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https://math.stackexchange.com/questions/3191496/how-do-i-solve-this-combinatorics-problem-with-conditions
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math
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I have $N$ lattice points which are arranged linearly and equally spaced. I want to make connections(say with some wire or thread) with each lattice site with another. The first one has $N-1$ possibilities and the second one has $N-3$ as each one cannot make connections itself and the first one has already formed one. So the total possibility is $$(N-1)(N-3)(N-5)(N-7).....$$ and so on. Now I want to impose two conditions.
Case(i): If I impose a condition that each site cannot be connected with the nearest neighbor, how many ways I can make the connections. How do complete this counting problem with this condition?
Case(ii): Apart from the above condition(immediate neighbors should not be connected), If I impose a further condition that each site can be connected with other or it can also be left unconnected. How do I count the number of ways doing this?
I know both case(i) and case(ii) will have different answers. I really don't know where to start this problem at all
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s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256381.7/warc/CC-MAIN-20190521122503-20190521144503-00220.warc.gz
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CC-MAIN-2019-22
| 982 | 4 |
https://chytugyhosszu.com/questions/how-does-a-hypothesis-becomes-a-theorypt5zs1497i0-or
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math
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The clonal selection hypothesis has become a widely accepted model for how the immune system responds to infection and how certain types of B and T lymphocytes are selected for destruction of specific antigens invading the body This is the Difference Between a Hypothesis and a Theory. In scientific reasoning, a hypothesis is an assumption made before any research has been completed for the sake of testing. A theory on the other hand is a principle set to explain phenomena already supported by data. Theories will pull together experimental results to provide full.
Over the past several years, Mitchell's chemiosmotic hypothesis has been widely accepted as the mechanism of coupling of electron transport and ATP synthesis. He was awarded the Nobel Prize in Chemistry in 1978. This acceptance by the scientific community is a result of accumulating experimental evidence supporting the hypothesis A scientific theory consists of one or more hypotheses that have been supported by repeated testing. Theories are one of the pinnacles of science and are widely accepted in the scientific. . Gerrig, Mahzarin R. Banaji, in Thinking and Problem Solving, 1994 A Color Memory. When researchers first turned their attention to the Sapir-Whorf hypothesis, memory for color was considered to be an ideal domain for study (see Brown, 1976).Whorf had suggested that language users dissect nature along the lines laid down by [their] native languages (1956, p. 213): Color is a. No, they can eventually graduate to the level of Theory. A theory is a well-established scientific principle that is widely accepted because it holds up to scrutiny
Eliminate Grammatical Errors Instantly and Enhance Your Writing. Try Now for Free! Check Grammar Errors Instantly and Enhance Your Writing. Try Now for Free A hypothesis that is widely accepted as correct is called a theory. What is correct a hypothesis or an hypothesis? A hypothesis is correct grammar here's why:A hypothesis is correct because 'h' is. 1) A hypothesis is. A) a widely accepted theory that is broad in scope and supported by a large body of evidence. B) an explanatory idea that is broad in scope and supported by a large body of evidence. C) the same as a theory. D) a widely accepted idea about a phenomenon. E) a tentative answer to some question Accept null hypothesis (H0) if 'p' value > statistical significance (0.01/0.05/0.10) For example, in the sample hypothesis if the considered statistical significance level is 5% and the p-value of the model is 0.12. Hence, the hypothesis of having no significant impact would not be rejected as 0.12 > 0.05 CH8: Hypothesis Testing Santorico - Page 272 We tend to want to reject the null hypothesis so we assume it is true and look for enough evidence to conclude it is incorrect. We tend to want to accept the alternative hypothesis. If the null hypothesis is rejected then we must accept that the alternative hypothesis is true. Note: H
The term hypothesis made up of two words, Hypo means a composition of two variables that need to verify whereas Thesis refers to the position of the variable in the frame of references. Every explanation is, after all, a Hypothesis by Ludwig Wittgenstein, A tentative hypothesis is a prediction of what you have proven during the research.This prediction set up the research goal usually based on. by pratyush4. Wed Dec 05, 2012 2:26 am. Sorry for bumping it up. According to OG- the correct answer is: Gall's hypothesis that different mental functions are localized in. different parts of the brain is widely accepted today. The two bold faces that are connected by 'that' are not being correlated in the statement Hypothesis testing is one of the most powerful and elegant concepts in the field of statistics. It is widely used in the market by data scientists, statisticians, and researchers in differen
Null Hypothesis Examples. A null hypothesis (H0) exists when a researcher believes there is no relationship between the two variables or a lack of information to state a scientific hypothesis. This is something to attempt to disprove or discredit. A null hypothesis example looks like the sample sentences below Scientific Theories. With repeated testing, some hypotheses may eventually become scientific theories. Keep in mind, a hypothesis is a possible answer to a scientific question. A scientific theory is a broad explanation for events that is widely accepted as true. To become a theory, a hypothesis must be tested over and over again, and it must be supported by a great deal of evidence The giant impact hypothesis has been a widely accepted theory for how the Earth-moon system formed. In the giant impact scenario, the moon forms from debris ejected into an Earth-orbiting disk by the collision of a smaller proto-planet with the early Earth. One of the challenges to the longstanding theory of the collision, is that a Mars-sized.
Gall's hypothesis of there being different mental functions localized in different parts of the brain is widely accepted today. (A) of there being different mental functions localized in different parts of the brain is widely accepted today (B) of different mental functions that are localized in different parts of the brain is widely accepted toda Alfred Wegener developed the continentaldrift hypothesis and died without his hypothesis being widely accepted. If you could travel back in time to meet him what would you tell him about the Theory of Plate tectonics, the Interior of the Earth the possible mechanisms that drive plate movement Which of the following astronomers introduced the most widely accepted hypothesis regarding the origin of the Solar System? Immanuel Kant in 1755 _____ is the reaction in which two or more atomic nuclei collide and join to form a new type element. Nuclear fusion The Sun is predominantly composed of the elements Input Field 1 of 2 hydrogen unavailable correct and Input Field 2 of 2 helium.
2.1 General Background and Definition of Output Hypothesis In the early 1980s, the burgeoning field of SLA was dominated by the concept of input hypothesis of Krashen, which was widely accepted and gradually adopted into teaching. However, the successive researchers have found The logic of hypothesis testing is based on these two basic principles: the formulation of two mutually exclusive hypothesis statements that, together, exhaust all possible outcomes; the testing of these so that one is necessarily accepted and the other rejected; OK, I know it's a convoluted, awkward and formalistic way to ask research questions Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore a number of factors to determine which ones might contribute to the ultimate outcome Step 4: Also, find the z score from z table given the level of significance and mean. Step 5: Compare these two values and if test statistic greater than z score, reject the null hypothesis.In case test statistic is less than z score, you cannot reject the null hypothesis. Examples of Hypothesis Testing Formula (With Excel Template The research hypothesis is supported by rejecting the null hypothesis. The null hypothesis locates the sampling distribution, since it is (usually) the simple hypothesis, testing against one specific value of the population parameter. Establishing the null and alternative hypotheses is sometimes considered the first step in hypothesis testing
Humans have been asking for millennia: Where does new life come from? Religion, philosophy, and science have all wrestled with this question. One of the oldest explanations was the theory of spontaneous generation, which can be traced back to the ancient Greeks and was widely accepted through the Middle Ages The Solar Nebular Hypothesis. The solar nebular hypothesis describes the formation of our solar system from a nebula cloud made from a collection of dust and gas. It is believed that the sun.
The Out of Africa hypothesis is an evolutionary theory of modern human origin that posits that modern humans arose in the late Pleistocene, about 100,000-200,000 years ago, in Africa. There are different versions of Out of Africa, but its major tenet is that modern humans originated as a discrete population or species that rapidly. scientific hypothesis, an idea that proposes a tentative explanation about a phenomenon or a narrow set of phenomena observed in the natural world.The two primary features of a scientific hypothesis are falsifiability and testability, which are reflected in an Ifthen statement summarizing the idea and in the ability to be supported or refuted through observation and experimentation Now Let's see some of widely used hypothesis testing type :-T Test ( Student T test) Z Test; ANOVA Test; Chi-Square Test; T- Test :- A t-test is a type of inferential statistic which is used to determine if there is a significant difference between the means of two groups which may be related in certain features.It is mostly used when the data sets, like the set of data recorded as outcome. The logic of null hypothesis testing involves assuming that the null hypothesis is true, finding how likely the sample result would be if this assumption were correct, and then making a decision. If the sample result would be unlikely if the null hypothesis were true, then it is rejected in favor of the alternative hypothesis
¨ A widely accepted standard is a probability ≤0.05 (1 in 20, or 5 in 100) provides sufficient evidence that the null hypothesis can be rejected. ¨ This means that if the exact same study was repeated 100 times, the results you obtained would occur in 5 (or fewer) of those studies if the null hypothesis was actually true Components of a Formal Hypothesis Test. The null hypothesis is a statement about the value of a population parameter, such as the population mean (µ) or the population proportion (p).It contains the condition of equality and is denoted as H 0 (H-naught).. H 0: µ = 157 or H 0: p = 0.37. The alternative hypothesis is the claim to be tested, the opposite of the null hypothesis If the hypothesis is true and we accept it, and if the hypothesis is false and we reject it, our decision will be correct. On the other hand, we could reject the hypothesis when it should be accepted (a type 1 error), or we could accept a hypothesis that should be rejected (a type 2 error). The risk of making such errors in testing a hypothesis using available sample data can be minimized
Otherwise, the null is accepted. These are the only correct assumptions, and it is incorrect to reject, or accept, H 1. Accepting the null hypothesis does not mean that it is true. It is still a hypothesis, and must conform to the principle of falsifiability, in the same way that rejecting the null does not prove the alternative 6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a In this case, you could say the alternative hypothesis was supported. Personally, I would avoid saying the alternative hypothesis was accepted because this implies that you have proven the alternative hypothesis to be true. Generally, one study cannot prove anything, but it can provide evidence for (or against) a hypothesis A hypothesis is a conjectural statement of the relation between two or more variables. (Kerlinger, 1956) Hypothesis is a formal statement that presents the expected relationship between an independent and dependent variable.(Creswell, 1994) A research question is essentially a hypothesis asked in the form of a question
Answer: a. Explanation: Test statistic provides a basis for testing a Null Hypothesis. A test statistic is a random variable that is calculated from sample data and used in a hypothesis test. 11. Consider a hypothesis H 0 where ϕ 0 = 5 against H 1 where ϕ 1 > 5 If the signal sequence is not the correct one, the ribosome is released before delivering its protein. The hypothesis, which was formulated in the early 1970s by workers including Gunter Blobel (1936- ) and César Milstein (1927- ), is now widely accepted. A Dictionary of Biology The widely accepted view that strategy and execution are separable activities sets companies up for failure in a fast-paced world. One of us (Paul) is a strategy scholar and economist; the other.
The Kurgan hypothesis is the most widely accepted proposal to identify the Proto-Indo-European homeland from which the Indo-European languages spread out (map). Close. So all in all, right now the steppe hypothesis is the one which is widely accepted and probably true. level 2 8. A hypothesis is a possible answer to a scientific _____. 9. Matters of _____ are outside the realm of science. 10. A scientific _____ is a broad explanation for events that is widely accepted as true. 11. The last step in a scientific investigation is _____ what you have learned with others A hypothesis is the cornerstone of the scientific method. It is an educated guess about how the world works that integrates knowledge with observation. Everyone appreciates that a hypothesis must be testable to have any value, but there is a much stronger requirement that a hypothesis must meet. A hypothesis is considered scientific only if. A step-by-step guide to hypothesis testing. Published on November 8, 2019 by Rebecca Bevans. Revised on February 15, 2021. Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics.It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories
The Acquisition-Learning distinction is the most fundamental of the five hypotheses in Krashen's theory and the most widely known among linguists and language teachers. According to Krashen there are two independent systems of foreign language performance: 'the acquired system' and 'the learned system'. The 'acquired system' or 'acquisition' is the product of a subconscious process very. The original Gaia hypothesis, that life controls planetary processes (i.e., life created Earth's system), has become known as the strong Gaia hypothesis. It is not widely accepted. It is not widely accepted The scientific method attempts to explain the natural occurrences ( phenomena) of the universe by using a logical, consistent, systematic method of investigation, information ( data) collection, data analysis ( hypothesis ), testing ( experiment ), and refinement to arrive at a well-tested, well-documented, explanation that is well-supported by. Calculating p-value. From the observations of the experiment, — If the p-value is less than or equal to 0.05 (critical value), the null hypothesis is rejected.Hence, the conclusion to be drawn is that there is a difference between means of heights of the population from two countries. — If the p-value is greater than 0.05 (critical value), the null hypothesis is accepted
S.3.2 Hypothesis Testing (P-Value Approach) The P -value approach involves determining likely or unlikely by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P -value is small, say less than (or. The Steady State theory became widely-known by 1948 with the publication of two papers: A New Model for an Expanding Universe by English astronomer Fred Hoyle, and The Steady-State Theory. Raymond (2000) found that null hypothesis significant testing (otherwise known as NHST) is the most widely used approach to hypothesis testing in among behavioral and social scientists. Frick (1995), believed that the null hypothesis can be correct in some situations, although critics disagree
The alternative hypothesis cannot be tested directly; it is accepted by exclusion if the test of statistical significance rejects the null hypothesis. One- and two-tailed alternative hypotheses A one-tailed (or one-sided) hypothesis specifies the direction of the association between the predictor and outcome variables Theory definition is - a plausible or scientifically acceptable general principle or body of principles offered to explain phenomena. How to use theory in a sentence. Two related, yet distinct, meanings of theory Synonym Discussion of theory Widely accepted theories are already well-confirmed, so if a hypothesis is incompatible with existing science, the default response should be that the hypothesis is mistaken. An extraordinary claim incompatible with scientific knowledge should require very strong evidence before it can be accepted Hypothesis Testing. Definition: The Hypothesis Testing is a statistical test used to determine whether the hypothesis assumed for the sample of data stands true for the entire population or not. Simply, the hypothesis is an assumption which is tested to determine the relationship between two data sets. In hypothesis testing, two opposing. Yes, there is change, thus it is the alternative hypothesis, H 1; No, there is no change, therefore is the null hypothesis, H 0; The correct answer is that there is change. Dead represents a change from the accepted state of alive. The null hypothesis always represents no change. Therefore, the hypotheses are: H 0: Patient is alive
It has two parts: the null hypothesis and the other is known as the alternative hypothesis. The null hypothesis is the one that the researcher tries to reject. It isn't easy to prove the alternate hypothesis, so if the null hypothesis is rejected, the remaining alternate theory gets accepted The facial feedback hypothesis states that our facial expressions affect our emotions. If the facial-feedback hypothesis is correct, then not only do we smile when we feel happy, but smiling can make us feel happy, too, even when we start out feeling sad. In these cases, it is the act of smiling that produces a happy feeling If enough evidence accumulates to support a hypothesis, it moves to the next step — known as a theory — in the scientific method and becomes accepted as a valid explanation of a phenomenon Hypothesis testing is the process that an analyst uses to test a statistical hypothesis. The methodology employed by the analyst depends on the nature of the data used and the reason for the analysis
In the last seconds of the video, Sal briefly mentions a p-value of 5% (0.05), which would have a critical of value of z = (+/-) 1.96. Since the experiment produced a z-score of 3, which is more extreme than 1.96, we reject the null hypothesis. Generally, one would chose an alpha (a percentage) which represents the tolerance level for making a. Statistical hypothesis tests are important for quantifying answers to questions about samples of data. The interpretation of a statistical hypothesis test requires a correct understanding of p-values and critical values. Regardless of the significance level, the finding of hypothesis tests may still contain errors The prevailing theory supported by the scientific community, the giant impact hypothesis suggests that the moon formed when an object smashed into early Earth. Like the other planets, Earth formed. Hypothesis Testing Step 1: State the Hypotheses. In all three examples, our aim is to decide between two opposing points of view, Claim 1 and Claim 2. In hypothesis testing, Claim 1 is called the null hypothesis (denoted Ho), and Claim 2 plays the role of the alternative hypothesis (denoted Ha). As we saw in the three examples, the.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362571.17/warc/CC-MAIN-20211203000401-20211203030401-00003.warc.gz
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CC-MAIN-2021-49
| 19,795 | 18 |
https://futur.upc.edu/19311167
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math
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The restricted planar elliptic three body problem models the motion of a massless body under the Newtonian gravitational force of two other bodies, the primaries, which evolve in Keplerian ellipses.
A trajectory is called oscillatory if it leaves every bounded region but returns infinitely often to some fixed bounded region. We prove the existence of such type of trajectories for any values for the masses of the primaries provided the eccentricity of the Keplerian ellipses is small.
Guardia, M., Martín, P., Sabbagh, L., Martinez-seara, Tere. Oscillatory orbits in the restricted elliptic planar three body problem. "Discrete and Continuous Dynamical Systems- Series A", 1 Gener 2017, vol. 37, núm. 1, p. 229-256.
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CC-MAIN-2021-21
| 720 | 3 |
http://www.bookrags.com/lessonplan/journey-through-genius/test5.html
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math
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|Name: _________________________||Period: ___________________|
This test consists of 5 short answer questions, 10 short essay questions, and 1 (of 3) essay topics.
Short Answer Questions
1. What was known about pi, during Archimedes' time?
2. In what century did Archimedes live?
3. Which shapes as described by Euclid, inspired the Greek philosopher Plato?
4. That properties of specific shapes were early Egyptians aware of?
5. Which of the following is true about pi, as described by Dunham.
Short Essay Questions
1. Describe the events that follow del Ferro's death between Fior and Tartaglia.
2. Describe Euclid's postulates and notions in how they were important in constructing his proofs.
3. Describe Lindeman's work on the square of a circle, and state what he discovered.
4. According the Dunham, how did Euclid prove his theory on the infinitude of primes?
5. Describe what Gauss discovered according to Dunham.
6. How did Archimedes find a number value for pi?
7. Describe Euclid's definition of prime numbers and the relationship he stated as existing between prime and composite numbers.
8. Describe why Dunham infers that Euclid's Elements was an evolutionary book not so much for what it said, but in how it was presented.
9. What did Dunham claim was Pythagoras's major contribution to geometry, and mathematical reasoning?
10. Explain why Archimedes finding a number value for pi was considered a great achievement according to Dunham.
Write an essay for ONE of the following topics:
Essay Topic 1
Describe Gauss's work on what was to be known as non-euclidean geometry. What was Gauss's system for triangles where angles added up to fewer than 180 degrees? What were some of his conclusions? Did he publish his work? Was their any controversy surrounding his work on this system? Explain.
Essay Topic 2
Explain the accuracy of Archimedes determination of pi. How did he determine the number value of pi? How accurate is Archimedes's measurement of pi? What other mathematician was able to determine a number value, though more accurate, for pi?
Essay Topic 3
Write a a three part essay to explain how Cantor's work in mathematics also fit into the cultural movements of the time.
Part 1) Describe the artistic movements of the 1860s and 1870s. In general, how could they be related to mathematical philosophy at the time?
Part 2) What was Cantor's work in mathematics in the 1860s and 1870s?
Part 3) Explain how Cantor's philosophy and mathematical theorems fit with the new artistic and philosophic ideas of the time.
This section contains 960 words
(approx. 4 pages at 300 words per page)
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s3://commoncrawl/crawl-data/CC-MAIN-2016-50/segments/1480698542250.48/warc/CC-MAIN-20161202170902-00315-ip-10-31-129-80.ec2.internal.warc.gz
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CC-MAIN-2016-50
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https://math.answers.com/Q/What_is_the_formula_to_find_volume_of_a_trapezoid
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math
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---- it is IMPOSSIBLE to find the volume of a trapezoid, because a trapezoid is a 2-dimensional figure, and volume is for 3-dimensional figures. ---- you may find the area though, because that is possible for 2-dimensional figures. ----A trapezoid is a 2-dimensional (plane) figure.Its volume is zero.
The formula isV = 0 . Being a 2-dimensional entity, a trapezoid has no volume.That is, a trapezoid can't hold any water.
the volume of a trapezoidal prism is equal to the height times the base area of the trapezoid. First you find the area of trapezoid h(a+b)/2 h is the height of the trapezoid, not the height of the prism a is the length of the top b is the length of the bottom Then you find the volume of the trapezoidal prism with this formula H*h(a+b)/2 H is the height of the prism. Multiply H by the area of the trapezoid that you found in step one.
there isn't one Geometry is bull.
There is none because a trapezoid is a 2D shape but the area is as follows measured in square units:- Area = 0.5*(sum of parallel sides)*height
The cross section volume of a trapezoid is found between 0 and 2.0.
by the formula of ---A*b
formula of find the volume of dish
With great difficulty because a trapezoid is a 2 dimensional shape which has no volume but it does have a surface area.
(a1+a2+sqrt(a1*a2)*h/3= volume of Trapezoid RCC Footing
The volume of any right prism is the area of the base, in this case a trapezoid, multiplied by the height of the prism. The formula for the area of a trapezoid is A = 1/2h(a + b) where a and b are the bases of the trapezoid (the parallel sides). Once you calculate the area of the trapezoidal base of the prism, multiply that number by its height to get its volume.
Area of a trapezoid = 0.5*(sum of parallel sides)*height
The formula of volume
leanth times width
There is none because a trapezoid is a 2D shape but if you meant the area it is:- Area in square units = 0.5*(sum of parallel sides)*height
The perimeter of a trapezoid is the sum of the lengths of each side. To find the area of a trapezoid: add base 1 and base 2 together then divide that answer by 2, then multiply it by the height of the trapezoid.
Nothing is "indicated".
(base1 + base2)/2 = midsegment
The formula to find the volume of an object is Length times Width times Height
There is no simple formula and, in any case, the answer will depend on what information about the trapezoid is given.
Area of a trapezoid = (1/2) x (height) x (length of the base + length of the top)
If the lengths of the bases are also given then rearrange the area of the trapezoid formula so that the height is the subject.
you just simply cut it in half and you'll have the median
A formula is a string of letters and numbers and other mathematical characters. It has no volume.
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| 2,774 | 24 |
http://slashdot.org/~Sun/tags/oops
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math
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Almost a decade ago, I was in a trip to the USA. I was very surprised to see Liter used for car engine sizes (here they usually use cubic centimeters, which are exactly 1/1000, so not a real problem).
I remember strolling through a supermarket, and looking at the soda bottles, which were bigger than the 1.5L bottles common here. I picked one up to see what size it was. I guess most readers know the answer - it was 2 liters. I remember wondering how come Americans are willing to use a metric unit.
So I asked a vendor. His answer was "This isn't a metric unit. It's liter".
So I asked him how much was a liter, and his answer was something along the lines of "33.8 ounces" (without blinking of stopping to think about it).
Which, of course, got me my answer. The reason Americans are using a metric unit is because they don't know it's metric.
The problem with your proposal is that, if implemented that way, means just adding another unit to the mix, without exposing people to the main advantage that the metric system has to offer. That does not bode well for a "migration path".
You should add to that the fact that volume realization is hard. I'll give a couple of examples. First, bear in mind that the two units people are, more or less, familiar with are a milliliter (1 cubic centimeter = 1/1000 of a liter) and a liter.
The first was when a company I worked for ordered a certain amount of boxes for their product. We were trying to figure out whether we have where to store them. I made the calculation, based on box size, and figured the entire bunch would require a little less than 2 cubic meters (around 1.8). We sort of made a hand gesture estimate and figured it was not that much. Boy, were we wrong. We ended up using up every spare cabinet and space in the office. Lesson learned: a cubic meter is a lot.
The happened just yesterday. I was telling my wife we will have to remove some soil from our garden to make space for extra flooring. She said "we'll be giving that to friends, right?". I told her it was about 500 liters of soil. I then made a quick mental calculation. We'll need about 12 squared meter of flooring, and the base is about half a meter deep. 6000 liters. Assuming soil is half as dense than water (it was while driving, so I couldn't look it up), you get 3 tons of soil. My instinct was off by a factor of 10, and her instinct was off by a factor of 1000.
This doesn't mean this is useless. Can you make this same calculation, off the top of your head, using imperial units? Metric does simplify things quite considerably. It's just that, specifically for volumes, that is a hard problem to solve.
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368707439012/warc/CC-MAIN-20130516123039-00064-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 2,642 | 10 |
https://raisingthebar.nl/2018/04/24/solution-to-question-1-from-uol-exam-2016-zone-b/
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math
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Solution to Question 1 from UoL exam 2016, Zone B
This problem is a good preparation for Question 2 from UoL exam 2015, Zone A (FN3142), which is more difficult.
Two corporations each have a 4% chance of going bankrupt and the event that one of the two companies will go bankrupt is independent of the event that the other company will go bankrupt. Each company has outstanding bonds. A bond from any of the two companies will return % if the corporation does not go bankrupt, and if it does, a bondholder will lose the face value of the investment, i.e., %. Suppose an investor buys $1000 worth of bonds of the first corporation, which is then called portfolio , and similarly, an investor buys $1000 worth of bonds of the second corporation, which is then called portfolio .
(a) [40 marks] Calculate the VaR at % critical level for each portfolio and for the joint portfolio .
(b) [30 marks] Is VaR sub-additive in this example? Explain why the absence of sub-additivity may be a concern for risk managers.
(c) [30 marks] The expected shortfall at the % critical level can be defined as . Calculate the expected shortfall for the portfolios and . Is this risk measure sub-additive?
There are a couple of general ideas to understand before embarking on calculations. The return on the bond of one company is a binary variable taking values 0% and -100%. All calculations involving it are similar to the ones for the coin. After doing calculations the return figures can be translated to dollar amounts by multiplying by $1000.
While the use of the notions of the distribution function and generalized inverse can be avoided, I prefer to use them to show the general approach.
(a) The return on one bond is described by the table
Table 1. Probability table for return on one bond
Therefore its distribution function can be found in the same way as for the coin:
The distribution function is shown in red. It is zero for , 0.04 for and 1 for . The definition of the VaR requires inversion of this function. The graph of this function has flat pieces and its usual inverse does not exist. We have to use the generalized inverse defined by
see the definition of the infimum here. In our case and the verbal procedure is: 1) find those returns for which (it's the half-axis ) and 2) among them find the least return. The answer is %. This is the Value at Risk for each of
What we do next is very similar to the derivation of the sampling distribution for two coins.
Table 2. Joint probability table for returns on two portfolios
The main body of the table contains probabilities of pairs of the two returns. For the total portfolio the possible return values are 0 (none of the companies goes bankrupt), -50 (one goes bankrupt and the other does not) and -100 (both go bankrupt). The corresponding probabilities follow from Table 2 and we get
Table 3. Probability table for return on the total portfolio
This table results in the following distribution function:
Since 0.0784>0.05, the Value at Risk is -50% (use the generalized inverse).
(b) Translating the percentages to dollars, at 5% the risk for each of the bonds is $0 and for the total portfolio it is $1000 (50% of $2000; I am passing from negative percentages to positive loss figures).
We say that Value at Risk is sub-additive if . Our calculations show that Value at Risk is not sub-additive in case of independent returns. This has an important practical implication. Suppose that a financial institution has several branches and each of them keeps their Value at Risk, say, at zero. Nevertheless, the Value at Risk for the whole institution may well be large and threaten its stability.
(c) Here we have to apply the definition of the conditional expectation: . Since , this is the same as
For the total portfolio we get
In monetary terms, this translates (again passing to positive values) to $40 for each bond and to $1020.40 for the total portfolio. The conclusion is that expected shortfall is not sub-additive.
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In ordinary parlance, investment means to buy shares, stocks, bonds and securities which already exist in stock market. But this is not real investment because it is simply a transfer of existing assets. Hence this is called financial investment which does not affect aggregate spending. In Keynesian terminology, investment refers to real investment which adds to capital equipment.
It leads to increase in the levels of income and production by increasing the production and purchase of capital goods. Investment thus includes new plant and equipment, construction of public works like dams, roads, buildings, etc., net foreign investment, inventories and stocks and shares of new companies. In the words of Joan Robinson, “By investment is meant an addition to capital, such as occurs when a new house is built or a new factory is built. Investment means making an addition to the stock of goods in existence.”
Capital, on the other hand, refers to real assets like factories, plants, equipment, and inventories of finished and semi-finished goods. It is any previously produced input that can be used in the production process to produce other goods. The amount of capital available in an economy is the stock of capital. Thus capital is a stock concept.
To be more precise, investment is the production or acquisition of real capital assets during any period of time. To illustrate, suppose the capital assets of a firm on 31 March 2004 are Rs 100 crores and it invests at the rate of Rs 10 crores during the year 2004-05. At the end of the next year (31 March 2005), its total capital will be Rs 110 crores. Symbolically, let I be investment and К be capital in year t, then It = Kt– Kt- 1.
Capital and investment are related to each other through net investment. Gross investment is the total amount spent on new capital assets in a year. But some capital stock wears out every year and is used up for depreciation and obsolescence. Net investment is gross investment minus depreciation and obsolescence charges for replacement investment. This is the net addition to the existing capital stock of the economy.
If gross investment equals depreciation, net investment is zero and there is no addition to the economy’s capital stock. If gross investment is less than depreciation, there is disinvestment in the economy and the capital stock decreases. Thus for an increase in the real capital stock of the economy, gross investment must exceed depreciation, i.e., there should be net investment.
Types of Investment
- Induced Investment
Real investment may be induced. Induced investment is profit or income motivated. Factors like prices, wages and interest changes which affect profits influence induced investment. Similarly demand also influences it. When income increases, consumption demand also increases and to meet this, investment increases. In the ultimate analysis, induced investment is a function of income i.e., I = f(Y). It is income elastic. It increases or decreases with the rise or fall in income, as shown in Figure 1.
I1 I1is the investment curve which shows induced investment at various levels of income. Induced investment is zero at OY1 income. When income rises to OY3 induced investment is I3Yy A fall in income to OY2 also reduces induced investment to I2Y2.
Induced investment may be further divided into
- The average propensity to invest
- The marginal propensity to invest
(i) The average propensity to invest is the ratio of investment to income, I/Y. If the income is Rs. 40 crores and investment is Rs. 4 crores, I/Y = 4/40 = 0.1. In terms of the above figure, the average propensity to invest at OY3 income level is I3Y3/ OY3
(ii) The marginal propensity to invest is the ratio of change in investment to the change in income, i.e., I/Y. If the change in investment, I=Rs 2 crores and the change in income, Y = Rs 10 crores, then I/∆Y = 2/10=0.2 In Figure 1, I/Y =I3a/Y2Y3
- Autonomous Investment
Autonomous investment is independent of the level of income and is thus income inelastic. It is influenced by exogenous factors like innovations, inventions, growth of population and labour force, researches, social and legal institutions, weather changes, war, revolution, etc. But it is not influenced by changes in demand. Rather, it influences the demand. Investment in economic and social overheads whether made by the government or the private enterprise is autonomous.
Such investment includes expenditure on building, dams, roads, canals, schools, hospitals, etc. Since investment on these projects is generally associated with public policy, autonomous investment is regarded as public investment. In the long-run, private investment of all types may be autonomous because it is influenced by exogenous factors. Diagrammatically, autonomous investment is shown as a curve parallel to the horizontal axis as I1I’ curve in Figure 2. It indicates that at all levels of income, the amount of investment OI1 remains constant.
The upward shift of the curve to I2I” indicates an increased steady flow of investment at a constant rate OI2 at various levels of income. However, for purposes of income determination, the autonomous investment curve is superimposed on the С curve in a 45° line diagram.
- Determinants of the Level of Investment
The decision to invest in a new capital asset depends on whether the expected rate of return on the new investment is equal to or greater or less than the rate of interest to be paid on the funds needed to purchase this asset. It is only when the expected rate of return is higher than the interest rate that investment will be made in acquiring new capital assets.
In reality, there are three factors that are taken into consideration while making any investment decision. They are the cost of the capital asset, the expected rate of return from it during its lifetime, and the market rate of interest. Keynes sums up these factors in his concept of the marginal efficiency of capital (MEC).
Marginal Efficiency of Capital
The marginal efficiency of capital is the highest rate of return expected from an additional unit of a capital asset over its cost. In the words of Kurihara, “It is the ratio between the prospective yield to additional capital goods and their supply price.” The prospective yield is the aggregate net return from an asset during its life time, while the supply price is the cost of producing this asset.
If the supply price of a capital asset is Rs. 20,000 and its annual yield is Rs. 2,000, the marginal efficiency of this asset is 2000/20000 × 100/1 = 10 per cent. Thus the marginal efficiency of capital is the percentage of profit expected from a given investment on a capital asset.
Keynes relates the prospective yield of a capital asset to its supply price and defines the MEC as “equal to the rate of discount which would make the present value of the series of annuities given by the returns expected from the capital assets during its life just equal to its supply price.”
Symbolically, this can be expressed as-
SP =R1/ (1+i) + R2 (1+i)2 + Rn/(1+i)n
Where Sp is the supply price or the cost of the capital asset, R1 R2… and Rn are the prospective yields or the series of expected annual returns from the capital asset in the years, 1, 2… and n, i is the rate of discount which makes the capital asset exactly equal to the present value of the expected yield from it.
This i is the MEC or the rate of discount which equates the two sides of the equation. If the supply price of a new capital asset is Rs 1,000 and its life is two years, it is expected to yield Rs 550 in the first year and Rs 605 in the second year. Its MEC is 10 per cent which equates the supply price to the expected yields of this capital asset.
(Sp) Rs 1000 = 550/(1.10) + (605)/(1.10)2 = Rs. 500 + 500
In equation (1), the term R1/(1+i) is the present value (PV) of the capital asset. The present value is “the value of payments to be received in the future.” It depends on the rate of interest at which it is discounted.
Suppose we expect to receive Rs 100 from a machine in a year’s time and the rate of interest is 5 per cent. The present value of this machine is
R1 / (1+ i) =100/(1.05) = Rs 95.24
If we expect Rs 100 from the machine after two years then its present value is100/ (1.05)2 = Rs 90.70. The present value of a capital asset is inversely related to the rate of interest. The lower the rate of interest, the higher is the present value, and vice versa. For instance, if the rate of interest is 5 per cent, PV of an asset of Rs 100 for one year will be Rs 95.24; at 7 per cent interest rate, it will be Rs 93.45; and at 10 per cent interest rate, it will be Rs 90.91.
The relation between the present value and the rate of interest is shown in Figure 3, where the rate of interest is taken on the horizontal axis while the present value of the project on the vertical axis. The curve PR shows the inverse relation between the present value and the rate of interest. If the current rate of interest is ii the present value of the project is P1 On the other hand, a higher rate of interest (i2) will lead to a lower present value (P2) when the present value curve (PR) cuts the horizontal axis at point (Z), the net present value becomes zero.
As a matter of fact, the MEC is the expected rate of return over cost of a new capital asset. In order to find out whether it is worthwhile to purchase a capital asset it is essential to compare the present value of the capital asset with its cost or supply price. If the present value of a capital asset exceeds its cost of buying, it pays to buy it. On the contrary, if its present value is less than its cost, it is not worthwhile investing in this capital asset.
The same results can be had by comparing the MEC with the market rate of interest. If the MEL of a capital asset is higher than the market rate of interest at which it is borrowed, it pays to purchase the capital asset, and vice versa. If the market interest rate equals the MEC of the capital asset, the firm is said to possess the optimum capital stock.
If the MEC is higher than the rate of interest, there will be a tendency to borrow funds in order to invest in new capital assets. If the MEC is lower than the rate of interest, no firm will borrow to invest in capital assets. Thus the equilibrium condition for a firm to hold the optimum capital stock is where the MEC equals the interest rate.
Any disequilibrium between the MEC and the rate of interest can be removed by changing the capital stock, and hence the MEC or by changing the rate of interest or both. Since the stock of capital changes slowly, therefore, changes in the rate of interest are more important for bringing equilibrium. The above arguments which have been applied to a firm are equally applicable to the economy.
Figure 4 shows the MEC curve of an economy. It has a negative slope (from left to right downward) which indicates that the higher the MEC, the smaller the capital stock. Or, as the capital stock increases, the MEC falls. This is because of the operation of the law of diminishing returns in production.
As a result, the marginal physical productivity of capital and the marginal revenue fall. In the figure, when the capital stock is OK1, the MEC is Or1. As the capital increases from OK1to ОK2 the MEC falls from Or1 to Or2 .The net addition to the capital stock K1K2 represents the net investment in the economy.
Further, to reach the optimum (desired) capital stock in the economy, the MEC must equal the rate of interest. If, as shown in the figure, the existing capital stock is OK1 the MEC is Or2 and the rate of interest is at Or1 Everyone in the economy will borrow funds and invest in capital assets.
This is because MEC (Or1) is higher than the rate of interest (at Or2). This will continue till the MEC (Or1) comes down to the level of the interest rate (at Or2). When the MEC equals the rate of interest, the economy reaches the level of optimum capital stock. The fall in the MEC is due to the increase in the actual capital stock from OK2 to the optimum (desired) capital stock OK2.
The increase in the firm’s capital stock by K1K2 is the net investment of the firm. But it is the rate of interest which determines the size of the optimum capital stock in the economy. And it is the MEC which relates the amount of desired capital stock to the rate of interest. Thus the negative slope of the MEC curve indicates that as the rate of interest falls the optimum stock of capital increases.
- The Marginal Efficiency of Investment (MEI)
The marginal efficiency of investment is the rate of return expected from a given investment on a capital asset after covering all its costs, except the rate of interest. Like the MEC, it is the rate which equates the supply price of a capital asset to its prospective yield. The investment on an asset will be made depending upon the interest rate involved in getting funds from the market. If the rate of interest is high, investment is at a low level.
A low rate of interest leads to an increase in investment. Thus the MEI relates the investment to the rate of interest. The MEI schedule shows the amount of investment demanded at various rates of interest. That is why, it is also called the investment demand schedule or curve which has a negative slope, as shown in Fig. 5(A). At Or1 rate of interest, investment is OF. As the rate of interest falls to Or2, investment increases to ОI”.
To what extent the fall in the interest rate will increase investment depends upon the elasticity of the investment demand curve or the MEI curve. The less elastic is the MEI curve, the lower is the increase in investment as a result of fall in the rate of interest, and vice versa.
In Figure 5 the vertical axis measures the interest rate and the MEI and the horizontal axis measures the amount of investment. The MEI and MEI’ are the investment demand curves. The MEI curve in Panel (A) is less elastic to investment which increases by I’I’’. This is less than the increase in investment I1I”2 shown in Panel (B) where the MEI’ curve is elastic. Thus given the shape and position of the MEI curve, a fall in the interest rate will increase the volume of investment.
On the other hand, given the rate of interest, the higher the MEI, the larger shall be the volume of investment. The higher marginal efficiency of investment implies that the MEI curve shifts to the right. When the existing capital assets wear out, they are replaced by new ones and level of investment increases.
But the amount of induced investment depends on the existing level of total purchasing. So more induced investment occurs when the total purchasing is higher. The higher total purchasing tends to shift the MEI to the right indicating that more inducement to investment takes place at a given level of interest rate.
This is explained in Figure 6, where MEI1 and МЕI2 curves indicate two different levels of total purchasing in the economy. Let us suppose that the MEI, curve indicates that at Rs 200 crores of total purchasing, OI1 (Rs 20 crores) investment occurs at Or1 interest rate. If total purchasing rises to Rs 500 crores, the MEI1 curve shifts to the right as МЕI2 and the level of induced investment increases to OI2 (Rs 50 crores) at the same interest rate Or1.
- Distinction between MEC and MEI
Keynes did not distinguish between the marginal efficiency of capital (MEC) and the marginal efficiency of investment (MEI).
But modern economists have made clear distinctions between the two concepts as follows:
(i) The MEC is based on a given supply price for capital, and the MEI on induced changes in this price.
(ii) The MEC shows the rate of return on all successive units of capital without regard to the existing stock of capital. On the other hand, the MEI shows the rate of return on only units of capital over and above the existing stock of capital.
(iii) In the MEC, the capital stock is taken on the horizontal axis of a diagram, while in the MEI the amount of investment is taken horizontally on the X-axis.
(iv) The MEC is a ‘stock’ concept, and the MEI is a ‘flow’ concept.
(v) The MEC determines the optimum capital stock in an economy at each level of interest rate. The MEI determines the net investment of the economy at each interest rate, given the capital stock.
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ACCOUNTING and FINANCE
An Integrated Resource Management Guide for the 21st Century
The St. Lucie Press Library of Executive Excellence Series
ACCOUNTING and FINANCE
An Integrated Resource Management Guide for the 21st Century
J A E K . S H I M , P h .D .
Professor of Business Administration California State University at Long Beach, California
St. Lucie Press
Boca Raton London New York Washington, D.C.
Library of Congress Cataloging-in-Publication Data
Shim, Jae K. Accounting and finance for the nonfinancial executive : an integrated resource management guide for the 21st century / Jae K. Shim. p. cm. — (The library for executive excellence) Includes index. ISBN 1-57444-287-2 (alk. paper) 1. Accounting. 2. Corporations—Finance. I. Title. II. Series. HF5635.S552899 2000 657′.024′655—dc21 00-039041 CIP
This book contains information obtained from authentic and highly regarded sources. Reprinted material is quoted with permission, and sources are indicated. A wide variety of references are listed. Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher. The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale. Specific permission must be obtained in writing from CRC Press LLC for such copying. Direct all inquiries to CRC Press LLC, 2000 N.W. Corporate Blvd., Boca Raton, Florida 33431. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe.
© 2000 by CRC Press LLC No claim to original U.S. Government works International Standard Book Number 1-57444-287-2 Library of Congress Card Number 00-039041 Printed in the United States of America 1 2 3 4 5 6 7 8 9 0 Printed on acid-free paper
This book is directed toward the businessperson who must have financial and accounting knowledge but has not had formal training in finance or accounting — perhaps a newly promoted middle manager or a marketing manager of a small company who must know some basic finance concepts. The entrepreneur or sole proprietor also needs this knowledge; he or she may have brilliant product ideas, but not the slightest idea about financing. The goal of the book is to provide a working knowledge of the fundamentals of finance and accounting that can be applied, regardless of the firm size, in the real world. It gives nonfinancial managers the understanding they need to function effectively with their colleagues in finance. We show you the strategies for evaluating investment decisions such as return on investment analysis. You will see what you need to know, what to ask, which tools are important, what to look for, what to do, how to do it, and what to watch out for. You will find the book useful and easy to read. Many practical examples, illustrations, guidelines, measures, rules of thumb, graphs, diagrams, and tables are provided to aid comprehension of the subject matter. You cannot avoid financial information. Profitability statements, rates of return, budgets, variances, asset management, and project analyses, for example, are included in the nonfinancial manager’s job. The financial manager’s prime functions are to plan for, obtain, and use funds to maximize the company’s value. The financial concepts, techniques, and approaches enumerated here can also be used by any nonfinancial manager, irrespective of his or her primary duties. This book is designed for nonfinancial executives in every functional area of responsibility in any type of industry. Whether you are in marketing, manufacturing, personnel, operations research, economics, law, behavioral sciences, computers, personal finance, taxes, or engineering, you must have a basic knowledge of finance. Because your results will be measured in dollars and cents, you must understand the importance of these numbers so as to optimize results in both the short and long terms. Knowledge of the content of this book will enable you to take on additional managerial responsibilities. You will be better equipped to prepare, appraise, evaluate, and approve plans to accomplish departmental objectives. You will be able to back up your recommendations with carefully prepared financial support as well as state your particular measure of performance. By learning how to think in terms of finance and accounting, you can intelligently express your ideas, whether they are based on marketing, production, personnel, or other concepts. You will learn how to appraise where you have been, where you are, and anywhere you are headed. Financial measures show past, current, and future performance. Criteria are presented to examine the performance of your division and product lines, and also formulate realistic profit goals.
You are often faced with a choice of alternative investment opportunities. Without adequate funds. cash flows. but need not be able to arrive at the mathematical answer (e. receivable. You may have to forecast future sales. You may have to decide whether to buy machine A or machine B. You will spot areas of inefficiency or efficiency by comparing actual performance to standards through variance analysis. You have to understand that money is associated with a time value. a lower price may still result in profitability. To facilitate this understanding.Nonfinancial managers should have a grasp of financial topics. You must know what your costs are in order to establish a suitable selling price. and inventory. Proper tax planning will make for wise decisions. You should have a basic understanding of financial information so as to evaluate the performance of your responsibility center. an understanding of basic accounting . What is the best financing source in a given situation? Taxes are important in any business decision. Nonfinancial managers mainly need to know enough to ask their financial colleagues what the discounted rate of return is for a variety of investment decisions. or whether to expand. You may also want to compute growth rates. discounted rate of return problem). the convention adopted in recording information. The financing mix of the company in terms of equity of debt affects the cost of financing and influences the firm’s risk position.g. In managing working capital. If you have idle facilities. the after-tax effect is what counts. Are things getting better or worse? What are the possible reasons? Who is responsible? What can you do about it? You need to know whether your business segment has adequate cash flow to meet requirements. What are the reasons that sales targets differ from actual sales? Why are costs much higher than expected? The causes must be searched out so that corrective action may be taken. Are you maximizing your allowable tax deductions? Financial decisions are usually formulated on the basis of information generated by the accounting system of the firm. You can undertake certain strategies to improve return on investment by enhancing profitability or using assets more efficiently. a decision has to be made whether short-term. whether to introduce a certain product line. and the limitation inherent in the information presented. you have to get the most out of your cash.. and costs to see if you will be operating effectively in the future. Thus. A decision can then be based on their answer. intermediate-term. you would prefer projects that generate higher cash flows in earlier years. your chances of growth are restricted. Should you extend credit to marginal customers? How much inventory should you order at one time? When should you order the inventory? In financing the business. What sales are necessary for you to break even? You may have to decide whether it is financially advantageous to accept an order at below the normal selling price. or long-term financing is suitable. You need to be able to express your budgetary needs in order to obtain proper funding for your department. Proper interpretation of the data requires an understanding of the assumptions and rules underlying such systems. How do you get cash faster and delay cash payments? Don’t forget that you need liquid funds to meet ongoing expenditures.
These techniques include horizontal.concepts and conventions is helpful. vertical. The balance sheet. the income statement. These financial statements are included in the annual report. and ratio analysis. Keep this book handy for easy reference throughout your career. and the statement of cash flows are the primary documents analyzed to determine the company’s financial condition. Jae K. it will help you answer financial questions in all the areas mentioned here and in any other matter involving money. Shim . What has been the trend in profitability and return on investment? Will the business be able to pay its bills? How are the receivables and the inventory turning over? Various financial statement analysis tools are useful in evaluating the company’s current and future financial conditions. You should be able to make an informed judgment on the financial position and operating performance of the entity.
About the Author Jae K. OMEGA. Shim is a coauthor of Handbook of Financial Analysis. Management Science.D. Corporate Controller. degrees from the University of California at Berkeley (Haas School of Business). and Journal of Systems Management. The Vest-Pocket CFO. Dr. Shim is Professor of Accountancy and Finance at California State University.B. Dr. Financial Management. Decision Sciences. Financial Accounting. Long Range Planning. Encyclopedic Dictionary of Accounting and Finance. Strategic Business Forecasting. . Managerial Accounting. Long Beach. He received his M. Shim has 45 other professional and college books to his credit. and Ph. He was a recipient of the 1982 Credit Research Foundation Outstanding Paper Award for his article on cash budgeting. Advances in Accounting. and the best selling Vest-Pocket MBA. Journal of Business Forecasting.A. Management Accounting. Dr. and Modeling. Journal of Operational Research Society. Forecasting. Shim has also published numerous refereed articles in such journals as Financial Management. Econometrica. Barron’s Accounting Handbook. CMA Magazine. The Vest-Pocket CPA. The CPA Journal.
..........................................................12 1......21 ...........14 Chapter 2 What Can You Do About Your Departmental Costs? .................................................5 1.....................................1 The What and Why of Finance ....................4............5 1.....3............2 Partnership ..............................................3 Basic Forms of Business Organizations.......3 Costs by Timing of Charges Against Revenue ...........................21 2...........................................2...............................2..4.......20 2......................................16 2....................1 Costs by Behavior............4............2 Financial Assets vs...............3.12 1.......................................11 1...........4 Financial and Operating Environment .....16 2......16 2.........2 What Are Financial Managers Supposed to Do?.........5 Costs by Averaging...............................................................1 Sole Proprietorship .......................2....................................4 How Do Your Costs Behave? ...............................................10 1.............................11 1...............6 1....................10 1..... Control.... Real Assets ..............3 What Is the Relationship Between Accounting and Finance? ....5 Conclusion ......................6 1......................5 Segregating Fixed Cost and Variable Cost....................................................4.........................2 Costs by Ease of Traceability....................................3 Other Important Cost Concepts Useful for Planning..........................................................................................2........9 Conclusion ....5 1.....................................................4.......1 The Nonfinancial Manager’s Concern with Finance ....4......................3 1......................4 Costs by Behavior...17 2........1 Costs by Function...15 2............8 What You Can Learn from the Japanese.........3.........15 2.....7 Cost Analysis ...........3 Corporation ...2 What Are the Scope and Role of Finance?...................3.............2 Types of Costs .Table of Contents Part I Thinking Finance Chapter 1 Financial Decision Making and Analysis .3 The Importance of Finance ......................17 2..................6 Costs by Controllability..................1 What Should You Know About Financial Institutions and Markets?...............................................................................3......10 1........2..................18 2..........................................................................17 2....1 Importance of Cost Data ................................18 2......3 1.6 Cost Allocation ..... and Decision Making.....................................4.............................................................15 2..................................................................3................15 2......................................20 2....20 2......................................................2......
.........29 4.9 Conclusion ......................................58 6..........37 Chapter 5 How to Make Short-Term......................................................7...............3 Determining Profit from Year to Year ........................61 6..............50 6..........2 How Do You Determine a Bid Price?....................9 The Budgeted Income Statement ..............................7 Conclusion .....5 Conclusion ........46 5..39 5.........6 Adding or Dropping a Product Line .................7...........................................1 Should You Accept a Special Order? ........23 3.......................................49 6.......................................................................8 Do Not Forget the Qualitative Factors.................................8 The Cash Budget ..7........39 5.....................58 6..............7.....7...........................................64 ...........2 The Production Budget.....................................................................................5 Determining Whether to Sell or Process Further .............................................4 Analyzing the Make-or-Buy Decision ....................4 Cash Break-Even Point .................................57 6.......7...............................60 6..................................................2 Accepting or Rejecting a Special Order ...............61 6...........4 The Direct Labor Budget ........................................34 4....................................5 What Is a Budget? .......28 Chapter 4 Are You Breaking Even?.........................59 6........36 4.....43 5...............33 4.................26 3..........33 4...........44 5................................................................................................................................................................4 Are You Utilizing Capacity? ....................................10 The Budgeted Balance Sheet ...........................................................................1 The Sales Budget.....3 How Do You Prepare a Financial Forecast? ..................1 What Costs Are Relevant to You? ...............................................5 The Factory Overhead Budget ..............................7 The Selling and Administrative Expense Budget ..6 Sales Mix Analysis ..................................................................................................................................7 What Is the Structure of the Budget? .......1 What Is a Forecast? .....................5 What Is Operating Leverage?..................3 Pricing Standard Products .........................................................60 6.40 5............................................................................55 6........7 Utilizing Scarce Resources.........................................................................2 How Can You Use Forecasts? .......24 3.........7...44 5.......................................45 5............49 6.........25 3........52 6.....7.................. Nonroutine Decisions.............................4 Percent-of-Sales Method of Financial Forecasting..........3 The Direct Material Budget .41 5....7.............................................55 6..................50 6..........................................................................6 What Assumptions Must Be Made?....2 What and Why of Break-Even Sales ..............................................................................Chapter 3 How You Can Use Contribution Margin Analysis..............47 Chapter 6 Financial Forecasting and Budgeting..6 The Ending Inventory.......7..............29 4........28 3.....29 4............................3 What Is Margin of Safety? .........1 What Is Cost-Volume-Profit (CVP) Analysis?..........49 6..........................................63 6....
.........................................................................................107 ..............................................................8 7.................................................................78 7.............................................................65 Can You Use an Electronic Spreadsheet to Develop a Budget Plan?..........10 Is There a Shortcut Approach to Formulating the Budget? .....................95 Chapter 9 How to Manage Your Accounts Receivable ......................................................................97 9.............5 7....................74 The Use of Flexible Budgets in Performance Reports........7 7.........................................................2 Inventory Analysis .............................4 Getting Money Faster .........................................................1 Credit References ............3 Analyzing Accounts Receivable....5 Delaying Cash Payments.....8 Conclusion .....................................1 Inventory Management Considerations....92 8...........................2 Credit Policy ................78 7.............................................76 Standards and Variances in Marketing..................................................7 Volume Discounts...........................................................99 9.....................................................103 Chapter 10 How to Manage Inventory .10 6....................6 Opportunity Cost of Foregoing a Cash Discount .......65 Conclusion ..........................................................79 Variances in Warehousing Costs .....................80 Conclusion ..................................11 Chapter 7 7........................................................3 Managing Cash Properly ....................1 7........4 Conclusion ...........105 10............................6..................................4 7............................66 Using Variance Analysis as a Financial Tool .........86 8........................................................................2 Analyzing Salesperson Variances....94 8.................................................................2 7.11 7...........97 9...............................................................85 8....................................................................3 7.94 8.......10...............................................................68 The Usefulness of Variance Analysis..........12 Part II Critical Asset Management Issues Chapter 8 Working Capital and Cash Management ....................10...........85 8.............................69 Determining and Evaluating Sales Variances ...................71 Materials Variances............65 Computer-Based Models for Financial Planning and Budgeting..............................................................................................................................................................................................................98 9......9 7................................................................................88 8...............................................68 Setting Standards ..............................2 Financing Assets ....................67 Defining a Standard .............................................85 8......73 Overhead Variances ..........1 Sales Standards ....105 10......1 Working Capital.....9 6..................8 6.........................6 7.....................................................71 Labor Variances ...................................................81 7......70 Cost Variances..
7 10.........3............112 Conclusion .................135 What Are the Features of Investment Projects?...................143 12..........4 12........143 12.........2 12.........................5 Profitability Index .................4 10..138 12.......................................................................128 Conclusion ................................13 11..............124 Annual Percentage Rate (APR)...7 11..............................................................................3 Understanding the Concept of Time Value..............6 10..................122 Perpetuities.................2 11......4 Internal Rate of Return (IRR) ..........................3.119 Present Value — How Much Is Money Worth Now? ................117 Intrayear Compounding ......126 Bond Values ........................................................................1 Payback Period .......123 Deposits to Accumulate a Future Sum (or Sinking Fund) ...16 Chapter 12 12........3 Double-Declining-Balance (DDB) Method ........................................................109 Avoiding Stockouts...................................................136 12..................118 Future Value of an Annuity .........6...............................8 Determining the Carrying and Ordering Costs..............125 Rates of Growth...................................................................1 12..................................2 Accounting Rate of Return (ARR) .............6......137 12.....11 11........................................5 12.....................................................15 11..............................141 Types of Depreciation Methods ...............................................................................3............114 Part III Financial Decision Making for Managers Chapter 11 11..........135 What Are the Types of Investment Projects?.........................................................12 11.....9 11...140 How Do Income Taxes Affect Investment Decisions? ....................................................3 Net Present Value (NPV)...............................................................................................................................122 Applications of Future Values and Present Values ....7 ..110 Determining the Reorder Point or Economic Order Point (EOP).................................117 Future Values — How Money Grows....................121 Present Value of an Annuity...136 How Do You Measure Investment Worth?....................5 10..........................3 11..................................................6...............................8 11...126 Compound Annual Rate of Interest ........3..............................128 Capital Investment Decisions ...10 11........................................127 Use of Financial Calculators and Spreadsheet Programs...140 How to Select the Best Mix of Projects with a Limited Budget .......144 How does MACRS Affect Investment Decisions? ...............................................6 11..........1 11.................10.......14 11...................................................5 11.......2 Sum-of-the-Years’-Digits (SYD) Method ...3.........................120 Present Value of Mixed Streams of Cash Flows ..111 The ABC Inventory Control Method ...143 12...........139 12.............108 The Economic Order Quantity (EOQ)..........3 10.....145 12....................6 12.......123 Amortized Loans ........................136 12...........4 11..............1 Straight-Line Method ..
.....153 ROI and Profit Planning .............................151 What is Return on Investment (ROI)? ............2.............161 14......................................2..........173 14..................................162 14.............................182 15.....4..........................................148 12........................151 What Does ROI Consist of? — Du Pont Formula .........................................185 15......2......................................2 Interest and Dividends Paid........................................154 ROI and Return on Equity (ROE)...............159 Conclusion ........................184 15.............................2 Responsibility Center .......8....185 15.............2 Cost Center ..................................180 15..1 Interest and Dividend Income ........147 12.......148 12.........1 Cost of Debt and Preferred Stock ........1 Return on Investment (ROI)...179 15........8 12.......................152 ROI and Profit Objective .2...........149 12...........................................9 Chapter 13 13...............5 13.....1 13..3...3 Profit Center..4 Capital Gains and Losses ...........................179 15.....2 Residual Income (RI) .175 14....................................................................8.........................185 ................................3 Cost of Retained Earnings..........184 15.............6 13....................2....4 Measuring the Overall Cost of Capital ....4 13........1 Tax Strategies and Planning .....156 A Word of Caution ...............7 What to Know About the Cost of Capital ..2 Limited Liability Companies...................................................2........................................................................................12..............................................181 15...................160 Chapter 14 How to Evaluate Your Segment’s Performance ........2..........162 14......................4...........2................................149 Conclusion ..........................4...3 Foreign Tax Credit...............8.....................1 S Corporations .............................2...........................1 Transfer Pricing .......................165 14........177 Chapter 15 How Taxes Affect Business Decisions ......8.........4 Conclusion .2....5 Modified Accelerated Cost Recovery System (MACRS)..............3 Conclusion .....................................................3 13...173 14......6...................................3 Operating Loss Carryback and Carryforward...........................................185 15...................183 15.........166 14............169 14..........2 13...............................2...1 Revenue Center........182 15...2.....2 Cost of Common Stock .......................2 Tax Computation ..............2............................................2.................6 Alternative “Pass Through” Tax Entities ....................................161 14.....................................................................176 14.....................................................4 Investment Center .....................1 Appraising Manager Performance........................6..................3 Decisions Under ROI and RI .........................................................................2....2...........................150 How to Analyze and Improve Management Performance........................
.......1 18.........2 The Pros of Going Public.................................................................3.................................207 Insurance Company Term Loans..1 17..........................1 Are You Eligible for an Unsecured Loan?..................................5 How Do You Compute Interest? .........................................3......................6 17...........................4 What Should You Know When Dealing With a Banker?...........................................................................192 16.......213 18........................3 18.....................222 18.....................9 Should Inventories Be Used for Financing? ..................................................3........................................................................................................................................................1 16.................2 16.......205 Using Revolving Credit ..................11 Conclusion ........218 18.197 16.............................207 Financing with Equipment ........3.....3...............192 16........5......................1 Mortgages .............................222 Chapter 17 17.3......4 18....................211 Publicly and Privately Placed Securities....................210 Conclusion ..214 18.............................................................2 18......................................................6 Alternatives to Going Public .......2 17...............205 Intermediate-Term Bank Loans.........................215 18........193 16.........................................................199 16..5 What Is the Process of Going Public? ...........................3.....217 18............................................2 What Will You Give to Obtain a Secured Loan?.....................5 ......219 Venture Capital Funding........3.196 16................................190 16..............................10 What Other Assets May Be Used for Financing? ...................201 16.......3 17...201 Looking at Term Loans and Leasing .............3..............................................................5 17.3 What Line of Credit Can You Get?..................207 Leasing..................3................................3.......Part IV Obtaining Funds Chapter 16 16.....197 16.189 How to Use Trade Credit ......................3 The Cons of Going Public ..........................................................4 What Is an Installment Loan? ..................212 Going Public — About an Initial Public Offering (IPO) ..4 How to Avoid the Drawbacks of Going Public ...................4 17...........194 16.................220 Types of Long-Term Debt and Their Usefulness ..........211 Investment Banking ......................214 18............5 What Are Banker’s Acceptances? ............190 When Are Bank Loans Advisable? .....................210 Deciding on Long-Term Financing..................................7 Are You Financially Strong Enough to Be Able to Issue Commercial Paper? ...................................8 Should Receivables Be Used for Financing?.............................207 Lease-Purchase Decision ..............7 Chapter 18 18...1 How Does Going Public Work? .................196 16..192 16...................................................3 What to Know About Short-Term Financing..............................6 Are You Forced to Take Out a Commercial Finance Company Loan?...................................189 Cash Discounts .197 16.........................................
...........6............2 Common Stock Features ..........4 A Chart of Accounts................2.................5 Liabilities ..............................................................................224 18.....1 FASB Requirements .............5......................2 The Statement of Cash Flows ..........................2.................2 Expenses .......................243 19..............1 Preferred Stock ......244 19..............................................1..............245 19............2 Conclusion .......................1........................3 Bond Ratings ...2 Types of Bonds ...........247 19.....1..........................................248 19...................5............3 Ledger .8 Bonds ................238 18.............................1...............................3 The Advantages and Disadvantages of Debt Financing ............................256 20......243 19......1 Working a Loan Online ...........................................................................................249 19.........................2 Raising Equity and Venture Capital Online.228 18..............................................................................................249 19...4 Assets ..234 How Should You Finance? ......................5 The System of Debits and Credits ....3 Net Income (Loss) ...................................................251 20............7 18..............................................................................228 18.......................1.5.........................2.....................................251 20.............235 18..7..2.................2 The Account...................................4 Bond Refunding...5....................................1 The Income Statement and Balance Sheet ..........18.......................................1 Computing Interest ........................................................250 Chapter 20 Recording Financial Information and Accounting Conventions ......1.............................................2..5.....244 19..............1 Double Entry and the Accounting Equation ..............................3 Conclusion ................................259 ..................256 20..............................230 18......................2........5 Financing Activities ...............251 20..............245 19...........227 Equity Securities...1.............249 19..............................243 19.............2 Accrual Basis of Accounting....222 18................225 18.............................6 18..................................1 Stock Rights.....................1 The Accounting Equation...6 Equity.......3 Operating Activities .........................................258 20.........4 Investment Activities .............1...............................................6 The “How and Why” of Debits and Credits...1 Revenue......2..................2.......1....1...........7 Journals ...............259 20....259 20.......................243 19..................................1.........240 Part V Dissecting Financial Statement Information Chapter 19 Understanding Financial Statements....256 20...............1.223 18..7................239 Conclusion ...................................................................................1................................6.5..............2.......................................................................................................................................................2 18..248 19................................222 18........6.......................................................................................
.........................................................................................3 21..........................2 21..............................271 An Overall Evaluation — Summary of Financial Ratios..261 Horizontal and Vertical Analysis......................3...............1 21....................................................5 Market Value..............................275 Conclusion .......4 21....3 Solvency (Leverage and Debt Service)...........269 21...................261 What and Why of Financial Statement Analysis................264 21....266 21..............................................278 Index.........2 Asset Utilization ....1 Liquidity..5 Analyzing Financial Statements....................3.............265 21..3......270 21.....................................................................3...........................................................................................................4 Profitability ............................279 ..........................................................262 Working with Financial Ratios.....3.........................Chapter 21 21.....................
Part I Thinking Finance .
There are many types of plans a nonfinancial manager might have to deal with: production plans. problem solving. the budget communicates overall corporate goals to the department managers so they clearly know what is expected of them. Even after the budget is implemented.1 Financial Decision Making and Analysis A company exists to increase the wealth of its owners. you will learn about the nonfinancial manager’s concern with finance. Financial management deals with planning decisions to achieve the goal of maximizing the owners’ wealth. the right questions to ask. Further. and all require some kind of financial knowledge. This is true whether you are a manager in production. They set objectives and plot efficient courses of action to obtain those objectives. financial plans. Management is concerned with determining which products and services are needed and putting them into the hands of its customers. marketing. and where to get the answers. You should know what to look for. nonfinancial managers. For example. and the financial and operating environment in which finance is situated.1 THE NONFINANCIAL MANAGER’S CONCERN WITH FINANCE You should have knowledge of finance and know how to apply it successfully in your particular departmental functions. You must identify any problems with the proposed budget so they are rectified before the budget is finalized. You are typically a participant providing input when the budget is prepared. Each of these plans is very different. and decision making. 1. the responsibilities of financial managers. the language of finance. In this chapter. you 3 . the relationship between accounting and finance. and so on. Also. personnel. cannot carry out their responsibilities without accounting and financial information. like financial managers. Finance provides a link that facilitates communication among different departments. or any other department. the scope and role of finance. you must have financial and accounting knowledge in order to understand the financial reports prepared by other segments of the organization. you as a department manager must present a strong case to upper management to justify budgetary allowances. you may suggest changes in subsequent budgetary formulations. marketing plans. Financial knowledge aids in planning. Finance provides a road map in numbers and analysis so that you can optimally perform your duties. it also provides guidelines for how each department may conduct its activities. You must know what the numbers mean even if you do not have to determine them. Nonfinancial managers spend a good portion of their time planning. personnel plans. operations. Because finance is involved in every aspect of a company’s operations. Most importantly.
there will be changes in plant and equipment requirements that dictate increased external funding. you have something of value that will pay off in future earnings. The cost of raw materials is one of the most important manufacturing costs. As one nonfinancial manager I interviewed who was working for an electronics company put it: My knowledge of accounting and finance helps me to report results. If you show signs of being ill prepared. Because many of your decisions have financial implications. you must consider the feasibility of the purchase. If you do not adequately understand the budget or communicate requirements. They can justify costs associated with an advertising campaign by estimating its value. as well as a host of others. you will give a negative impression that may result in the loss of resources. you are continually interacting with financial managers. and decide the direction of my department. . plant. and my financial knowledge is a very important tool in my career development.4 Accounting and Finance for the Nonfinancial Executive must intelligently discuss the budget with other organizational members. Thus. understand reports. such as equipment or an automobile. The cost of alternative materials along with their quality must be known since cost affects selling price. marketing. budget for proper staffing. Therefore. You may be involved in a decision of whether to lease or buy an asset. new product lines). Thus. The purchasing manager must know whether sufficient funds exist to take advantage of volume discounts. Capital investment projects (property. For instance. thus adversely affecting future sales.. Here. marketing decisions influence growth in sales and. your department may fail to achieve its goals. customer orders may not be filled in a timely fashion. if materials are not delivered on time. the marketing manager must have knowledge of the constraints of fund availability. as a result. managers in these areas must be involved with planning and analyzing project performance. control expenses. Further. You should be able to understand such data in order to make intelligent decisions. Your request for resources will entail financial plans for the contemplated project. Advertising managers also make key decisions related to finance. In certain situations you may obtain financial information about competitors. and equipment) are closely tied to plans for product development. If customers want to buy your products. and plant utilization. and production. You must evaluate and appraise monetary and manpower requests before submission. and inferior materials may create production problems that eat into divisional profitability. For these reasons. allocate resources. I need every edge I can get in order to continue moving ahead. You have to formulate and provide upper management with documented information to obtain approval for activities and projects (e. a knowledge of forecasting and capital budgeting (selecting the most profitable of several alternative long-term projects) is required. inventory policies. and we work in a very competitive environment as the company only promotes from within. Thus. There are thirty nonfinancial managers at my level within the company.g. you need basic financial knowledge to successfully conduct daily activities.
Therefore. you need knowledge of it to perform effectively. and the relationship between accounting and finance will be explained. concepts. For effective communication. and other aspects of finance. You will see the responsibilities of financial managers. Accounting is generally broken down into two categories: financial accounting and managerial accounting. for example. and monitoring performance. You can “open the door” to the finance department by having a better understanding of the finance function. the less inventory (merchandise held for resale) you keep.3. but also the greater the risk of running out of stock and thus losing sales and customer goodwill. which helps to determine if the expected return is sufficient to justify the risks taken. the greater the return required. 1.1 THE WHAT AND WHY OF FINANCE Finance involves many interrelated areas such as obtaining funds. One important aspect of finance is the analysis of the return-risk tradeoff. Financial and managerial accounting are discussed later in this chapter.g. 1. taxes. and applications aids in the overall management of your departmental affairs. and communicate clearly about the quantitative aspects of performance and results.Financial Decision Making and Analysis 5 1. you must be able not only to understand what financial people are saying. you have to be familiar with the basics of accounting. new product line. In managing your inventory of stock. use that information effectively.. Finance uses accounting information to make decisions regarding the receipt and use of funds to meet corporate objectives. thus leading to more productive working relationships with finance professionals.. It enables you to look at current and prospective problems and find ways of solving them. To do so. The greater the risk with any decision (e. but also to express your ideas in their language. You must clearly and thoughtfully express what you need to financial officers in order to perform effectively. you will learn the language of finance as well as the what and why.3 THE IMPORTANCE OF FINANCE Finance provides discipline to all the components of the organization involved in decision making.2 WHAT ARE THE SCOPE AND ROLE OF FINANCE? In this section. you will be able to comprehend financial information (e. new territory). Managerial accounting provides financial information useful in making better decisions regarding the future. . the higher the expected return (since less cash is tied up).g. A knowledge of finance terminology. using funds. If you master the finance vocabulary. economics. techniques. Financial accounting records the financial history of the business and involves the preparation of reports for use by external parties such as investors and creditors. budgets). Chapters 19 to 21 cover financial accounting while Chapters 2 to 7 and 13 to 14 zero in on managerial accounting.
1 presents the functions of the financial manager. as well as modification or replacement of assets. operations research staff. Financial managers must know how to manage assets so as to optimize the rate of return. If you are employed by a large firm. business managers. the financial responsibilities are probably carried out by the treasurer. Timing and risk of earnings. 2. production personnel. Public relations managers must know about the financial strengths of the business. For instance. lawyers. controller. Figure 1.6 Accounting and Finance for the Nonfinancial Executive No matter who you are.2 WHAT ARE FINANCIAL MANAGERS SUPPOSED TO DO? The financial manager plays an important role in the company’s goals. and inventory to accomplish higher returns without undue risk. Present and future earnings per share (EPS). and tax experts. Production managers have to be familiar with budgeting and effective handling of productive assets. The primary distinctions between accounting and finance relate to the treatment of funds and decision making. public relations managers. bonds. 4. Table 1. • Financing and capital structure decisions — Raising funds on favorable terms. The financial manager makes decisions regarding the mix and type of assets acquired.1 shows an organization chart of the finance structure within a . investment planners. and financial success. Operations research staff has to know about the time value of money.3 WHAT IS THE RELATIONSHIP BETWEEN ACCOUNTING AND FINANCE? Accounting is a necessary input and subfunction to finance. Personnel executives must know about planning.3. The financial manager affects stockholder wealth maximization by influencing: 1. 3. economists. For example. Manner of financing. policies. • Investment decisions — Allocating funds to specific assets (things owned). marketing managers have to know product pricing and variance analysis.3. you are involved with finance in one way or another. Dividend policy. 1. that is. among others. 1. determining the nature of the company’s liabilities (obligations). designating the size of the firm and its rate of growth. and other investments. Financial knowledge is required of marketing managers. Investment planners have to be familiar with the valuation of stocks. receivables. that is. and financial vice president (chief financial officer). The financial manager’s responsibilities include the following: • Financial analysis and planning — Determining the proper amount of funds to employ in the firm. should funds be obtained from short-term or longterm sources? • Management of financial resources — Managing cash.
Evaluation and Consulting Consultation with and advice to other corporate executives on company policies. Provision of Capital Short-term sources. cost and arrangements Long-term sources. custody. objectives.1 Functions of the Financial Manager A. Planning Long.and short-range financial and corporate planning Budgeting for operations and capital expenditures Evaluating performance Pricing policies and sales forecasting Analyzing economic factors Appraising acquisitions and divestment B. Accounting and Control Establishing accounting policies Development and reporting of accounting data Cost accounting Internal auditing System and procedures Government reporting Report and interpretation of results of operations to management Comparison of performance with operating plans and standards E. Tax Administration Establishing tax policies Preparation of tax reports Tax planning G. Administration of Funds Cash management Banking arrangements Receipt. Investor Relations Maintaining liaison with the investment community Counseling with analyst-public financial information H. and their degree of effectiveness I. cost and arrangements Internal generation C. operations.Financial Decision Making and Analysis 7 TABLE 1. Management Information Systems Development and use of computerized facilities Development and use of management information systems Development and use of systems and procedures . Protection of Assets Providing for insurance Establishing sound internal controls F. and disbursement of companies’ securities and moneys Credit and collection management Managing pension moneys Investment portfolio management D.
The controller prepares the annual report and Securities and Exchange Commission (SEC) filings as well as tax returns. and timely handling of controllership and treasurer functions will ensure corporate success. company. The primary function of the controller is ensuring that funds are used efficiently. Managerial accounting is the preparation of reports used by management for internal decision making.8 Accounting and Finance for the Nonfinancial Executive President (CEO) Vice President Manufacturing Vice President Finance (CFO) Vice President Marketing Treasurer Controller Cash Manager Credit Manager Tax Manager Cost Accounting Manager Financial Accounting Manager Financial Planning Manager Capital Expenditure Manager Fund Raising Manager Investment Manager Computer Manager FIGURE 1. competent. but typically controllers are concerned with internal functions whereas treasurers are responsible for external functions. The internal matters of concern to the controller include financial and cost accounting. this function is of internal nature. Form 10-Q. Management is involved with finance primarily in two ways. control. and Form 8-K. He or she has financial and managerial responsibilities. First. there is the record keeping. and serves as the financial adviser to the board of directors. The external function involves outside entities. costing. The control features of the finance function are referred to as managerial accounting. as well as obtaining funds to satisfy current and future requirements. The effective. You should know the responsibilities of these financial officers within your own organization and how the function of each affects you. The functions may differ slightly between organizations because of personality and company policy. The controller is primarily involved in collecting and presenting financial information. pricing. The financial vice president is involved with financial policy making and planning. capital .1 Financial activity organization. The SEC filings include Form 10-K. and audit functions. and controlling of the financial effects of prior and present operations. including budgeting.2 lists the typical responsibilities of the treasurer and controller. supervises all phases of financial activity. Table 1. but there is no universally accepted precise distinction among the two jobs. He or she typically looks at what has happened instead of what should or will happen. Note that the controller and treasurer report to the vice president of finance. tracking. taxes.
The treasurer’s responsibility is mostly custodial in obtaining and managing the company’s capital. Managerial accounting relies heavily on historical information generated in the financial accounting function.Financial Decision Making and Analysis 9 TABLE 1. He or she deals with creditors (e. the break-even point is useful to marketing managers in deciding whether to introduce a product line. The controller function also involves reporting to top management and analyzing the financial implications of decisions. planning capital expenditures. accounts receivables inventory) and debt. investors. and governmental regulatory bodies such as the SEC. and emerging patterns. Whereas the accountant concentrates on profitability. the treasurer emphasizes the . but managerial accounting differs from financial accounting in that it is future-oriented (making decisions that ensure future performance). underwriters for equity (stock) and bond issuances. current. Unlike the controller. and rate of return analysis. performance evaluation. obtaining funds. stockholders. bank loan officers). The treasurer concentrates on keeping the company afloat by obtaining cash to meet obligations and to buy the assets needed to achieve corporate objectives. The treasurer is responsible for managing corporate assets (e. formulating credit policy.. Budgets provide manufacturing guidelines to production managers. the treasurer is involved in external activities primarily involving financing matters. Many controllers are involved with management information systems that analyze prior. break-even analysis (sales necessary to cover costs).2 Responsibilities of Controller and Treasurer Controller Accounting Reporting of financial information Custody of records Interpretation of financial data Budgeting Controlling operations Appraisal of results and making recommendations Preparation of taxes Managing assets Internal auditing Protection of assets Reporting to the government Payroll Treasurer Obtaining financing Banking relationship Investment of funds Investor relations Cash management Insuring assets Fostering relationship with creditors and investors Credit appraisal and collecting funds Deciding on the financing mix Dividend disbursement Pension management budgeting. For example. and managing the investment portfolio. Managerial accounting information is vital to the nonfinancial person. planning the finances.g. transfer pricing (pricing of goods or services transferred between departments).g.. Variance analysis is used to compare actual revenue and costs to standard revenue and costs for performance evaluation so that inefficiencies can be identified and collective action taken.
a company may fail. and makes decisions based on the analysis. Even a company that has been profitable may have a significant negative cash flow. REAL ASSETS The two basic types of investments are financial assets and real assets. formulates additional data. the financial manager should prevent bankruptcy and accomplish corporate goals. The financial manager appraises the financial statements.S. The financial markets are composed of money markets and capital markets.1 WHAT SHOULD YOU KNOW ABOUT FINANCIAL INSTITUTIONS AND MARKETS? A healthy economy depends heavily on efficient transfer of funds from savers to individuals. is an example of a major capital market. In addition. and governments who need capital. By concentrating on cash flow. including financial institutions. Figure 1. 1. For example. and negotiable certificates of deposit issued by government. there may exist substantial long-term receivables (debts owed to the company but not yet paid). which handles the stocks of many of the larger corporations. companies demanding funds are brought together with those having surplus funds. 1. and financial institutions. In this section we will discuss financial institutions and markets. Treasury bills. or they show your right to buy or sell your ownership interest at a . Most transfers occur through specialized financial institutions. or they provide evidence that someone owes you a debt. Your financial assets comprise intangible investments (things you cannot touch). The New York Stock Exchange. securities are traded through the thousands of brokers and dealers on the over-the-counter (OTC) market.4 FINANCIAL AND OPERATING ENVIRONMENT You operate in the financial environment and are indirectly affected by it.2 depicts the general flow of funds among financial institutions and markets. Capital markets are the markets for long-term debt and corporate stocks. In the financial markets. In fact.2 FINANCIAL ASSETS VS. businesses. a term used to denote all buying and selling activities in securities that do not occur on an organized stock exchange.10 Accounting and Finance for the Nonfinancial Executive sources and uses of cash flow. financial vs. Financial markets provide a mechanism through which the financial manager obtains funds from a wide range of sources. real assets. commercial paper. They represent your equity ownership of a company.4. Examples of money market securities include U.4. which serve as intermediaries between suppliers and users of funds. without sufficient cash flow. and the alternative forms of business organizations. The American Stock Exchange and the regional stock exchanges are still other examples. business. Money markets are the markets for short-term (less than one year) debt securities. 1.
partnership. subsequent date. The income of the business is taxed as personal income. or number of employees). Sole proprietorships are the most numerous of the three types of organizations. Funds are raised from personal resources or through borrowings. usually. savings accounts.2 General flow of funds among financial institutions and financial markets.4. bonds. money market certificates. precious and common metals. they include real estate. and corporation. and financial futures (contracts to buy financial instruments at a later date).3 BASIC FORMS OF BUSINESS ORGANIZATIONS The basic types of businesses are sole proprietorship. preferred stock. Financial assets include common stock. Real assets are investments you can put your hands on. Confidentiality is maintained.Financial Decision Making and Analysis 11 Financial Institutions Commercial banks Mutual savings banks Savings and loan associations Pension funds Life insurance companies Credit unions Investment banking houses (or brokerage houses) Others Suppliers and Users of Funds Individuals Businesses Governments Financial Markets Money markets Capital markets FIGURE 1. Profits and control are not shared with others. only the proprietor and a few employees work in it. . and service sectors. Sole proprietorships are common in the retail.3. and oil. Treasury bills. Organizational costs are minimal. The sole proprietor makes all the decisions. total assets. The advantages of a sole proprietorship are: • • • • • No formal charter is required. corporations are usually of the largest size (in terms of sales. 1. Of the three. machinery and equipment. wholesale. whereas partnerships and proprietorships emphasize entrepreneurship to a greater degree. The typical sole proprietorship is a small business. 1. commercial paper (unsecured short-term debt).4. options and warrants to buy stock at a later date.1 Sole Proprietorship A sole proprietorship is owned by one individual. Sometimes referred to as real property.
• More funds are typically obtained than by a sole proprietorship.4. However. brokerage.3. • Partnerships are free from special governmental regulation. Each partner’s interest in the property is based on his or her proportionate capital balance. the partnership is not bound by acts committed beyond the scope of the partnership. Partnerships are often formed to bring together different skills or talents. Unlimited liability exists for the owner. • Income of the partnership is taxed as personal income to the partners. The partnership (and thus each individual partner) is legally responsible for the acts of any partner. If nothing about distribution is stated. at least compared to corporations.3. • Because it cannot sell stock. The life of the business is limited to the life of the owner. its ability to raise significant capital is limited. Ownership is evidenced by possession of shares of stock. The partnership contract (articles of partnership) spells out the rights of each partner concerning such matters as profit distribution and fund withdrawal. • It dissolves upon the withdrawal or death of any partner. Forming a partnership creates these advantages: • Partnerships can be easily established. Partnerships are common in finance.2 A partnership is similar to the sole proprietorship except that the business has more than one owner. The sole proprietor must be a “jack-of-all-trades.4. they are not typically large businesses.” Partnership 1. public accounting. or to obtain the necessary capital. and law. Profits and losses are divided in accordance with the partnership agreement. Partnership property is jointly owned. insurance. Each partner acts as an agent for the others. each member is held personally liable for all partnership debts. • Better credit standing results from the availability of partners’ personal assets to meet creditor claims. with minimal organizational effort. • Partnerships attract good employees because of potential partnership opportunities. 1. real estate. they are distributed equally. Although partnerships are generally larger than sole proprietorships. The corporate form is not the .3 Corporation A corporation is a legal entity existing apart from its owners (stockholders).12 Accounting and Finance for the Nonfinancial Executive The disadvantages are: • • • • The ability to raise large sums of capital is limited. which may restrict growth. Its disadvantages are as follows: • It carries unlimited liability for the partners.
c. Its disadvantages are: a. It cannot have any nonresident foreigners as shareholders. A corporation cannot have more than 35 shareholders. but it is the most important in terms of total sales. b.4.3. d. profits. It cannot have more than one class of stock. The corporate form is implicitly assumed throughout this book. and contribution to national income.3. c. Difficult and costly to establish.1 Subchapter S Corporation A Subchapter S Corporation is a form of corporation whose stockholders are taxed as partners.Financial Decision Making and Analysis 13 FIGURE 1. Unlimited life. . b. Corporations are governed by a distinct set of state or federal laws and come in two forms: a state C Corporation or federal Subchapter S Corporation. Limited liability for its owners. c. The general structure of a corporation is depicted in Figure 1. Note: Not all states recognize Subchapter S Corporations. Ease of transfer of ownership through transfer of stock. To qualify as an S Corporation. as a formal charter is required. as long as no personal guarantee on a business-related obligation such as a bank loan or lease exists. most numerous type of business.3. Subject to double taxation on its earnings and dividends paid to stockholders. does not discharge tax obligations. d. It must properly elect Subchapter S status. Bankruptcy. assets. even at the corporate level. The advantages of a C corporation are: a. b.3 Corporate structure. 1. The S Corporation can distribute its income directly to shareholders and avoid the corporate income tax while enjoying the other advantages of the corporate form. the following is necessary: a. Ability to raise large sums of capital.
Profits and losses can be split among members any way they choose. The members run the company unless they hire an outside management group. medicine. procedures. The nonfinancial manager must comprehend the goals.5 CONCLUSION This chapter discussed the functions of finance. Most states permit the establishment of LLCs.14 Accounting and Finance for the Nonfinancial Executive 1. performance evaluation. The financial functions of the business impact nonfinancial activities in such areas as record keeping. as a corporation does. promotion. An LLC provides limited personal liability. Owners. advertising. Ignorance of finance will not only lead to incorrect analysis and decisions but will also prevent you from moving within the organization. law. The LLC can choose whether to be taxed as a regular corporation or pass through to members. and accounting).3. whose recommendations you may not be able to totally understand or. Note: Rules governing LLCs vary by state. if necessary.g. A successful operation blends sales.3. yardsticks. marketing. 1. you cannot contribute sound input to the decision process. An important reason why you need the financial and accounting knowledge edge is that without a good understanding of these disciplines you do not have the tools needed for effective management decision making. You would have to rely totally on the financial manager.. can be other corporations. and the acquisition and utilization of resources. and functions of finance to optimally perform his or her duties. and how the nonfinancial manager fits in a typical company’s structure. LLCs are typically not permitted to carry on certain service businesses (e. and finance with some degree of goal congruence. variance analysis. the environment in which finance operates. Decisions that make sense in terms of marketing and sales must also make financial sense.4. dispute. techniques.2 Limited Liability Company Limited Liability Companies (LLCs) are a relatively recent development. who are called members. . Without some financial background.
by telephone.g. territory. Cost information also assists in determining: (1) the minimum order to be accepted. direct labor. First.. and other expenses) when determining a selling price that accounts for expected inflationary price increases. and other important cost concepts. Cost information is also useful in planning and budgetary decisions. Your budgeted costs must be sufficient to meet your needs.2 TYPES OF COSTS Costs are classified according to function. and factory overhead. you must know total costs and costs per unit. averaging.2. and control. cost information allows the purchasing manager to evaluate which suppliers are the least costly to use (i. (2) the profitability of a particular product.e. and planning. and (3) the method of servicing particular types of accounts (e.. 2. through jobbers. and proper costing will ensure the appropriate use of and accountability for your department’s resources. You must also be familiar with the various cost concepts that are useful for income determination.1 IMPORTANCE OF COST DATA Obtaining and understanding cost information is essential to your business success. including any transportation charges). selling. or customer. or by mail order). In establishing a price for your product or service. Different types of costs are used for different purposes. behavior. the selling price should similarly be increased by 6%. controllability. if inflation is expected to be 6% next year. you will incur a loss. All costs applicable to a product or service must be considered (including manufacturing. your costs determine your selling price. short-term and long-term decision making. 2. ease of traceability. if your costs exceed your selling price. the total cost associated with buying their merchandise. 2. For example. 15 .1 COSTS BY FUNCTION Manufacturing costs include any costs to produce a product consisting of direct material. In addition. timing of charges against revenue.2 What Can You Do About Your Departmental Costs? Cost is an expenditure incurred to obtain revenue. evaluation.
insurance). insurance.g. They are charged against revenue in full in the year incurred.16 Accounting and Finance for the Nonfinancial Executive Direct material becomes an integral part of the finished product (e. and administrative salaries). therefore. Indirect (common) costs are more difficult to trace to a specific costing object because they are shared by different departments. profits can increase rapidly during good times. fixed costs do not increase.g.. ..4 COSTS BY BEHAVIOR Fixed costs include the costs that remain constant regardless of activity (e.g. They are charged to inventory first and then to cost of sales when sales are made. salespersons’ salaries. sales commissions. Selling expenses include the cost of obtaining the sales commission. territory.g.. general. advertising costs.g.g. however. However. rent. rent. the wages of assembly workers on an assembly line). in an analysis by product. These costs include sales. rent is allocated to a department based on square footage). customer class.2.g.. Product costs are related to manufacturing a product (e. property taxes. For example. or territory (e. which causes profits to fall rapidly.. Therefore. material and labor costs). Nonmanufacturing costs (operating expenses) are expenses related to operating the business rather than producing the product. in analyzing salespeople. Marketing costs should be evaluated based on the success of distribution methods (e. during bad times fixed costs do not decline. mail order sales). product. 2.g. 2. direct selling to retailers and wholesalers vs. such costs are allocated on a rational basis (e. jobs. taxes.. delivery charges).g. and method of sale. distribution outlet. job. products.. Selling costs may be analyzed for reasonableness by product. Factory overhead includes all costs of manufacturing except direct material and direct labor (e. General and administrative expenses include the costs incurred for administrative activities (e.. and fringe benefits). these expenses are indirect. depreciation on machinery in a department and advertising geared to a particular sales territory). depreciation. As sales increase. traveling and entertainment expenses are direct.2.. and administrative expenses.. steel used to make an automobile). executive salaries and legal expenses). or territories. or distributing the product to the customer (e.2 COSTS BY EASE OF TRACEABILITY Direct costs are directly traceable to a particular object of costing such as a department. Direct labor is labor directly involved in making the product (e.g.g.3 COSTS BY TIMING OF CHARGES AGAINST REVENUE Period costs are related to time rather than to producing the product (e..2. 2. A cost may be direct in one area and indirect in another.
Such examples include telephone bills.3 OTHER IMPORTANT COST CONCEPTS USEFUL FOR PLANNING. Uncontrollable costs are those costs over which a manager has no control (e.5 COSTS BY AVERAGING Average costs are the total costs divided by total units. Semivariable (mixed) costs include the costs that are part fixed and part variable. Standard costs are compared with actual costs in order to measure the performance of a given department.000 book value is a sunk cost that does not affect a future decision. direct labor). Joint costs are incurred for the benefit of the entire company (e. and short-term decision making. will not change regardless of which alternative is chosen.000. advertising if it is at the manager’s discretion). The breakdown of costs into their variable and fixed components is important in many areas.000 units. the incremental cost is $5. A semivariable cost varies with changes in volume but. Relevant costs include expected costs that will differ between alternatives. CONTROL. therefore. and car rentals charged as fixed rental fees plus variable mileage fees.2.000. property taxes). if total cost is $10. a 20% increase in variable cost accompanies a 20% increase in sales. Sunk costs are those costs of resources that have already been incurred. .000. legal fees). respectively. For example. if you have the choice of using your department’s capacity to produce an extra 10. For example. break-even analysis. the average cost is $10 per unit.g..000 units or renting it out for $20.2.6 COSTS BY CONTROLLABILITY Controllable costs are those costs over which a manager has direct control (e. and.000. but the sunk cost is irrelevant.. AND DECISION MAKING Standard costs are the carefully predetermined production or operating costs that serve as target costs.000 for the production of 1. 2. This $20.000. Incremental (differential) costs are determined by calculating the difference in costs between two or more alternatives.000 and $15.g. They represent past or historical costs. 2. if the direct labor costs for products A and B are $10. For example. 2.g. including flexible budgeting.000 machine paid for three years ago now has a book value of $20. unlike a variable cost. electricity bills.What Can You Do About Your Departmental Costs? 17 Variable costs include the costs that vary directly with changes in activity (e. The incremental cost is relevant to a decision. the opportunity cost of using the capacity is $20.. Thus. Opportunity costs include the net revenue foregone by rejecting an alternative. For example.. a $50. direct material.g. does not vary in direct proportion.
If production increases to 110.1 shows the behavior pattern for a fixed cost. such as rent.2 Cost Behavior for Rent Volume 100.000 units. and Figure 2.000 200.1. bonuses). and variable cost per unit is $3. Example 2.000 units) Total variable cost is $330. perhaps the most important way to classify costs is by how they behave in accordance with changes in volume or some measure of activity. Total fixed cost is $100..000. such as a product line. Table 2.000.2 shows the behavior pattern for a variable cost. the following results: 1.18 Accounting and Finance for the Nonfinancial Executive TABLE 2. 2.91 ($100.000/110. Variable cost per unit is $3.000 100. You can estimate the total cost of an item.4. Assuming idle capacity (not using all your department’s capacity). the cost behavior relationships of fixed cost. and Figure 2.2 illustrates the cost behavior for a fixed cost.1 COSTS BY BEHAVIOR From a planning and control standpoint.000 units.1 — Your company is operating at idle capacity. variable cost. .000 Unit Cost $1.1 Cost Behavior Unit Cost Fixed Variable Semivariable Up/down to volume Constant Up/down to volume Total Cost Constant Up/down to volume Up/down to volume TABLE 2.g. such as commissions.000 Rent $100. 3. Total fixed cost is still $100. 2.000 100. and semivariable cost are shown in Table 2. Table 2.50 Discretionary costs are those costs that can be discontinued without affecting the accomplishment of essential managerial objectives in the short term (e.3 illustrates the cost behavior for a variable cost.00 .4 HOW DO YOUR COSTS BEHAVE? 2.67 . Current production is 100. Fixed cost per unit is $. by combining the variable cost and fixed cost.000. 4.000 150.
10 .2 — There are 100 estimated units for product line X. The fixed cost is $600.25) .000 20.What Can You Do About Your Departmental Costs? 19 FIGURE 2. TABLE 2.000 Unit Cost $.000 Commissions $10.3 Cost Behavior for Commissions Volume 100.000 200.2 Variable cost behavior pattern. The total cost is: Fixed cost Variable Total cost $ 600 + 225 $ 825 (100 × $2.1 Fixed cost behavior pattern.25 per unit. FIGURE 2.000 150.10 . and the variable cost is $2.000 15.10 Example 2.
and industry standards.200 $1. aids efficiency evaluation. For example. Example 2.000 12. ease of use.000 20.5 SEGREGATING FIXED COST AND VARIABLE COST If you know the total cost you can determine the fixed and variable costs using the high-low method.7 COST ANALYSIS Cost analysis allows management to move carefully and accurately to control costs in the following ways: • Compensation and expenses for salespeople should be analyzed and compared to budget.g. using the high point: Total Fixed Cost = Total Cost – Total Variable Cost Total Fixed Cost = $4. • Cost estimates may be made for alternative methods of selling products (e. Total Cost High point (May) Minus low point (February) Change due to volume Change in cost per unit = $4. the variable cost per unit is $. The lowest volume occurred in February.10 × 32.20 Accounting and Finance for the Nonfinancial Executive 2.200 $12.6 COST ALLOCATION Cost allocation assigns a common cost to two or more departments.. evaluation can be performed related to the distribution of samples and the effect on costs and sales trends).10 Thus. You can now determine the fixed portion of the expense using either the lowest or highest volume level. direct labor cost.800 $1.000 = Unit Volume 32. The variable cost per unit may be computed by comparing the change in expense between high and low levels with the change in volume. and number of employees.000 $. . • Cost data of potential sales by product or territory may aid in the assignment of sales people.000 – ($.10. 2. Accurate cost figures are necessary for product costing and pricing. Possible allocation bases include units produced. Cost allocation enhances control. salary structure. Criteria in selecting an allocation base include cost benefit. direct labor hours. and industry standards. and promotes sound decision making. machine hours.3 — Your company reached its sales volume high in May.000 2. The costs are allocated in proportion to each department’s responsibility for their incurrence.000) = $800 2.
• Material costs should be evaluated for changes. cost per shipment. and difference in the quality of material. or they may change due to substitution of different materials. In an attempt to improve machine efficiency. Also. timely delivery. and evaluation of project status. or territory. . • The cost per month and cost per mile for auto expenses should be considered for reasonableness. instead of breakdown maintenance. changing suppliers.What Can You Do About Your Departmental Costs? 21 • Cost information for advertising programs helps in making decisions for future media communications. • An analysis of entertainment expenses should be made by customer. and low-cost production. Note that such selling prices may be lower than that supported by current manufacturing costs. salesperson. Japanese companies practice preventative and corrective maintenance. cost plus contracts. • Direct labor costs should also be evaluated for changes.9 CONCLUSION Cost information is imperative in the decision-making process and is necessary for operational and control purposes as well. and cost per order filled. equipment purchasing and rentals. cost per item handled. 2. Japanese companies also recognize that the best area to support low-cost production is usually in a product’s design stage. 2. Special cost structure may be formulated for market test cases to examine cost effectiveness. The project manager should have a basic knowledge of cost control so as to keep track of the expenses of his or her product. Such knowledge would be useful in analysis of payment requests to vendors. They design and build products and sell them at prices that will ensure market success. preparation of the progress report. in order to determine whether expenses are in line with the revenue obtained and whether the cost per dollar of net sales and the cost per customer are reasonable. • The following costs should also be analyzed for control purposes: cost per order received. new material waste will decline as the operation attains increased maturity. lump-sum vs. analysis of labor cost. Costs per unit may drop as a result of quantity discounts and changes in the suppliers’ freight charges and terms. To lower costs they reduce the number of parts and use standard parts across product lines with a variety of products. Costs per unit may decline due to increased worker experience in performing the task. cost per customer account.8 WHAT YOU CAN LEARN FROM THE JAPANESE Japanese manufacturing companies place high standards on quality.
000. In the contribution margin approach.1 — If the selling price is $10 per unit and the variable cost is $8 per unit. this procedure would be useful to formulate a bid price on a contract. For instance. and to decide whether to accept an order even if it is below the normal selling price. the contribution margin income statement is as follows: Sales (40.000 Example 3.3 How You Can Use Contribution Margin Analysis Contribution margin analysis is another tool managers use for decision making. expenses are categorized as either fixed or variable. The format of the contribution margin income statement follows: Sales Less: Variable cost of sales Variable selling and administrative expenses Contribution margin Less: Fixed cost Net income Example 3.000 × $5) Contribution margin (40.000 × $15) Less: Fixed Cost Net Income $ 800.000 units of a product at $20 per unit.000 $ 600. The contribution margin ratio (contribution margin/sales) is 20% ($2/$10). the expected departmental income will be as follows: 23 . The variable costs are deducted from sales to obtain the contribution margin. and fixed cost $3.000.000. variable cost $45. and so on.000 250. This information helps the manager to: (1) decide whether to drop or push a product line. The variable cost per unit is $5. (3) decide on pricing strategy and products or services to emphasize. and (4) appraise performance. Fixed costs are then subtracted from contribution margin to obtain net income.000 × $20) Less: Variable cost (40. a contribution margin of $2 per unit is earned.000 $ 350. Example 3.000. If there is an expected 10% increase in sales. and the fixed cost is $250. special advertising.3 — The following data applies to your department: sales $50.2 — You sell 40. (2) evaluate alternatives arising from production.000 200.
which are 14% of the selling price. Idle capacity exists.000) Contribution margin Less: Fixed cost Net income * $ 9.4 — You currently sell 8.400 $ 4. by $1.000 (fixed cost per unit is $60.200 to buy a special tool for this job. If idle capacity exists.000 0 $ 3.500 3.1 SHOULD YOU ACCEPT A SPECIAL ORDER? When idle capacity exists.000 × $9) Less: Variable manufacturing cost (1.800 ($3.10) Less: Variable cost ($45. even if fixed costs were to increase. an order should be accepted at below the normal selling price.000 × 1. The contribution margin income statement for this special order would be as follows: Sales (1. A potential customer is willing to purchase 500 units at $21 per unit.5 — Financial data for your department follows: Selling price Direct material Direct labor Variable overhead Fixed overhead ($100.000 .50 = $4.340 0 $ 3.$1. it still would be financially attractive to accept this order because you would still realize a profit of $1.24 Accounting and Finance for the Nonfinancial Executive Sales ($50.500 3.50 $ 5.000 49. or $7. You receive an additional order for 1.260 $ 3.000 4.000 × $4. the acceptance of an additional order does not increase fixed cost.000.90 + $.500 7.40 .000/$20.200). The contribution margin income statement for this special order would be as follows: Sales (500 × $21) Less: Variable cost (500 × $15) Contribution Margin Less: Fixed cost Net Income $ 10.500 $ 5. provided a contribution margin is earned.00 Selling and administrative expenses are fixed except for sales commissions.500 $ 3.10) Contribution margin Less: Fixed cost Departmental income $ 55. The variable cost per unit is $15. Example 3. say.000 You should accept this order because it increases your profitability. and the fixed cost is $60. However.00 $ 2.90 $ .600 1.00 + $1.00 $ 1.000 units at $30 per unit.340 Variable manufacturing cost = $2.000/8. because fixed cost will not change.50).40)* Manufacturing contribution margin Less: Variable selling and administrative expenses (14% × $9.000 units from a potential customer willing to pay $9 per unit.000) units $ 15.000 × 1. Idle capacity exists.000 $ 2. Example 3.
A knowledge of your variable and fixed costs is necessary to make an accurate bid price determination.000 $1.400 $ 25 Total direct labor for the year is $1.700 19. you still need to understand why your company asks you to sell an item at a lower price. when it may be financially beneficial to bid on extra business at a competitive price that covers all variable costs and makes some contributions to fixed costs plus profits. you should accept the incremental order since it will be profitable.000 4.000 = $540.= 22. computed as follows: 0. Example 3.000.000 2. 000 $405.2 HOW DO YOU DETERMINE A BID PRICE? Pricing policies using contribution margin analysis may be helpful in contract negotiations.5% (% of direct labor) $1.000 12.000 In this case.5% of direct labor.75 × $540.6 — You want a markup of 40% over cost on a product. . variable overhead = 22.800.= -------------------. There is idle capacity. Total overhead for the year is 30% of direct labor. The following contribution margin income statement will show you whether you should accept the special offer.How You Can Use Contribution Margin Analysis Even though the offered selling price of $9 is much less than the current selling price of $15.300 0 $ 3.000.000 8.700 19.300 $ Total overhead 0. the order should be accepted.700 3. Often such business is sought during the slack season.000 12.000 $ 5.000 Variable overhead = -------------------------------.800.800.400 $ 29. if you are not the one who decides whether to accept or reject special orders. Selling price Less: Variable costs Direct material Direct labor Variable overhead ($12.000 × 22.000.5%)* Contribution margin Less: Fixed cost Net income * $ 23. A customer offers to buy the item for $23. The overhead is 25% fixed and 75% variable.30 × $1.000 $ 21. 3. You can determine your selling price by using the following data: Direct material Direct labor Overhead Total cost Markup on cost (40%) Selling price 5.800. However.
000 30.000 units. The current income statement is as follows: Sales (50.30) Fixed overhead Gross margin Less: Selling and administrative expenses Variable (includes freight costs of $0.000 units should be $122.000 expenditure on the special tool.000 units × $25) Less: Cost of sales Direct material Direct labor Variable overhead ($200.3 DETERMINING PROFIT FROM YEAR TO YEAR Contribution margin analysis also aids in determining how to obtain the same profit as the previous year even with decreased sales volume. In 2001.000 increase in profits.40 4.000. Keep in mind that total fixed cost is the same except for the $8.26 Accounting and Finance for the Nonfinancial Executive Example 3. sales volume was 200.400 ($1. provides more information on how to determine a bid price. sales volume is expected to total only 150.000 will be required and will not be reused again.20 A forecasted income statement. 40.000 units. As a result.000 Cost patterns for the incremental order are the same except that: • Freight costs will be borne by the customer: • Special tools costing $8.000) Direct labor ($200.000 units have already been sold.250.000 units and want to know the minimum bid price that will result in a $20.000 $770. The contract price for the 10.000).000 $ 60.000 480.00 1.000 90.250.1.000 60.000/50. .000 $ 680.400/10.7 — You receive an order for 10.000) $2.40 per unit) Fixed cost Net income $1. • Direct labor time for each unit under the order will be 20% longer. You wish to compute the contribution margin that must be earned on the remaining units for 2001 in order to make the same net income as in 2000.000.000/50.000 100. or $12. fixed costs have been slashed by $80. 3.400 – $1.8 — In 2000.372.24 is below the $25 current selling price per unit.000 200. like the one on Table 3. the selling price was $25. Example 3.24 per unit ($122.000) Variable selling and administrative expense ($60.000 × 0.000 480. the variable cost per unit was $15. and the fixed cost was $500. In 2001.000/50.000). Preliminary computations indicate the following per-unit costs: Direct material ($120.000 $120. The contract price per unit of $12.000 90.
000 $68.000) Net income Contribution margin needed for year Contribution margin already earned: (Selling price – variable cost) × units ($25 – $15) $10 × 40.000 100.20 = $4.000 units Contribution margin remaining Contribution margin per unit needed $ 420.000 – $80.000 = P Contribution margin to be earned in 2001: Total fixed cost ($500.How You Can Use Contribution Margin Analysis 27 TABLE 3.000 .000 1.000 + [10.372.000 = = Contribution margin remaining ----------------------------------------------------------Units remaining $1.000 $1.80(c)]) Net income + selling and administrative expense + cost of sales = sales: $700.000 -------------------------.000 + $98.000 $1.000 $700.82 110.000 + $20.000 + $574.400 (b) $4 × 1.80 (c) $1.000 $1.000) ($200.000 Net income (P) computation for 2000: Sales = Fixed Cost + Variable Cost + P $25 × 200.000 $90.400 50.000 + ($15 × 200.000 $680.000 = $700.400 = $1.000 × $4.000 $574.520.20 – $0.520.000 $98.000 248.80(b)]) ($248.80 (d)$680.000(d) ($60.500.000 200.000 $480.= $13.000 30.500. 000 = $500.40 = $0.000 400.920.000 $120.372.40 × 60.000 60.250.1 A Forecasted Income Statement Current Units Sales Cost of sales Direct material Direct labor Variable overhead Fixed overhead Total Selling and administration costs Variable Fixed Total Net income (a) Projected 60.000 74.000 30.000 + [10.400 108.000 × 30%) $60.000 Computed last ($2.000 × $0.000) + P $1.400(a) $144.000 $1.
There is unlimited demand for both products. Three hours are required to produce the raw metal. your bonus may be based on the contribution margin you earn for your department.000 hours of capacity are interchangeable between the products.28 Accounting and Finance for the Nonfinancial Executive 3. Is an order worth accepting even though it is below the normal selling price? What should the price of your product or service be? Is a proposed contract advantageous? What is your incremental profitability? What is the best way of using departmental capacity and resources? In some cases.5 CONCLUSION Contribution margin analysis aids you in making sound departmental decisions. Thus. Raw Material Selling price Variable cost $200 90 Alloy $315 120 Total fixed cost is $400. . an understanding of the computation of contribution margin is necessary. and 100.9 — You can produce a raw metal that can either be sold at this stage or processed further and sold as an alloy.67 Alloy $315 120 $195 5 $ 39 You should sell only the alloy because it results in the highest contribution margin per hour. Example 3. Fixed costs are not considered because they are constant and are incurred irrespective of which product is manufactured. 3.4 ARE YOU UTILIZING CAPACITY? Contribution margin analysis can be used to determine the best way of utilizing capacity. The contribution margin per hour is as follows: Raw Metal Selling price Less: Variable cost Contribution margin Hours per ton Contribution margin per hour $200 90 $110 3 $ 36.000. and five hours are needed to make the alloy.
” you must first understand the concept of breaking even. CVP analysis tries to answer the following questions: 1. it would cost the company money. starting a new business. you must be able to calculate the sales volume needed to cover your costs and how to use this information to your advantage. To break even on your department’s product lines and/or services. We always had to attain an advertising percentage of . 29 . CVP information helps you to predict the effect of any number of contemplated actions and to make better planning decisions. What profit can be expected on a given sales volume? 4. the more profit the company would make on a given issue.1 WHAT IS COST-VOLUME-PROFIT (CVP) ANALYSIS? Cost-volume-profit (CVP) analysis relates to the way profit and costs change with a change in volume. fixed cost. fixed costs. The break-even point that is arrived at by such analysis is important to the profit planning process. is the process of calculating the sales needed to cover your costs so that there is zero profit or loss. What sales volume is required to break even? How long will it take to reach that sales volume? 2. modernizing facilities. volume. because at this percentage our revenue from advertisers is equal to the costs incurred from printing and distributing the paper. The higher the percentage above . which is part of CVP analysis.67. If the number fell below . Such knowledge allows managers to maintain and improve operating results. or appraising production and administrative activities.2 WHAT AND WHY OF BREAK-EVEN SALES Break-even analysis. a nonfinancial manager employed by a publishing company commented that: Our advertising percentage (paid advertisements appearing in a given issue) represents our break-even point.67 is the paper’s break-even point.67 or better. and output affect profits? 5.4 Are You Breaking Even? Before your business can realize “profit. How would a change in the mix of products sold affect the break-even and target volume and profit potential? 4. You must also be familiar with how your costs react to changes in volume. .67 and the paper was printed. Thus. variable costs. In an interview. More specifically. 4. and product mix. It is also important when introducing a new product or service. How would changes in selling price. CVP analysis examines the impact on earnings of changes in such factors as variable cost. What sales volume is necessary to earn a desired profit? 3. selling price.
Economic conditions. The guidelines for breaking even are: • An increase in selling price lowers break-even sales. In deciding which products to push. Break-even analysis can also be used as a screening device. supply and demand.1 Break-even chart. is not just to break even. The break-even sales can be determined using the graphic and equation approaches. You can extend break-even analysis to concentrate on a desired profit objective. total cost. Figure 4. and the long-term impact on customer relations must also be considered.1 also depicts profit potentials over a wide range of activity. Variable cost per unit is constant.30 Accounting and Finance for the Nonfinancial Executive Relevant Range Dollars Break-even point Loss Revenue Profit Total Cost Variable Cost Total Cost Fixed Cost Volume FIGURE 4. of course. Using the graphic approach (see Figure 4. such as the first attempt to determine the economic feasibility of an investment proposal. pricing may be aided by knowing the break-even point for a product. continue. Manufacturing efficiency is constant. revenue. There is only one product or a constant sales mix. What other situations can you think of where break-even analysis is useful? The assumptions of break-even analysis follow: • • • • • Selling price is constant. Inventories do not significantly change from period to period. and fixed cost are plotted on a vertical axis and volume is plotted on a horizontal axis. Also. • An increase in fixed cost increases break-even sales. Your objective. or discontinue. the break-even point is not the only important factor. The break-even point occurs at the intersection of the revenue line and the total cost line. • An increase in variable cost increases break-even sales. but to earn a profit. The equation approach uses the following equation: S = VC + FC .1). It shows how profits increase accordingly with increases in volume.
If desired profit is $40. solve for P in the following equation: S = VC + FC + P Example 4.000.000 ($900. and FC = fixed cost.000 units × $30 = $1. the variable cost per unit is $20.000. The point of break-even sales can be calculated as follows: S = FC + VC 1S = $270. The variable cost is $2. VC = variable cost.000) .000 S = $900.000 + ($2.000 + 0.7S + $40.3S = $270. break-even units are 9.44 to break even: S = FC + VC 800.2 — If the selling price per unit is $30.033.333 Example 4.000.000 The break-even dollar amount is: 40.50 × 800.7S 0.000 Example 4.000 0.3S = $310. The selling price (SP) per unit should be $3. and the fixed cost is $400.000 If the selling price per unit is $100. the break-even units (U) can be calculated as follows: S = FC + VC $30U = $400.1 — A product has a fixed cost of $270.000 units of an item.Are You Breaking Even? 31 where S = sales. An example is selling price. 000 + 0.000/$100). This approach allows you to solve for break-even sales or for other unknowns as well. the sales needed to obtain that profit (P) can be calculated as follows: S = FC + VC + P 1S = $270.000 U = 40. Fixed cost totals $750.000 + $20U $10U = $400.3 — You sell 800.000 S = $1.000SP = $750. If you want a desired before-tax profit.000 and a variable cost of 70% of sales.50 per unit.200.
5 — Assume your selling price is $40.70 = $735.000 + $24 U + $400.= Before-tax profit 0. your fixed cost is $120.4 — Assume your selling price is $40. your sales volume is 20.000) = ($15 × 20. and your tax rate 30%. your variable cost is $15 per unit.000) + P 1. To determine the after-tax profit. your variable cost is $30 per unit.000.000. your variable cost is $24.000 = R Example 4. consider the following equation: S = FC + VC + P $40 U = $150.000SP = $2.050.000 units.000 U = 34.000 units. your after-tax profit is $240.6 × Before-tax profit $240. and your tax rate is 40%.000 × 0.6 $400.000 + $100.000 SP = $3.000) + $120.000. your fixed cost is $150. To determine how much you have available to spend on research (R).000 = 0. use the following equation: S = FC + VC + P ($50 × 60. and your tax rate is 40%. your fixed cost is $150.44 Example 4.32 Accounting and Finance for the Nonfinancial Executive 800.000 --------------------.000) = 150.6 $100.000 = Before-tax profit ** After-tax profit: $240.000 + ($30 × 60.000.6 × Before-tax profit $60.6 — Assume your selling price is $50 per unit. your after-tax profit is $60.000 = Before-tax profit . your sales volume is 60.000.000** $16 U = $550.000* + R $280.000 = P $1.375 Example 4. To determine how many units you must sell to earn the after-tax profit. consider this equation: S = VC + FC + P + R ($40 × 20.750.= Before-tax profit 0.000 = 0.000 -----------------.000 * After-tax profit: $60.050.
The fixed cost is $10.000 + $0. $0.000 4. . This is known as the cash break-even point. For example.000 U = 250.000 – $34. Not all fixed costs involve cash payments. Example 4. or if the opportunity cost of holding excess cash is high. the greater the risk of reaching the break-even point.12 U = $10. you may want to know the volume of sales that will cover all cash expenses during a period.= 15% $40.000. and the variable cost per unit is $0.08. To find the cash break-even point.000 and break-even sales are $34. and total fixed cost is $50. depreciation expense is a noncash charge.000 $10 U = $48.000 Margin of safety = -------------------------------------------. Therefore. Budget sales – Break-even sales Margin of safety = ---------------------------------------------------------------------------Budget sales The lower the ratio.40 U = $10. what is your margin of safety? $40. which includes depreciation of $2.12 per unit.4 CASH BREAK-EVEN POINT If you have a minimum of available cash.800 You must sell 4.000.000.3 WHAT IS MARGIN OF SAFETY? The margin of safety is a risk indicator that stipulates the amount by which sales may decline before losses are experienced.7 — You are considering making a product presently purchased outside for $0.000 U = 4. Use the following equation to determine the number of units you must sell so that the annual cost of your machine equals the outside purchase cost.9 — If the selling price is $25 per unit.08 U $0.8 — If budget sales are $40.000 33 4.000.Are You Breaking Even? Example 4. the cash break-even point is lower than the usual break-even point. the variable cost is $15 per unit. the cash break-even point is: $25 U = $15 U + $48. the noncash charges must be subtracted from total fixed costs.800 units at $25 each to meet your break-even point. The cash break-even point equation is as follows: S = VC + FC (after deducting depreciation) Example 4.
If sales increase by 10%.10%. Hence.000.12 — You are evaluating operating leverage.5% for 2000 $65. income will increase by 1.= 1. there is greater earnings instability. your variable cost is $18 per unit.000 × $2) – .000 ) $96.000. $55. It is easier to adjust variable cost than fixed cost when demand for your products decline. net income will rise by 17. Your selling price is $2 per unit. The operating leverage in 2001 compared to 2000 was higher.000 in 2001. your fixed cost is $50. Example 4. However. You can determine the extent of operating leverage as follows: ( Selling price – Variable cost ) ( Units ) ------------------------------------------------------------------------------------------------------------------------( Selling price – Variable cost ) ( Units ) – Fixed cost ( $30 – $18 ) ( 8.71 ( $30 – $18 ) ( 8. and that variable costs were $25.000 $143. as indicated by the increase in the ratio of fixed costs to total costs. But a high ratio of variable cost to total cost indicates stability. your fixed cost is $40.000 ) – $40.000 units.34 Accounting and Finance for the Nonfinancial Executive 4.000 Example 4.000 $67.000 × $2) – (130. high operating leverage means risk because fixed costs cannot be decreased when revenue drops in the short run. and your sales volume is 8.10 — Assume that fixed costs were $40. It is the extent to which you commit yourself to high levels of fixed costs other than interest payments in order to leverage profits during good times.000-unit volume.10 per unit.= -----------------.000 $56.5 WHAT IS OPERATING LEVERAGE? Operating Leverage is the degree to which fixed costs exist in your cost structure.000 -----------------. A high ratio of fixed cost to total cost over time may cause variability in profit.000 (100.000 $50.= 67.000 units. Example 4. the second assumes a sales volume of 130.000 -----------------.000 -----------------------------------------------------------------------.= 61. The first example assumes a sales volume of 100.71%.000 – – $110. Sales Volume (in dollars) – Fixed Cost – Variable Cost = Net Income $50. and your variable cost is $1.11 — Assume that your selling price is $30 per unit.000 in 2000 and $27.000 $40.000 = = $40.000 in 2000 and $55.000 units.000 This means that for every 1% increase in sales above the 8.1% for 2001 $82.000 in 2001.
With subcontracting. While a high degree of operating leverage is sometimes a desirable objective.25 figure tells you that for every 1% increase in sales above the 100.= -------------30. contracts can be terminated when demand declines.25% increase in net income.000 – $40. Managers must determine whether the risks associated with higher fixed costs are worth the potential returns. a 10% jump in sales will boost net income 22. Operating leverage is an issue that directly impacts line managers.000-unit volume there will be a 2.000 ----------------------------------------------------------------------------------------------------------------Quantity $100.000 $40. newer technology has a higher fixed cost and lower variable cost than older technology.000 – $100.000 $27. . The tradeoffs determine how much financial and operating leverage to use. It should also be noted that the more unpredictable sales volume is.Are You Breaking Even? The ratio of the percentage change in net income to the percentage change in sales volume is as follows: Change in net income $67.= --------------------. If you buy them. If there is a rental with a short-term lease. the more desirable it is to have a high degree of operating leverage. If you have a high degree of operating leverage. the annual cost is likely to be more.000-unit level. One example of an operating leverage question you may face is whether to buy buildings and equipment or rent them.5%. the fixed cost remains even if demand declines. In general.5% Net Income $40. if you have a low degree of operating leverage you can often take on a higher level of financial leverage.000 $30. there is the risk of financial damage caused by a drop in sales. Remember: Fixed costs magnify the gain or loss from any fluctuation in sales.25 35 If fixed cost remains the same.000 = 2. fixed operating costs should constitute a larger proportion of the total cost at a particular sales level so as to enhance the gains realized from any subsequent rise in sales. Presumably.000 $100. but it is easier to terminate the fixed cost in a business downturn. Alternatively. you incur fixed costs even if volume declines.0% Change in quantity $130. Another operating leverage decision involves whether to purchase plant and facilities and manufacture all components of the product or to subcontract the manufacturing and just do assembly. The opportunity to magnify the increase in earnings that arises from any increase in sales suggests that you should use a high degree of operating leverage. you should not simultaneously use a high degree of financial leverage (debt) because the combination makes the risk associated with your operations too severe for a volatile economic environment. The level of operating leverage selected should not be made without input from the production managers. The lower risk of operating leverage balances the higher risk of financial leverage (debt position).= -------------------------------------------------. the 2.000 --------------------------------------------------------------------------------------------------------------67.000 --------------------------------------------------. The same proportionate operating leverage develops regardless of the size of the sales increase above the 100. Thus. If plant and equipment are bought.
000 units Example 4.000 69. Different selling prices and different variable costs result in different unit contribution margins.000 and two products with the following contribution margin data: Product A Selling price Less: Variable cost Unit contribution margin Sales mix $15 12 $3 60% Product B $10 5 $5 40% The weighted average unit contribution margin is: $3(.000 24. Example 4.000 20% 30% Product B $60.000 $31. the break-even point in dollars is: $18.000 33. called the sales mix.80 Your department’s break-even point in units is: $76.600 and produces and sells three products: Product A Sales Less: Variable cost Contribution margin Contribution margin ratio Sales Mix $30. It is also necessary to assume that the sales mix does not change for a specified period.000 units Product B: 20.000 $6.13 — Your department has fixed costs of $76.80 = 20.3% 60% Product C $10.000 $20.000 31% 100% Since the contribution margin ratio for your department is 31%.000 .000 50% 10% Total $100.6 SALES MIX ANALYSIS Break-even analysis requires some additional considerations when your department produces and sells more than one product.000 $5.000 5.000/$3.000 units × 40% = 8. it is necessary to predetermine the sales mix and then compute a weighted average contribution margin.14 — Your department has total fixed costs of $18.4) = $3. In break-even analysis.000 40. break-even points vary with the relative proportions of the products sold. As a result.600/.6) + $5(.36 Accounting and Finance for the Nonfinancial Executive 4.31 = $60.000 units × 60% = 12.000 units which is divided as follows: Product A: 20.
you may improve departmental profitability by reducing your variable cost of manual labor through a fixed cost investment in plant.000 $ 6.000 $60. and C: Product A: Product B: Product C: $60. 4. you must consider the risk that sales may decline below the break-even point.Are You Breaking Even? which will be split in the mix ratio of 3:6:1 to give us the following break-even points for the individual products A. If the sales mix does change. however.000 × 60% $60.000 × 30% $60. the break-even point will also change. because it will reduce your contribution margin. rather than converting variable cost to fixed.000 × 10% = = = $18. B.7 CONCLUSION If your sales volume consistently exceeds the break-even point. . However. Generally. which will decrease your profitability.000 37 One important assumption in a multiproduct department is that the sales mix will not change during the planning period. you should aim to convert fixed cost to variable cost. But this must be done carefully.000 $36.
1 WHAT COSTS ARE RELEVANT TO YOU? In each of these situations. The plan consists of purchasing a new machine for $50.5 • • • • • • How to Make Short-Term. 4. Nonroutine Decisions When analyzing the manufacturing and/or selling functions of your department. The relevant costs are the future costs that differ between the decision alternatives. What should you produce? How should you manufacture it? Where should you sell the product? What price should you charge? In the short run.1 — You are planning to expand your department’s productive capacity. and other criteria. and you must identify the costs that are relevant to a decision. not all costs are of equal importance in decision making. the cost to be paid for the new business is relevant. 3. However. you may be confronted with the following nonroutine. For example. Cost data. 2. Select the best alternative based on the remaining cost data. or relevant cost approach. The incremental or differential costs are relevant because they are the ones that differ between the alternatives. behavior patterns. you are faced with the problem of choosing between alternative courses of action. the sunk costs are not relevant to these decisions because they are past costs. Under the concept of relevant costs. which may be appropriately titled the incremental. nonrecurring situations: Whether to accept or reject a special order How to price standard products Whether to sell or process further Whether to make or buy Whether to add or drop a certain product line How to utilize scarce resources 5. However. Therefore. Gather all costs associated with each alternative.000 and disposing of the old 39 . Drop the sunk costs. decision making involves the following steps: 1. Drop those costs that do not differ between alternatives. the ultimate management decision rests on cost data analysis. Example 5. which are classified by function. differential. in a decision on whether to sell an existing business for a new one. are the basis for profit calculations. the initial cost of the old business is not relevant because it is a sunk cost.
A price that is lower than the regular price is called a contribution price.000 units of a product each year at a regular price of $2.500 4. the income statement follows: . such an order should be accepted if the incremental revenue obtained from it exceeds the incremental costs involved.40 Accounting and Finance for the Nonfinancial Executive without receiving anything. if sales are slumping.500 New Machine $60.000 2.000 10.000-unit capacity. Annual sales and operating costs of the present machine and the proposed replacement are based on normal sales volume of 20. sales and fixed costs such as insurance and taxes are irrelevant because they do not differ between the two alternatives.000 $18. (2) there is idle capacity. This contribution approach to pricing is most appropriate when: (1) there is a distressing operating situation where demand has fallen off.000 35.000 4.000 $26.000 20.000 cost of the new machine is relevant.000 At first glance. The company should accept this price since it is better to receive some revenue than to receive nothing at all.000. it appears the new machine provides an increase in net income of $7.000 units and are estimated as follows: Present Machine Sales Less: Variable costs Less: Fixed costs: Depreciation (straight-line) Insurance.000 Exclusive of $2. but will substantially cut down on variable operating costs.2 ACCEPTING OR REJECTING A SPECIAL ORDER You may receive a short-term. However. The old machine has a 5-year remaining life and a book value of $17. Example 5. the book value of the present machine is a sunk cost and is irrelevant in this decision. The new machine will generate the same amount of revenue as the old one. However. Eliminating all the irrelevant costs leaves only the incremental costs: Savings in variable costs Less: Increase in fixed costs Net annual cash saving arising from the new machine * $15.2 — Your department has a 100. The new machine has a 5-year life. Normally.000 10. however. or (3) there is sharp competition or a competitive bidding situation. special order for your products at a lower price than usual.000* $5. you may refuse such an order since it will not yield a satisfactory profit. If the variable cost per unit is $1 and the annual fixed cost is $45.500 sunk cost You must also consider that the $50. etc.500 per year.500. You are producing and selling only 90. 5. taxes. Net income $60.
You must consider. and profit will increase by $2. pricing standard products requires long-term considerations.00 + $0.50 The company received an order calling for 10.3 PRICING STANDARD PRODUCTS Unlike pricing special orders.000 90.000 45. At a price of $1. The key concept is to recognize that the established unit selling price must be sufficient in the long run to cover all manufacturing.000 Units) $180. Note that the fixed costs will not increase.000 units × $0. that you can add to total profits by accepting this special order even though the price offered is below the unit factory cost. the variable cost of $1 will be a better guide than the full unit cost of $1.000 (10.00 1. as well as to provide for an adequate return and for future expansion.000 45.20) toward fixed cost.50).000 $2.000 Per Unit Sales Less: Variable costs Contribution margin Less: Fixed cost Net income $2. Without Special Order (90.20).000 Per Unit $2.000 10. the order will contribute $0. Although the acceptance of this order will not affect regular sales.50 $0.00 1. both of which use some kind of cost-plus pricing formula.20.000 90.00 0. for a total of $12.000. Nonroutine Decisions 41 Total Sales (90. The buyer will pay the shipping expenses.000 Units) $192.000 $ 2. both fixed and variable.50.000 units at $1.000 units) Less: Variable costs (90.50 factory unit cost ($1.000 100. selling. Selling and administrative costs are provided for through the markup that is added to the cost base.50 = $1.000 $90.50 $0.000 $ 90. The full-cost approach defines the cost base as the full unit manufacturing cost. 1. .50 Difference $12.000 $ 92.20 per unit (contribution margin per unit = $1.000 With Special Order (100.000 $45. Fixed costs are provided for through the markup that is added to this base.20 price is below the $1.00 $1. Using the contribution approach to pricing.000 $47.How to Make Short-Term. you are reluctant to accept it because the $1.00 = $0. The contribution approach defines the cost base as the unit variable cost.00 $1.000 5.000 units) Contribution margin Less: Fixed cost Net income $180. and administrative costs.20 per unit. 2.00 0.000 $45. There are two primary approaches to pricing standard products that are sold on the regular market. however.20 – $1.000 45.
4 — Your company has determined that a $500. If your company desires a 20% return on investment.000 Assume that in order to obtain its desired selling price.3 — You have prepared the following cost data on your company’s regular product: Per Unit Direct material Direct labor Variable overhead Fixed overhead (based on 20.000 $200.000 100.50% of full unit cost Desired selling price $6 4 10 $20 10 $30 Under the contribution approach.000 50% .000 units) $6 4 4 6 1 2 Total $120. Under the full-cost approach. the firm has a general policy of adding a markup equal to 50% of the full unit cost or 100% of the unit variable cost.000.100% of unit variable cost Desired selling price $6 4 5 $15 15 $30 Example 5.000 $40. and administrative expenses) Unit variable cost Markup to cover fixed costs. and total selling and administrative expenses are estimated to be $100. what will be the markup using the full-cost approach? Desired rate of return (20% × $500.000 units of its product every year.000 units × $20) Required markup (Total/Full unit cost) $100. and desired profit . selling. the desired unit selling price is: Direct material Direct labor Factory overhead Full unit cost Markup to cover selling and administrative expenses.000 $400. It will cost $20 to manufacture each unit at a 20.000-unit level of activity.000 units) Variable selling and administrative expenses Fixed selling and administrative expenses (based on 20. the desired selling price is determined as follows: Direct material Direct labor Variable costs (overhead.000) Selling and administrative expenses Total Full unit cost (20.42 Accounting and Finance for the Nonfinancial Executive Example 5.000 investment is necessary to manufacture and market 20. and desired profit .
and taxes.g.000 Total of 8.How to Make Short-Term.000 $152.000 $48.000 Units Make Buy 128. Leaving facilities idle. or 3..000 32.. Renting out idle facilities.5 — You have prepared the following cost estimates for manufacture of a subassembly component based on an annual product of 8.000 $ 8. . Assuming productive capacity will be idle if not used to produce the subassembly.000 The make-or-buy decision must be evaluated in the broader perspective of considering how best to utilize available facilities. The alternatives include: 1. the analysis is as follows: Per Unit Make Purchase price Direct material Direct labor Variable overhead Fixed overhead that can be avoided by not making Total relevant costs Difference in favor of making Buy 16 $5 4 4 2 $15 $ 40.4 ANALYZING THE MAKE-OR-BUY DECISION Deciding whether to produce a component part internally or to buy it from a supplier is called a make-or-buy decision.000 units: Per Unit Direct material Direct labor Variable factory overhead applied Fixed factory overhead applied (150% of direct labor cost) Total Cost $5 4 4 6 $19 Total $40.000 32. depreciation.000 $16 $1 $128. rent. The quantitative effects of the make-or-buy decision are best seen through incremental analysis.000 A supplier offers the subassembly at a price of $16 each. which represent executive salaries. Two thirds of fixed factory overhead. Nonroutine Decisions 43 5. Using idle facilities for other products.000 32.000 32.000 $120. cost). product quality and long-term business relationships with subcontractors) and quantitative factors (e. To determine whether to make or buy the product. continue regardless of the decision. Example 5.000 16. This decision involves both qualitative factors (e. 2. you must evaluate the relevant costs that can change between the alternatives.g.
000 13. and all additional processing costs are variable. and C from a joint process. is irrelevant to the decision.000 4.000 It is profitable for product A to be processed further.000 Product B $15.000 7. since the joint costs have already been incurred at the time of the decision and. Incremental sales revenue Incremental costs of additional processing Incremental revenue of additional processing $30. However. these products are called joint products.000 26.000 Total $50. 5. therefore.5 DETERMINING WHETHER TO SELL OR PROCESS FURTHER When two or more products are produced simultaneously from the same input by a joint process. and C. Keep in mind that the joint production cost of $120. the split-off point. B.000 6. any final decision should be based primarily on the impact on contribution margin or net income.000 25. The decision will rely exclusively on additional revenue compared to the additional costs incurred due to further processing. The sales value at the split-off point of 3.000 5.000 24. The additional processing requires no special facilities.000 units is $60.000 units after further processing is $90. The income statement for these product lines follows: Product A Sales Less: Variable costs Contribution margin $10.000 and the additional processing cost is $25. The sales value for 3.000 . that is.000.6 — Your company produces products A. B. Joint costs are considered irrelevant to this sell-or-process-further decision.6 ADDING OR DROPPING A PRODUCT LINE Deciding whether to drop an old product line or add a new one requires an evaluation of both qualitative and quantitative factors.000 8. whereas others require additional processing. represent sunk costs. Example 5.7 — Your department has three major product lines: A. you might have an option: you can sell the goods at the split-off point or process them further in the hope of obtaining additional revenue. You are considering dropping product line B because it is being sold at a loss. therefore. Joint production costs for the year are $120.000 is not included in the analysis. Product A may be sold at the splitoff point or processed further.000 12. At the splitoff point some of the joint products are in final form and can be sold to the consumer.000.000 Product C $25. The term joint costs is used to describe all the manufacturing costs incurred prior to the point at which the joint products are identified as individual products.000. since it is a sunk cost and.44 Accounting and Finance for the Nonfinancial Executive 5. In many cases. Example 5. however.
000 Difference $(15.000) (6.500) $ 500 Alternatively.g.000 17.000 2. Therefore. when there are constraining factors or scarce resources. if product line B were dropped..500 12.500 6.000) (7. whereas allocated fixed costs are common fixed costs allocated to the product lines using some base (e. The following calculations show the effects on your department with and without product line B.000 17.000 $(1.500 1.How to Make Short-Term.500 Direct fixed costs are identified directly with each of the product lines.000 $8. Nonroutine Decisions 45 Product A Less: Fixed costs Direct Allocated Total Net income Product B Product C Total 2.000 26.000 5.500 14. 5.000 $ 6. One of the great dangers in allocating common fixed costs is that such allocations can make a product line look less profitable than it really is.000 11. Because of such an allocation.000 but it actually contributes $500 ($7. the incremental approach would show the following: Sales revenue lost Gains: Variable cost avoided Directed fixed costs avoided Increase (decrease) in net income $15. product line B should be kept.000 24.500 $ 6.500 5. A constraining factor restricts or limits the production . product line B showed a loss of $1.7 UTILIZING SCARCE RESOURCES In general. the emphasis on products with higher contribution margins maximizes your department’s net income.500 5.500) to the recovery of common fixed costs.000 17. Keep Product B Sales Less: Variable cost Contribution margin Less: Fixed costs Direct Allocated Total Net income $50. Common fixed costs typically continue regardless of the decision and thus cannot be saved by dropping the product line to which they are distributed.000 6. space occupied).500 $ (500) Both methods demonstrate that by dropping product line B your department will lose an additional $500.500 Drop Product B $35.000) (8.000 6. This is not true.000 3.500) (6.500 8.500 $ 6.000 .000) 4.000 6.000 12. however.000 $ 1.$6.500 14.000 18.000 1.500 $ 6.
Qualitative factors. it should be produced and product B should be dropped. $8. Another way to look at the problem is to calculate the total contribution margin for each product. 5. product B is more profitable than product A since it contributes more to your department’s profits ($4 vs.00 5 $0.000). maximizing profit depends on getting the highest contribution margin per unit of the factor (rather than the highest contribution margin per unit of product output).8 — Your department produces products A and B with the following contribution margins per unit and an annual fixed cost of $42. product A should be produced since it contributes more than product B ($10.000 vs. In the presence of these constraining factors.80 Since product A returns the higher contribution margin per labor hour.000 hours/2 hours) (10. Product A Sales Less: Variable costs Contribution margin $8 6 $2 Product B $24 20 $4 As is indicated by the contribution margin. Further. Product A Maximum possible production Contribution margin per unit Total contribution margin * ** Product B 2. include: . which are difficult to measure in terms of money.00 Product B $4.46 Accounting and Finance for the Nonfinancial Executive or sale of a given product.000 hours/5 hours) Again.00 2 $1. Product A Contribution margin per unit Labor hours required per unit Contribution margin per labor hour $2.000 units** × $4 $8. Example 5. But assume that your department has a limited capacity of 10.000 labor hours. incremental qualitative factors must also be considered in the decision making. assume that product A requires 2 labor hours to produce and product B requires 5 labor hours. It may be machine hours.000 units* × $2 $10. $2).000.000 5. labor hours.000 (10. or cubic feet of warehouse space. One way to express this limited capacity is to determine the contribution margin per labor hour.8 DO NOT FORGET THE QUALITATIVE FACTORS In addition to the quantitative factors.
2. whether to sell or process further. . In some decision-making situations. Effect on present and future customers. The relevant costs are the expected future costs that differ between the decision alternatives.9 CONCLUSION Not all costs are of equal importance in decision making. the sunk costs are irrelevant since they are past costs.How to Make Short-Term. nonroutine decisions such as whether to accept a below-normal selling price. 5. Relationships with and commitments to suppliers. which products to emphasize. The relevant cost approach assists you in making short-term. Effect on employee morale. Therefore. qualitative factors are more important than immediate financial benefit. The costs that continue regardless of the decision are also irrelevant. 3. schedules. and Long-term future effect on profitability. Nonroutine Decisions 47 1. and other internal factors. and how to optimize utilization of capacity. 4. remember that qualitative factors must also be considered in many decision-making situations. In addition to these quantitative aspects. whether to make or buy.
Financial Forecasting and Budgeting
To accomplish your department’s goals you must be familiar with financial forecasting and budget planning. Without these instruments you have no plan on which to base future financial decisions, and without a plan you cannot make things happen. As a nonfinancial manager, you may have to forecast sales, production, and costs under varying assumptions. Learning to prepare and use financial forecasts and budgets will help you to accurately plan and control your department’s future.
6.1 WHAT IS A FORECAST?
Despite the uncertainties in life, it is important to attempt to forecast what will happen in the future. A forecast is a starting point for planning. It may simply be a projection that what happened last year will happen this year, or it may be quite complex, using statistical techniques and seasonal patterns. Although you can base your projection on historical patterns, you must also take into account any important changes taking place in the current environment, as these changes will make the future different from the past. Examples of relevant changes are better technology, changes in laws and regulations, and increased competition. Forecasts are the basis for capacity planning, inventory planning, planning for sales and market share, and budgeting. Sales forecasts are particularly important in many financial activities, including budgets, profit planning, capital expenditure analysis (whether to buy long-term assets), and acquisition and merger analysis (when two companies combine into one). You must realize that forecasts are guesses regarding the future. The guesses principally arise from hard data rather than from subjective judgment; therefore, certain variables may not be accounted for in this process. Hence, you should question forecasted figures that seem unreasonable and illogical based on your experience. After all, you are most familiar with the financial factors that relate to your job.
6.2 HOW CAN YOU USE FORECASTS?
Forecasts are needed for marketing, production, manpower, and financial planning and are used for planning and implementing long-term objectives. If you are a marketing manager, for instance, you can use sales forecasts to determine optimal sales force allocations, establish sales goals, and plan promotions and advertising. If you are a production planner, you need forecasts to schedule production activities, order materials, and plan shipments. If you are a purchaser,
Accounting and Finance for the Nonfinancial Executive
you need forecasts to aid you in determining what quantity of merchandise is needed and when to satisfy projected sales. Figure 6.1 illustrates the relationship between forecasting and managerial functions. For example, as soon as your company is sure that it has sufficient capacity, the production plan is developed. If the company does not have enough capacity, planning and budgeting decisions will be required for capital spending to expand capacity. In planning for capital investments, predictions of economic activity are required so that the returns, or cash inflows, accruing from the investment may be estimated. Borrowing needs for future operations should also be estimated through forecasts. Financial managers must make forecasts of money and credit conditions and interest rates so that the cash needs of the firm may be met at the lowest possible cost (e.g., should the company issue stock or debt to maintain its desired financial structure?). Long-term forecasts are needed to plan changes in the company’s capital structure.
6.3 HOW DO YOU PREPARE A FINANCIAL FORECAST?
To prepare a financial forecast you must begin by forecasting sales. Production and related cost forecasting will follow. Forecasting is easiest when stability exists in relationships that can be captured in mathematical terms (e.g., s = a + bA + cp where s = sales, A = advertising expenses and p = price). The sequence for forecasting financing needs is: 1. Project your sales. 2. Project variables such as cost of sales and operating expenses. 3. Estimate the level of investment in assets required to support the projected sales. 4. Calculate financing needs. 5. Consider external factors affecting the forecast. Political concerns, economic environment, tax law, technological developments, and demographic factors may be applicable in certain cases. Most other forecasts (budgets) follow the sales forecast. Sales estimates may be based on several factors including your instincts, past experiences, feedback from the sales force, and consumer surveys. If any changes are expected in your product mix (lines added or deleted), the projected change in volume is a consideration in projecting sales. If competition or cost reductions necessitate price changes, these must also be considered in making your sales forecast. A sales forecast of major product lines for a 6-month period is shown in Figure 6.2.
6.4 PERCENT-OF-SALES METHOD OF FINANCIAL FORECASTING
When constructing a financial forecast, the sales forecast is used to estimate various expenses, assets, and liabilities. Often, sales forecasting is done by product line. The
Financial Forecasting and Budgeting
Forecasts of Money and Credit Conditions Sales Forecast
FIGURE 6.1 Sales forecasts and managerial functions.
Sales Forecast (in thousands)
800 700 600 500 400 300 200 100 Jan Feb Mar
Product Line C
Product Line B
Product Line A
FIGURE 6.2 Sales forecast by product line.
most widely practiced method for formulating projections is the percent-of-sales method, in which the various expenses, assets, and liabilities for a future period are estimated as a percentage of sales for the present period. These percentages, together with the projected sales for the upcoming year, are then used to construct pro forma (planned or projected) balance sheets.
Accounting and Finance for the Nonfinancial Executive
The computations for a pro forma balance sheet follow: 1. Express balance sheet items that vary directly with sales as a percentage of sales. Any item that does not vary directly with sales (e.g., long-term debt) is considered not applicable (n.a.). 2. Multiply the percentages determined in Step 1 by the projected sales figure to obtain the amounts for the future period. 3. Where no percentage applies (e.g., for long-term debt, common stock, and paid-in-capital), simply insert the figures from the present balance sheet in the column for the future period. 4. Compute the projected retained earnings as follows: Projected retained earnings = present retained earnings + projected net income – cash dividends (You will need to know the percentage of sales that represents net income and the dividend payout ratio.) 5. Sum the asset accounts to obtain a total projected assets figure. Then add the projected liabilities and equity accounts to determine the total financing provided. Since liabilities plus equity must balance the assets when totaled, any difference is a shortfall, which is the amount of external financing required. Let us numerically work one out.
Example 6.1 — For the pro forma balance sheet shown in Table 6.1, net income is assumed to be 5% of sales and the dividend payout ratio is 40%.
One important limitation of the percent-of-sales method is that your company is assumed to be operating at full capacity. Based on this assumption, the firm does not have adequate productive capacity to absorb projected increases in sales and may require an additional investment in assets. The prime advantage of the percent-of-sales method of financial forecasting is that it is simple and inexpensive. To obtain a more precise projection of future financing needs, however, the preparation of a cash budget is required.
6.5 WHAT IS A BUDGET?
In a personal interview with the author, a nonfinancial manager discussed the budgeting process as follows:
Budgeting at the firm follows the traditional top-down planning strategy. Sales budgets are set up for the firm as a whole, then broken out into the four sales regions — eastern, central, western, and control states. At the Eastern Region we then receive our share of the corporate budget, which we must then subdivide among the territories in the region. The two key budgets that must be given considerable thought in their divisions are the
Financial Forecasting and Budgeting
TABLE 6.1 Pro Forma Balance Sheet in Millions of Dollars
Present (2000) Assets Current Fixed Total assets Liabilities and stockholders’ equity Current liabilities Long-term debt Total liabilities Common stock Paid-in-capital Retained earnings Total equity Total liabilities and stockholders’ equity % of Sales (2000 Sales = $20) Projected (2001 Sales = $24)
2 4 6
2.4 4.8 7.2
2 2.5 4.5 0.1 0.2 1.2 1.5 6
10 n.a. n.a. n.a.
2.4 2.5 4.9 0.1 0.2 1.92 2.22 7.12 0.08 7.2 Total financing provided External financing needed Total
2001 retained earnings = 2000 retained earnings + projected net income – cash dividends paid = $1.2 + 5%($24) – 40%[5%($24)] = $1.2 + $1.2 – $0.48 = $2.4 – $0.48 = $1.92 External financing needed = projected total assets – (projected total liabilities + projected equity) = $7.2 – ($4.9 + $2.22) = $7.2 – $7.12 = $0.08
sales quotas themselves and the promotional local funding dollars. Travel and expense dollars for the field representatives must be allocated. On a less formal, periodic basis, we receive allocations of promotional items that are charged to a national budget or charged in whole to our region and also must be allocated to the territories in the region.
In a personal interview with the author, another nonfinancial manager commented:
We use our projected sales forecasts for determining our increase in [insurance] policies in force. I am directly involved in our direct labor budget as we plan out our total people needs. I also must budget what each of my people will cost the company in terms of salary expense. I must budget for a certain percentage of promotions and also budget for the dollar amount and frequency of merit increases. This along with other aspects combine to formulate our yearly plan. After that is established we have everything in terms of variances to plan. Our management staff is then evaluated on our results in terms of variances. I am responsible for overtime dollars, additions to staff, and our in-house efficiencies in terms of production plans.
Accounting and Finance for the Nonfinancial Executive
Budgets are very important to nonfinancial managers. They are useful for planning your goals, evaluating your progress, motivating your people, and communicating your results. Often your attainment of budget goals is measured in terms of variances. Budgeting is also very useful on a personal level, as you always want to know where you are in relation to your goals. A budget is an annual projection of what you expect to achieve financially and operationally. It is a plan that commits resources to activities or projects and makes formal (written) statements of your expectations of sales, expenses, production, volume, and various financial transactions for the coming period A budget places guidelines and limitations on spending. The most common budget types that a nonfinancial manager might have to deal with are fixed budgets and flexible budgets. A fixed budget allocates a specific amount of resources that can be used to complete a specific task — this amount cannot be exceeded. A flexible budget allows the amount of allocated resources to vary along with the various levels of activity on a specific project. Almost all nonfinancial managers are responsible for either planning and submitting a budget for a specific period of time or for conforming to one that has already been laid out. In a personal interview, a nonfinancial manager employed by a computer company commented:
Although the company’s attitude toward the budgeting process is a bottom-up approach, the calculation of the budget is almost entirely a top-down method. My immediate superior hands me the annual budget and discusses it with me for any discrepancies. Our basic strategy to budgeting can be viewed as follows: first, strategic aspects are analyzed for both the short and long term; next, specific plans are developed; and last, the actual budgets are formulated.
The budget coordinates the activities of all the departments in your company. It communicates companywide goals to nonfinancial managers in different departments so they know what direction to take. You have no choice but to be familiar with your departmental budget and determine ways to keep within it. Many nonfinancial managers also believe that they must use all the money allocated to them in the budget, so as not to lose funding next year; however, this does not mean that funds should be spent foolishly just to meet the budget. A budget should be realistic (e.g., feasible in marketing and production capabilities) and consistent with company policy. It should take into consideration what your department’s or company’s mission is. For instance, does your company want to hold the line against the competition or does it want to grow? Should your company take an aggressive or a conservative approach in achieving these goals? The budget should be constantly evaluated since external or internal conditions may warrant changes. A budget is only an estimate, and deviation from that estimate should be expected. The budget must be adaptable to changing circumstances in your department. What will happen to sales if conditions change? What problems will be caused if initial sales expectations prove wrong? It is best to develop cost figures for different sales levels (e.g., high, low, expected) to assure flexibility.
(3) estimating manufacturing costs and operating expenses. reviewing technological changes. monthly.7 WHAT IS THE STRUCTURE OF THE BUDGET? The master (comprehensive) budget contains a projection of each of the key financial statements. you have no idea of what you want to accomplish. If you do not know where you are going. and taking corrective action. It enables you to see your role and set goals accordingly. it is hard to tell whether or not you have arrived. If you have no initial plan. developing strategies.. appraising industry trends. 6. Supporting schedules are also prepared for each of the major components in the financial statements. looking at economic and political conditions. quarterly. what will occur if you raise your selling price? What will be the effect if one variable (e. The budgetary process involves establishing goals. certain questions must be asked and certain assumptions must be made. analyzing competition. A manager with a poor understanding of budgets may fail to correctly anticipate the future and commit to objectives for which his or her budget is inadequate. The operational budget includes the following: • The sales budget • The direct materials budget .3. identifying the life cycle of the product. reviewing suppliers. formulating plans of action.g. the budget is a control device to measure your department’s performance against the plan so that future performance may be improved. which may result in a budget overrun. The budgetary time period depends on many factors. advertising) is changed? 6. and daily. At the end of the period. A simplified diagram of the various components of the comprehensive budget is shown in Figure 6. evaluating the market. For instance. The master budget is classified broadly into two categories — the operational budget and the financial budget.6 WHAT ASSUMPTIONS MUST BE MADE? Prior to the budget being developed. including how crucial the budget is to control costs. (4) determining cash flow and other financial effects. However. budgeting is a waste of time and money. and (5) preparing projected financial statements. appraising financial strength. The financial budget shows the financial decisions of your company and includes the cash budget and financial statement projections other than the income statement. noting changes in the customer base. the budget is a standard.Financial Forecasting and Budgeting 55 The budget is a blueprint for planning and control. What will the inflation rate be? Where is competition headed? Will suppliers increase prices? Will customer tastes change? You also must explore the financial alternatives available to you. The operational budget reflects the results of operating decisions and provides data needed to prepare a budgeted income statement. The period for a budget can be any appropriate time frame such as yearly. without competent management. (2) determining expected production volume. At the beginning of the period. The major steps in preparing the budget are: (1) completing a sales forecast. weekly.
3 A comprehensive (master) budget. . We will highlight the variable cost-fixed cost breakdown throughout this example. • • • • The The The The direct labor budget factory overhead budget selling and administrative expense budget pro forma income statement The financial budget includes the following: • The cash budget • The pro forma balance sheet To illustrate how all these budgets are put together. which produces and markets a single product.56 Accounting and Finance for the Nonfinancial Executive Sales Budget Desired Ending Inventory Budget Production Budget Direct Material Direct Labor Factory Overhead Cost of Goods Sold Budget Selling Expense Budget Administrative Expense Budget Budgeted Income Statement Capital Budget Budgeted Balance Sheet Cash Budget FIGURE 6. we will focus on a manufacturing company called the Johnson Company. We will assume that the company develops the master budget in contribution format for 2001 on a quarterly basis.
200 × $80 $256.000) Second quarter sales ($56. Nonfinancial managers must also carefully appraise the sales estimates of other departments.500 62. 70% are collected in the quarter of sale.920c 39.000 Total 3.000 The schedule of expected cash collections for the Johnson Company is as follows: Quarter 1 Accounts receivable (12/31/2000) First quarter sales ($64. a very pessimistic forecast may cause a shortage in staff and facilities so that consumer demand cannot be met. the marketing department may give optimistic sales estimates because it may try to stimulate the sales effort. Accurate sales forecasting is important since an exaggerated sales forecast may result in your company’s hiring too many staff members or acquiring excessive facilities.7.000) Total cash collections a 2 3 4 Total $ 9.000 4 800 × $80 $64. sales forecast figures determine staffing needs to reach targeted goals. this translates into lost business. Of the total quarter’s sales. After sales volume has been estimated.200b $15.120 $66. b .800b $17. Example 6. 28% are collected in the quarter following. the remaining 2% are uncollectible. On the other hand.800b $64. which translates into unneeded costs. it may not realistically appraise consumer demand.460 $ 9. which ordinarily indicates the quantity of each product expected to be sold.2 — The Johnson Company’s sales budget for the year ending December 31.000) Third quarter sales ($72. Further.1 THE SALES BUDGET The sales budget is the starting point in preparing the master budget.960 $54. allows all departments to plan their needs.300 $57.680c 50.Financial Forecasting and Budgeting 57 6.000 3 900 × $80 $72. the sales budget includes a computation of expected cash collections from credit sales. The sales budget.880 70. c Of the total quarter’s sales. 2001 is as follows: Quarter 1 Expected sales in units Unit sales price Total sales 800 × $80 $64. Generally.800 $242. For instance.080 All of the $9.160c 44.400b $20.000 2 700 × $80 $56. As a result.000) Fourth quarter sales ($64. which will be used later for cash budgeting.560 44. the sales budget is constructed by multiplying the expected sales in units by the expected unit sales price. since estimated sales volume influences nearly all other items appearing in the master budget.500a 44.500 accounts receivable balance is assumed to be collected in the first quarter.720 54.
7.2 THE PRODUCTION BUDGET After sales are budgeted.2) Desired ending inventorya Total needs Less: Beginning inventoryd Units to be produced a b c d 2 700 90 790 70 720 3 900 80 980 90 890 4 800 100 b 900 80 820 Total 3. Example 6. Example 6.4 — The Johnson Company’s direct material budget for the year ending December 31. The same as the previous quarter’s ending inventory. The purchase will depend on both expected usage of material and inventory levels. The formula for computation of the purchase is as follows: Purchase in units = Usage + Desired ending material inventory units – Beginning inventory units The direct material budget is usually accomplished by a computation of expected cash payments for materials. The expected volume of production is of the units expected to be produced and the desired inventory at the end of the period.220 800 70 870 80 790 This figure is calculated as 10% of the next quarter’s sales. 2001 is as follows: Quarter 1 Planned sales (see Example 6. The number of units expected to be manufactured to meet budgeted sales and inventory requirements (determined by subtracting the estimated inventory at the beginning of the period from the sum) is set forth in the production budget. For example a computer or an assembly line is down for an extended period of time. Estimated. 6. Good managers constantly evaluate whether production is on schedule with proposed budgets and make adjustments accordingly. a direct material budget should be constructed to show how much material will be required for production and how much material must be purchased to meet this production requirement.7.58 Accounting and Finance for the Nonfinancial Executive 6.200 100 c 3. the production budget can be determined.300 80 3. 2001 is as follows: .3 THE DIRECT MATERIAL BUDGET When the level of production has been computed. The ending inventory for the year is the same as the one for the fourth quarter.3 — The Johnson Company’s production budget for the year ending December 31. the attentive manager knows that production and output will probably be low for that time period.
250 4 820 ×5 4.349a $2.082 $2.422 5.710 246 2.464a $5.) Desired ending inventory of materials (in lbs.)c Materials to be purchased Unit price Purchase cost a b c 2 720 ×3 2.500 .160 267 2. The remaining 50% of a quarter’s purchases are paid for in the following quarter.427 216 2.500 Total 3. To compute direct labor requirements.916 627 2.464 × $2 $4.549 $4. The schedule of expected cash disbursements for the Johnson Company is as follows: Quarter 1 Accounts payable (12/31/2000) First quarter purchases ($4. The same as the prior quarter’s ending inventory.298) Fourth quarter purchases ($4.698) Second quarter purchases ($4.3) Material needs per unit (in lbs.928 Total 3. 2001 is as follows: Quarter 1 Units to be produced (see Example 6.698 4. Example 6. 50% are paid for in the quarter of purchases.560 Of the total quarter’s purchases.)a Total material needs (in lbs.673 × $2 $19.450 × $5 $22.211a 3 4 Total $2.928) Total disbursements a b 2 $2.7.860 $2.298 4 820 ×3 2.649 a $4.670 246 2. expected production volume for each period is multiplied by the number of direct labor hours to produce a single unit.) Less: Beginning inventory of materials (in lbs.698 10% of the next quarter’s units needed for production multiplied by 3 (material needs per unit).950 × $5 $19.3) Direct labor hours per unit Total hours Direct labor cost per hour Total direct labor cost 790 ×5 3.Financial Forecasting and Budgeting 59 Quarter 1 Units to be produced (see Example 6.100 × $5 $80.211b 2.370 216 2.5 — The Johnson Company’s direct labor budget for the year ending December 31.586 237 2.660 250 9.220 ×3 9.649b 2.464 $19.211 × $2 $4.298 2. 6.200 2.346 790 ×3 2.750 2 720 ×5 3. Estimated.422) Third quarter purchases ($5.349 × $2 $4.910 237 9.100 × $5 $20.) Material needs for production (in lbs.200 4.460 250b 2.349 b 2.200 ×5 16.113 $4. The direct labor hours required to meet production needs are then multiplied by the direct labor cost per hour to obtain budgeted total direct labor costs.600 × $5 $18.4 THE DIRECT LABOR BUDGET The production requirements provide the starting point for the direct labor budget.649 × $2 $5.000 3 890 ×5 4.422 3 890 ×3 2.
• Depreciation expenses are $3.950 Total 16.650 2 3. Example 6.60 Accounting and Finance for the Nonfinancial Executive 6.200 3.600 . • All overhead costs involving cash outlays are paid for in the quarter incurred.900 3.000 14.5) Variable overhead rate Variable overhead budgeted Fixed overhead budgeted Total budgeted overhead Less: Depreciation Cash disbursement for overhead 3. we will assume the following: • Total factory overhead budgeted = $6.250 9.3) Unit Cost $2 $ 41 Total $ 500 $ 4.200 3. It will also give the dollar value of the ending materials and finished goods inventory to appear on the budgeted balance sheet.000 13. it must be deducted from the total factory overhead in computing cash disbursement for factory overhead.200 13. and factory utilities.650 4 4. remember that depreciation is not a cash outlay.6 THE ENDING INVENTORY The desired ending inventory budget provides information for the construction of budgeted financial statements.4) 100 units (see Example 6.000 56.7.100 × $2 8. 2001 is as follows: Quarter 1 Budgeted direct labor hours (see Example 6.900 3.600 × $2 7. factory property taxes.950 × $2 7.6 — To illustrate the factory overhead budget. Example 6.950 3 4.250 10.200 24.000 fixed (per quarter) plus $2 per hour of direct labor.000 43. Using the contribution approach to budgeting requires the development of a predetermined overhead rate for the variable portion of the factory overhead. factory insurance. therefore.250 11.200 6.200 6. it will help compute the cost of goods sold on the budgeted income statement.200 6.000 14. The Johnson Company’s factory overhead budget for the year ending December 31.000 13.100 × $2 32.7 — The Johnson Company’s ending inventory budget for the year ending December 31. Specifically. These costs include factory rent.7.450 × $2 8.5 THE FACTORY OVERHEAD BUDGET The factory overhead budget provides a schedule of manufacturing costs other than direct materials and direct labor.250 10.250 each quarter.900 6.900 6.100 $ 4. In developing the cash budget. 2001 is as follows: Ending Inventory Units Direct materials Finished goods Total 250 pounds (see Example 6.
000 1.400 2.800 34.800 800 × $4 $3.8 THE CASH BUDGET The cash budget is prepared to forecast financial needs. .8 — The Johnson Company’s selling and administrative expense budget for the year ending December 31.100 8.750 $13. Because the cash budget details the expected cash receipts and disbursements for a designated time period. the variable selling and administrative expense per unit must be computed.500 350 1. 6.200 $56.200 $14.200 1. Example 6.800 3 900 × $4 $3.150 Includes sales agents’ commissions.800 8.500 350 1. In order to complete the budgeted income statement in contribution format.7. and supplies. Paid for in the quarter incurred.200 × $4 $12.200 Total 3.500 350 1.500 350 4.950 $12.600 4 800 × $4 $3. 2001 is as follows.100 8. shipping.600 $15. Quarter 1 Expected sales in units Variable selling and administrative expense per unita Budgeted variable expense Fixed selling and administrative expenses: Advertising Insurance Office salaries Rent Taxes Total budgeted selling and administrative expensesb a b 2 700 × $4 $2. It is a tool for cash planning and control and for formulating investment strategies.750 1.7 THE SELLING AND ADMINISTRATIVE EXPENSE BUDGET The selling and administrative expense budget lists the operating expenses incurred when selling the products and managing the business. 6.100 8.Financial Forecasting and Budgeting The unit variable cost of $41 is computed as follows: 61 Unit Cost Direct materials Direct labor Variable overhead Total variable manufacturing cost a Units 3 pounds 5 hours 5 hoursa Total 6 25 10 $41 $2 5 2 Variable overhead is applied on the same basis as direct labor hours.7.400 1.100 2.
Interest is computed and paid as the principal is repaid. the company may be missing opportunities to use its cash for the greatest profit possibilities.g.g. On the other hand. Just as you pay cash for living costs (e. The disbursements section shows all cash payments listed by purpose. If a cash shortage is experienced. cash collections from customers. selling assets). The financing section provides a detailed account of the borrowings and repayments expected during the budget period.000 minimum cash balance at the end of each quarter. the company may even go out of business because it cannot pay its bills. if the cash position is excessive. Borrowing takes place at the beginning of each quarter. Note that cash receipts are not necessarily the same as revenue (e. cash collections from customers are cash payments (e.g. which gives you the total amount available to spend. Example 6.g. food and shelter). purchase of assets.9 — To illustrate the cash budget we will make the following assumptions: • The company desires to maintain a $5. To the beginning cash balance.. the cash budget must also be periodically updated for changing conditions. borrowing money. • All borrowing and repayment must be in multiples of $500 at an interest rate of 10% per annum. and repayment is made at the end of each quarter. a company has more alternative sources of cash than you do. however.. you add the period’s cash receipts. 2001 is shown as follows: . 4. The receipts section gives the beginning cash balance. and other receipts (e... you instead must estimate when credit sales will be collected. a company also pays cash to operate and generate revenue (e. A cash budget for your department is similar to a cash budget you would prepare for yourself. leaving the ending cash balance. The cash budget usually is comprised of four major sections: 1. advertising).g. Just as forecasts must be continuously evaluated for changing internal and external circumstances. 2. Unlike your personal cash budget. a company may issue stock but a person does not. You then subtract cash payments. However. 3. depreciation). the cash budget indicates whether the shortage is temporary or permanent and whether short-term or long-term borrowing is needed.62 Accounting and Finance for the Nonfinancial Executive it helps avoid the problem of either having idle cash on hand or suffering a cash shortage. The Johnson Company’s cash budget for the year ending December 31. and payment of debt.. Examples include cash expenses. For example. credit sales). the company’s cash budget cannot count on receiving a paycheck each period. The receipts section gives the beginning cash balance. The cash surplus or deficit section simply shows the difference between the cash receipts section and the cash disbursements section. Is a line of credit necessary? Should capital expenditures be cut back? If the cash position is very poor.
200 56. Example 6.950 4.925) $9.9 THE BUDGETED INCOME STATEMENT The budgeted income statement summarizes the various component projections of revenue and expenses for the budgeting period (for control purposes.500 $5.750 24.8 6.300 4.560 18.755 $35.200 units @ $41) Variable selling and administrative Contribution margin Less: Fixed expenses Factory overhead Selling and administrative Net operating income Less: Interest expense Net income before taxes Less: Income taxes Net income 6.800 $131.713 24.300 69.750 10.960 74.000 6.113 20.353 6.860 22.460 19.549 19.6 6.899 9.000 54.066 5.6 6.950 12.9 20% 24.000 9. depending on need).4 6.Financial Forecasting and Budgeting 63 Quarter Example No.650 14.353 $9.5 6.461 $24.200 144.500 43.200 units @ $80) Less: Variable expenses Variable cost of goods sold (3.800 44.401 57.775 8.600 24.000 112.250 11.2 1 $10.500) (425) (8.106 3 $5.000 43. beginning Receipts Collection from customers Total cash available Less: Disbursements Direct materials Direct labor Factory overhead Selling and administrative Machinery purchase Income tax Total disbursements Cash surplus (deficit) Financing Borrowing Repayment Interest Total financing Cash balance.120 66.541 4.080 71.8 12.020 .510 18.2 $256.401 2 $9.650 15.7.800 67. ending Given 6.000 242. 2001 is as follows: Example No.10 — The Johnson Company’s budgeted income statement for the year ending December 31.750 4 $9.778 8.682 24.521 4.031 49.401 8.500 (8.8 Given Given 53. the budget can be divided into quarters or even months.200 425 43.560 (3. Sales (3.460 252.082 80. Cash balance.353 6.039) 8.106 64.950 13.150 Total $10.500 (8.000 227.300 4.7 6.000 54.500 10.461 66.000 6.500) (425) (425) $24.300 64.
460 receipts (from Example 6.040b 500c 4.040.11 — To illustrate. 2001 is shown as follows: Assets Current assets Cash Accounts receivable Material inventory Finished goods inventory Total current assets Fixed assets Land Buildings and equipment Accumulated depreciation Total fixed assets Total assets a b c Liabilities and Stockholders’ Equity Current liabilities Accounts payable Income tax payable Total current liabilities Stockholders’ equity Common stock. 2000.280 23.7. Assets Current assets Cash Accounts receivable Material inventory Finished goods inventory Total current assets Fixed assets Land Buildings and equipment Accumulated depreciation Total fixed assets Total assets Liabilities and Stockholders’ Equity Current liabilities Accounts payable Income tax payable Total current liabilities Stockholders’ equity Common stock.000)g 101. and highlights future resources and obligations.464h 8. The budgeted balance sheet is prepared by adjusting the previous year’s balance sheet based on expectations for the budgeting period.293 From Example 6.254 $2.054 Total liabilities and stockholders’ equity $113.7 (ending inventory budget).000 6.64 Accounting and Finance for the Nonfinancial Executive 6.500 474 3. From Example 6.000 37.254 50. .000 j 72.100d $ 51. Example 6. $9.353a 23.300 $153.200 4. It also serves as a final check on the mathematical accuracy of all the other schedules. no-par Retained earnings $24.300f (73.074k Total liabilities and stockholders’ equity $153.000) 90.219 70. we will use the Johnson Company’s balance sheet as of December 31.10 THE BUDGETED BALANCE SHEET The budgeted balance sheet alerts you to unfavorable financial conditions that you might want to avoid.200 70.9) = $23. helps you perform a variety of ratio calculations.000 100.9 (cash budget). no-par Retained earnings $10.000 $113.755 i 11.2) – $242.000 (60.293 $2.993 50.000e 124.254 The Johnson Company’s budgeted balance sheet as of December 31.000 9.500 + $256.000 sales (from Example 6.
The value of certain variables (e. This is a version of the percent-ofsales method previously discussed. if a budgetary figure is changed (e.8 IS THERE A SHORTCUT APPROACH TO FORMULATING THE BUDGET? There is a shortcut approach that is widely used in formulating a budget.000 + $24. k $37.Financial Forecasting and Budgeting 65 d e From Example 6. it is easy to make different sales projections and see what the resulting costs and profitability will be. sales). 2. These percentages are then applied to forecasted sales. There are primarily two approaches to modeling the corporate budgeting process: simulation and optimization . mechanical calculations including addition. the electronic spreadsheet will change all other budgetary amounts related to it (e. Second. cash. Such software carries out tedious.346 (from Example 6.020 (from Example 6..g.464 (all accounts payable relate to material purchases). More importantly. and division. and accounts receivable) can be forced to take on specified desired values. 6. cost of sales. g $60. 6. Hence.4) – $19.9) = $124.464.054 + $35. 6.10) net income = $72. j No change. a pro forma balance sheet is estimated by determining the desired level of certain balance sheet items and by making additional financing conform to those desired figures.000 + $13. f $100. No change.928) = 2.200 + $19.000 (from Example 6.300 (from Example 6.300. h $2.4) = $2.000. the remaining items are estimated to make the balance sheet even. subtraction.9 CAN YOU USE AN ELECTRONIC SPREADSHEET TO DEVELOP A BUDGET PLAN? An electronic spreadsheet may be used to efficiently and quickly develop a budget (examples of available software are Lotus 1-2-3 and Microsoft Excel).10 (budgeted income statement)...g. a pro forma income statement is developed using past percentage relationships between relevant expense and cost items and sales.7 (ending inventory). or 50% of fourth quarter purchase = 50% ($4. Previous financial condition is a reliable predictor of future condition. Its calculations provide a basis for choice among alternatives under conditions of uncertainty. selling expenses).10 COMPUTER-BASED MODELS FOR FINANCIAL PLANNING AND BUDGETING A computer-based quantitative model may be used to construct a profit planning budget and to help answer a variety of “what-if” questions.082 (from Example 6.6) = $73. There are two basic assumptions underlying this approach: 1.074. Thus. inventory. In the first step of this approach.g. multiplication. i From Example 6.
6. the budget helps you achieve departmental goals. Venture. other departments. Encore! Plus. among the wellknown system packages are Comshare’s Interactive Financial Planning System (IFPS). you can better understand the impact of your decisions on your department. they will be more receptive to meeting its objectives. There are many user-oriented modeling languages specifically designed for budgeting. You have a reference point for control reporting. Further. It assists you in anticipating problems in time to deal with them effectively. The budgetary process also assists you in searching for weaknesses. If the people operating under the budget have helped prepare it. Budgets must also be realistic if they are to be accepted by the staff and if the company’s objectives are to be met. and the company as a whole. . and MicroFCS. A budget helps you direct attention from the present to the future. and the budget process should be decentralized to departmental cost centers with responsible managers. and it reveals whether you can expand. You can also determine how to best use allocated funds to strengthen your department’s position.66 Accounting and Finance for the Nonfinancial Executive (see an advanced finance text for more information on these models).11 CONCLUSION Budgets should be participative. which you can strengthen before they become a major problem. not authoritative. If you feel a budget is fair and you have participated in the budgetary process.
You would want to know whether the sales manager can control the problem (e. who should get credit for it? If it is unfavorable. you can spot and correct problems. as well as identify areas of success.g. To help you interpret variance analysis reports. an economic depression). and distribution. and remedy any problems. With the aid of variance analysis. and whether it is controllable or not. If the variance is significant (or controllable). you would want to know what you and your employees are doing correctly so as to capitalize on the situation. you would want to know the reasons for the discrepancy and the severity of the situation. factory workers. understand which variances are important for your position. (4) the use of flexible budgeting. among others. In this event. is it controllable? 3. you can then decide whether the problem lies with buying. Locating deviations between expected and actual figures through variance analysis helps you not only to identify problems but also to determine how large the problem is. poor salesperson effort) or not (e. What trends do the variances reveal? 6. By using variance analysis. Do your actual sales and expenses match your estimates? Why or why not? 2. only significant variances warrant investigation. You can carry out variance analysis for such areas of the company as sales. If the actual cost of a product is less than expected. (2) the use of variance analysis to monitor performance. who is responsible. you would want to reward superior performances by employees or to know that the company is using new technological processes that successfully keep costs down. if the cost of manufacturing a product or rendering a service is higher than expected. planning. Is the variance uncontrollable because of external factors such as a strike? 4. for instance.. (3) the evaluation of sales and cost variances. Variance analysis can also help you appraise the productivity of your employees.7 Using Variance Analysis as a Financial Tool Variance analysis is a tool managers use to evaluate financial performance. purchasing. what are the reasons and who is responsible? What corrective actions should be taken? 67 . and (5) analysis of warehouse problems and sales performance. Are your standards too tight? 5. Is the variance favorable or unfavorable? if it is favorable. Variance analysis also spotlights positive performances. For example.g. or general productivity. this chapter will cover the following topics: (1) the standards of revenue and cost. including sales personnel. Or perhaps you find that actual sales fall short of expectations. You will learn to calculate and appraise variances so as to answer these questions: 1. Typically. and delivery personnel..
Variance analysis compares standard to actual costs or performances. and standard volume. A nonfinancial manager commented in an interview that his facilities department uses standard costs for equipment installation and relocation to determine the cost to charge to the ordering unit. you set standards such as sales quotas.. Generally. material price. when a product or activity is critical to the proper functioning of the business (e.g. working conditions). or marketing an item during a given future period. or hourly. you should understand the concept of and calculations for standard costs. We have a weekly production meeting where we must report on our variances to plan in a number of areas. or immaterial. For example.g. Contingent on the cost-benefit relationship.000 units. repairs). This norm is also dependent upon quantitative and qualitative measurements (e. quarterly. monthly. whichever is less. For example. which you are about to learn: Let’s say production has dropped and I am below plan. Guidelines for materiality should be set to reflect the importance of an element to the corporation’s performance and decision making. Let us focus on standard cost.. standard costs (e. which is the predetermined cost of manufacturing. the company may set a policy looking into any variance that exceeds $10.000 or 20. Insignificant. these analyses may be as detailed as necessary. For material variances.1 DEFINING A STANDARD At the beginning of the period. materiality is measured by dollar amount or by volume level. wage rate). One way to measure if a variance is significant is to divide the variance by the standard cost. servicing. depending on how quickly you need to identify a problem. hours spent) until the end of the period.g. a variance of more than 5% may be deemed material. Also. 7. you must identify the responsible departments or persons and take corrective action. promotion. Some specific advantages of standards and variances are that they: . 7. It is based on current and projected conditions.. budgeting our people if you will.68 Accounting and Finance for the Nonfinancial Executive In an interview. variances can only be computed at that time. We do this in order to maintain tight management control and also to be responsive to our changing environment. variances need not be looked into further unless they recur and/or reflect potential difficulty. limits for materiality should be such that early reporting of variances is encouraged. Evaluation of variances may be done yearly. But since you do not know actual figures (e. There are two types of variances: material and immaterial.g. I must take appropriate action to get back on course. statistical techniques can be used to ascertain the significance of cost and revenue variances. this is a very important tool for planning as we each week determine the best use for our resources. critical part. In some cases. For determining the projected cost of a job.2 THE USEFULNESS OF VARIANCE ANALYSIS Setting standards and analyzing variances are essential in financial analysis and decision making. Further. a nonfinancial manager neatly summarized the virtues of variance analysis. daily.. Both activities tell you how you are doing and what is going wrong or right.
• Expected — These are expected figures. Therefore. • Simplify bookkeeping procedures by keeping the records at standard cost. because everyone knows the standard to accomplish. optimal conditions. • Facilitate communication within the organization. 7. biases in deriving standards can exist. • Currently attainable — These are based on efficient activity. They are possible goals but difficult to achieve.g. quantity. • Establish cost control since cost inefficiencies and overruns are pinpointed.3 SETTING STANDARDS There are four types of standards: • Basic — These are not changed from period to period. however. which is an unrealistic basis. • Establish bid prices on contracts because desired profit goals can be determined. • Help formulate sales price because you can determine what the item should cost. which assume ideal. Although standard costing and variance analysis are exceptionally important tools. Variances in product activity (cost. • Set and evaluate objectives by comparing budgeted to actual figures. You should base standards on the situation being appraised. • Pinpoint responsibility for undesirable performance so that corrective action may be taken. certain inefficiencies will occur. such as anticipated machinery failure. Variances in sales are often the responsibility of the marketing manager. you should use these tools with caution. Normal occurrences. For example. they can have their drawbacks. quality) are typically the foreman’s responsibility.. Here are some examples of how to match standards with particular situations: Situation Cost reduction Pricing policy High-quality good Standard Tight Realistic Perfection . Further. • Maximum efficiency — These are perfect standards. cash requirements). Realistically.Using Variance Analysis as a Financial Tool 69 • Assist in decision making because areas of inefficiency are identified. such as between management and supervisors. Note that variances indicating strengths should be further taken advantage of. Variances in profit usually relate to overall operations. which should come very close to actual figures. They form the basis with which later period performance is compared. is given to a change in the environment. • Highlight problem areas through the “management by exception” principle. No consideration. • Assist in planning by forecasting needs (e. are considered in the calculation at currently attainable standards. material variances can sometimes be due to out-of-date standards or poor budgetary processes rather than actual performances.
000 Unfavorable Favorable Favorable By looking at the trend in sales.100 $303.4 DETERMINING AND EVALUATING SALES VARIANCES Actual and budgeted sales figures should be compared by territory. and product to see if expectations are being realized.1 — Western Corporation’s budgeted sales for 2001 were: Product A: 10.000 – 10. or returns. When you appraise changes in gross profit.000 $12. Sales variances are computed to gauge the performance of the marketing function. it is a legitimate measure of performance. . Although gross profit may not necessarily translate into net profit because of high selling and advertising expenses.000 units at $6. salesperson.700.20 – $6.000 units at $8. volume. consisting of the sales price variance and sales volume variance.00) × 8.000 Sales price variance $1.70 – $8. sales plans.00) × 33. selling price.000 Actual sales for the year were: Product A: 8.00 per unit Expected sales revenue $ 60. To evaluate sales performance.70 Accounting and Finance for the Nonfinancial Executive 7.600 254. Do not be misled by high sales volume.000) × $6.20 per unit Product B: 33.000 $300. The sales price variance equals: (Actual selling price – Budgeted selling price) × Actual units sold Product A ($6. the report will reveal where to put sales effort. you should focus on profitable sales volume.000 units at $6.900 $8.00 Product B (33.300 Favorable Unfavorable Unfavorable The sales volume variance equals (Actual quantity – Budgeted quantity) × Budgeted selling price Product A (8. industry comparisons. high sales volume does not automatically mean high profits because the high costs associated with products need to be subtracted.000 24.000 – 30. a complete analysis of sales volume should include consideration of budgets. you have to recognize that these changes may be caused by changes in sales mix. Overall. standards. reports by salespersons should show not only revenue derived but also gross profit earned.00 per unit Product B: 30.70 per unit Actual sales revenue $ 49.000 240.000 units at $7.000) × $8. you may identify unfavorable trends requiring a reduction of the sales effort or a change in product.00 Sales volume variance $12.700 There is a favorable sales variance of $3. and manufacturing costs. Example 7. Also. Thus.000 Product B ($7.699 9.
1 depicts the variance analysis for total cost. where standard quantity equals standard quantity per unit of work times actual units of work produced. spending) variance is calculated as follows: (Standard price – Actual price) × Actual quantity Quantity (usage. An unfavorable total sales variance may signal a problem with the marketing manager because he or she has control over sales. 7. Figure 7. Example 7. and often pricing. You should also compare your divisional sales figures with the sales figures of competing companies’ divisions and with industry averages. • Standard cost equals standard price times standard quantity. And.6 MATERIALS VARIANCES The materials price variance allows you to evaluate the activity of the purchasing department and to see the impact of raw materials’ cost changes on profitability. efficiency) variance is formulated in the following manner: (Standard quantity – Actual quantity) × Standard price These figures are computed for both material and labor. advertising. Total cost variance has these two elements: price variance and quantity variance. if unfavorable volume variance is coupled with favorable price variance. • Total cost variance equals actual cost less standard cost. you may have lost sales by raising your prices. Unfavorable sales situations may also be caused by a lack in quality control. . 7.5 COST VARIANCES When a product is made or a service is performed. where actual quantity equals actual quantity per unit of work times actual units of work produced. Price (rate. or deficient product design based on poor engineering. an unfavorable sales volume variance may arise from poor marketing procedures. For example. Sometimes an unfavorable sales volume variance is caused by the price cuts of competing companies. substitution of poorer quality components because of deficient purchasing. you have to determine these three cost measures: • Actual cost equals actual price times actual quantity. while the materials quantity variance helps you to judge the performance of the production supervisor.Using Variance Analysis as a Financial Tool 71 You have to evaluate the meaning of sales variances to your department.2 calculates the three types of materials variances you need to know.
000 U $40. use of an improper production method. failure to take a discount on quantity purchases.2 — The standard cost of one unit of output (product or service) was $15. improperly adjusted machines.000) × $5 $32.000 × $7) $120. Total Materials Variance Standard quantity × Standard price (24. The actual cost was $14 per unit. scarcity in raw material supplies resulting in higher prices. and purchasing department inefficiencies.000 112. 8. Once the reasons for unfavorable materials variances have been determined. outright waste on the production line. and/or use of a lower-grade material. Example 7. purchased to save money.000 F Actual Materials Price Variance (Standard price – Actual price) × Actual quantity ($5 – $7) × 16.72 Accounting and Finance for the Nonfinancial Executive Price Actual Price Variance Standard Quantity Variance Quantity Standard FIGURE 7. or three pieces at $5 per piece.000 × $5) Actual quantity × Actual price (16.000 – 16. or two pieces at $7 per piece.000 $8.1 Variance analysis of total cost. Unfavorable materials quantity variances result from poorly trained workers. you can then locate the responsible departments or key personnel: .000 Materials Quantity Variance (Standard quantity – Actual quantity) × Standard price (24. inflationary cost increases.000 F Unfavorable materials price variances may be caused by one or more of the following factors: inaccurate standard prices. During the period.000 units were made. failure to shop for bargains.
000 × $8) $252. you can increase selling price. who will bear the ultimate cost increase. and emphasize vertical integration to reduce the price and supply risk of raw materials. remember that you cannot control materials price variances when higher prices are caused by inflation or shortage situations or when rush orders are required by the customer.000 Labor Efficiency Variance (Standard quantity – Actual quantity) × Standard price (28. look at price instability in trade publications. The actual cost is six hours times $8 per hour.000) × $9 $42. or engage in a cost reduction program.000 U Labor Rate Variance (Standard price – Actual price) × Actual quantity ($9 – $8) × 42. Labor efficiency standards are typically estimated by engineers based on an analysis of the production operation.7 LABOR VARIANCES The standard labor rate is based on the contracted hourly wage rate.000 U . Example 7. 7. Labor variances are determined in a manner similar to that of materials variances.000 F $126. as illustrated in Example 7. During the period. Lastly. you should examine the variability in raw material costs.000 units were produced. substitute cheaper materials.Using Variance Analysis as a Financial Tool 73 Reason Overstated price paid Failure to detect defective goods Inefficient labor or poor supervision Poor mix in material Rush delivery of materials Unfavorable quantity variance Unexpected change in production volume Responsible Party Purchasing Receiving Foreman Production manager Traffic Foreman Sales manager To correct an unfavorable materials price variance. or $48 per unit. or $36 per unit. To achieve some of these ends. Where salary rates are set by union contract. change a production method or specification. the labor rate variance will usually be minimal.000 – 42.000 336.3.000 $84. Total Labor Variance Standard quantity × Standard price (28.3 — The standard cost of labor is four hours times $9 per hour.000 × $9) Actual quantity × Actual price (42. 7.
as follows: Reason Use of overpaid or an excessive number of workers Poor job descriptions Overtime Responsible Party Production manager or union contract Personnel Production planning In the case of a shortage of skilled workers. Labor efficiency (quantity) variances can be attributed to one or more of the following: • Poor supervision • Use of unskilled workers. or the wrong mixture of labor for a given job • Use of poor quality machinery • Improperly trained workers • Poor quality of materials. Relevant computations follow. Standard overhead (standard hours × standard overhead rate). and (3) use of workers commanding higher hourly rates than expected. it may be impossible to avoid an unfavorable labor price variance.8 OVERHEAD VARIANCES The overhead variance is composed of the controllable and volume variances. Overhead control variance = Actual overhead vs. requiring more labor time in processing • Machine breakdowns • Employee unrest • Production delays due to power failure The reasons and responsible parties for unfavorable labor efficiency variances can then be matched in these ways: Reason Inadequate supervision Improper functioning of equipment Insufficient material supply or poor quality Responsible Party Foreman Maintenance Purchasing 7. who are paid lower rates. Budget adjusted to standard hours.74 Accounting and Finance for the Nonfinancial Executive Possible causes of unfavorable labor rate variance include the following: (1) an increase in wages. Possible reasons for labor rate variances can be matched with responsible parties. Controllable variance = Actual overhead vs. (2) poor scheduling or production resulting in overtime work. .
500 and variable overhead of $10.Using Variance Analysis as a Financial Tool 75 Note: Budget adjusted to standard hours equals fixed overhead plus variable overhead (standard hours times standard variable overhead rate).000 4.000/10.500 11.000 $7. Volume variance = Standard overhead vs.500 4. Example 7.500 10.500F Volume Variance Standard overhead Budget adjusted to standard hours 7.75 $4.000 8.500/10.75 1.000 $1.000 hr × $1. Example 7.000 7.500U .000 hrs) Standard hours (800 units × 5 hrs per unit) Total Overhead Variance Actual overhead Standard overhead Standard hours Standard overhead rate $8.000 × $1) $8.00 $1.75 7.500 $4.4 — The following data are provided: Budgeted overhead (includes fixed overhead of $7.000 800 5 Preliminary calculations are as follows: Budgeted fixed overhead ($7. Budget adjusted to standard hours.000 0.000 hrs) Total budgeted overhead ($17.000 11.000) Budgeted hours Actual overhead Actual units produced Standard hours per unit of production $17.000U Controllable Variance Actual overhead Budget adjusted to standard hours: Fixed overhead Variable overhead (Standard hours × Standard Variable overhead rate: 4.500/10.000 hrs) Budgeted variable overhead ($10.4 uses the equations to illustrate a hypothetical situation.500 $3.000 11.
On the other hand. The flexible budget is geared toward a range of activities rather than a single level of activity. 7. since they are involved with plant utilization. The controllable variance is the responsibility of the foreman. you would want to locate the responsible parties. The possible reasons for recurring unfavorable overhead volume variances include the following: • • • • • • • The purchase of the wrong size plant Improper scheduling Insufficient orders Shortages in material Machinery failure Long operating time Inadequately trained workers When idle capacity exists. Table 7. You can then see how your department is performing at varying capacity levels. Example 7.9 THE USE OF FLEXIBLE BUDGETS IN PERFORMANCE REPORTS The static (fixed) budget is geared to only one level of activity and thus has problems in cost control because it does not distinguish between fixed costs and variable costs. The volume variance is the responsibility of management executives and production managers. and full (150%) capacity levels. Flexible budgeting distinguishes between fixed and variable costs. A flexible budget employs budgeted figures at different capacity levels.76 Accounting and Finance for the Nonfinancial Executive Because unfavorable variances exist. fixed overhead variance data provide information regarding decision-making astuteness in relation to the purchase of some combination of fixed plant size and variable production inputs.5 illustrates the differences between static and flexible budgets. this may indicate long-term operations’ planning problems. since he or she influences actual overhead incurred. Note that flexible budgets are primarily used to accurately measure performance because they compare actual costs for a given output with the budgeted costs for the same level of output. Fixed costs remain constant as long as you operate below full capacity. Thus. . thus allowing for a budget that can be automatically adjusted (via changes in variable cost totals) to the particular level of activity actually attained. It allows you to choose the best expected (normal) capacity level (100%) and to assign pessimistic (80%). On the one hand. It also assists in appraising decisions regarding variable inputs.1 presents an example of a flexible budget. variable overhead variance information is helpful in arriving at output level and output mix decisions. optimistic (110%). variances between actual costs and budgeted costs are adjusted for volume ups and downs before differences due to price and quantity factors are computed.
000(F) 4.000 Spending Variance $2.200 Actual 5. .30 4.000 hrs.000 6.000 74.) $54.000 $39.000(U) 6.000 70. it makes no sense to compare costs at one activity level with costs at a different one.000 293.800 $38.000(F) $60.000 21.000 $700.000 32.000 $200.000 58. Assume further that only 5.800 units were produced. From a control standpoint.000 units 5.000 234.000 2.80 4.000 287. the budget costs are based on an activity level of 6.20 Fixed Cost $6.1 Flexible Budget Cost Indirect material Indirect labor Supervision Depreciation Power and light Maintenance Total Variable Cost $.000 hrs.000 276.70 $10.500 5.000 Actual (60.950 870 295 $45.000 40. For our current examples.000 6.5 — Assume that the Fabricating Department of Company X is budgeted to produce 6.000 70. Such comparisons make a production manager look good as long as the actual production is less than the budgeted production.000 40.000 20.000 Budget (50.800 units).200 If a static budget is used.00 Example 7.000 340.000 units.000 units during June.000 40.000 $740.) $46.000 17.) $56.000 $820.000 900 300 $46.000 270.000(F) 1.Using Variance Analysis as a Financial Tool 77 TABLE 7. whereas the actual costs were incurred at an activity level below this figure (5.800 units $39.000(F) . The direct labor and variable overhead budget for the month of June follows: Budgeted production Actual production Direct labor Variable overhead costs Indirect labor Supplies Repairs 6. the performance report for Company X’s Fabricating Department will appear as follows: Variance (U or F) 200U $500F 50F 30F 5F $585F Budget Production in units Direct labor Variable overhead costs Indirect labor Supplies Repairs 6.000(U) 53.000 900 300 $46.000 hrs.000 Budget (60.000 24.000(U) 8.800 units.000 70. we should compare costs at the actual production of 5. That is.615 These cost variances are useless: They compare oranges with apples.
000 units 5. as compared to the favorable cost variance on the performance report using the static budget approach. Of the numerous marketing standards and variances. minimum cost traffic routes should be selected based on the distribution pattern. the salesperson meets a standard.660 All cost variances are unfavorable. we will focus on. or the relationship between effort and accomplishment. which are in turn based on the type of customers the advertising is intended to reach as well as the nature of the competition. . Direct selling expenses should be related to distance traveled.800 870 290 $44. for the purpose of illustration.50 per unit 1.10 STANDARDS AND VARIANCES IN MARKETING Prior to setting a marketing standard in a given trade territory. to reward merit. standards can be based on a percentage of net sales. You should also make adjustments for standards that vary with geographical location. By making 100 calls.10. Standards for advertising cost in particular territories will vary depending upon the types of advertising media needed. etc. Some direct selling costs can be standardized.800 units) $38. such as product presentations for which a standard time per sales call can be established. a different standard is accomplished.800 units Actual (5. a salesperson may be expected to make 100 calls per month. By doing so. and forecasted conditions.700 5. and to encourage sales effort.05 $7. 7.00 .800 units) Direct labor Variable overhead Indirect labor Supplies Repairs $6. you should examine prior. You need to set sales standards to control sales activities.500 5.15 . since past strategies may have been inefficient. 7.615 Variance (U or F) $800U 150U 0 5U $955U Budget (5. accomplishments.70 $37.1 SALES STANDARDS Sales standards may be set in terms of effort. frequency of calls made. He or she may be expected to obtain 60 orders or $300.950 870 295 $45. current. If sales commissions are based on sales generated. Time and motion studies are usually a better way of establishing sales standards than prior performance. For example. those associated with sales. In formulating standard costs for the transportation function.78 Accounting and Finance for the Nonfinancial Executive Budgeted production Actual production 6.000 in business based on the 100 calls.
800 of merchandise.7 provide you with the data and computations for analyzing variances in two hypothetical situations. product.000 $34.000 120 238.Using Variance Analysis as a Financial Tool 79 7.2 ANALYZING SALESPERSON VARIANCES You should appraise sales force effectiveness within a territory.800) Standard calls × Standard sales (50 × $2. or personnel.700 $34. Examples 7. including time spent and expenses incurred. Variance in Salesperson Days (Actual days – Standard days) × Standard rate per day (1.000 U An unfavorable variance results because the actual rate per day is greater than the expected rate per day.000 F The variance is favorable because the territory was handled in fewer days than expected.000 120. The control variance is broken down into salesperson days and salesperson costs.000 2.10.000 F .000 240.6 — Sales data for your department follows. Standard cost Standard salesperson days Standard rate per salesperson day Actual cost Actual salesperson days Actual rate per salesperson day Total Cost Variance Actual cost Standard cost $238.000 1.000F $240. Total Variance Actual calls × Actual sales (55 × $2. Variance in Salesperson Costs (Actual rate – Standard rate) × Actual days ($140 – $120) × 1.700 – 2.7 — A salesperson called on 55 customers and sold each an average of $2. Example 7. Example 7.400.000) × $120 $36. Variance analysis of calls and sales follows.000 $ 2.700 140 Note: Cost variances may be determined by territory.6 and 7. The standard of calls is 50 and the standard sale is $2.400) $154.
100 $ 2.500 2.8 provides the data and calculations of the warehousing cost variance for a hypothetical situation. Example 7. and the relationship between salesperson costs and revenue obtained.000 F $2.030 12. Additional performance measures of sales force effectiveness include meeting sales quotas.80 Accounting and Finance for the Nonfinancial Executive The $34. resulting in huge sales returns and allowances. Variance in Calls Actual calls – Standard calls) × Standard sale (55 – 50) × $2. .000F You should encourage your sales staff to push products with the highest profitability rather than the highest selling price or least sales resistance. 7.11 VARIANCES IN WAREHOUSING COSTS Variance in warehousing costs can be calculated by looking at the cost per unit to store the merchandise and the number of orders anticipated.000 favorable variance can be broken down as follows.20 14.800 – $2.8 — The following information applies to a product: Standard cost Standard orders Standard unit cost Actual cost Actual orders Actual unit cost $12.930 U The total variance is segregated into the variance in orders and variance in cost.30 Total Warehousing Cost Variance Actual cost Standard cost $14.400) $12.030 6. Example 7. profitability per order. Avoid paying your salespeople commissions on gross sales because you may encourage them to sell to anyone.000 F $20.400) × 50 Joint Variance (Actual calls – Standard calls) × (Actual sale – Standard sale) (55 – 50) × ($2. Instead. the commission should be tied to net sales.100 5.400 Variance in Sales (Actual sale – Standard sale) × Standard calls ($2. as follows.100 $1.800 – $2. the number of orders from current and new customers.
Standard orders) × Standard unit cost (6. you are using a tool to protect savings and to cut inefficiencies and losses. immediate corrective action must be taken to handle the problem. with the quality of service or product at a constant level. marketing. Variances are red (or green) flags to watch for and become monitoring and control devices. When a variance is controllable. By analyzing variances. Unfavorable variances must be examined to ascertain whether they are controllable by you or uncontrollable because they solely relate to external factors. or a large loss. $2. 5. including manufacturing. By looking at variances. if unfavorable. you make your department more efficient and less costly to run.30 vs. Further. the party responsible for a favorable variance should be recognized and rewarded.20) × 6. and service. an examination should still be made so that corporate policy may include the positive aspects. .500) × $2.100 $1.12 CONCLUSION Variance analysis is essential for the appraisal of all aspects of the business.320 U $610 U 7.Using Variance Analysis as a Financial Tool 81 Variance in Orders (Actual orders vs. Even a small variance can mean a large savings. if favorable.100 vs. Standard cost per unit) × Actual orders ($2. If a variance is favorable. You should also determine an acceptable range of variances.20 Variance in Cost (Actual cost per unit vs.
Part II Critical Asset Management Issues .
The short-term debt provides flexibility to meet seasonal needs within your ability to repay the loan. 8. affects the amount of cash held. The longer it takes to acquire or produce goods. There are various ways of managing working capital to achieve success. you are financing assets with liabilities of similar maturity so the proceeds and return from the assets may be used to pay off the debt.000 in patents. in turn. $30. Your working capital needs will partly depend on how long it takes your company to turn raw materials into sold products.000 in inventory. $90. Short-term credit. Long-term assets should be financed with longterm debt because the assets last longer and the financing can be spread over a longer time period.8 Working Capital and Cash Management The ability to manage working capital will improve return and minimize the risk of running short of cash. These two strategies are called hedging.1 illustrates how to calculate working capital. These methods will be discussed in this chapter.000 42. 85 .000 The liquidity of the current assets will influence the terms and availability of short-term credit.1 WORKING CAPITAL Briefly. $42. generally the easier it is for you to obtain short-term credit at favorable terms.000 $82.1 — The following assets exist: $10. $36. 8.000 in machinery. The working capital consists of the total current assets: Cash Accounts receivable Inventory Total working capital $10. resulting in less financing risk.000 in cash.2 FINANCING ASSETS When you need funds to buy seasonal inventory. you should finance with short-term debt because the sale of the inventory will generate funds in the near term to pay off the obligation. the greater the working capital needed. Example 8.000 30.000 in long-term investments. and $4. that is. The more liquid your business is. working capital equals total current assets — the most liquid assets of the company. Example 8.000 in accounts receivable.
maturity dates of debt. longterm savings accounts. Before you plan a cash management strategy. For example. You can invest funds in the following ways: • Time deposits. Cash management also requires knowing the amount of funds available for investment and the length of time they can be invested. highgrade debt instruments such as Treasury bills and commercial paper. Thus. Forecasting assists in properly timing financing. • Money market funds. such as under a line of credit agreement. current liquidity position. you need to determine your cash management objective. you have to plan when to have excess funds available for investment and when money needs to be borrowed. For example. Also.3 MANAGING CASH PROPERLY Sound cash management requires you to know how much cash is needed. which are managed portfolios of short-term. issued at face value and providing for interest at maturity). which allows you to borrow instantly up to a specified maximum amount. how much cash you have. You want to invest excess cash for a return but have adequate liquidity to meet your needs.86 Accounting and Finance for the Nonfinancial Executive 8. including savings accounts earning daily interest. negotiable time deposits with banks. You can get away with a smaller cash balance when cash receipts and cash disbursements are highly synchronized and predictable. you may be able to guard against accumulating excessive balances. and where that cash is. forecasted short. liquidity risk preferences. You need less cash on hand if you can borrow quickly from a bank. you need to take care of some basic cash-handling needs. and the probabilities of different cash flows under varying circumstances. and its destination. which in effect represents restricted cash. and certificates of deposit (short-term. when a bank tends your money. You have to accurately forecast the amount of cash needed. But some available cash is needed for unexpected demands or for customer collection problems. This deposit is referred to as a compensating balance. it may require you to retain funds on hand as collateral. and the amount to be transferred between accounts. its source. What determines how much cash you should hold? The key factors are cash management policies. These data are needed on both a short. This knowledge is particularly crucial during inflationary periods. ability to borrow. You do not want an excessive cash balance because no return can be earned on it.and long-term cash flow. Next. Demand deposits that pay interest. If you have many bank accounts. The minimum cash to hold is the greater of (1) compensating balances (a deposit held by a bank to compensate for providing services) or (2) precautionary balances (money held for emergency purposes) plus transaction balances (money to cover checks outstanding). debt repayment. make certain that cash receipts are deposited promptly. make sure that cash is not unnecessarily tied up in other accounts such as advances or loans to employees and insurance deposits. . Warning: Cash in some bank accounts may not be available for investment.and a long-term basis.
government securities.S. marketability. Treasury bills are exempt from state and local income tax. A good secondary market exists for resale. In deciding on an investment portfolio. Banker’s acceptances are time drafts drawn on and accepted by a banking institution. Ninety. government. They have a maturity typically ranging from 90 days to 1 year.2 — A $10.S. The borrower will repurchase at the contract price plus an interest charge. The maturity typically ranges from 6 to 12 months. • Commercial paper. The return for three months is Return $10. which in effect substitutes its credit for that of the importer or holder of merchandise. which is a short-term. unsecured debt instrument issued by financially strong companies (see Chapter 16 for a more detailed discussion). Treasury bills are issued at a discount. you should consider return rate. They are legal contracts between a borrower (security seller) and lender (security buyer). three-month Treasury bill is purchased for $9. • Short-term tax exempts issued by states and local government agencies in denominations up to $1 million.and 180-day bills are auctioned weekly. the return is 2% × 12/3 = 8% (annual return) By holding marketable securities. which are short-term (up to six months). No secondary market exists.800 On an annual basis.000 – $9. which are backed by the U. You may also invest in marketable securities when funds are being held temporarily in anticipation of shortterm capital expansion.and 360-day bills are auctioned monthly. noninterest-bearing notes up to $1 million issued at a discount.000 or more.= ----------------------------------------.= --------------.800. The maturity ranges from 1 day to 3 months. Interest is paid at maturity.2 demonstrates how to calculate the annual return of a Treasury bill. and maturity date. default risk. • Repurchase agreements issued by dealers in U.Working Capital and Cash Management 87 • Banker’s acceptances. If your business is seasonal. They come in denominations of up to $1 million and are highly liquid. Example 8. Example 8.800 $9.= 2% Investment $9. which means that interest represents the difference between the price paid and the face value of the instrument at the maturity date.000. They come in typical amounts of $500. • Treasury bills. you may buy marketable securities when excess funds exist and then sell the securities when there is a cash deficit. . Acceptances are mostly traded internationally and enjoy their preferred credit status because of their “acceptance” (guarantee) for future payment by commercial banks. you can protect against cash shortages.800 $200 ------------------------. whereas 270.
Check issued and mailed by payer company to payee company
Accounting and Finance for the Nonfinancial Executive
Check received by payee company Journal entries prepared and check deposited by payee company Check clears the bank and monies are available to payee company
Mail float (3 days) 0
Processing float (2 days)
Transit float (4 days)
Total float (9 days)
FIGURE 8.1 Total float time.
In deciding on a cash management system, you should consider its associated costs compared to the return earned from implementing the system. The costs include bank charges, your time, and office employee salaries. You can make use of your personal computer in making transactions with the computers of banks and money market funds. Computer systems are also useful for buying and selling securities in the money market. The thrust of cash management is to accelerate cash receipts and delay cash payments. Analyze each bank account as to its type, balance, and cost so that return is maximized.
8.4 GETTING MONEY FASTER
To accelerate cash inflow, you must: (1) know the bank’s policy regarding fund availability; (2) know the source and location of cash receipts; and (3) devise procedures for quick deposit of checks received and for quick transfer of receipts in outlying accounts into the main corporate account. Before you draw up plans for quick deposits and transfers, you need to understand the check processing delays. Delays include: (1) mail float–the time a check moves from a debtor to a creditor; (2) processing float–the time it takes for a creditor to deposit the check after receipt; and (3) deposit collection (transit) float–the time for a check to clear. Figure 8.1 illustrates the float resulting from a check issued and mailed by the payer company to the payee company. Figure 8.2 illustrates a cash collection system for a hypothetical business. You can minimize mail float by making sure that the collection center is close to the customer. Local banks should be selected to hasten the receipt of funds for subsequent transfer to the central corporate account. Alternatively, strategic post office lockboxes may be used for customer remissions. The local bank collects from these boxes periodically during the day and deposits the funds in the corporate account. The bank also provides a computer listing of payments received by account
Working Capital and Cash Management
Mail Float (1) Puts checks in the mail (2) Mail is delivered U.S. Mail
Checks are paid (6) (5)
Funds are now available in company’s bank account (7)
(4) Clearing Company’s system bank Checks are forwarded Transit Float
FIGURE 8.2 Cash collection system.
Lockbox (1) Puts checks in the mail (2) U.S. Mail Funds are now available in the company’s bank account (8) Company’s headquarters
Checks are paid (7)
(5) Clearing Company’s system bank Checks are forwarded by the company’s bank for payment by the customer’s bank
FIGURE 8.3 Lockbox system.
and a daily total. Because the lockbox system has a significant per-item cost, it is most effective with low-volume, high-dollar collections. But the system is becoming increasingly more available to firms with high-volume, low-dollar receipts because technological advances (such as machine-readable documents) are lowering the peritem cost of lockboxes. Example 8.3 calculates, for a hypothetical situation, the amount of money that can be tied up by mailing delays.
Accounting and Finance for the Nonfinancial Executive Example 8.3 — You obtain average cash receipts of $300,000 per day. It typically takes 6 days from the time a check is mailed to its availability for use. The amount tied up by the delay is
6 days × $300,000 = $1,800,000
Before implementing a lockbox system, you need to undertake a cost-benefit analysis considering the average dollar amount of checks received, the costs saved by having lockboxes, the decline in mailing time per check, and the processing cost. Figure 8.3 depicts a simple lockbox system. Example 8.4 shows you how to calculate the maximum monthly payment for a lockbox.
Example 8.4 — It takes about 8 days to receive and deposit payments from customers. Thus, a lockbox system is being considered. It is anticipated that the system will reduce the float time to 5 days. Average daily collections are $400,000. The return rate is 11%. The reduction in outstanding cash balances occurring if the lockbox system is initiated is
3 days × $400,000 = $1,200,000
The return that could be earned on these funds is
$1,200,000 × .11 = $132, 000
The maximum monthly charge that should be paid for the lockbox arrangement is therefore
$132,000 --------------------- = $11,000 12
Example 8.5 illustrates the financial advantage of a lockbox system.
Example 8.5 — You are considering the use of a lockbox system costing $130,000 per year. Daily collections average $360,000. The lockbox arrangement will reduce the float period by 3 days. The rate of return is 14%. The cost-benefit analysis is shown below:
Return on early collection of cash (.14 × 3 × $360,000) Less: Cost Advantage of lockbox $ 151,200 (130,000) $ 21,200
You may also have to determine whether or not it would be financially beneficial to split a geographic collection region into a number of pans. Example 8.6 demonstrates how geographical splitting can be advantageous.
Working Capital and Cash Management Example 8.6 — You have an agreement with Harris Bank, which handles $4 million in collections a day and requires a compensating balance of $600,000. You are contemplating canceling the agreement and dividing the eastern region so that two other banks will handle the business instead. Bank X will handle $1 million a day in collections, requiring a compensating balance of $300,000, and Bank Y will handle the other $3 million a day, requiring a compensating balance of $500,000. It is expected that collections will be hastened by 1 day if the eastern region is divided. The rate of return is 12%. The new arrangement is financially beneficial, as indicated below.
Acceleration in cash receipts ($4 million × 1/4) Less: Additional compensating balance ($800,000 – $600,000) Increased cash flow Times: Rate of return Net annual savings $1,000,000 (200,000) $ 800,000 × .12 $96,000
Concentration banking should also be considered where funds are collected by several local banks and transferred to a main concentration account in another bank. The transfer of funds may be accomplished through the use of depository transfer checks (DTCs) or wire transfers. In the DTC arrangement, you make a resolution statement with the bank, whereby signatureless checks are deposited. As the initial banks collect the funds, information is immediately transferred to the concentration bank, which then issues a DTC to collect the outlying funds. The funds may be available the same day. With wire transfers (e.g., bank wire, federal reserve wire), funds are moved immediately between banks. This eliminates transit float in that only “good funds” are transferred. Other ways to accelerate cash receipt deposits include the following: • Arrange for preauthorized checks where the company writes the checks for its customers to be charged against their demand deposit accounts. • Send customers preaddressed, stamped envelopes. • Require deposits on large or custom orders or progress billings as the work progresses. • Charge interest on accounts receivable after a certain amount of time. • Encourage postdated checks from customers. • Have cash-on-delivery terms. In accelerating cash receipts, we may want to determine the return on the cash balance.
Example 8.7 — Your company’s weekly average cash balances follow:
Week 1 2 3 4 Total Average Cash Balance $14,000 16,000 11,000 15,000 $56,000
Accounting and Finance for the Nonfinancial Executive The monthly average cash balance is
56,000 --------------- = $14,000 4
Assuming an annual interest rate of 12%, the monthly return on the average cash balance is
$14,000 × 1% = $140
By accelerating remissions, freed cash can be invested in marketable securities for a return or used to pay off short-term debt.
8.5 DELAYING CASH PAYMENTS
You should try to keep money longer to earn greater interest! Never pay bills, for example, before their due dates. Other ways to delay cash payments include the following: 1. Make partial payments. 2. Use drafts to pay bills because drafts are not due on demand. When a bank receives a draft it must return the draft to you for acceptance before payment. When you accept the draft, you then deposit the funds with the bank; therefore, you can maintain a smaller average checking balance. 3. Mail checks from post offices with limited service or from locations where the mail must go through several handling points, lengthening the payment period. 4. Draw checks on remote banks or establish cash disbursement centers in remote locations so that the payment period is lengthened. For example, you can pay someone in New York with a check drawn on a California bank. 5. Use credit cards and charge accounts to lengthen the time between your purchase of goods and the payment date. 6. Delay the frequency of payments to employees (e.g., expense account reimbursements, payrolls). 7. Disburse sales commissions when the receivables are collected rather than when the sales are made. 8. Maintain zero balance accounts where zero balances are established for all of the company’s disbursing units. These accounts are in the same concentration bank. Checks are drawn against these accounts, with the balance in each account never exceeding $0. Divisional disbursing authority is thus maintained at the local level of management. The advantages of zero balance accounts are better control over cash payments, reduction in excess cash balances held in regional banks, and a possible increase in disbursing float.
Working Capital and Cash Management
You can control cash payments by centralizing the payment operation so that obligations are satisfied at optimum times. Centralization will also aid in predicting the disbursement float. You can minimize cash balances by using probabilities of the expected time checks will clear. Deposits, for example, may be made to a payroll checking account based on the anticipated time of check clearance. Examples 8.8 and 8.9 illustrate this principle.
Example 8.8 — You write checks averaging $50,000 per day; each check takes 3 days to clear. You will have a checkbook balance $150,000 less than the bank’s records. Example 8.9 — Every 2 weeks, you make out checks that average $600,000 and take 3 days to clear. How much money can you save annually if you delay transfer of funds from an interest-bearing account that pays 0.0384% per day (annual rate of 14%) for those 3 days? The interest for three days is
$600,000 × (.000384 × 3) = $691
The number of 2-week periods in a year is
52 weeks --------------------- = 26 2 weeks
The savings per year is
$691 × 26 = $17,966
Although not a delay of cash payment, you may reduce cash outflow by the early repayment of a loan, thus avoiding some interest. A cash management system that incorporates the suggestions in the last two sections is shown in Figure 8.4. Finally, in planning cash flows, make sure to consider that some types are more uncertain than others. For example, a major uncertain cash flow is cash sales. A major known cash flow is payroll payments. Make adjustments accordingly.
Acceleration of Cash Receipts Lock box system Concentration banking Preauthorized checks Preaddressed stamped envelopes Obtain deposits on large orders Charge interest on overdue receivables Delay of Cash Payments Pay by draft Requisition more frequently Disbursing float Make partial payments Use charge accounts Delay frequency of paying employees
FIGURE 8.4 Cash management system.
If you are short of funds to pay the supplier early. 8. An opportunity cost is the net revenue you lose by rejecting an alternative action.6 OPPORTUNITY COST OF FOREGOING A CASH DISCOUNT Many companies establish credit terms that authorize cash discounts in exchange for early payment of the amount purchased. Example 8.× ----------------. it can increase the carrying cost of holding a greater amount of merchandise. For example.= ----. The numerator of the first term (discount percent) is the cost per dollar of credit. net/30. if the terms are 2/10. net/60. The second term represents the number of times this cost is incurred in a year. A larger order usually provides a higher trade discount.= 24. holding the higher level of . you should hold on to the money as long as possible.× -------. you will receive a 2% discount off the purchase of $2 per unit. You should typically take advantage of a discount offered by a creditor because of the high opportunity cost. If you take advantage of the cash discount. you have 30 days to pay the bill but will get a 2% discount if you pay in 10 days. whereas the denominator (100 – discount percent) represents the money available by forgoing the cash discount.000 units instead of 5.10 — The opportunity cost of not taking a discount when the terms are 3/15. you should borrow the money when the interest rate on the loan is below the annual rate of the discount. you should not pay for 60 days.1 presents possible credit terms and the associated opportunity cost of not paying within the discount period. if the terms of sale are 2/10. However.7 VOLUME DISCOUNTS A volume discount is a reduction in the price you pay if a large quantity of goods is ordered. You can use the following formula to compute the opportunity cost percentage on an annual basis: Discount percent 360 Opportunity cost = ------------------------------------------------------. For example. Although a trade discount reduces the cost of buying goods.× -------100 – Discount percent N where N = the number of days payment can be delayed by forgoing the cash discount. Example 8.94 Accounting and Finance for the Nonfinancial Executive 8. you will reduce the purchase cost.7% 100 – 3 60 – 15 97 45 Table 8.000 units. If you elect not to pay within the discount period. This equals the number of days credit is outstanding less the discount period. net/60 is computed as follows: 3 360 3 360 Opportunity cost = ----------------.11 — If you buy 10.
6% 8. net/30 3/30. You should attempt to accelerate cash receipts and delay cash payments as much as is feasible.3% 36. Savings due to trade discount: 10. The larger order is warranted as indicated below. net/90 Opportunity Cost 10.7% 18.000 × 0. or ($2 × . you can increase your rate of return.Working Capital and Cash Management merchandise will increase carrying costs by $300.04.8 CONCLUSION By properly managing your cash. . net/45 2/10.02) Less: Increase in carrying costs Net advantage of higher value order 95 $400 (300) $100 TABLE 8.1 Opportunity Cost of Not Taking a Discount Credit Terms 1/10.
you must consider whether it is financially prudent to hold receivable balances. terms of sale.. This. audit opinion. To be successful in managing accounts receivable. You must also consider the costs of giving credit. The opportunity cost of tying up money in accounts receivable is the loss of return that could have been earned if those funds had been invested in marketable securities. banking relationships and account information (e. there will be higher sales and gross profit but greater bad debts and a higher opportunity cost of carrying the investment in accounts receivable because marginal customers take longer to pay. In evaluating a potential customer’s ability to pay. The management of these accounts receivable also involves having appropriate credit and collection policies. 9. Bad debt losses can be estimated reliably when you sell to many customers and when credit policies have not changed for a long time. if credit terms are lax.1 CREDIT REFERENCES Retail credit bureaus and professional credit reference services should be used to appraise a customer’s ability to pay. your decisions regarding accounts receivable must include whether to give credit. current bank loans). This information is provided in several 97 . product line. On the other hand. management. lawsuits. For example. amounts. including administrative costs of the credit department. if credit terms are tight. financial soundness. previous payment history as reported by suppliers. you must determine eligibility.g. location of business. a longer credit term will probably result in increased sales. As a manager. fees to rating agencies. in turn. if so.9 How to Manage Your Accounts Receivable Most business transactions are carried out on a credit basis. there will be less investment in accounts receivable and less bad debt losses. and terms. The type of credit terms extended to customers determines the length of time a customer has to pay for the purchase. financial statement information. and. One such service is Dun and Bradstreet (D&B) reports. and seasonality aspects. and periodic field investigations. amounts currently owed and past due. The credit terms have a direct bearing on the associated costs and revenue to be generated from accounts receivable. but there will also be lower sales and reduced profits. computer services. which contain information about a company’s nature of business. leases. criminal proceedings. insurance coverage. affects sales volume. while a shorter credit term will likely result in less sales. and collateral to be pledged. number of employees. For example. consider the customer’s integrity.
It is based upon past experience (e. 3. consumers are more protected by fair trade laws. examining the characteristics of good accounts. the competitive factors of the customer’s business. marginal accounts. you may offer liberal payments during slow periods to stimulate business by selling to customers who are unable to pay until later in the season.1 shows an illustrative classification of customers by credit risk for a hypothetical company. As customer financial health changes. you may relax the credit policy because you need the business. credit limits should be revised. and D&B Business Information Reports. 5. delinquent accounts.. 2. in times of short supply.g. If seasonal datings are used.” 1.98 Accounting and Finance for the Nonfinancial Executive D&B publications such as the D&B Reference Book. customers in a financially troubled industry or region). the D&B Consolidated Reports. If the credit standing of a customer is dubious. This policy is financially appropriate when the return on the additional sales plus the lowering in inventory costs is greater than the incremental cost of the additional investment in accounts receivable. The customer’s previous repayment record. 7. Marketing factors must be noted since an excessively restricted credit policy will lead to lost sales. 3. and the economy must also be considered. Note that consumer receivables have a greater risk of default than corporate receivables. It is quick — otherwise. and outright rejected applications). clear. Avoid high-risk receivables (e. You want to know whether there is sufficient cash flow to repay the debt. Table 9. 4. and uniformly applied. A detailed review of a potential customer’s soundness should be made prior to extending credit. 6. 1. However. the customer may do business elsewhere. 5. . In recession.. credit policy may be tightened because the seller is in the “driver’s seat. It does not intrude into a customer’s personal affairs. you should practice the following procedures.2 CREDIT POLICY A good credit system has the following characteristics: It is straightforward. First..g. 9. consistent. It is inexpensive (e. 4. Further. Individuals have less money than companies. 2. there is centralization of credit decisions by experienced staff). Competition and economic conditions must be considered.g. establish a credit policy. collateral equal to or greater than the balance of the account should be pledged. In managing accounts receivable. and financial service reports should be reviewed. Careful attention is given to the reasons for previous uncollectibility. The customer’s financial statements and credit rating should be examined.
3 ANALYZING ACCOUNTS RECEIVABLE The average sales volume affects the size of the investment in accounts receivable. 1. the higher the likelihood of uncollectibility. A larger quantity results in a larger investment. Finally.How to Manage Your Accounts Receivable 99 TABLE 9. 9. Use collection agencies when warranted. establish a billing policy. Large sales should be billed immediately. establish a collection policy. 4. Sell (factor) accounts receivable when net savings occur (see Chapter 16 for a more detailed discussion of factoring). Collection efforts should be undertaken at the very first sign of customer financial unsoundness. holding sales volume constant. However. The billing process will be more uniform if cycle billing is employed. The calculation that defines this relationship follows: Annual credit sales × Days to collect/360 = Investment in accounts receivable . Aging is determining the length of time an account is past due. 3. The aging should be compared to industry norms.1 shows the factoring procedure. Billing for services should be done on an interim basis or immediately prior to the actual services.1 Types of Customers and Expected Bad Debts Risk Category A B C D Description Large. 3. Customers should be invoiced for goods when the order is processed rather than when it is shipped. Figure 9. 1. 2. financially strong companies having minimal credit risk Financially strong companies lacking a proven track record Companies with financial status of some risk and on which credit limit should be placed Marginal accounts needing reacted credit and careful monitoring Bad Debt Percent None 2% 3% 5% Second. 2. Credit insurance will protect against unusual bad debt losses. Customer statements should be sent within 1 day subsequent to the close of the period. Accounts receivable should be aged to identify delinquent and high-risk customers. 4. the size of that investment becomes directly attributable to how long average receivables are outstanding. The longer receivables are outstanding.
accounts are 30 days past due.4 — Your credit sales are $120.000 Example 9. and the cost is 80% of sales price.= $100.000 360 Example 9.000.000 per month.000 × (0.000.000 × (0.40 + 0.1 Factoring procedure. accounts are paid 90 days after the sale date. the collection period is 60 days.12) = $62.000 The investment in accounts receivable is $120.000 × (0. On the average.000. Annual credit sales are $400. Sales average $40.3 — You have accounts receivable of $700.1 — You sell on terms of net/60. The investment in accounts receivable is 90 $400.000 × -------. 51) = $357. 40 + 0.100 Accounting and Finance for the Nonfinancial Executive Factor nd pro s rem ed it a val o itted pp rov f cred al req it ue ste d (5 ) Me rch for aid ep dis an (2) Cr (3 ) (6) Ap Fu (1) Order placed (4) Merchandise shipped Customer Company FIGURE 9. The sales commission is 8% of the sales. The average manufacturing cost is 40% of the sales price.000 sales = $120. On the average. The carrying cost of inventory is 3% of the selling price.400 Example 9. Example 9. The accounts receivable turnover is 360 -------.= 6 60 . The before-tax profit margin is 10%. Your accounts receivable for this product are calculated as follows: 3 months × $40. and the carrying cost is 12% of the selling price.03 + 0. The investment in accounts receivable is $700.08) = $700.2 — The cost of a product is 40% of the selling price.
000/6) Average accounts receivable balance-after policy change ($12. and your collection period is 2 months.25 × $12. Therefore.000 90.= --------------------. net/30 discount. a variable cost of $50.000 units annually. and each unit has a selling price of $80. You anticipate 25% of your customers will take advantage of the discount. An analysis of this discount policy indicates that it would not be financially prudent. Sales will increase by 20%.000 × . Example 9. and a fixed cost of $10.6 — Currently. The collection period is 2 months.5 — Your current annual credit sales are $12.000 --------------------------. Here. the profitability on additional sales must be compared with the amount of additional bad debts expected. Bad debt losses are expected to be 3% of the increased sales. and the rate of return is 16%. Current average accounts receivable balance ($12. You could expect a 15% rate of return. As a result of the discount policy. Or you may consider other alternatives at slow business periods.000. 3. The following information applies to the proposal: 1. You propose to offer a 3/10.000 It is good business practice to give a discount for early payment by customers when the return on the funds received is greater than the cost of the discount.000 Instead.000/8) Reduction in average accounts receivable Rate of return Dollar return earned Cost of discount (0.000 × . The incremental investment in receivables is determined by multiplying the average accounts receivable by the ratio of per unit cost to selling price.000 × 0. and the opportunity cost of tying up funds in receivables for a longer period of time. You are experiencing a period of idle capacity and are considering a change in policy that will relax credit standards.03) Disadvantage of discount policy $2.500. the collection period will be reduced to 11 months (turnover of 8 times). the additional profitability is represented by the incremental contribution margin (sales less variable costs) since fixed costs remain the same (see Chapter 3). you sell 300.000 Turnover 6 101 The average investment in accounts receivable is $20.000. Example 9.000.000 1. you may consider offering credit to customers with a higher-than-normal risk rating.000 $15. 2.000.How to Manage Your Accounts Receivable The average accounts receivable balance is Credit sales $120. When idle capacity exists. .15 75. 4.000 500.000. Collection costs are expected to increase by $20. You sell on terms of net/30. the turnover of accounts receivable is 6 times (12/2).80 = $16. higher investing and collection costs.000.000.= $20. The collection period will increase to 3 months.
= $3.000 300.000 3.000 The new average unit cost is determined by using the following information: Units Current Increment Total a Unit Cost $60 50 a Total Cost $18.000) Rate of return Additional cost $2.249.= $58. $21.03 $ 144. you must subtract the current investment in average accounts receivable: $24.000.000 × $80) Bad debt percentage Additional bad debts $4.× -------.000 The additional cost of higher investment in average accounts receivable is determined by calculating the investment in average accounts receivable after the change in policy: Credit sales Unit cost --------------------------.000 6 $80 This results in the following information: Incremental investment in average accounts receivable ($5.000 $60 ----------------------------.00 From this amount.000.000.000 $21.000 60.000 New average unit cost = ----------------------------.700 × .700 – $3.000 Since idle capacity exists.33 360.20) Per-unit contribution margin ($80 – $50) Incremental profit 60.952 .249.000 × $30 $1.000.000 × .000.× --------------.000 Additional bad debts are calculated as follows: Incremental dollar sales (60.× ----------------------------Turnover Selling price $28.102 Accounting and Finance for the Nonfinancial Executive An analysis of the proposed credit policy shows incremental profitability to be calculated as follows: Increased unit sales (300.16 $ 359.33 ----------------------------.700 4 $80.000.000.800.249.800.= $5.000 360.000 $58. the per-unit cost on the incremental sales is solely the variable cost of $50.000.000 × .
000 × 0. you should relax the credit policy.000 $240.952 103 523.952 $1. Other relevant data are included here.4 CONCLUSION You should carefully evaluate the credit and collection policies of your department to be certain that your accounts receivable are being aggressively managed.7 — You are considering liberalizing the credit policy to encourage more customers to purchase on credit.000 53.952 523.276. and there is a gross margin of 30%.333 $66. the analysis yields the following results: Expected increase in credit sales ($360.000 $360.000/3) Current average accounts receivable ($240.400 $120.30 $ 36. 9.04 × $240. it might be necessary to tighten policies at other times .000 $144.667 You would benefit from a more liberal credit policy.000 359. Example 9.000 – $240. For example.000 9. 80% of your sales are made on credit. Currently.How to Manage Your Accounts Receivable The net advantage/disadvantage is Incremental profitability Less: Additional bad debts Additional collection costs Opportunity cost Net advantage/disadvantage $1.000 4% of credit sales 4.048 Since the net advantage is considerable. during times of idle capacity. 000) Current collection expenses (0. it may be advantageous to alter credit policies to attract business.000 $120.600 $ 8. Current Sales Credit sales Collection expenses Accounts receivable turnover $300.000 20.05 × $360.5 Proposed $450.000) Gross profit rate Increase Collection expenses are calculated as follows: Expected collection expenses (0.000/4. Similarly.800.000 5% of credit sales 3 An analysis of the proposal yields the following results for average accounts receivable balance (credit sales/accounts receivable turnover): Expected average accounts receivable ($360.5) Increase For gross profit. 000) Increase $18.
.104 Accounting and Finance for the Nonfinancial Executive in order to make better use of investment opportunities. Decisions regarding when to extend credit to whom and for how much must be made in light of these changing circumstances.
remember that you want to avoid placing too many funds in inventory because it will result in declining profitability and retarded cash inflow. condition of equipment. 3. 8. 105 . Examine the quality of merchandise received. Table 10. Guard against inventory buildup.10 How to Manage Inventory When managing inventory. For the former. Plan for a stock balance that will guard against and cushion the possible loss of business from a shortage in materials. inventory balances are updated daily. The reason is that back orders may be used as indicators of the production required. Discard slow-moving products to reduce inventory carrying costs and to improve cash flow. Minimize inventory levels when liquidity and/or inventory financing problems exist. The timing of an order also depends on seasonal factors. 2. In areas where control is weak. 9.1 INVENTORY MANAGEMENT CONSIDERATIONS In managing inventory. resulting in improved production planning and procurement. and (3) finished goods (completed goods awaiting sale). The two types of inventory systems are perpetual and periodic. Appraise the adequacy of the raw materials level. since it is associated with substantial carrying and opportunity costs. But some inventory must be maintained to meet customer orders and ensure smooth production activity. inventory balances should be restricted. 6. Keep a careful record of back orders. 5. and any seasonal considerations.2 presents the periodic inventory method. The trend in the ratio of the dollar amount of back orders to the average per-day sales will prove useful. A sales forecast is the starting point for effective inventory management since expected sales determines how much inventory is needed. additional materials are purchased at the lower price.1 illustrates the perpetual inventory method. if prices are expected to increase. 4. 10. (2) working-process (partially completed goods). A high back-order level indicates that fewer inventory balances are needed. which depends on expected production. The three types of inventories are: (1) raw materials (materials acquired from a supplier that will be used in the manufacture of goods). whereas Table 10. you should perform the following tasks: 1. there is a physical count of inventory each period. Forecast future movements in raw materials prices so that. 7. Monitoring the ratio of purchase returns to purchases should be enlightening: A sharp increase in the ratio indicates that a new supplier may be warranted. Any problems must be identified and rectified. For the latter. Appraise the acquisition and inventory control functions.
12.000 6. 13.e.000 4.000 8.. 15. Closely supervise warehouse and materials handling staff to guard against theft and to maximize efficiency. due to an increase in oil prices or to managerial inefficiencies). The register continually updates inventory for sales and purchases. Scrutinize the trend in the unit cost of manufactured items. 11. a point-of-sale computerized electronic register may be used by a retail business.000 2.000 4. Units) August 1 Balance Add: August purchases Total stock available Less: August 31 physical count Sold or used during August 10. Minimize the lead time in the acquisition. .000 30. Reasons for variations should be analyzed to see if they are caused by factors within or beyond your control (i. units) Date 8/1 8/5 8/10 8/13 8/17 8/29 8/30 Receipts Issuances Balance 10.000 20. For example.000 8. 16.000) 22. an increase in inventory stocking may be required or the purchasing pattern may have to be altered.2 Periodic Inventory (Product X.1 Perpetual Inventory (Product X.106 Accounting and Finance for the Nonfinancial Executive TABLE 10.000 2.000 12. Examine the time between raw materials input and the completion of production to see if production and engineering techniques can be implemented to hasten the production operation. manufacturing. Have economies in production run size to reduce setup costs and idle time. 14.000 6.000 10. Examine the degree of spoilage and take steps to reduce it. such as through the application of computer techniques.000 10. and distribution functions.000 10. The lead time is how long it takes to receive merchandise from suppliers after an order is placed.000 TABLE 10. These data facilitate the computation of reorder points and quantity per order.000 (8. Maintain proper inventory control.000 12. Depending upon lead times.
Inventory levels are also affected by short-term interest rates.360 . Cyclic counting has the following advantages: 1. fashionable. Additionally. Enables the timely detection and correction of the causes of inventory error. as Example 10. The quantity discount is 4%.2 shows. However. Example 10. The discount reduces the acquisition cost of materials. as does a year-end count. and specialized goods usually have a high salability risk. full-time experienced counters throughout the year.How to Manage Inventory 107 10.000 (640) $15. spoilage. 2. Does not require a plant shutdown.000) Net cost $16. The net cost of the item is calculated as follows: Acquisition cost (2. and interest on borrowed funds to finance inventory acquisition. an increase in inventory lowers the possibility of lost sales from stockouts and the incidence of production slowdowns from inadequate inventory. higher property taxes for larger facilities. cyclic intervals because this method allows you to check inventory on an ongoing basis as well as to reconcile the book and physical amounts. A quantity discount may be received when purchasing large orders. The nature of the risk should be taken into account in computing the desired inventory level for the item.000 units of an item with a list price of $8 each. Inventory management involves a trade-off between the costs of keeping inventory vs. You may have to decide whether it is more profitable to sell inventory as is or to sell it after further processing. flammable. the benefits of holding it. Permits the efficient use of a few.000 as is or sell it for $80.000 if you put $20. Facilitates the modification of computer inventory programs. Higher inventory levels result in increased costs from storage. Different inventory items vary in profitability and the amount of space they take up. large volume purchases will result in greater purchase discounts. For example. as short-term interest rates increase. For instance. 3.1 — You can sell inventory for $40. perishable.04 × $16. Example 10. Inventory should be counted at regular. the optimum level of holding inventory will be reduced.000 profit relative to $40.000 for the current sale. 4. The latter should be selected because further processing yields a $60.2 — You purchase 2.000 × $8) Less: Discount (.1 provides a hypothetical situation that involves making this decision. technological. Example 10.000 into further processing.2 INVENTORY ANALYSIS You must consider the obsolescence and spoilage risk of inventory. if needed. increased manpower requirements. casualty and theft insurance.
4 uses this equation in a hypothetical situation. handling.3 — You place an order for 7.000 units at the beginning of the year. The average investment is Average inventorya Unit cost Average investment 3. and property taxes. . as Example 10.= 3. insurance. you also have to consider your sales volume and cost estimates.3 DETERMINING THE CARRYING AND ORDERING COSTS Inventory carrying costs include warehousing.3 illustrates.× C 2 where Q/2 represents average quantity and C is the carrying cost per unit. ordering cost includes scheduling cost. An additional item should be held as long as the increase in sales revenue from storing the item equals the cost of holding it. the lower the average investment will be.000 a Quantity (Q) 7.000 -----------------------------.500 2 2 The more frequently you place an order. Carrying cost is calculated as follows: Q Carrying cost = --. They include freight and the clerical costs. Inventory ordering costs are the costs of placing an order and receiving the merchandise. In inventory planning.500 × $12 $42. In the case of produced items.= -----------. Example 10. the greater its carrying cost.× P Q where S = total usage Q = quantity per order P = cost of placing an order Example 10. Ordering cost is formulated as follows: S Ordering cost = --. Further. Each unit costs $12. the opportunity cost of holding inventory balances should be taken into account. A provisional cost for spoilage and obsolescence should also be included in an analysis of inventory. The more the inventory held. enter the fewest number of orders possible. If you want to minimize ordering costs.108 Accounting and Finance for the Nonfinancial Executive The average investment in inventory should be considered. 10.
1 EOQ point. .4 THE ECONOMIC ORDER QUANTITY (EOQ) The economic order quantity (EOQ) is the optimum amount of goods to order each time so that total inventory costs are minimized. The total ordering cost for the year is: 8. EOQ is calculated as follows: EOQ = 2SP --------C The number of orders for a period is the usage. The cost per order is $13.6 calculate the frequency of ordering for hypothetical situations. Figure 10. A greater order quantity will increase carrying costs but lower ordering costs. S.× $13 = $552.1 graphs the EOQ point.50 200 Order size (units) The total inventory cost is therefore QC SP -------. You should apply EOQ analysis to every product that represents a significant proportion of sales.500 -----------.5 and 10. Example 10. divided by the EOQ.4 — You use 8. 10. while Examples 10.500 units per year.How to Manage Inventory 109 Cost (dollars) Total cost Carrying cost Ordering cost EOQ FIGURE 10.+ -----2 C A trade-off exists between ordering and carrying costs. Each order is for 200 units.
= 5 2. . based on expected usage and delivery time of materials. Its desired average inventory level is 40. The need for a safety stock increases the total inventory required.5 AVOIDING STOCKOUTS Stockout of raw materials or work-in-process can cause a slowdown in production. To avoid a stockout situation. The following information is provided: S = 500 units per month P = $40 per order C = $4 per unit EOQ = 2SP --------. 10. Example 10.000 = 100 units The number of orders each month is S/EOQ = 500/100 = 5 Therefore. The ordering cost is $10.6 — A store is determining its frequency of orders for blenders.= -------. For example.= 5 12. S = 50 × 12 = 600 P = $10 C = Purchase price × Carrying cost = $15 × $200 = $5 -------------------------------------------------------------------------------------------------Average investment EOQ = 2SP --------. an order should be placed about every 6 days (31/5).000 --------------. During periods of inflation and tight credit. you should be flexible with your inventory management policies.110 Accounting and Finance for the Nonfinancial Executive Example 10.= C 40 × $15 2 ( 600 ) ( 10 ) --------------------------.400 = 49 (rounded) The number of orders per year is: S 600 ----------. The annual carrying cost is $200.= C 2 ( 500 ) ( 40 ) --------------------------. Safety stock is the minimum inventory for an item. a safety stock should be kept.= 4 10. Safety stock helps to prevent the potential damage to customer relations and to future sales that can occur when you lack the inventory to fill an order immediately. The store anticipates selling 50 blenders each month. the EOQ computation will have to be adjusted for increasing costs.= 12 orders (rounded) EOQ 49 The store should place an order about every 30 days (365/12). Each blender costs $15. This cushions against unusual product demand or unexpected delivery problems.5 — You want to know how frequently to place orders.
calculating the reorder point requires you to know the lead time from placing to receiving an order.000 × $2. However. The increased carrying cost equals the carrying cost per unit multiplied by the safety stock: usage Stockout cost = Number of orders × --------------------------------- × Stockout units order quantity × Unit stockout cost × Probability of a stockout Example 10. The optimum safety stock is the point where the increased carrying cost equals the opportunity cost of a potential stockout. Example 10.7 illustrates the safety stock principle.30 × .900 10. In other words. The safety stock is 30 units. . then add this amount to the EOP.900 = $5X 1. you expect to be stocked with 30 units when the new order is received.000 units.6 DETERMINING THE REORDER POINT OR ECONOMIC ORDER POINT (EOP) The reorder point tells you when to place an order. Each order calls for 10. If you need a safety stock.8 — You use 100. ignoring a safety stock factor.000 units annually.30.000 Stockout cost = -----------------. Example 10.8 uses the safety stock equation in a hypothetical situation. The carrying cost per unit is $5. this amount is the difference between the maximum daily usage during the lead time less the reorder point.3 = $6. Stockout cost = Carrying cost of safety stock $6. You expect a stockout probability of 30%.How to Manage Inventory 111 Example 10.× 1. the reorder point is computed as follows: EOP = Lead time × Average usage per unit of time This tells you the inventory level at which a new order should be placed.380 units = X 10. Stockout is 1.000 Let X represent the safety stock.000 units. The stockout cost and the amount of safety stock are determined as follows: 100. The per-unit stockout cost is $2.7 — You place an order when the inventory level reaches 210 units rather than 180 units. Thus.
The reorder point is 6. Group A items are the most expensive.400 units evenly throughout the year. B. The product that results in the highest contribution margin per cubic foot should typically have the most priority in space allocation.2 Changes in level of inventory over time. or C. An inventory control model appears in Figure 10. group B less expensive. The higher the value of the inventory items.2 shows the changes in level of inventory over time. the more control needed. There is a lead time of 1 week.4 for an illustration of the ABC inventory control system.9 — You need 6.112 Accounting and Finance for the Nonfinancial Executive Inventory Level Reorder Point Delivery Interval EOQ Safety Stock Time FIGURE 10. Table 10. We now turn to determining what inventory items should have priority in space. and group C the least costly. Example 10.3.10 — For Product X: Sales price Variable cost per unit Contribution margin per unit Contribution margin per dozen Storage space per dozen (cubic feet) Contribution margin per cubic foot Number of units sold per period Expected contribution margin per cubic foot $ 15 5 $ 10 $120 ÷2 $ 60 ×4 $240 10.3 illustrates an ABC distribution. There are 50 working weeks in the year. See Figure 10. .= 1 week × 128 units/week = 128 units 50 weeks Figure 10.7 THE ABC INVENTORY CONTROL METHOD The ABC method of inventory control requires the classification of inventory into one of three groups — A. Example 10.400 1 week × --------------------.
How to Manage Inventory 113 7000 6000 Peak investment in inventory Units in stock 5000 Average investment in inventory 4000 3000 2000 1000 7 7 7 Days between orders (entered and received) FIGURE 10.3 Inventory control model.4 ABC inventory control system. Dollar value of total inventory (percent) 100 90 80 70 60 50 40 30 20 10 0 (C) Loose Control (B) Average Control (A) Tight Control 10 20 30 40 50 60 70 80 90 100 Number of items (percent) FIGURE 10. .
The amount you need may change daily and require close evaluation. an excessively low inventory may result in less profit because of lost sales.8 CONCLUSION Deciding on the proper amount of investment in inventory is not an easy task. improper inventory management can unnecessarily tie up money in inventory funds that can be used more productively elsewhere. A buildup of inventory may lead to obsolete inventory.114 Accounting and Finance for the Nonfinancial Executive TABLE 10. However. .3 ABC Inventory Distribution Inventory Classification A B C Population (Percent) 20 30 50 Dollar Usage (Percent) 80 15 5 10. On the other hand.
Part III Financial Decision Making for Managers .
Time value of money is a critical consideration in financial and investment decisions.n) where T1(i. Discounting.11 Understanding the Concept of Time Value A dollar now is worth more than a dollar to be received later. 117 . For example. There are plenty of applications of time value of money in finance. and applications of future values and present values. let us define the following: Fn = P = i = n = Then. which is inversely related to compounding. or the calculation of present value. F1 = = F2 = = the amount of money at the end of year 1 principal and interest = P + iP = P(1 + i) the amount of money at the end of year 2 F1(1 + i) = P(1 + i)(1 + i) = P(1 + i)2 future value = the amount of money at the end of year n principal annual interest rate number of years The future value of an investment compounded annually at rate i for n years is Fn = P(1 + i)n = P × T1(i. Compounding interest means that interest earns interest. is used to evaluate the future cash flow associated with capital budgeting projects. For example.1 at the end of the chapter.1 FUTURE VALUES — HOW MONEY GROWS A dollar in hand today is worth more than a dollar to be received tomorrow because of the interest it could earn from putting it in a savings account or placing it in an investment account. This statement sums up an important principle: money has a time value. how do you determine the periodic payout of an auto loan or a mortgage loan? This chapter discusses the concepts.n) is the compounded amount of $1 and can be found in Table 11. The reason is that you could invest the dollar now and have more than a dollar at the specified later date. The truth of this principle is not that inflation might make the dollar received at a later time worth less in buying power. For the discussion of the concepts of compounding and time value. compound interest calculations are needed to determine future sums of money resulting from an investment. 11. calculations.
the above formula becomes Fn = P(1 + i/2)n × 2 = P × T1(i/2. The interest rate is compounded quarterly.728) = $5. If interest is compounded m times a year.08)4 = $1.2)1 = $3 T1(20%. Therefore.1 — You place $1.361) = $1.118 Accounting and Finance for the Nonfinancial Executive Example 11. Fn = P(1 + i)n F1 = $3(1 + 0.000 (1. compound interest quarterly.440) = $4. The accumulated amount at the end of the fifth year is calculated as follows: i n×m Fn = P 1 + --.2)2 = $3 T1(20%. m The formula reflects more frequent compounding (n·m) at a smaller interest rate per period (i/m). You wish to project the dividends for years 1 through 3.1. n·m) m .3 — You deposit $10. in the case of semiannual compounding (m = 2).000 (1 + 0. = P × T1(i/m. the T1 for 4 years at 8% is 1. and even continuously.60 F2 = $3(1 + 0. For example.361. You will keep the money on deposit for 5 years.2 — You invested a large sum of money in the stock of TLC Corporation.3) = $3 (1. Banks.18 11. How much money will you have in the account at the end of 4 years? Fn = P(1 + i)n F4 = $1.000 in an account offering an annual interest rate of 20%.2) = $3 (1. The dividend is expected to increase by 20% per year for the next 3 years.000 T1(8%.32 F3 = $3(1 + 0. for example.2)3 = $3 T1(20%. Example 11.2 INTRAYEAR COMPOUNDING Interest is often compounded more frequently than once a year.361. The company paid a $3 dividend per share. then the general formula for solving the future value becomes i n×m = P × T1(i/m. n·m) Fn = P 1 + --.1) = $3 (1.000 in a savings account earning 8% interest compounded annually. n·2) Example 11.200) = $3.4 years) From Table 11. F4 = $1. daily.
166 Semiannual compounding (m = 2): 0.000 i/m = 20%/4 = 5% n × m = 5 × 4 = 20 Therefore. F5 = $10.000 (2.000.170 Quarterly compounding (m = 4): 0.04)4 = $1.08 F2 = $1.000(1 + 0.166) = $1.08 2 × 4 F2 = $1. The future value of an annuity is a compound annuity.3 FUTURE VALUE OF AN ANNUITY An annuity is defined as a series of payments (or receipts) of a fixed amount for a specified number of periods.20) = $10.4) = $1.000 1 + --------.08)2 = $1.8) = $1.2) = $1. 4 = $1. Each payment is assumed to occur at the end of the period.172) = $1.000 T1(4%. Let Sn = the future value on an n-year annuity A = the amount of an annuity .000(1 + .000(1 + .02)8 = $1. 11. 2 2×2 = $1.000 1 + --------.05)20 = $10.000 T1(2%.000 T1(5%.Understanding the Concept of Time Value where P = $10.000(1 + 0. This is true for any interest for any period of time.530 119 Example 11. which involves depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow. Then for annual compounding (m = 1): F2 = $1.4 — Assume that P = $1.653) = $26. the more frequently interest is compounded. i = 8% and n = 2 years.000(1.000 T1(8%. the greater the amount accumulated.172 As the example shows.000(1.170) = $1.000(1.
340 11.= F n × T 3 ( i.000 at the end of each year for the next 6 years.5 — You wish to determine the sum of money you will have in a savings account at the end of 6 years by depositing $1. Recall that Fn = P (1 + i)n.= A × T 2 ( i. n ) i n t=0 n–1 where T2(i.= F n ----------------. or discounting.336.6 years) is given in Table 11.000 semiannually into a fund for 10 years.20) = $30.000 (7. Fn 1 P = ----------------.120 Accounting and Finance for the Nonfinancial Executive Then we can write Sn = A(1 + i)n–1 + A(1 + i)n–2 + … + A(1 + i)0 = A[(1 + i)n–1 + (1 + i)n–2 + … + (1 + i)0] (1 + i) – 1 t = A × ∑ ( 1 + i ) = A -------------------------.n) where A = $30.2 as 7.6) = $1. Therefore.000 (29.2 at the end of the chapter. is actually the opposite of finding the compounded future value.n) represents the future value of an annuity of $1 for n years compounded at i percent and can be found in Table 11.000 T2(4%.336) = $7. The T2(8%. The annual interest rate is 8 percent. Therefore. Sn = $30. In connection with present value calculations.000 i = 8%/2 = 4% n = 10 × 2 = 20 Therefore.n ) n n (1 + i) (1 + i) . The process of calculating present values.336 Example 11. The amount accumulated at the end of the tenth year is calculated as follows: Sn = A × T2(i.778) = $893. Example 11. the interest rate i is called the discount rate. The annual interest rate is 8%. S6 = $1.4 PRESENT VALUE — HOW MUCH IS MONEY WORTH NOW? Present value is the present worth of future sums of money.6 — You deposit $30.000 T2(8%.
Example 11.8 — You are thinking of starting a new product line that initially costs $32.n) represents the present value of $1 and is given in Table 11. 1 P = $2.000 6 years from today since the amounts are time equivalent.000 × T3(10%. In other words. you must compute the present value of $20.000 $20.909 0.1 ) = $20. Example 11. you could invest $11.365 Since the present value of your projected cash inflows is less than the initial investment. We know that the present value of each individual payment is the payment times the appropriate T3 value.000. T3(10%.5 PRESENT VALUE OF MIXED STREAMS OF CASH FLOWS The present value of a series of mixed payments (or receipts) is the sum of the present value of each individual payment.3 at the end of the chapter. you should not undertake this project. what is the most you should pay for this opportunity? To answer this question. If you can earn 10% on your investments. and n is 6 years. n) 0.000 T3(10%.300 now or $20.000 6 years from now. should you undertake this new product line? The present value of this series of mixed streams of cash inflows is calculated as follows: Year 1 2 3 Cash inflows $10.Understanding the Concept of Time Value 121 where T3(i.000. .000 ----------------------6 ( 1 + 0. 11.000 Year 2 $20. Your annual projected cash inflows are: Year 1 $10.090 16.6) from Table 11. i is 10%. F6 is $20.000 If you must earn a minimum of 10% on your investment.000(0.300 today at 10 percent and have $20.751 Present value $9.7 — You have been given an opportunity to receive $20.300 This means that you can earn 10% on your investment.000 in 6 years.755 $29.565) = $11.3 is 0.000 to be received 6 years from now at a 10% rate of discount. and you would be indifferent to receiving $11.000 Year 3 $5.6) = $20.520 3.000 $5.826 0.565.
6 PRESENT VALUE OF AN ANNUITY Interest received from bonds.9 — Assume that the cash inflows in Example 11. we need to know the present value of each. called perpetuities. it is actually paying you only $340.000 for 3 years.000 × T4 (10%.000 T4(10%.n) where T4(i.560 rather than $800. If the discount rate is 10%. how much is the lottery amount worth to you? Then the present worth is Pn = A × T4(i.+ … + ----------------1 2 n (1 + i) (1 + i) (1 + i) 1 1 1 = A × ∑ ----------------t ∑ A × -.+ A × ----------------. An example of a perpetuity is preferred stock that yields a constant dollar dividend indefinitely.000. and insurance obligations all involve annuities.000. 3 years) = $10.000 after taxes).n) P3 = $10.000 (8. The present value of a perpetuity is found as follows: .n) P20 = $40.487) = $24. Then the present value is Pn = A × T4(i.514) = $340. 11.560 This means that if the state can make a 10% return on its lottery sales receipts.+ ----------------. 20 years) = $40.+ … + A × ----------------1 2 n (1 + i) (1 + i) (1 + i) 1 1 1 = A × ----------------.000 each year for the next 20 years.n) represents the present value of an annuity of $1 discounted at i percent for n years and is found in Table 11.8 form an annuity of $10. the state pays you $40.870 n Example 11. The present value of an annuity (Pn) can be found by using the following equation: 1 1 1 P n = A × ----------------.000 (2. pension funds.4 at the end of the chapter.10 — Suppose that you have just won the state lottery in the amount of $1 million (or $800.122 Accounting and Finance for the Nonfinancial Executive 11.7 PERPETUITIES Some annuities go on forever. To compare these financial instruments.1 – --------------i (1 + i) t=1 ( 1 + i ) = A × T4(i. Instead of paying you the lump sum of $800. Example 11.
Understanding the Concept of Time Value 123 receipt A Present value of a perpetuity = -----------------------------.n) Solving for A.000 A = --------------. you will have accumulated $5. Sn = A × T2(i. The interest rate is 10%. if you deposit $819 at the end of each year for 5 years at 10% interest.2) $5.= $819 6.= $800 i 0.9 DEPOSITS TO ACCUMULATE A FUTURE SUM (OR SINKING FUND) An individual might wish to find the annual deposit (or payment) that is necessary to accumulate a future sum. The annual year-end contribution needed to accumulate $1.11 — Assume that a perpetual bond has an $80-per-year interest payment and that the discount rate is 10%.000. Example 11. we obtain: Sn Annual deposit amount = A = ---------------T 2 ( i.000 at the end of the fifth year. The interest rate is 10%.8 APPLICATIONS OF FUTURE VALUES AND PRESENT VALUES Future and present values have numerous applications in financial and investment decisions.10 11. To find this future amount (or sinking fund) we can use the formula for finding the future value of an annuity.000 is: .= --------.000 T2(10%.13 — You need a sinking fund for the retirement of a bond 30 years from now.000 at the end of 5 years in a fund. The annual deposit is: S5 = $5. 11.105 (from Table 11.12 — You wish to determine the equal annual end-of-year deposits required to accumulate $5. Six of these applications are presented below.105 In other words. The present value of this perpetuity is: A $80 P = --.= --discount rate i Example 11. 5 years) = 6.n ) Example 11.
= 6. we obtain: Pn Amount of loan = A = ---------------T 4 ( i. 40 months) = 32.08 T 4 ( 14%.000 Amount of loan = A = ----------------------------------------.124 Accounting and Finance for the Nonfinancial Executive S30 = $1. 12%. you have to pay $152.n ) Example 11.14 — You borrow $200.835 (from Table 11.000 T4(14%. The amount of each payment is .15 — You take out a 40-month bank loan of $5.10 AMORTIZED LOANS If a loan is to be repaid in equal periodic amounts. mortgage loans.4) $5.28 a month for the next 40 months.000 at a 12% annual interest rate.433 Example 11. Example 11.000 T4(1%.433 (from Table 11. A = --------------.835 So.= --------------------.000 A = -------------------------. The bank charges 12% interest. 5 years ) 3.28 32. i = 12%/12 months = 1% P40 = $5. 5 years) = 3. and most commercial loans.000. The annual year-end payment on the loan is calculated as follows: P5 = $200.000.000 T2(10%.000 for 5 years at an interest rate of 14%.000. 40-month loan. 30 years) = 164.258.49 $1. You want to find out the monthly loan payment.49 11. to repay the principal and interest on a $5.4) P5 $200. The periodic payment can easily be computed as follows: Pn = A × T4(i.000 to be repaid in three equal installments at the end of each of the next 3 years.n) Solving for A.000 Therefore.079.= $152. it is said to be an amortized loan.16 — Assume that a firm borrows $2.40 164.= $58. Examples include auto loans.
0 m where i = the stated.407. or effective annual rate.0 = (1.015)4 – 1. nominal.64 2. most bonds pay interest semiannually.17 — Using the same data as in Example 15. – 1.0 = 1 + --------. 11. The breakdown is often displayed in a loan amortization schedule.0614 – 1.Understanding the Concept of Time Value P3 = $2. he or she needs to put them on a common basis.402 $2. banks generally pay interest quarterly. If a financial manager wishes to compare investments with different compounding periods. – 1. b The reduction in principal equals the payment less the interest portion ($832.18 — If the nominal rate is 6%.64b $663.00 a $168.23 $592. A = --------------.11 ANNUAL PERCENTAGE RATE (APR) Different types of investments use different compounding periods. Therefore. whereas the principal portion is smallest in the first period (because of the high interest) and increases thereafter. 3 years) = 2.000 T4(12%.000.0 = 0.64 – $240.00 $1.00 = $592.64 $832.407. we set up the following amortization schedule: Repayment of Principal Remaining Balance $2.14% m 4 .12) = $240.= $832.88. compounded quarterly.64 $832. Example 11. – 1. All figures are rounded.76 $743.60 Year 0 1 2 3 a Payment Interest $832.36 $ 743. the APR is i m 0. Example 11.64 $240. as shown in the following example.12) = $89.000 Therefore. is used for this purpose and is computed as follows: i m APR = 1 + --.0 = 1.88 $89. For example.23.64). in year 2 interest is $1.000(0. The interest component of the payment is largest in the first period (because the principal balance is the highest) and subsequently declines. interest in year 1 is $2. The annual percentage rate (APR).402 125 Each loan payment consists partly of interest and partly of principal.60(0.41c Interest is computed by multiplying the loan balance at the beginning of the year by the interest rate.06 4 APR = 1 + --.12) = $168.36(0. c Not exact because of accumulated rounding errors. and in year 3 interest is $743.0614 = 6. or quoted rate and m = the number of compounding periods per year.
n) = ---P Example 11.50 Therefore. we obtain .70 and P = $2. The compound annual growth rate in earnings per share is computed as follows: Fn = P × T1(i.70 T1(i.70.19 — Assume that your company has earnings per share of $2.48 $2. $3.126 Accounting and Finance for the Nonfinancial Executive This means that if one bank offered 6% with quarterly compounding. it is necessary to calculate the compound annual rate of growth. associated with a stream of earnings.10) = -----------. Annual percentage rate (APR) also is a measure of the cost of credit.48 at 10 years is at i = 4%. while another offered 6. we obtain Fn T1(i.1 a T1 of 1. 11. The compound annual rate of growth is therefore 4%.n) or Sn = P × T2(i. including mortgage plans.n) Solving this for T1 (or T2). they would both be paying the same effective rate of interest. 11. It includes interest as well as other financial charges such as loan origination and certain closing fees. The compound annual rate of growth in earnings per share is computed as follows: F10 = $3. expressed as a yearly rate. and 10 years later the earnings per share has increased to $3.14% with annual compounding.50 From Table 11.13 COMPOUND ANNUAL RATE OF INTEREST The compound annual interest rate is computed as follows: Fn = P × T1(i.50 in 2001.= 1.n) Solving this for T1. The lender is required to tell you the APR.12 RATES OF GROWTH In finance. It provides you with a good basis for comparing the cost of loans.
11.20 — You agree to pay back $3.000 T1(i.000 per year. Thus.2).000 loan made today.21 — You want to have $500. You deposit $30.n) = ---P $500. from Table 11.000 so that i = 7% (from Table 11.n) = ---P Example 11. Thus. usually $1. or maturity value.n) = ---P Sn or T2(i.n) + M × T3(i.5 $2. Its value is found as the present value of the payment stream.000 in 6 years on a $2.000 T2(i.14 BOND VALUES Bonds call for the payment of a specific amount of interest for a stated number of years and the repayment of the face value at the maturity date. You are being charged an interest rate of 7%.= 16.n) where I = M= i = n = interest payment per period par value.000 so that i = 15% (approximately. a bond represents an annuity plus a lump sum. V = ∑ ----------------t + ----------------n (1 + i) (1 + i) I M t=1 n = I × T4(i.n) = ---P $3.000 investor’s required rate of return number of periods . 9 years) = --------------------. Example 11. Fn T1(i. The interest is usually paid semiannually.1).667 $30. 6 years) = --------------. Thus.= 1.Understanding the Concept of Time Value 127 Fn T1(i.000 accumulated in a pension plan after 9 years. Sn T2(i.
11. 11. such as finding the amount of deposits to accumulate a future sum and the periodic payment of an amortized loan.00 = $885. 20) + $1. Sharp EL733. They include Radio Shack EC5500.312) = $573. the present value (V) of this bond is: V = $50 · T4(6%. term) in Lotus 1-2-3 or Excel calculates the amount of the periodic payment to payoff a loan. given a specified periodic interest rate and number of payment periods.000(0.16 CONCLUSION The basic idea of the time value of money is that money received in the future is not as valuable as money received today. The time value of money is a critical factor in many financial and investment applications.000 × T3(6%. Since interest is paid semiannually. Furthermore. For example. This chapter developed two basic concepts: future value and present value. the number of periods involved is 20 and the semiannual cash inflow is $100/2 = $50. PMT (principal.000. Hewlett-Packard 10B. The development of the time value of money concept permits comparison of sums of money that are available at different points in time.470) + $1. paying interest semiannually and having a face value of $1. spreadsheet software such as Microsoft Excel has built-in financial functions to perform many such applications.50 + $312.50 Note that the required rate of return (12%) is higher than the coupon rate of interest (10%). .128 Accounting and Finance for the Nonfinancial Executive Example 11.15 USE OF FINANCIAL CALCULATORS AND SPREADSHEET PROGRAMS There are many financial calculators that contain preprogrammed formulas to perform many present value and future applications. Assume that you have a required rate of return of 12% for this type of bond. and Texas Instruments BA35. It showed how these values are calculated and can be applied to various financial and investment situations.22 — Assume there is a 10-year bond with a 10% coupon. interest. 20) = $50(11. so the bond value (or the price investors are willing to pay for this particular bond) is less than its $1. Then.000 face value.
574 1.380 1469.661 10.405 1.773 3.887 5.133 2.012 2.996 4.479 3.611 1.898 2.211 2.772 1.Understanding the Concept of Time Value 129 TABLE 11.690 8.540 2.925 2.866 7.160 6.286 8% 1.801 1.172 3.583 4.474 6.316 4.397 2.800 .195 2.595 5.361 1.1 The Future Value of $1.217 1.137 9.186 26.106 3.732 1.100 1.338 1.139 3.801 6% 1.192 7.896 4.107 2.055 5.261 2.700 3.714 1.798 4.359 2.260 1.252 3.518 2.191 1.974 2.853 3.261 7.056 13.762 1.482 1.937 3.693 2.026 3.791 1.332 2.492 6.949 2.300 5.177 4.140 1.880 20% 1.277 10.594 2. n) Periods 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 40 4% 1.074 2.125 1.210 1.601 1.124 1.080 1.646 29.948 38.853 3.407 18.699 12.120 1.594 1.950 188.720 2.986 3.613 9.560 6.728 2.063 21.300 1.430 8.476 2.00 (Compounded Amount of $1.744 10.707 4.450 45.260 12% 1.999 2.243 4.689 1.587 1.480 1.166 1.138 8.040 1.026 2.665 1.873 1.369 1.623 31.207 5.265 1.502 2.170 1.575 12.364 4.419 1.116 6.426 3.051 14% 1.452 3.469 1.851 1.464 1.159 2.082 1.960 93.488 2.839 15.690 1.130 6.916 10.728 17.743 50.854 3.423 1.263 1.948 2.200 1.316 1.191 3.818 5.00) (1 + i)n = T1(i.254 1.331 1.488 22.060 1.144 2.504 1.226 4.540 1.440 1.338 237.725 10% 1.
773 35.200 3.= T 2 ( i.762 113.580 15.496 442.972 16.000 2.00) Periods 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 30 40 a (1 + i) – 1 --------------------------.778 79.627 18.882 21.324 33.368 7.300 14.000 2.716 9.698 25.247 5.105 7.600 51.080 3.976 31.506 5.150 39.271 32.246 4.130 Accounting and Finance for the Nonfinancial Executive TABLE 11.089 37.921 6.160 57.969 91.930 12.499 20.950 40.633 7.025 356.085 19.580 48.089 12.276 25.214 10.393 37.416 6.000 2.930 128.975 8.655 24.000 2.026 6% 1.181 14.762 Payments (or receipts) at the end of each project.310 4.959 32.024 21.597 12% 1.646 18.057 10% 1.440 4.374 4.900 n 4% 1.292 20.906 33.394 78.842 50.2 The Future Value of an Annuity of $1.330 767.491 13.353 8.637 6.115 10.276 164.152 30.673 28.870 18.581 43.040 3.026 16.000 2.898 11.000 2.898 9.00a (Compounded Amount of an Annuity of $1.884 55.523 27.283 259.122 4.085 95.196 72.006 13.750 37.546 45.753 48.778 56.140 3.776 17.923 10.336 8.120 3.640 5.760 36.900 7343.488 14. .825 23.671 29.060 3.035 87.215 27.000 2.916 16.058 154.442 105.487 11.977 21.536 10.497 59.549 20.100 3.280 42.015 23.779 6.446 45.637 12.233 16.394 9.000 20% 1.583 12.641 6.867 7.740 186.450 41.980 59.120 154.486 15.938 18.495 24.440 75.436 13.385 24.133 28.531 21. n ) i 8% 1.118 68.213 30.045 27.029 32.730 13.090 14% 1.487 16.610 8.645 27.750 63.375 5.337 23.052 241.690 1181.790 1342.799 25.442 9.184 4.
006 .146 .051 .672 .137 .042 .609 .085 .630 .052 .218 .003 .003 .442 .002 .650 .168 .364 .028 .410 .116 .005 .012 .099 .075 .797 .073 .625 .390 .675 .476 .354 .233 .239 .347 .035 .185 .056 .028 .003 .108 .331 .636 .112 .621 .060 .031 .3 1 Present Value of $1.500 .004 .002 .184 .002 .423 .007 .592 .029 .123 .093 .890 .610 .183 .162 .833 .013 .207 .497 .160 .220 .053 .266 .370 .001 .024 .031 .164 .018 .107 .125 .076 .001 .516 .712 .162 .229 .002 .714 .186 .681 .422 .174 .008 .020 .386 .551 .406 .650 .319 .437 .340 .270 .012 .002 .630 .033 .592 .025 .494 .140 .159 .056 .003 .204 .513 .040 .061 . n ) Periods 4% 6% 8% 10% 12% 14% 16% 18% 20% 22% 24% 26% 28% 30% 40% 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 40 .262 .275 .025 .064 .676 .519 .889 .094 .439 .456 .014 .092 .199 .925 .049 .308 .071 .167 .877 .370 .260 .350 .208 .066 .583 .050 .001 .001 .025 .043 .182 .195 .769 .054 .022 .078 .059 .130 .361 .008 .012 .007 .170 .705 .095 .011 .031 .066 .290 .747 .194 .893 .207 .135 .552 .215 .123 .046 .037 .006 .010 .011 .051 .133 .144 .034 .018 .001 .025 .703 .247 .394 .149 .015 .001 .026 .452 .292 .962 .163 .002 .002 .004 .002 .017 .002 .397 .315 .044 .002 .010 .001 .855 .534 .010 .093 .001 .006 .943 .048 .003 .263 .022 .287 .751 .Understanding the Concept of Time Value 131 TABLE 11.826 .004 .080 .014 .005 .145 .196 .009 .116 .001 .057 .012 .510 .558 .564 .026 .735 .004 .007 .001 .455 .743 .038 .335 .112 .402 .135 .350 .641 .001 .222 .294 .227 .794 .015 .003 .047 .665 .322 .601 .069 .042 .097 .577 .001 .270 .123 .862 .208 .020 .084 .049 .806 .006 .019 .033 .093 .001 .108 .016 .003 .009 .463 .250 .400 .524 .527 .227 .909 .039 .062 .060 .308 .038 .781 .404 .125 .475 .116 .043 .456 .303 .191 .033 .233 .019 .225 .006 .137 .022 .429 .592 .694 .250 .451 .205 .022 .00 -------------n (1 + i) = T 3 ( i.500 .016 .068 .198 .341 .063 .008 .350 .005 .857 .032 .627 .001 .333 .146 .198 .180 .361 .482 .125 .840 .014 .002 .076 .790 .371 .006 .004 .001 .084 .018 .015 .074 .002 .051 .507 .417 .135 .397 .375 .021 .794 .007 .116 .001 .040 .469 .158 .023 .112 .083 .278 .094 .005 .269 .062 .092 .718 .009 .579 .003 .005 .820 .178 .007 .351 .232 .567 .037 .424 .015 .540 .555 .315 .249 .099 .073 .157 .291 .847 .312 .179 .314 .513 .045 .368 .257 .102 .926 .099 .016 .104 .083 .769 .013 .009 .467 .760 .033 .021 .005 .683 .011 .108 .038 .305 .019 .095 .043 .477 .065 .069 .013 .321 .004 .026 .237 .279 .032 .007 .079 .026 .263 .731 .822 .005 .003 .792 .020 .009 .373 .010 .139 .
837 4.820 1.886 2.910 3.395 3.224 1.497 0.459 3.120 7.414 2.167 3.366 7.162 5.929 5.438 2.342 5.022 8.483 3.118 7.467 6.083 3.042 2.468 5.402 3.303 4.008 5.122 9.387 3.798 3.421 3.812 4.192 3.494 2.106 2.577 3.465 4.791 6 7 8 9 10 5.991 0.559 6.745 1 1 – --------------.335 5.563 11.139 7.604 9.037 3.372 9.689 0.811 6.775 3.327 4.868 2.216 3.166 12.736 2.571 2.465 2.416 3.265 4.656 3.910 5.442 4.659 13.993 0.853 9.092 3.250 7.269 3.675 5.127 4.002 6.436 0.194 6.849 2.799 3.385 9.968 5.943 1.477 2.353 4.206 5.288 4.539 3.974 7.470 8.184 3.373 6.726 3.080 4.912 3.103 7.952 2.424 6.669 5.981 2.607 4.786 3.793 4.242 6.673 3. n ) n (1 + i) 14% 16% 18% 20% 22% 24% 30% 40% Periods 4% 6% 8% 10% 1 2 3 4 5 0.814 7.366 3.111 4.564 4.242 3.842 6.244 8.859 4.824 8.035 2.355 4.925 3.433 3.575 5.092 4.938 6.456 2.331 2.589 2.544 3.329 3.496 2.760 9.316 5.783 2.367 7.818 7.029 5.495 6.682 4.463 3.460 4.582 6.477 10.142 6.833 2.887 8.605 3.002 6.468 2.818 5.492 2.147 3.212 0.335 3.111 4.824 3.158 11.914 3.315 3.868 5.546 2.776 3.962 4.283 2.606 3.885 3.639 4.263 2.812 4.391 4.097 4.174 2.851 9.710 4.357 4.320 2.923 3.440 1.166 2.566 2.311 3.889 4.532 2.769 1.222 5.847 1.589 1.619 3.828 11.550 6.365 8.132 TABLE 11.223 3.489 2.203 4.937 3.494 3.808 3.786 3.833 1.059 4.322 2.946 5.328 5.606 Accounting and Finance for the Nonfinancial Executive 16 17 18 19 20 11.503 3.806 1.628 6.962 1.031 4.690 3.039 4.326 3.492 2.870 4.494 2.656 3.247 6.033 4.241 3.759 6.533 4.453 5.035 4.690 2.712 7.771 3.781 1.469 0.833 5.623 5.986 10.168 2.643 2.780 3.145 11 12 13 14 15 8.249 3.877 1.862 1.529 3.747 6.452 0.161 3.904 8.635 0.887 3.001 2.392 1.751 3.528 2.749 5.419 4.439 4.201 8.170 3.656 4.076 3.652 12.802 7.536 7.590 10.518 3.954 3.928 3.923 2.362 2.816 2.775 4.078 4.623 3.484 4.= T 4 ( i.273 5.197 5.942 3.106 10.020 3.877 5.794 1.514 .759 2.361 1.435 8.660 5.274 0.730 4.210 6.695 3.605 0.611 4.265 6.360 4.650 5.951 3.685 4.647 2.917 5.127 0.498 3.844 4.605 2.344 4.427 3.909 1.110 3.316 0.926 1.864 0.802 2.725 3.379 2.4 1 Present Value of an Annuity of $1.487 3.424 1.404 2.246 2.019 3.190 3.241 2.630 4.851 3.800 1.304 3.134 13.733 7.384 8.268 3.893 1.457 1.00a i 12% 25% 26% 28% 0.295 9.312 3.566 3.714 1.
591 13.970 4.499 4.564 3.499 3.500 2.147 3.983 16.332 3.784 7.765 10.055 16% 18% 20% 22% 24% 40% 30% Periods 4% 6% 8% 10% Understanding the Concept of Time Value 21 22 23 24 25 14.011 6.480 5.556 3.840 3.097 6.143 4.303 12.500 3.622 11.244 7.985 9.891 4.488 4.507 4.003 5.923 4.925 9.793 15.822 3.524 4. 133 .499 2.500 2.994 3.645 7.258 9.017 10.529 10.961 6.550 12.988 3.330 16.292 13.161 9.975 4.997 4.177 5.559 3.843 7.TABLE 11.792 6.332 2.467 4.051 11.073 6.320 3.649 8.984 17.331 3.943 7.158 11.857 15.810 10.044 6.783 10.157 4.384 5.105 6.956 4.985 25% 7.4 (continued) 12% 14% 26% 28% 3.909 4.827 3.837 3.499 2.300 3.211 13.663 16.999 3.964 4.842 6.077 26 27 28 29 30 15.743 6.151 4.029 14.981 3.476 4.325 3.323 3.247 15.568 3.329 3.935 6.846 3.544 4.022 8.160 3.970 3.973 6.130 4.551 3.370 9.831 3.502 5.883 8.571 a Payments (or receipts) at the end of each period.154 4.136 6.327 3.995 6.675 8.841 3.042 12.983 7.569 3.873 5.718 7.779 8.528 4.510 5.517 4.816 8.451 5.137 4.500 2.764 12.410 5.534 4.432 5.121 4.839 3.003 13.990 3.976 3.520 4.562 3.451 14.567 3.331 3.569 3.371 10.984 8.118 6.835 6.834 3.152 6.548 4.166 3.772 8.406 13.237 9.687 6.492 5.979 4.937 4.166 6.046 11.514 4.531 4.427 40 19.963 3.566 3.498 2.307 9.500 2.201 10.498 2.234 5.500 2.992 3.948 4.935 11.906 6.896 7.562 7.333 2.159 4.
introduction of a computer. The effect of the Modified Accelerated Cost Recovery System (MACRS) on capital budgeting decisions. market research. etc. (c) Mergers and acquisitions in the form of buying another company to add a new product line. refunding of long-term debt. How income tax factors affect investment decisions.1 WHAT ARE THE TYPES OF INVESTMENT PROJECTS? There are typically two types of long-term investment decisions made by your company: 1. keep-or-sell a business segment decisions. How to select the best mix of projects with a limited capital spending budget. 12. The types of depreciation methods. plant. lease or buy decisions. Replacement decisions in terms of replacing existing facilities with new facilities.12 Capital Investment Decisions Capital budgeting is the process of making long-term investment decisions. These decisions should be made in light of the company’s goals. (b) Resource commitments in the form of new product development. you must perform three tasks in evaluating capital budgeting projects: (1) estimate cash flows. Basic capital budgeting techniques. Examples include replacing an old machine with a high-tech machine. Also see Chapter 17. and equipment as well as other types of assets. Investments in fixed assets should be consistent with the goal of maximizing the firm’s market value. (2) estimate the cost of capital (or required rate of return). To make long-term investment decisions in accordance with your goal. Examples include: (a) Investments in property. 2. Selection decisions in terms of obtaining new facilities or expanding existing facilities. 135 .” This chapter discusses: • • • • • • The types and special features of capital budgeting decisions. There are many investment decisions that the company may have to make in order to grow. • How to compute a firm’s cost of capital. The stockholders have entrusted the company with their money and they expect the firm to invest it wisely. and (3) apply a decision rule to determine if a project is “good” or “bad. Examples of capital budgeting applications are product line selection. and determination of which assets to invest in.
Income taxes could make a difference in the accept or reject decision. There are expected recurring cash inflows (for example.000 $3. Each of these methods is discussed below. Therefore. 3.3 HOW DO YOU MEASURE INVESTMENT WORTH? Several methods of evaluating investment projects are as follows: 1.2 WHAT ARE THE FEATURES OF INVESTMENT PROJECTS? Long-term investments have three important features: 1.136 Accounting and Finance for the Nonfinancial Executive 12.3. Therefore. 12. They typically involve a large amount of initial cash outlays that tend to have a long-term impact on the firm’s future profitability. 4.= 6 years Cost savings $3.000 Then.1 and 12. 2. 3. savings in cash operating expenses. It is computed by dividing the initial investment by the cash inflows through increased revenues or cost savings. Example 12. 12. Payback period Accounting rate of return (ARR) Net present value (NPV) Internal rate of return (IRR) Profitability index (or cost/benefit ratio) The NPV method and the IRR method are called discounted cash flow (DCF) methods.000 Payback period = ----------------------------------------. the payback period is formulated as follows: Initial investment $18.000 . Examples 12.) over the life of the investment project.2 calculate the payback periods for two different situations.= -----------------. income tax factors must be taken into account in every capital budgeting decision. these initial cash outlays need to be justified on a cost-benefit basis. etc. increased revenues.1 — Consider the following data: Cost of investment Annual after-tax cash savings $18. 2. This frequently requires considering the time value of money. 5.1 PAYBACK PERIOD The payback period measures the length of time required to recover the amount of initial investment.
Example 12.000 = $500 + $400 + $100): $100 2 years + ----------. Example 12.= 2 1/3 years $300 Project B is the project of choice in this case.3 — Consider the following investment: Initial investment Estimated life Cash inflows per year Depreciation per year (using straight line method) $6. essentially. The advantages of using the payback period method of evaluating an investment project are that (1) it is simple to compute and easy to understand. The rationale behind this choice is: The shorter the payback period. The payback period of project A is ($1.2 ACCOUNTING RATE OF RETURN (ARR) Accounting rate of return (ARR) measures profitability from the conventional accounting standpoint by relating the required investment — or sometimes the average investment — to the future annual net income.500 20 years $1.000 $325 . Decision rule: Under the ARR method.000= $100 + $200 + $300 + $400) 4 years.Capital Investment Decisions 137 Decision rule: Choose the project with the shorter payback period. the payback period has to be found by trial and error. Cash Inflow Year 1 2 3 4 5 6 A($) 100 200 300 400 500 600 B($) 500 400 300 100 When cash inflows are not even.000. and the greater the liquidity. The shortcomings of this method are that (1) it does not recognize the time value of money.3. The payback period of project B is ($1. and (2) it handles investment risk effectively.2 — Consider the two projects whose after-tax cash inflows are not even. cash flows after the payback period determine profitability of an investment. 12. since it has the shorter payback period. the less risky the project. and (2) it ignores the impact of cash inflows received after the payback period. Assume each project costs $1. choose the project with the higher rate of return.
950 10 years $3.3 NET PRESENT VALUE (NPV) Net present value (NPV) is the excess of the present value (PV) of cash inflows generated by the project over the amount of the initial investment (I): NPV = PV – I The present value of future cash flows is computed using the so-called cost of capital (or minimum required rate of return) as the discount rate.138 Accounting and Finance for the Nonfinancial Executive The accounting rate of return for this project is: Net income $1. The value of T4 is found in Table 11. .4. Otherwise. 12.000 × T4 (12%.4% Investment $6. Example 12. reject it. accept the project.650) Initial investment (I) Net present value (NPV = PV – I) $16.4 — Consider the following investment: Initial investment Estimated life Annual cash inflows Cost of capital (minimum required rate of return) $12.000 Since the NPV of the investment is positive. 10 years) = $3.= --------------------------------.3. The shortcomings of this method are that it fails to recognize the time value of money.950 $ 4.500 If average investment (usually assumed to be one-half of the original investment) is used. then: $1.000 – $325 APR = --------------------------. and it uses accounting data instead of cash flow data. In the case of an annuity.950 12. Decision rule: If NPV is positive.250 The advantages of this method are that it is easily understandable.= 10. and recognizes the profitability factor.000 12% Present value of the cash inflows is: PV = A × T4 (i.000 – $325 APR = --------------------------------.000 (5. n) where A is the amount of the annuity. the investment should be accepted.= 20. is simple to compute. the present value would be PV = A × T4(i. n) = $3.8% $3.
5 — Assume the same data given in Example 12.= 4.950 T4(i. In other words.000 × T4(i.177 4.494 4. Otherwise. 0. I = PV or NPV = 0 Decision rule: Accept the project if the IRR exceeds the cost of capital.3.(20% – 18%) 0.10 years) = -----------------.4. especially .177 IRR = 18% + -----------.Capital Investment Decisions 139 The advantages of the NPV method are that it obviously recognizes the time value of money and it is easy to compute whether the cash flows form an annuity or vary from period to period.4 INTERNAL RATE OF RETURN (IRR) Internal rate of return (IRR) is defined as the rate of interest that equates I with the PV of future cash inflows.495 4. The advantage of using the IRR method is that it does consider the time value of money and.317 $3. therefore.10 years) $12.302 Therefore. reject it.302 = 18% + 0.950 = $3.10 years) 18% IRR 20% Difference 4. The interpolation follows: PV of an Annuity of $1 Factor T4(i.000 which stands somewhere between 18 and 20% in the 10-year line of Table 11.17% = 19. and set the following equality (I = PV): $12. The shortcomings of this method are that (1) it is time-consuming to compute.586(2%) = 18% + 1. accept the project.317 0. Example 12.17% Since the IRR of the investment is greater than the cost of capital (12%). 12. is more exact and realistic than the ARR method.192 0. for an IRR.4.
= -----------------.000 15.000 NPV($) 42. accept the project. which is not discussed here.000 145. then accept the project. The profitability index has the advantage of putting all projects on the same relative basis regardless of size. This index is used as a means of ranking projects in descending order of attractiveness.000 45. When cash inflows are not even.= 1. Example 12.000 –2.000 60. 12.15 1.140 Accounting and Finance for the Nonfinancial Executive when the cash inflows are not even. PV/I. 12.6 — Using the data in Example 12.000 Profitability Index 1. The profitability index is used widely in ranking projects competing for limited funds.31 $12.000 needs to select a mix of acceptable projects from the following: Projects A B C D E F I($) 70.000 PV($) 112.000 80.000 110.7 — A company with a fixed budget of $250.32 0. and (2) it fails to recognize the varying sizes of investment in competing projects.000 126.000 95.4.950 PV ------.5 PROFITABILITY INDEX The profitability index is the ratio of the total PV of future cash inflows to the initial investment. and D.000 100. its profitability index is greater than 1).500 79. Capital rationing is concerned with the problem of selecting the mix of acceptable projects that provides the highest overall NPV.e. B.4 HOW TO SELECT THE BEST MIX OF PROJECTS WITH A LIMITED BUDGET Many firms specify a limit on the overall budget for capital spending.19 Ranking 1 2 5 3 6 4 The ranking resulting from the profitability index shows that the company should select projects A.45 1.000 40.500 19.000 16. that is. the profitability index is $16.3. Decision rule: If the profitability index is greater than 1..000 38.950 I Since this project generates $1.95 1.31 for each dollar invested (i. Financial calculators such as Texas Instruments and Sharp have a key for IRR calculations. IRR is computed by the trial-and-error method. Example 12. although most business calculators have a program to calculate IRR.6 1. .
000 100. the project that is attractive on a before-tax basis may have to be rejected on an after-tax basis. NPV = $336.000 60. Income taxes typically affect both the amount and the timing of cash flows.000 12. By definition.000 $336.000 = $106. Tax shield = Tax savings on depreciation = (d)(t) = Sales = Cash operating expenses = Depreciation = Tax rate . In other words. is subject to tax.000 – $230. Before-tax cash inflows (or before-tax cash savings) = S – E and net income = S – E – d.000 Therefore. the deductibility of depreciation from sales in arriving at net income subject to taxes reduces income tax payments and thus serves as a tax shield.000 79. Let us define: S E d t Then.5 HOW DO INCOME TAXES AFFECT INVESTMENT DECISIONS? Income taxes make a difference in many capital budgeting decisions.000 $230.000 145. After-tax cash inflows = Before-tax cash inflows – Taxes = (S – E) – (S – E – d) (t) Rearranging gives the short-cut formula: After-tax cash inflows = (S – E) (1 – t) + (d)(t) As can be seen. Since net income. not cash inflows.000 PV $112. after-tax cash inflows are not usually the same as after-tax net income.Capital Investment Decisions 141 I A B D $70.
10 years) = $2. Thus.597.000 d = $500 per year using the straight line method t = 30% Then After-tax cash inflow = ($12. Therefore.25.597. NPV = PV – I = $12.500(1 – 0.142 Example 12.597. the higher the tax savings on depreciation will be.400 + $150 = $1. an accelerated depreciation method (such as double-declining balance) produces higher tax savings than the straight-line method. the net present value can be calculated.3) = $1.3) = ($2.050 To see if this machine should be purchased.000. and the after-tax cost of capital (minimum required rate of return) is 10%.000(0.000)(1 – 0.000/10 = $1.500 a year in cash operating costs for the next 10 years if it buys a special-purpose machine at a cost of $10.000 E = $10.3) = $150 Since the tax shield is dt. Accelerated methods produce higher present values for the tax savings that may make a given investment more attractive. .750 + $300 = $2. After-tax cash savings = (S – E) (1 – t) + (d)(t) = $2.000 – $10.25 – $10.050 T4(10%.3) + ($500)(0. PV = $2.25 Since NPV is positive.8 — Assume: Accounting and Finance for the Nonfinancial Executive S = $12. No salvage value is expected.000 per year. Assume that the income tax rate is 30%. the higher the depreciation deduction. Example 12.000)(0.7) + ($500)(0.3) + $1. After-tax cash savings can be calculated as follows: Note that depreciation by straight-line is $10. the machine should be bought. Thus.145) = $12.500.3) = $1.550 Note that a tax shield = tax savings on depreciation = (d)(t) = ($500)(0. Here beforetax cash savings = (S – E) = $2.050 (6.9 — The Shalimar Company estimates that it can save $2.000 = $2.
6. Among the commonly used depreciation methods are straight-line and accelerated methods.000 × 12. .6 TYPES OF DEPRECIATION METHODS We saw that depreciation provided the tax shield in the form of (d)(t).000 – $2. The following formula may be used to quickly find the sum-of-the-years’-digits (S): (N)(N + 1) S = --------------------------2 where N represents the number of years of expected life. The sum of these digits is 36. 7. the number of years of life expectancy is enumerated in reverse order in the numerator. The result is the same: $18.250. 2.10 — An auto is purchased for $20. write the numbers in reverse order: 8. The two major accelerated methods are sum-of-the-years’-digits (SYD) and double-declining-balance (DDB). which is 12. 12. The annual depreciation expense is calculated by using the following formula: Cost – Salvage value Depreciation expense = ----------------------------------------------------------------------Number of years of useful life Example 12. The method is most appropriate when an asset’s usage is uniform from period to period.Capital Investment Decisions 143 12. or 1.000 = ----------------------------------------. It results in equal periodic depreciation charges. while the fraction for the last year is 1/36. 4. 5.5% = $2.5% in this example. the machine is completely written down to its salvage value.6. 3.= $2.250 / year 8 years An alternative means of computation is to multiply the depreciable cost ($18. 6. Thus. The sum of the eight fractions equals 36/36. as is the case with furniture. the fraction for the first year is 8/36.000.000 and has an expected salvage value of $2. For example. if the life expectancy of a machine is 8 years. and the denominator is the sum of the digits.000) by the annual depreciation rate.5%).1 STRAIGHT-LINE METHOD This is the easiest and most popular method of calculating depreciation. The annual rate is calculated by dividing the number of years of useful life into one (1/8 = 12. Therefore. The auto’s estimated life is 8 years.2 SUM-OF-THE-YEARS’-DIGITS (SYD) METHOD In this method. or (8 + 7 + 6 + 5 + 4 + 3 + 2 + 1). Its annual depreciation is calculated as follows: Cost – Salvage value Depreciation expense = ----------------------------------------------------------------------Number of years of useful life $20. 1. at the end of 8 years. 12.
000 3.000 3.250 8.109 1.000 18. the depreciation expense for the eighth year would have been $569 ($2.000 11.11 — In Example 12.6.000 2.746 3.000 Year 1 2 3 4 5 6 7 8 Total Fraction 8/36 7/36 6/36 5/36 4/36 3/36 2/36 1/36 × = 12.000 1.144 Accounting and Finance for the Nonfinancial Executive Example 12. since the asset cannot be depreciated below its salvage value.000 18.187 667 Year-end Book Value $15. the depreciable cost is $18.750 2.000 – $2.746 3. Since book value declines over time.500 2.5% (1/8).000 18. depreciation expense is highest in the earlier years and lower in the later years.= ---------.500 3.000 15. the double-declining-balance rate is 25% (2 × 12.000).669 . if an asset has a life of 10 years. the depreciation expense decreases each successive period.12 — Assume the data in Example 12.3 DOUBLE-DECLINING-BALANCE (DDB) METHOD Under this method.000 500 $18. Second. the straight-line rate is 1/10 or 10%.000 ($20.= ----. the computation for each year’s depreciation expense is (N)(N + 1) 8(9) 72 S = --------------------------.500 1.328 4.10.000 18.000 18.437 6. Since the straight-line rate is 12. However.000 Depreciation Expense $ 184.108.40.2069 Year 1 2 3 4 5 6 7 × Rate (%) 25% 25 25 25 25 25 25 = Depreciation Expense $5.328 4.000 11.437 6. and the double-declining rate is 20%. The depreciation expense is computed as follows: Book Value at Beginning of Year $20.582 1.813 2. depreciation expense is computed by multiplying the rate by the book value of the asset at the beginning of each year. the book value of the fixed asset at the end of its useful life cannot be below its salvage value.100) rather than $667. Example 12. a depreciation rate is determined by doubling the straight-line rate.000 18. First.250 8.002 Note: If the original estimated salvage value had been $2. Using the SYD method.559 2.5%).000 18. This method ignores salvage value in the computation. .= 36 2 2 2 Depreciation Amount ($) $18.$2. For example.
Capital Investment Decisions 145 TABLE 12.0 14.6a 6.4 4.0% 18.9 5.5 14.5 4.5 12.0 20-year 3.9 6.9 5.5 4.4 5-year 20.9a 8. That rule is called the Modified Accelerated Cost Recovery System (MACRS) rule.2 6. based on an allowable percentage of the asset’s original cost (see Tables 12.2 7. It abandons the concept of useful life and accelerates depreciation deductions by placing all depreciable assets into one of eight age property classes.2 5.7 6.5 9.9 5.5 8.9 8.5 8. It calculates deductions.9 4.5 4.7 5.9 5.2 100% 100% 100% 100% 100% 100% Denotes the year of changeover to straight-line depreciation.9 5.4 4. 12.5 6.4 6.5 4. The rationale behind the system is that this way the . 1981 saw a new way of computing depreciation deductions for tax purposes.3% 24.9 3.5 a 4.6 6.4 4.2).8 7-year 14.8% 7.3 15-year 5.1 and 12.5 4.4 2.5 4.5 3.5 17.7 HOW DOES MACRS AFFECT INVESTMENT DECISIONS? Although the traditional depreciation methods still can be used for computing depreciation for book purposes.5 5.7 6.3 4.1 Modified Accelerated Cost Recovery System Classification of Assets Property Class Year 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Total a 3-year 33.0 19.9 5.9 5.0% 9.3% 44.2 5.2 11.0% 32.4 4.4 11. This rule is characterized as follows: 1.5 4.5 10-year 10. thereby making an investment more attractive.5 a 11.6 7.8 a 7.9 a 5.9 4. With a shorter life than useful life. the company would be able to deduct depreciation more quickly and save more in income taxes in the earlier years. as enacted by Congress in 1981 and then modified somewhat under the Tax Reform Act of 1986.
2 MACRS Tables by Property Class MACRS Property Class and Depreciation Method 3-year property 200% declining balance 5-year property 200% declining balance Useful Life (ADR Midpoint Life)a 4 years or less Examples of Assets Most small tools are included. Service stations and other real property with an ADR midpoint life of less than 27. . the law specifically excludes autos and light trucks from this property class. telephone and electrical distribution facilities. This means that the company can deduct only half of the regular straightline depreciation amount in the first year. the larger the tax shield (d)(t)). there is no need to consider the salvage value of an asset in computing depreciation. More than 4 years to less than 10 years 7-year property 200% declining balance 10-year property 200% declining balance 15-year property 150% declining balance 20-year property 150% declining balance 27. and research and experimentation equipment are included. and land improvements are included.5-year property straight-line 31. The reason for electing to use the MACRS optional straight-line method is that some firms may prefer to stretch out depreciation deductions using the straight-line method rather than accelerate them. (Remember that the higher d. duplicating equipment. 2. All residential rental property is included. 3.5 years are included. computers. Office furniture and fixtures. the appropriate ADR midpoint lives for assets are designated in the tax regulations. Since the allowable percentages in Table 12.146 Accounting and Finance for the Nonfinancial Executive TABLE 12. Autos and light trucks. Sewage treatment plants. Various machinery and equipment.5-year property straight-line a 10 years or more to less than 16 years 16 years or more to less than 20 years 20 years or more to less than 25 years 25 years or more Not applicable Not applicable The term ADR midpoint life means the “useful life” of an asset in a business sense. copiers. most items of machinery and equipment used in production are included. The straight-line convention must follow what is called the half-year convention. The company may elect the straight-line method. heavy general-purpose trucks. or have little or no income and wish to show more income on their income statements. All nonresidential real property is included. government encourages the company to invest in facilities and increase its productive capacity and efficiency. are included. typewriters. Those firms are the ones that just start out. such as that used in petroleum distilling and refining and in the milling of grain.2 add up to 100%.
000 = $359. often called the minimum required rate of return. Therefore.000 × × × × MACRS% 33.000/3 years = $1.34 15.5 14.359. Project managers must know the cost of capital.170 (from Table 11.000.4 d $333 445 148 74 (d)(t) $99. 4 years) = 3.08.109.3 ) = $350 for 4 years a b T4(10%.683b 90.9 133.08 – $1.13 — Assume that a machine falls under a 3-year property class and costs $3.826b .8 7.5 14.000 $1.170 a Year 1 2 3 4 Cost $1. . NPV = PV – I = $1.08 Present Value $1.Capital Investment Decisions 147 Example 12.000 Example 12. The NPV analysis can be performed as follows: Present Value Factor @ 10% 3.000 500 $3. The estimated life of the machine is 4 years.2 .000 3. The machine will be depreciated using the MACRS rule and will fall under the 3-year property class. The formula for computation of after-tax cash inflows (S – E)(1 – t)+ (d)(t) needs to be computed separately. T3 values obtained from Table 11.3% 44. The cost of capital is computed as a weighted average of the various capital components.14 — A machine costs $1.751b .000 Year 1 2 3 4 Cost $3.335 444 222 $3. Annual cash inflows are expected to be $500.000 3.909b .3. 12. Straight-Line (half-year) Depreciation $ 500 1.8 WHAT TO KNOW ABOUT THE COST OF CAPITAL The cost of capital is defined as the rate of return that is necessary to maintain the market value of the firm (or price of the firm’s stock).000 initially.50 ( S – E ) ( 1 – t ): ------------------------------------------------------------------------------$500 ( 1 – 0. The table below compares the straight-line with half-year convention with the MACRS. The tax rate is 30%.000 1.359.000. The cost of capital after taxes is 10%. The straight-line option under MACRS differs from the traditional straight-line method in that under this method the company would deduct only $500 depreciation in the first year and the fourth year ($3.5 44. so that the machine should be bought.8 7.000/2 = $500).4).27 33.000 3.000 $1. was used either as a discount rate under the NPV method or as a hurdle rate under the IRR method earlier in the chapter and in calculating the residual income (RI) in Chapter 13.16 $1.3% 44.000 × × × × MACRS % 33.4 22.81 110. $1.4 MACRS Deduction $ 999 1. which is positive.000 $1.
The dividend to be paid at the end of the coming year is $4 per share and is expected to grow at a constant annual rate of 6%.148 Accounting and Finance for the Nonfinancial Executive which are items on the right-hand side of the balance sheet such as debt.4) = 4. unlike debt interest. common stock. 8%. is not a deductible expense in computing corporate income taxes.8.1 COST OF DEBT AND PREFERRED STOCK The cost of debt is stated on an after-tax basis. Then. since the interest on the debt is tax deductible. This rate is not adjusted for income taxes because the preferred dividend.8.16 — Suppose that the Hume company has preferred stock that pays a $12 dividend per share and sells for $100 per share in the market.00% (1 – 0. Then the cost of this common stock is: . preferred stock. the after-tax cost of debt is: 8. 20-year bond whose net proceeds are $940.000. and retained earnings. the cost of preferred stock is the stated annual dividend rate.17 — Assume that the market price of the Hume Company’s stock is $40. One way to measure the cost of common stock is to use the Gordon’s growth model.= ----------. Example 12. The model is D1 P o = ---------r–g where Po = D1 = r = g = value (or market price) of common stock dividend to be received in 1 year investor’s required rate of return rate of growth (assumed to be constant over time) Solving the model for r results in the formula for the cost of common stock: D1 r = ----.15 — Assume that the Hume Company issues a $1.= 12% Price per share $100 12. 12. The tax rate is 40%. However.+ g Po Example 12. Then the cost of preferred stock is: Dividend per share $12 -------------------------------------------.2 COST OF COMMON STOCK The cost of common stock is generally viewed as the rate of return investors require on a firm’s common stock.8% Example 12.
00 16.60 11.92%.000 4.00% 16. with the weights being the proportions of each type of capital used.80% 12.000 $50.+ 6% = 16% Po $40 149 12.20 6.Capital Investment Decisions D1 $4 ----.+ g = -------.000 5. 12. that is.92%b 1.000 = .40 = 40%.000. we can determine its minimum rate of return.000.000 par) Preferred stock ($100 par) Common stock ($40 par) Retained earnings Total $20.000 20. (percentage of the total capital structure supplied by each source of capital × cost of capital for each source). since the cost of equity obtained by retained earnings is the same as the rate of return investors require on the firm’s common stock.8. ∑ The computation of overall cost of capital is illustrated in the following example.00 16. 4.000. Example 12.12% a b $20.80% × 40% = 1.000.80% 12.8. By computing a company’s cost of capital.000.00 These proportions would be applied to the assumed individual explicit after-tax costs below: Source Debt Preferred stock Common stock Retained earnings Weights 40%a 10 40 10 100% Cost 4.000/$50. Overall cost of capital is 11.18 — Assume that the capital structure at the latest statement date is indicative of the proportions of financing that the company intends to use over time: Cost Mortgage bonds ($1.000 5.00% Weighted Cost 1. A company’s cost of capital .40 1.000.000. which is used as the discount rate in present value calculations and in calculating an investment center’s residual income (RI).4 MEASURING THE OVERALL COST OF CAPITAL The firm’s overall cost of capital is the weighted average of the individual capital costs.00% 16.12%.3 COST OF RETAINED EARNINGS The cost of retained earnings is closely related to the cost of existing common stock.
tax factors must be taken into account in every decision. Since income taxes could make a difference in the accept or reject decision. if your company’s cost of financing increases. who are demanding higher return on their investments in the form of higher dividend and interest rates. it is being viewed as more risky by investors and creditors. Although the traditional depreciation methods still can be used for computing depreciation for book purposes.150 Accounting and Finance for the Nonfinancial Executive is also an indicator of risk. and presented an overview of the traditional depreciation methods. We also covered how to calculate a firm’s cost of capital. 12. For example. We illustrated the use of MACRS. We have also discussed five commonly used criteria for evaluating capital budgeting projects. 1981 saw a new way of computing depreciation deductions for tax purposes. .9 CONCLUSION We have examined the process of evaluating investment projects. including the net present value (NPV) and internal rate of return (IRR) methods. which is used either as a discount rate under the NPV method or as a hurdle rate under the IRR method earlier in the chapter and in calculating the residual income (RI) in Chapter 13. It was enacted by Congress in 1981 and then modified somewhat under the Tax Reform Act of 1986. This rule is called the Modified Accelerated Cost Recovery System (MACRS). The problems that arise with mutually exclusive investments and capital rationing were addressed.
whether that dollar came from owners or creditors. In this chapter. ROI = Net profit after taxes = --------------------.000 $18. Related is the return to stockholders.13 How to Analyze and Improve Management Performance The ability to measure managerial performance is essential in controlling operations toward the achievement of organizational goals.1 WHAT IS RETURN ON INVESTMENT (ROI)? ROI relates net income to invested capital (total assets). They do this by restructuring the firm into several divisions and treating each as an independent business. The managers of these subunits or segments are then evaluated on the basis of the effectiveness with which they use the assets entrusted to them. known as the return on equity (ROE).000 Then. ROI is calculated as: Net profit after taxes ROI = ------------------------------------------------Total assets Example 13. Furthermore.1 — Consider the following financial data: Total assets = Net profit after taxes = $100. a better ROI can also translate directly into a higher return on the stockholders’ equity. As companies grow or their activities become more complex.000 18. Perhaps the most widely used single measure of success of an organization and its subunits is the rate of return on investment (ROI). you will learn: • What ROI is • The basic components of the Du Pont formula and how it can be used for profit improvement • How ROI can be increased • How financial leverage affects the stockholder’s return 13.= 18% ------------------------------------------------Total assets $100.000 151 . they attempt to decentralize decision making as much as possible. ROI provides a standard for evaluating how efficiently management employs the average dollar invested in a firm’s assets.
ROI = Net profit margin × Total asset turnover = 9% × 2 times = 18% .= 9% Sales $200. Net profit after taxes Sales Net profit after taxes ROI = ------------------------------------------------. total asset turnover measures how well a company manages its assets.1. known as the Du Pont formula.000 Then.× --------------------------Sales Total assets Total assets = Net profit margin × Total asset turnover The Du Pont formula combines the income statement and balance sheet into this otherwise static measure of performance. The ROI breakdown.000 Sales $200. The breakdown of ROI is based on the thesis that the profitability of a firm is directly related to management’s ability to manage assets and control expenses effectively.= --------------------. $18. ROI = Net profit after taxes = --------------------.= ------------------------------------------------.152 Accounting and Finance for the Nonfinancial Executive The problem with this formula is that it only tells you about how a company did and how well it fared in the industry.= 2 times Total assets $100. It is important to realize that excessive funds tied up in assets can be just as much of a drag on profitability as excessive expenses.= 18% ------------------------------------------------Total assets $100. The Du Pont Corporation was the first major company to recognize the importance of looking at both net profit margin and total asset turnover in assessing the performance of an organization. In the past. Net profit margin is a measure of profitability or operating efficiency. as shown below.000.2 WHAT DOES ROI CONSIST OF? — DU PONT FORMULA ROI can be broken down into two factors — profit margin and asset turnover. Example 13. is expressed as a product of these two factors. It is the percentage of profit earned on sales. This percentage shows how many cents attach to each dollar of sales. It is the number of times by which the investment in assets turns over each year to generate sales.= --------------------.000 Therefore. managers have tended to focus only on the profit margin earned and have ignored the turnover of assets.000 Total asset turnover = --------------------------. Net profit after taxes $18.000 Net profit margin = ------------------------------------------------. It has very little value from the standpoint of profit planning. On the other hand. 13.2 — Assume the same data as in Example 13. Also assume sales of $200.000 Alternatively.
13. They are: 1. An industry with products tailor-made to customers’ specifications will have different margins and turnover ratios. In other words.e. The margin and turnover complement each other. but with varying income statements and balance sheets. In fact. The combination will necessarily vary depending upon the nature of the business and the characteristics of the product. (Note that net profit margin and total asset turnover are hereafter called margin and turnover. 2.25 3 4. Sound and successful operation must point toward the optimum combination of profits. The breakdown stresses the possibility of trading one for the other in an attempt to improve a company’s overall performance. sales. Weak margin can be complemented by a strong turnover.How to Analyze and Improve Management Performance 153 The breakdown provides numerous insights to financial managers on how to improve profitability of the company and investment strategy. Example 13. and capital employed. a low turnover can be made up by a high margin. as shown below: Margin (1) (2) (3) (4) (5) (6) 9% 8 6 4 3 2 × × × × × × × Turnover 2 times 2. There is no ROI that is satisfactory for all companies. respectively. turnover is just as important as profit margin in enhancing overall return. the combination (4) may describe a supermarket operation that inherently works with . The importance of sales is explicitly recognized.3 ROI AND PROFIT OBJECTIVE Figure 13. In effect. and vice versa.1 can also be looked at as showing six companies that performed equally well (in terms of ROI). which is not in the original formula..5 6 9 = ROI = = = = = = 18% 18 18 18 18 18 The margin-turnover relationship and its resulting ROI are depicted in Figure 13.1. It also shows how turnover is an important key to profit making. For example.) Specifically.3 — The breakdown of ROI into its two components shows that a number of combinations of margin and turnover can yield the same rate of return. As the figure shows. The importance of turnover as a key to overall return on investment is emphasized in the breakdown. 3. compared with industries that mass-produce highly competitive consumer goods. and vice versa. net profit after taxes/total assets) for profit planning. it has several advantages over the original formula (i. the margin and turnover factors complement each other. these two factors are equally important in overall profit performance.
low margin and high turnover. Margins may be increased by reducing expenses. Some of the ways to reduce expenses are: (a) Use less costly inputs of materials. with various programs either curtailed or eliminated. management can: 1.154 Accounting and Finance for the Nonfinancial Executive 10 8 (6) Turnover Ratio (5) 6 4 2 (4) (3) (2) (1) 0 2 4 6 8 10 Margin (%) FIGURE 13. Improve margin 2. although this can be dangerous in today’s quality-oriented environment. 13. Various actions can be taken to enhance ROI. and management development programs. Generally.4 ROI AND PROFIT PLANNING The breakdown of ROI into margin and turnover gives management insight into planning for profit improvement by revealing where weaknesses exist: margin or turnover. Improve both Alternative 1 demonstrates a popular way of improving performance. or increasing sales faster than expenses. Improve turnover 3. Discretionary fixed costs arise from annual budgeting decisions by management. (c) Bring the discretionary fixed costs under scrutiny. The cost-benefit analysis is called for in order to justify the budgeted amount of each discretionary program. Examples include advertising. while the combination (1) may be a jewelry store that typically has a low turnover and high margin. or both. thereby reducing turnover. . research and development.1 The margin-turnover relationship. (b) Automate processes as much as possible to increase labor productivity. raising selling prices. But this will probably increase assets.
new entrants.000 without affecting sales and investment to yield a 20% target ROI. or by reducing assets. political opposition. which will improve margin as well as turnover. EXAMPLE 13. By doing so. Pricing power is the ability to raise prices even in poor economic times when unit sales volume may be flat and capacity may not be fully utilized. or threats of product substitution. making continuous monitoring of inventory more feasible for better control.× -----------------200. This will help identify more detailed strategies to improve margin.000 200. (b) Devise various methods of speeding up the collection of receivables and also evaluate credit terms and policies. Alternative 1: Increase the margin while holding turnover constant. It is currently making an 18% return on its investment.= ------------------------------------------------. Net profit after taxes Sales Net profit after taxes ROI = ------------------------------------------------. Figure 13. Companies that offer unique.2 shows complete details of the relationship of ROI to the underlying ratios — margin and turnover — and their components.4 — Assume that management sets a 20% ROI as a profit target.× --------------------------Sales Total assets Total assets Present situation: 18. Pursuing this strategy would involve leaving selling prices as they are and making every effort to increase efficiency so as to reduce expenses. (c) See if there are unused fixed assets. turnover.000 18% = -----------------.How to Analyze and Improve Management Performance 155 A company with pricing power can raise selling prices and retain profitability without losing business. Some of the strategies to reduce assets are: (a) Dispose of obsolete and redundant inventory. It is also the ability to pass on cost increases to consumers without attracting domestic and import competition. (d) Use the converted assets (primarily cash) obtained from the use of the previous methods to repay outstanding debts or repurchase outstanding issues of stock. The company with pricing power must have a unique economic position. Alternative 2 may be achieved by increasing sales while holding the investment in assets relatively constant. expenses might be reduced by $2. high-quality goods and services (where the service is more important than the cost) have this economic position. The computer has been extremely helpful in this regard. You may use those funds elsewhere to get more profit.000 100.000 The following are illustrative of the strategies which might be used (each strategy is independent of the other). or both. Alternative 3 may be achieved by increasing sales or by any combinations of alternatives 1 and 2. regulation. as follows: .
which is the ratio of a company’s total asset base to its equity investment. For example. Another version of the Du Pont formula. trimming down $5.000 200.5 ROI AND RETURN ON EQUITY (ROE) Generally. called the modified Du Pont formula.000 90. It is calculated by dividing total assets by stockholders’ equity. the ratio of how many dollars of assets held per dollar of stockholders’ equity.000.000 20% = -----------------. 19.156 Accounting and Finance for the Nonfinancial Executive 20.000 without affecting sales and net income to yield the 20% target ROI as follows: 18. The return on equity (ROE) is calculated as: Net profit after taxes Total assets Net profit after taxes ROE = ------------------------------------------------.= ------------------------------------------------. The financial leverage is measured by the equity multiplier.000 200. However. reflects this effect. In this case.000 200.000 worth of investment in inventories would also reduce the inventory holding charge by $1.000 Alternative 3: Increase both margin and turnover by disposing of obsolete and redundant inventories or through an active advertising campaign. a better management performance (i. stated another way.× -----------------200. even a poorly managed company that suffers from a below-average performance can generate an above-average return on the stockholders’ equity.000 20% = -----------------.000 Excessive investment in assets is just as much of a drag on profitability as excessive expenses. The formula ties together the ROI and the degree of financial leverage (use of borrowed funds). simply called the return on equity (ROE).000 95. This measurement gives an indication of how much of a company’s assets are financed by stockholders’ equity and how much are financed with borrowed funds. 13. a high or above-average ROI) produces a higher return to equity holders. This strategy would increase ROI to 20%.e.000 Alternative 2: Increase turnover by reducing investment in assets while holding net profit and sales constant. Working capital might be reduced or some land might be sold. This is because borrowed funds can magnify the returns a company’s profits represent to its stockholders. so that both margin and turnover are improved at the same time. cutting unnecessary inventories also helps cut down expenses of carrying those inventories. or.000 100.× ------------------------------------------------Total assets Stockholders’ equity Stockholders’ equity = ROI × Equity multiplier .× -----------------200.000 20% = -----------------. alternative 3 is much more common than alternative 1 or 2. In practice. reducing investment in assets by $10..× -----------------200.
2 Relationships of factors influencing ROI.3 ROI. and financial leverage. Net profit margin Return on investment (ROI) Net profit after taxes Total assets Return on equity (ROE) Net profit after taxes Stockholders’ equity Divided by Net profit after taxes Sales Multiplied by Total asset turnover Sales Total assets (1 – Debt ratio) 1 – Total liabilities Total assets FIGURE 13. ROE. .How to Analyze and Improve Management Performance 157 Sales Cost of goods sold Selling expenses Administrative expenses minus Total cost Net income Net profit margin Divided by Cash Sales Multiplied by Return on investment (ROI) Marketable securities Accounts receivable Current assets Sales Inventories Divided by Total asset turnover Others Long-term investments Total assets Land Building Fixed assets Machinery and equipment FIGURE 13.
000 = 45% is the equity-to-asset ratio. ROE. assume stockholders’ equity of $45.5 — In Example 13. let us compare two firms that generate $300.000 = 2.000 in total assets. who put up only 45% of the capital. The use of the equity multiplier to convert the ROI to the ROE reflects the impact of the leverage (use of debt) on the stockholders’ return. Since the 18% ROI all goes to stockholders. the ROE is higher than 18%. Equity multiplier = ------------------------------------------------.158 Accounting and Finance for the Nonfinancial Executive ROE measures the returns earned on the owners’ (both preferred and common stockholders’) investment.45 $18.= -----------------.000 Net profit after taxes ROE = ------------------------------------------------. but they have different capital structures.000 ROE = ROI × Equity multiplier = 18% × 2. Total assets The equity multiplier = ------------------------------------------------Stockholders’ equity Total assets = --------------------------------------------------------------------Total assets – Total liabilities 1 = --------------------------------------------Total liabilities 1 – ----------------------------------Total assets 1 = ------------------------------------( 1 – Debt ratio ) Figure 13.000.22 = 40% If the company used only equity.= $100.000/$100. Example 13. $55.000 1 1 1 = ----------------------------------. Example 13. This example indicates the company was using leverage (debt) favorably.55 ) 0.3 shows the relationship among ROI. One firm employs no debt. Both firms employ $800.= 2.= --------. Total assets Then. and financial leverage.6 — To further demonstrate the interrelationship between a firm’s financial structure and the return it generates on the stockholders’ investments.22 ( 1 – debt ratio ) ( 1 – 0. the 18% ROI would equal ROE.000 = 55% is the debt ratio).= ----------------------.000 in operating income.1. 55% of the firm’s capital is supplied by creditors ($45.000 in borrowed funds. However.000/$100. whereas the other uses $400.= 40% Stockholders’ equity $45. The comparative capital structures are shown as: .22 --------------------Stockholders’ equity $45.
The advantage of this formula is that it enables the company to break its ROE into a profit margin portion (net profit margin).000 Firm B pays 10% interest for borrowed funds.000 $800.000 400. and a use-of-leverage portion (equity multiplier).000 $800.5% The absence of debt allows firm A to register higher profits after taxes. 13. within the context of the whole. Yet the owners in firm B enjoy a significantly higher return on their investments. Financial managers have the task of determining just what combination of asset return and leverage will work best in its competitive environment. Since financial leverage affects net profit margin through the added interest costs.000 $300. Too much debt can increase the firm’s financial risk and thus the cost of financing.How to Analyze and Improve Management Performance 159 A Total assets Total liabilities Stockholders’ equity (a) Total liabilities and stockholders’ equity $800. Most companies try to keep at least a level equal to what is considered to be “normal” within the industry. then the stockholder suffers.000 45.000) $210. and he/she will be left with a smaller return than would otherwise have been earned. .000 B $800.000) $260. The reason is that part of the profits from the assets which the stockholder has provided to the firm will have to go to make up the shortfall to the long-term creditors. the leverage is positive and the common stockholders benefit. but within a certain limit.6 A WORD OF CAUTION Unfortunately. management must look at the various pieces of this ROE equation. It shows that the company can raise shareholder return by employing leverage — taking on larger amounts of debt to help finance growth.000 26. The comparative income statements and ROEs for firms A and B would look as follows: A Operating income Interest expense Profit before taxes Taxes (30% assumed) Net profit after taxes (b) ROE [(b)/(a)] $300.000 — 800.25% B $300. This provides an important view of the positive contribution debt can make to a business.000 (90. an efficiency-of-asset-utilization portion (total asset turnover).000) $182. If the assets in which the funds are invested are able to earn a return greater than the fixed rate of return required by the creditors.000 (78.000 (40.000 400. to earn the highest return for stockholders. If assets are unable to earn a high enough rate to cover fixed finance charges. leverage is a double-edged sword.
Another version of the Du Pont formula — the modified Du Pont formula — relates ROI to ROE (stockholders’ return) through financial leverage. and (b) what needs to be done in order to improve performance.7 CONCLUSION This chapter covered in detail various strategies to increase the return on investment (ROI). popularly known as the Du Pont formula. It shows how leverage can work favorably for the owners of the company. The breakdown of ROI into margin and turnover. . provides much insight into: (a) the strengths and weaknesses of a business and its segments.160 Accounting and Finance for the Nonfinancial Executive 13.
For example. product lines. which sales territories have a poor sales mix. as well as whether or not the division meets overall goals. manufacturing plants.14 How to Evaluate Your Segment’s Performance In the previous chapter. You will have to determine whether to drop unprofitable products or substantially raise prices. consideration should be given to profitability. Why? Perhaps some customers need more extensive services (e.g. if any..g. Within a customer class. 14. We touched on a broad measure of performance — that is. there may also be a difference in selling costs to different customers within that class. what profit you are earning from each customer. and whether or not production workers are performing effectively. A segment is a part or activity of a company for which a manager desires cost or revenue data. distribution channels. to improve performance. we discussed how to analyze and evaluate managerial performance. types of customers. sales territories. growth. advertising budget) and which factors 161 . we will focus on the performance of a segment within a firm. In evaluating a product line. Examples of segments are divisions. divisional performance measures are concerned with the contribution of the division to profit and quality. and what actions you should take. It will help you determine the impact on profitability of proposed price and volume changes. Customer analysis will show the difference in profitability among customers so that corrective action may be taken. individual stores. return on investment (ROI). sales departments. It also shows whether or not your product lines are profitable. processes. The ability to measure performance is essential in developing management incentives and controlling the operation toward the achievement of organizational goals. competition. whether or not your salespeople are doing a good job. In this chapter. and capital employed. jobs. programs. you must determine which factors were under your control (e. Segment reports will help you determine what types of goods are being bought by your customers. depending on your needs. geographic areas. Segmental reports may be prepared for activity at different levels within your responsibility center and in varying formats. The analysis will aid in formulating selling prices and monitoring and controlling distribution costs. warehousing)..1 APPRAISING MANAGER PERFORMANCE In appraising your performance as the manager of the segment. You should know the financial strengths and weaknesses for your responsibility center. delivery. and contracts. Analysis of segmental performance helps you evaluate the success or failure of your segment. service centers. Segmental reporting reveals your department’s performance.
you are responsible for obtaining a target level of sales revenue. • It points to trouble spots needing attention. Responsibility accounting: (1) facilitates delegation of decision making. • It helps you determine who is not doing well so that corrective action may be taken. • It aids in allocating time among projects. economic conditions). Responsibility centers are found in both centralized and decentralized organizations. and (3) permits effective use of “management by exception. (2) helps promote “management by objective. To understand these lines.” in which managers agree on a set of goals (your performance is evaluated based on the attainment of these goals). while a cost center is usually associated with a centralized one. a cost center.” Figure 14. as well as to similar divisions in competing companies. and an investment center. a profit center. is organized primarily by business functions: exploitation. • It helps you determine who should be rewarded for good performance. including evaluation.2. A responsibility center is a unit that has control over costs. The reasons to measure your performance as a division manager are as follows: • It assists in formulating incentives and controlling operations to meet company and departmental goals. you should know how your company is organized. Comparison should be made of the performance of your division to other divisions in the company. for example. It is both a planning and control technique. while Figure 14.2 RESPONSIBILITY CENTER Responsibility accounting is the system for collecting and reporting revenue and cost information by areas of responsibility.1 shows responsibility centers within an organization. This center may be responsible for all three functions or for only one function.. Shell. . refining. revenues. There are lines of responsibility within a company. which is composed of a revenue center. 14. It operates on the premise that you should be held responsible for your performance.2 presents an organization chart of a company. 14. is organized by product lines. and investment funds.g. and for all activities within your responsibility center. An example is a district sales office. A profit center is often associated with a decentralized organization. Appraisal should also be made of the risk and earning potential of your division.1 REVENUE CENTER As the manager of a revenue center. on the other hand. General Foods. the performance of your subordinates. The performance report contains the budgeted and actual sales for the center by product. and marketing. Divisional performance is analyzed by a responsibility center. • It provides job satisfaction since you receive feedback.162 Accounting and Finance for the Nonfinancial Executive were not (e.
But a revenue center typically has a few costs (e. consideration should be given to the number of calls. After studying the information.How to Evaluate Your Segment’s Performance 163 Company Headquarters Divisions or Groups Investment Centers Companies or Subsidiaries Profit Centers Plants Departments Cost Centers Operations FIGURE 14. you must know which areas have the greatest profitability. terms of sale. Further. This requires sound sales analysis and cost evaluation. you are responsible for marketing a product line. Sales analysis may involve one or more of the following: prior sales performance. Sales analyses can help you uncover unwanted situations. . If you are to generate profitable sales. and comparing actual sales to budgeted sales. resulting in fewer selling expenses. you may more narrowly focus your sales effort. you are responsible mostly for revenues and only incidentally for some costs (typically not product costs). Subanalyses may also be made for evaluating product sales in each territory. order size. and mailings. Usually. You should keep a record of sales levels for the same product at varying prices so as to establish a relationship of volume to price. you may see that only a few customers give you most of your sales volume. looking at sales trends over the years. salaries. sales orders and back orders may be used as measures of projected volume. channel of distribution. Sales analysis will also allow you to see if sales effort is directed toward the wrong products and if sales of products are going toward less profitable lines. and territory.g. Analyses may be in dollars and/or units. Thus. Also. a small part of the selling effort is needed for a high percentage of your business. Territorial assignments may be changed. or the product line may be simplified. Accountability for departmental sales revenue also assumes that you have the authority to determine product sales prices. The types of analysis include those by salesperson. and their results. product. such as when most of your division’s sales are derived from a small share of your product line. ads placed.. In appraising sales effort.1 Responsibility centers within a company. customer. Hence. rent). You can determine whether orders have been lost by stockouts or delayed shipments.
Production Vice President .2 Organization chart of a company. .Research Vice President .164 President Vice President .Sales Treasurer Secretary Director of Engineering Manager of Advertising Manager of Marketing National Sales Manager Manager of Plant A Manager of Plant B Manager of Plant C Director of Research Accounting Purchasing Personnel Director of Special Products Director of Legal Affairs Engineering District Manager Division A District Manager Division B District Manager Division C Engineering Science } Profit Centers Pilot Plant ( Maintenance Finishing Similar for each plant ) Fabricating Assembling Toolmaking } Cost Centers Accounting and Finance for the Nonfinancial Executive FIGURE 14.
Cost center evaluation is most suitable for the following functions. For instance. optimistic capacity. Generally. such as an administrative area of a large company or an entire factory. necessary corrective action is taken to correct problems. you can budget figures for expected capacity. marketing. however. Such costs should. a factory may be segmented into numerous departments. Departmental profit is difficult to derive because of problems in allocating revenue and costs. Some cost centers may be composed of smaller cost centers. Your performance depends on your ability to achieve output levels given budgetary constraints. usually a department head.How to Evaluate Your Segment’s Performance 165 14. For example. where problems in quantifying the output in financial terms occur: accounting and financial reporting. Managers of cost centers. Incremental costs are those expenditures that would not exist if the center were abandoned. Actual expenditures are compared to budget. general administration) should not be included in appraising your performance. allocated common costs (e. The cost center approach is useful when you possess control over your costs at a specific operating level.2 COST CENTER A cost center is typically the smallest segment of activity or responsibility for cost accumulation. Flexible budgets should be prepared to enable you to look at costs at different levels of capacity. You may use the cost center approach when problems arise in relating financial measures to output. The cost center manager.g. comparisons of budget to actual cost can thus be made. and pessimistic capacity. In such a case. legal. personnel. A cost center manager is responsible for direct operational costs and for meeting production budgets and quotas. however. actual cost should be compared with the initial budget figure (original goal) and the revised budget. and public relations. computer services. carries the authority and responsibility for costs and for quantity and quality of not only products but also services. When looking at your performance. Hence. Examples of cost centers include the maintenance department or the fabricating department in a manufacturing company. each of which is a cost center. If a division’s situation significantly changes. Variances are investigated to determine the reasons for particular costs. cost centers pertain more to departments than to divisions. have no control over sales or marketing activities. given changing circumstances. You will also find the cost center approach appropriate for nonprofit and governmental units where budgetary appropriations are assigned. an adjustment to the initial budget is necessary. you must compare budgeted cost to actual cost. and efficiencies are accorded recognition. Better still. be allocated in determining the profit for the division. the personnel manager oversees both the costs and the quality of services rendered.2. the relevant costs are those incremental costs you have control over. . Cost allocation must conform to department goals and should be applied consistently among divisions. With a cost center. For example. say at bonus time. Cost center evaluation will not be worthwhile unless reliable budget figures exist. Cost centers may be relatively small — a single department with few employees — or very large..
However. such as advertising and research. controllable profit. For example. or any other quantifiable unit. When a transfer occurs between cost centers. and cost per labor hour. product line. By including just controllable cost. using one of these expressions. A center thus measures the performance of a division. capacity utilization. net income and contribution margin can be computed for them. A profit center demonstrates the following characteristics: (1) defined profit objective. There is no incentive to control costs. Solution: Using standard cost affects this problem because the selling division will only be credited for what the item should cost. and invoices processed. Discretionary costs are those that can be easily changed. the former should be charged with the increased costs necessary to meet acceptable standards incurred by the purchasing department. Warning: Using actual cost can pass cost inefficiencies on to the next division. The cost center should be charged with actual controllable cost and credited with standard controllable cost for the assembled product or service passed to other divisions. gross profit. and incremental profit. and (3) the use of profit-oriented decision rules. where appropriate. A good transfer price is a controllable cost. number of rejects. On the other hand. Transfer price is the price charged between divisions for a product or service. profit centers may not have significant amounts of invested capital.3 PROFIT CENTER Profits can be expressed in several ways including net income. The reason is that the profit reported by the . It should be used if your division is self-contained (with its own manufacturing and distribution facilities) and when there is a limited number of interdivisional transfers. The profit center provides not only goods and services but also the means for marketing them. 14. profit centers have associated revenues and expenses. For example. you should consider factory performance measures such as yield percentages for direct materials. profit centers are formed when products or services are used solely within the company. phone calls taken. or controllable cost. the transfer price should be based on either actual cost. standard cost. margin. In evaluating administrative functions. The profit center approach enhances decentralization and delineates units for decision-making purposes. A cutback in discretionary costs will prompt short-term improvements in profitability but in the long run will likely have a negative effect. as it bills each of the administrative and operating units for services rendered.2. Provision should exist for chargebacks.166 Accounting and Finance for the Nonfinancial Executive If you are a manager in the factory. You should be aware of the effects of discretionary costs when evaluating performance. if the quality control department makes an effort in its evaluation which leads to acceptance of the product by the purchasing department. the subjectivity of the allocation of fixed noncontrollable cost does not exist. In some instances. A typical profit center is a division selling limited numbers of products or serving a particular geographic area. (2) managerial authority for making decisions that have an impact on earnings. the computer department may be considered a profit center. performance reports should examine such dollar indicators as executive salaries and service departments as well as nondollar measures such as number of files handled. graphic area.
contribution margin may be a good indicator of your division’s performance because it emphasizes cost behavior patterns and controllability of costs that are generally useful for evaluating performance and making decisions. Ultimately. Further. it is not essential to allocate fixed costs.How to Evaluate Your Segment’s Performance 167 TABLE 14. Table 14. fixed costs are much less controllable than variable costs. Hence. any excess will be adequate to cover general corporate expenses. Also. divisional earnings should not be increased by any action reducing overall corporate profitability. with a profit center. In using the profit center approach.1 presents a contribution margin income statement by division.200 (700) 500 (200) 300 (180) 120 (70) 50 (23) $27 $300 $100 (100) (50) 200 50 (200) (500) 100 400 (100) (250) 100 (40) 60 (50) 10 (5) 5 50 (30) 20 (15) 5 (4) 1 (50) (150) 50 250 (40) (140) 10 (6) 4 110 (64) 46 (40)a (40) (20) (60) (40) (40) 160 10 (30) 130 (5) 5 (20) (15) 110 (10) Only those costs logically traceable to a product line should be allocated. with a further breakdown into product lines. output levels. Table 14. the price to accept an order given an idle capacity situation.2 illustrates product line profitability. In general. To evaluate divisional and managerial performance.1 Contribution Margin Income Statement By Segments Divisional Breakdown Entire Company Sales Less: Variable manufacturing cost of sales Manufacturing contribution margin Less: Variable selling and administrative costs Contribution margin Less: Controllable fixed costs by segment managers Contribution controllable by segment managers Less: Fixed costs controllable by others Segmental contribution Less: Unallocated costs Net income a Breakdown of Division Y Product Unallocable 1 2 3 $200 4 $300 Division X Y $300 $900 $1. . maximization of resource uses. which are common to a group of divisions. performance efficiencies. net income is determined as if the division were a separate economic entity. if your division meets its target contribution margin. use the profit center approach when you have decision-making authority in terms of the quantity and mix of goods or services. and break-even analysis. The contribution margin approach aids in computing selling price. you should be more cognizant of outside market considerations. Because. and managerial decisions. division is basically independent of other divisions’ operating activities. a contribution income statement can be prepared.
It is important to recognize that.000 (14.1 — It is important to know at what point to sell an item in order to maximize profitability.000) 42.000) $35. An example is the effect of foreign exchange transaction gains and losses because you may have no control over it.000 Product B $40. The ensuing profit figure may be erroneous. Example 14.000 2.g.000 8.000 4.000 (35. Advantages of the profit center approach are that it creates competition in a decentralized company.000) 65. provides goal congruence between a division and the company.000 5. Policies optimizing divisional earnings will likewise optimize corporate earnings even before the allocation of nondivisional expenses. it should not be used in evaluating you.000 10.000 (23.000 (7.000 (3.000) 16.000) 19.000) 46.000 1.2 Contribution by Products Entire Company Projected sales Variable costs Goods sold Marketing Less: Total variable costs Contribution margin Direct fixed costs Production Marketing Less: Total direct fixed costs Profit contribution Common fixed costs Production Marketing Administrative and general Less: Total common costs Income before tax $100.000 (21.000) 58. cost allocation is required.000 30.000 Product A $60. . while an uncontrollable income statement item is included in appraising the performance of a profit center.000 A difficulty with the profit center approach is that profit is calculated after subtracting noncontrollable costs or costs not directly related to divisional activity that have been arbitrarily allocated.000 1.000 20. Also. and aids performance evaluation.000 2.168 Accounting and Finance for the Nonfinancial Executive TABLE 14.000 5. this approach does not consider the total assets employed in the division to obtain the profit.000 3. A drawback is that profits can be manipulated since expenses may be shifted among periods. Examples of discretionary costs where management has wide latitude are research and repairs. However. you are responsible for not only profit and loss items attributable directly in your division but also costs incurred outside of the center (e. headquarters. You can sell a product at its intermediate point in Division A for $170 or its final point in Division B at $260.000 10.000 2. since divisions must incorporate nondivisional costs that have to be met before the company will show a profit.000 (4.. other divisions) for which your center will be billed directly. The outlay cost in Division A is $120.000 4. As a profit center manager.
g.. Transfer prices are not only important in performance.. • Productivity measures.. customer service). turnover). 14. top management. . Thus. market share. consumer medals). for each division. An example is labor hours in a production run. safety record). employee turnover rate. there is no single transfer price that will please everybody — that is. Further. • Product leadership indicators (e. • Social responsibility measures (e. including on-time deliveries). you need to know what monetary values and market prices to assign to these exchanges or transfers — some version of either. customer relations. Divisional performance follows: Division A Selling Price Less: Outlay cost A Outlay cost B Profit $178 (120) $ 50 Division B $260 (120) (110) $ 30 Sell at the intermediate point because of the higher profit. You have to consider the input in time and money. whether to sell or process alternative production possibilities..1 Transfer Pricing The transfer price is the one credited to the selling division and charged to the buying division for an internal transfer of an assembled product or service.g. The transfer resembles. product leadership. patented products. an “arm’s length” transaction. number of promotions. You need to know what transfer price is being used for transfers in a department and why it is being used.g. Does the maintenance of equipment ensure future growth? • Personnel development (e. growth rate. and the resulting output in quantity and quality. the selling division. A transfer price has to be formulated so that a realistic and meaningful figure can be determined for your division. • Human resource relationships (e.g. including input-output relationships. and the buying division — involved in the transfer.. It should be established after proper planning. Capacity is interchangeable. Unfortunately.3.How to Evaluate Your Segment’s Performance 169 while the outlay cost in Division B is $110. but also in decisions involving whether to make or buy.2.g. product quality. innovative technology. Other measures in appraising divisional performance that are not of a profit nature but that must be considered are the following: • Ratios between cost elements and assets to appraise effectiveness and efficiency. • Market measures (e. Unlimited product demand exists for both the intermediate product and the final product. understanding the transfer pricing can help you account for possible cost overruns.
You can suggest that the company buy the item through a vendor. absence of replacement market.. the selling division is encouraged to be cost-inefficient. product line) rather than the overall corporate profit margin. due to a strike situation causing a supply shortage) should not be employed. this could tell management that the cost of the materials is too high. and auxiliary conditions are precisely the same) less internal cost savings that result from dealing within the organization (e. advertising. If two divisions cannot agree on the transfer price. Market price may be determined from price catalogues. There is an incentive to the selling division to control costs because it will not be credited for an amount exceeding budgeted cost plus a markup. The market value of services is based on the going rate for a specific job (e. If the item is a by-product.g.g. sales commission. Even though actual cost plus profit markup may be used. delivery. and published data on complete market transactions. If the negotiated market value is too high. For example.. outside bids. A negotiated transfer price works best when outside markets for the intermediate product exist.. the transfer price will be $12. due to oversupply of the item) or high transfer price (e. the cost-based .g. since the higher its actual cost is. Some division managers use actual cost as the transfer price because of its ease to use. all parties have access to market information. If the outside market price is inappropriate or not ascertainable (e. The negotiated market price can tell you whether an item should be produced internally or bought through an outside vendor. credit.. if the selling division’s inefficiencies result in excessive actual costs.g. and collections costs). If the cost of an item produced internally is more than the market price. it would have to absorb the decline in profit to the extent that actual cost exceeds budgeted cost. equipment tune-up) and/or the standard hourly rate (e. If one of these conditions is violated.. it has the drawback of passing on cost inefficiencies. it may be settled by arbitration at a higher level. In fact. saving the company money overall. An average long-term market price should be used.g. The negotiated market value equals the outside service fee or selling price for the item (a quoted price for a product or service is only comparable if the credit terms. the hourly rate for an engineer). the higher its selling price (since it shows a greater profit) will be.. grad. Further.g. delivery charges.170 Accounting and Finance for the Nonfinancial Executive The best transfer price is the negotiated market value of the assembled product or service since it is a fair price and treats each profit center as a separate economic entity.g. but the problem is that no profit is shown by the selling division and cost inefficiencies are passed on. or too costly to be used for transfer pricing). you may want to go to your superiors and suggest that the item no longer be supplied internally. Thus. and you are permitted to deal externally if a negotiated settlement is impossible. Profit market should take into account the particular characteristics of your division (e. A temporarily low transfer price (e. you should use budgeted cost plus profit markup because this transfer price approximates market value and will highlight divisional inefficiencies. equality. the negotiated price may break down and cause inefficiencies. new product.. if budgeted cost is $10 and a profit markup on a cost of 20% is desired. it could also show that the selling department is wasting money. This could make the purchasing department look for another vendor.
and the discount offers an incentive to buy the company’s brand over a competitor’s.How to Evaluate Your Segment’s Performance 171 method treats the divisions as cost centers rather than profit or investment centers. the providing department has an incentive to do a good job. Division profit is computed as follows: Division A Sales Transfer price Product cost Transfer price Profit $ 7.500 30. is sold (or leased) to my department at a discount over the price offered to the general public.500) $30. They were sold outside at $45.600 We now see whether a buying division should buy inside or outside. Computer equipment. a cost-based transfer price may be used since the receiving department will select the services of the department providing the highest quality. We now see how transfer prices are used to determine divisional profit. Example 14.600 Company $61.500 $61.000 $54. Relevant information for the period follows: Division A Production Transferred to Division B Sold outside Selling price $25 Unit cost $5 Units 1. Training.500 ($ 7.500 $ 7. Therefore. is also offered to the public.2 — Division A manufactures an assembled product that can be sold to outsiders or transferred to Division B.200 300 The units transferred to Division B were processed further at a cost of $7.900 $15. on the other hand.000 $ 8. although internal. training costs are charged to my department at the same amount as to outside companies.500 $15. If other departments provide identical or very similar services.500 1. Because of this competitive situation. Transfers are at market value.000 $37.900 $45. This is attributable to the fact that computer sales for the company have been rather sluggish.000 $38.400 $15. Thus. . A transfer price based on cost may be appropriate when minimal services are provided by your department to another.000 Division B $54. A nonfinancial manager neatly illustrates this situation: The two major areas of transfer pricing that directly affect my department are internal training and computer equipment.400 30. measures such as return on investment and residual income cannot be used for evaluation purposes.
there are items that can also be bought in any stationery store. If he determines that he can get the material for a lower price from an outside vendor and that vendor can produce the quantity he needs at the time he needs them. Current production is 10. If the manager can lower the price and believes you are serious. He could tell the other manager either lower the price or he will go to the other location. One. Most of the items in the inventory are special orders. Transfer pricing could help him determine which course of action to take. The variable cost per unit is $50. Idle capacity exists. Whether the buying division should be permitted to buy the item outside or be forced to buy inside depends on what is best for overall corporate profitability. The finishing division purchases the item outside for $73 per unit. no one wants the auditors in their department. The stationery department in my company handles the supplies for the various departments. and make him look good to his superiors.000 58. Even if there is nothing to hide. since the selling division still has to meet its fixed cost when idle capacity exists. However.400. The impact on corporate profitability of having the buying division go outside is determined as follows: Savings to assembly division [Units (800) × Variable cost per unit ($50)]: Cost to finishing division [Units (800) × Outside selling price ($73)]: Stay inside savings $40. Second. A nonfinancial manager summarizes the importance of transfer pricing policy: The nonfinancial manager needs to know what the transfer pricing policy of the company is. Total fixed cost in the assembly division is $200. The cost for most of the . the buying division is required to purchase inside at the maximum transfer price ($73). They also do not want the auditing division to check their records. even though it’s an internal department. it could prove embarrassing to the selling department.3 — An assembly division wants to charge a finishing $80 per unit for an internal transfer of 800 units. The maximum transfer price should be $73 because the finishing division should not have to pay a price greater than the outside market price. If he thinks he is being overcharged by a department. he should go to the manager of the other department and tell him that he can get the item from another location for a better price.400 The buying division will be asked to purchase inside the company because. This will cut costs and give him a higher profit margin. the manager can make a strong case for eliminating the operation and using an outside source. A manager may be trying to decide whether he should shut down an operation due to the lack of profit. he would probably lower the price for two reasons.000. if it went outside. the manager can determine what the actual cost to produce the material is. he still needs the business. corporate profitability would decline by $18.000 units. if upper management finds out that people are using outside vendors. Typically.400 $18. If the operation produces a material that is used in other departments to create a good product.172 Accounting and Finance for the Nonfinancial Executive Example 14. The selling department does not want upper management to think they are mismanaged.
First. Assets assigned to a division include direct assets in the division and allocated corporate assets. A divisional investment is the amount placed in that division and put under your control. and investment funds. Two major divisional performance indicators are return on investment (ROI) and residual income (RI). For the specialized products. we would like to focus on its usefulness as a measure of a manager’s performance. Investment centers are widely used in highly diversified companies. The stationery department charges the other departments based on their actual costs. the latter is used to evaluate the entire division.4 INVESTMENT CENTER An investment center has control over revenue. 14. As an investment center manager. Return on investment equals: Operating income -----------------------------------------Operating assets An alternative measure is: Controllable operating profit ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------Controllable net investment ( Controllable assets – Controllable liabilities ) Example 14. You should be able to distinguish between controllable and noncontrollable investment.2. Another possibility is that someone in the stationery department is getting a kickback from a vendor. Assets are reflected at book value. While the former is helpful in appraising your performance. you accept responsibility for both the center’s assets and the controllable income. the other departments have no choice but to use the stationery department. Controllable investment depends on the degree of your division’s autonomy. the price is lower.1 Return on Investment (ROI) Although ROI was discussed in a prior chapter. There is no incentive for the managers to buy within. It is a profit center whose performance is evaluated on the basis of the return earned on investment capital.How to Evaluate Your Segment’s Performance 173 items in the stationery department is higher than the price the other departments would pay from an outside source. it takes several weeks for the merchandise to arrive. An example is an auto product line that is manufactured on company premises. This leads me to the conclusion that either the stationery department is getting overcharged from outside vendors or that the department is wasting a lot. the manager will buy it externally.2. The company has no policy which states that the departments must buy from the stationery department. if it’s available on the outside. If the manager needs the item in a rush the stationery department can do an emergency delivery but the cost is so much.4. .4 computes ROI for a hypothetical situation. 14. cost. Second. Most departments will get items from the outside for several reasons.
. • It focuses on maximizing a ratio instead of improving absolute profits. • A lack of goal congruence may exist between the company and your division.4 — The following financial data pertains to your division: Operating assets Operating income Sales $100. For example. • It represents a cumulative audit or appraisal of all capital expenditures incurred during your division’s existence. • It highlights unprofitable divisions. Alternative profitability measures could be used in the numerator besides net income (e. Because divisions are often geographically far apart. • If the projected ROI at the beginning of the year is set unrealistically high. it does not show future flows. • It helps make your goals coincide with those of corporate management. • ROI is a static indicator. discouragement of investment center incentive could result. and a project’s ROI is 16%.000 $200. • It assigns profit responsibility. you may be motivated to reject other profitable investment opportunities. you are given broad authority in using division assets and acquiring and selling assets. if your company’s ROI is 12%.= 18% Operating assets $100. • It aids in appraising performance.000 -----------------------------------------.000 $ 18. • It can be used as a base against which to evaluate divisions within the company and to compare the division to a similar division in a competing company. • ROI emphasizes short-run performance instead of long-term profitability. • It places emphasis on high-return items. segment margin). regardless of the asset risk. • ROI ignores risk. you will not accept the project because it will lower your ROI. . To protect the current ROI.000 The advantages of ROI as a performance indicator are as follows: • It focuses on maximizing a ratio instead of improving absolute profits. • It is the broadest possible measure of financial performance.000 Your ROI is: Operating income $18. • Different assets in the division must see the same return rate. contribution margin.g.= --------------------. • Established rate of return may be too high and could discourage incentive.174 Accounting and Finance for the Nonfinancial Executive Example 14. gross profit. your division’s ROI is 18%. even though the project may be best for the entire company. A labor-intensive division generally has a higher ROI than a capitalintensive one.
How to Evaluate Your Segment’s Performance 175 An understanding of ROI enables you to see how your performance is measured and how your department compares with other departments in the organization. As a nonfinancial manager. and the cost of capital is 9%. you must be fully aware of these factors so that you can evaluate your position accurately as each option presents its own set of consequences. and contribute premium dollars. Manager B increases his department’s ROI by increasing income while holding invested capital steady. Without a full understanding of the implications and limitations of ROI. Taking a closer look at ROI reveals three added viewpoints.000.000. Manager B decides to appeal to the existing sales force to increase their efficiency and production with promises of no further hiring and encourages them to push the more profitable property lines.5 — Divisional operating income is $250. Manager B has not invested wisely in human resources leaving you one year later with a sales force working to capacity with limited growth potential. Therefore. Manager A on the other hand has increased his potential by investing wisely and now has 15 additional agents who are fully trained and prepared to lead future company growth by expanding into untapped markets.000 per agent.000 The minimum return rate is based upon the company’s overall financial cost adjusted for your division’s risk. but has actually jeopardized the company in the long run by his failure to adequately forecast and plan accordingly. along with allowing you to plan and monitor your financial position as you move the organization towards its goals. In an interview. total operating assets are $2 million. Example 14. a vice-president of a company commented on the usefulness of ROI in evaluating nonfinancial managers: There are two department managers in separate areas with a goal of 15% ROI. which equals divisional operating income less minimum return times total operating assets. 14. Manager A decides that to reach the goal he must increase the sales force by 15 agents. You must evaluate these two managers one year later with regard to the company’s goal of 15% ROI and profitable growth. or decreasing total assets.000) $70.000 (180. It takes six months to complete the training. being knowledgeable in accounting.2 Residual Income (RI) An alternative measure of divisional performance is residual income.4. However. . so we see that Manager A has invested heavily in human resources to increase income and affect his ROI. The proper use of accounting allows you to exercise the proper management controls. ROI can be positively affected by decreasing costs. as they have saturated their markets and are not prepared to invade new markets. become fully functional.2.000) Residual income $250. increasing revenue. Residual income equals: Divisional operating income Less: Minimum × total operating assets (9% × $2. while Manager A has only had his people functional for six months and has not reached his 15% goal. The training costs come to $60. you decide that Manager B has achieved his goals. you determine that Manager B has merely opted to look good in the short term.
• RI maximizes dollars instead of a percentage. • RI identifies operating problem areas. there is no segregation. depending on the risk of those divisions. The advantages of residual income are as follows: • The same asset may be required to earn the same return rate irrespective of the division the asset is in. The addition of such an investment will increase the division’s overall RI. depending on riskiness. • RI cannot be used to compare divisions of different sizes. center. • It may be difficult to determine the valuation basis and means of allocating assets to divisions. Under the ROI method. A target residual income may be formulated to act as your objective.3 Decisions Under ROI and RI The decision whether to use ROI or RI as a measure of your division’s performance affects your investment decisions. residual income will artificially increase over time. • Since it is a mixture of controllable and uncontrollable elements. you tend to accept only the investments whose returns exceed the division’s ROI. The disadvantages of residual income include the following: • Assigning a minimum return involves estimating a risk level that is subjective. 14. thereby motivating you to accept all profitable investments. • Different return rates may be employed for different types of assets. or specific program to ensure that the rate of return on alternative investments is met or improved on by each segment. The trend in residual income to total available assets should be examined in appraising divisional performance. Residual income tends to favor the larger divisions due to the large amount of dollars involved. • If book value is used in valuing assets. Otherwise. Under the RI method. • Different return rates may be assigned to different divisions. • RI provides an economic income.176 Accounting and Finance for the Nonfinancial Executive Residual income may be projected by division. the division’s overall ROI would decrease if the investment were accepted. since the minimum return times total assets becomes lower as the assets become older.4.2. on the other hand. . taking into account the opportunity cost of tying up assets in the division. you would accept an investment as long as it earns a rate in excess of the minimum required rate of return.
emphasizing profitable products. profit center. Product line analysis identifies areas that need corrective action such as changing the selling price.500 Under the RI approach. Proper analysis under each method is vital in appraising operating efficiency.3 CONCLUSION It is essential to evaluate your segment’s performance to identify problem areas. You should understand the advantages and disadvantages of each method as well as determine which method is most appropriate for a situation.000 × 13% = $1.000 19.000 1.73% $100.6 — The following data apply to your division: Operating assets Operating income Minimum required rate of return ROI RI $100. customer.200 $100.300 14.000 18.000 18.500* 15% Overall $110. The various means of evaluating performance include cost center.000 (13. as shown below: Present Operating assets (a) Operating income (b) ROI (b/a) * New Project $10. modifying advertising strategy.500 (l. You would not accept this project under the ROI approach since the division is already earning 18%. and salesperson. eliminating unprofitable products.000 $10.300)* $ 200 Overall $110.How to Evaluate Your Segment’s Performance Example 14.200.000 13% 18% $5. the manager would accept the new project because it provides a higher rate than the minimum required rate of return (15% vs.000) $ 5.000 $18. 13%).000 1. .300) $ 5. revenue center. as shown below: Present Operating assets (a) Operating income (b) Less: Minimum required income at 13% (c) RI (b – c) * New Project $10. Acquiring this project will bring down the present ROI to 17. method of sale. Controllable and uncontrollable factors must be considered.000 18% $10.73%.000 investment. and investment center.000 19. The profit and loss figures will indicate areas of strength or weakness.500 17. commodity.000 × 15% = $1. and selecting a center of distribution. Accepting the new project will increase the overall residual income to $5.500 (14.000 177 Assume that you are presented with a project that would yield 15% on a $10. You should be familiar with the profit and loss statements by territory.
g. number of new customers). and cost per hour of employee time. reduction in per unit cost). If you are in a service business.g. average billing rates.g. . and improving employee morale (e. turn revenue per employee).178 Accounting and Finance for the Nonfinancial Executive There are other goals that managers have which include increasing market share (e. some performance measures include billable time. your division’s sales relative to sales of divisions in c companies.. improved productivity (e...
tax credits. Corporate taxes should be deferred when: (1) there will be a lower tax bracket in a future year.. and local taxes may be levied on income. and S corporations. You must analyze the tax consequences of such alternative approaches. By donating appreciated property to a charity. taxable income computations. It is important that you understand the federal corporate tax because it is the largest in magnitude and thus influences your managerial decisions. and property. ignoring taxes will cause an overstatement in estimated income. Try to convert income to less-taxed sources. accelerate deductions in the current year if you anticipate lower rates in the next year and accelerate expenses that will no longer be deducted or that will be restricted in the future. which means you have to keep up to date with the changes in the tax law that affect your business. business can deduct the full market value and avoid paying tax on the gain. it is important that you have an understanding of the basic concepts underlying the prevailing tax structure and of how these concepts affect your decisions. deductible expenses. you should be familiar with tax strategies. sales. a 179 . For example.g. operating loss carrybacks and carry forwards. you can reduce the tax obligation by deferring income to next year. 15. tax laws of foreign countries must also be understood.1 TAX STRATEGIES AND PLANNING Sound planning minimizes tax obligations and postpones the payment of taxes to later years.15 How Taxes Affect Business Decisions Since your company must pay taxes. (4) the tax payment will be in “cheaper” dollars. If your company is operating internationally. (3) the business earns a return on the funds for another year that would have had to have been paid to the federal and local taxing authorities. You should also properly time the receipt of income and the payment of expenses to minimize tax payment. state. (2) the firm lacks the funds to meet the present tax requirement. As a result. capital gains and losses. However. A good tax strategy is to receive income in a year it will be taxed at a lower rate. To make sound financial and investment decisions. Federal. Income and expenses must be shifted into tax years that will result in the least tax. an investment alternative may be chosen that does not sufficiently generate the needed return for the risk exposure taken. or (5) there may eventually be no tax payment (e. if you expect tax rates to drop next year. Also. For example. In some cases. as a result of a new tax law). Another tax strategy your company might consider is to donate appreciated property instead of cash. pay deductible expenses in a year in which you will receive the most benefit.
000.2 TAX COMPUTATION Corporations pay federal income tax on their taxable income. The equivalent rate on a taxable instrument is: .000 next $ 25.000 in taxable income.34 .000 × 15%). the market value of the bond changes with changes in the going interest rate.000.000 next $ 5.333.= 9. Of course. Tax-free income is worth much more than taxable income. The capital gain or loss (difference between cost and sell price) is subject to tax when your company sells the bond.06 . Example 15.06 --------.3 — If a firm has $20. Obtaining tax-exempt income is another tax strategy your company should consider. Federal income taxes are imposed at the following tax rates: 15% 25% 34% 39% 34% 35% 38% 35% on on on on on on on on the the the the the the the the first $ 50. The company’s tax rate is 34%.665. This is referred to as interperiod tax allocation because the temporary difference eventually reverses.000 ($20.000 next $ 9. for example. the tax is calculated as follows: .1 — A municipal bond pays an interest rate of 6%. You can determine the equivalent taxable return as follows: Tax-free return Equivalent taxable return = ------------------------------------------------1 – Marginal tax rate Interest earned on municipal bonds. the tax liability is $3. taxes can be reduced in the initial years by using the modified accelerated cost recovery system (MACRS) depreciation rather than straight-line depreciation for tangible assets.000 next $ 25. For example.= -----. Example 15.333 remaining income Example 15. which is the corporation’s gross income reduced by the deductions permitted under the Internal Revenue Code of 1986.1% 1.000 in taxable income.66 15.000 next $ 3.2 — If a firm has $20.180 Accounting and Finance for the Nonfinancial Executive company can use one method of accounting for books and another method for tax.000 next $ 235. A company that uses an accounting method that results in less taxable income initially will lower its tax in the earlier years due to the time value of money. is not subject to federal tax and is exempt from tax of the state in which the bond was issued.
A corporation pays income tax on its taxable income.000.000.3 is 35%.333.416. The income tax rate increases to 35% at taxable incomes of $10.000).266. Average tax rates are computed as follows: Average tax rate = Tax due/taxable income Example 15. The purpose of the 38% tax bracket is to wipe out the effect of the 34% tax bracket and to raise the average tax rate to 35%. the amount of the reduction depends upon the .286.333. corporate shareholders are entitled to reduce their income by a portion of the dividends received in a given year. This is accomplished at taxable income of $18.333. As suggested in Example 15.0000 of corporate income. Thereafter.333 1.650 3. which results in an average tax rate of 34% ($113.500 91. The 15%.667. If a corporation owns stock in another corporation. The income tax on $18.333.000.000 25.900/$335.3 is 35% (7.000 25.4 — The average tax rate for the corporation in Example 15. and the individual shareholder).900.667/$18. Generally.100 1.333.666. Because of the fluctuations in the corporate tax rates. at taxable incomes beyond $18.000 235.750.000 9. and when the corporation pays dividends to its individual shareholders.000/20.333. corporations pay a tax of 35% on all of their taxable income. The effect of the 39% tax bracket is to wipe out the early low tax brackets.How Taxes Affect Business Decisions Income × $ 50.000.000 3.2.000 $7. To avoid this result.000. parent.000). and 34% tax brackets demonstrate the intent that there should be a graduated tax rate for small corporate taxpayers. then the income of the subsidiary corporation could be subject to triple taxation (income tax paid by the subsidiary.1 INTEREST AND DIVIDEND INCOME Interest income is taxed as ordinary income at the regular corporate tax rate.333). 25%.000 Financial managers often refer to the federal tax rate imposed on the next dollar of income as the “marginal tax rate” of the taxpayer. financial managers also talk in terms of the average tax rate of a corporation.000. which results in an average tax rate of 35% ($6. the cumulative income tax is $113.250 8.667 181 Marginal Tax Rate (%) 15% 25% 34% 39% 34% 35% 38% 35% = $ Taxes 7.665.333.416.000 5.000.000 1.4.667 583.333 of taxable income is $6. The marginal tax rate for the corporation in Example 15.333 $20. 15. At $335. the tax rate is reduced back to 35%. the dividends are subject to a second tax.500 6. Corporate income is subject to double taxation. This fact demonstrates the reasoning behind the patch-quilt of corporate tax rates.
2. these dividends are taxed at an effective federal tax rate of 10. and ABC Corporation receives dividends of $10. As a result of the dividends received deduction. Note that dividends are paid with after-tax dollars.182 Accounting and Finance for the Nonfinancial Executive percentage of the stock of the subsidiary corporation owned by the parent corporation as shown below: Percentage of Ownership by Corporate Shareholder Less than 20% 20% or more.000. As a result of these dividends.000. The loss can be carried back 3 years and then forward 15 years.000 in a given year from XYZ Corporation. during the 15-year period of 2000 through 2014. and pays dividends of $40. The company’s taxable income is: $125. To illustrate. however. if any.500 + $6.2. any loss remaining may no longer be used as a tax deduction. Thus. but less than 80% 80% or more Deduction Percentage 70% 80% 100% Example 15.000 $75.2. The corporate taxpayer may elect to first apply the loss against the taxable income in the 3 prior years. At that time. This means that our tax system favors debt financing over equity financing.000). Dividends on stock (common and preferred). If the loss is not completely absorbed by the profits in these 3 years. is $13.5%. The corporation may choose to forego the loss carryback. Example 15. pays interest charges of $50. are not deductible and are therefore paid with after-tax dollars. 1997.000 and an offsetting dividends received deduction of $7. as calculated in Example 15. its tax liability on the dividends is $1. .050 (35% × $3.5 — ABC Corporation owns 2% of the outstanding stock of XYZ Corporation. and 1998.000 (70% × $10. If any part of the loss remains. it may be carried forward to each of the 15 following years.2 INTEREST AND DIVIDENDS PAID Interest paid is a tax-deductible business expense. which results in a net $3.750 ($7. interest is paid with before-tax dollars.000). ABC Corporation will have ordinary income of $10. and to instead carry the net operating loss to future years only.000 –50. 1999 operating loss may be used to recover.3 OPERATING LOSS CARRYBACK AND CARRYFORWARD If a company has an operating loss.000. in whole or in part. which is tax-deductible) (taxable income) The tax liability. this amount may be used to reduce taxable income.000 being subject to federal income tax. If ABC Corporation is in the 35% tax marginal tax bracket. 15. the loss may be applied against income in other years.250).000 (operating income) (interest charge. 15. the taxes paid during 1996.6 — Yukon Company has an operating income of $125.
000 100.000 100. the firm was able to “zero-out” its before-tax income as follows: Remaining 1999 Net Operating Loss ($) $600.750 ($22.250 In 1999.250 22.250 22.500) for the years 1996 through 1998. The remaining capital loss is carried forward to future . Like all taxpayers.000 100. corporations net any capital gains and capital losses that they have.000 (700.000 100. it was able to file for a tax refund of $66.000 100.7 — The Loyla Company’s taxable income and associated tax payments for the years 1994 though 2001 are presented below: Year 1996 1997 1998 1999 2000 2001 2002 2003 Taxable Income ($) 100.250 22. then part or all of the gain from the sale may be taxed as ordinary income.000 $700. corporations pay tax on their capital gains at the same rate as any other income.000 100.250 + $22.000 Tax Savings ($) $ 22.250 22. Loyla Company had an operating loss of $700.000 Tax Payments ($) 22.000 100.How Taxes Affect Business Decisions 183 Example 15.000 100.4 CAPITAL GAINS AND LOSSES Capital gains and losses are a major form of corporate income and loss. By carrying the loss back 3 years and then forward.250 22.250 0 22.250 0 22.000 100. 2000 through 2003.000) 100.000 in 1999.000 0 100.000 200.000 100. If depreciation has been taken on the asset sold.000.250 22.250 22.000 300. The maximum tax rate on the capital gains of individuals is 28%.250 22. It then carried forward the portion of the loss not used to offset past income and applied it against income for the next four years.250 22. Corporations include any net capital gains as part of their taxable income.000 0 Year 1996 1997 1998 1999 2000 2001 2002 2003 Total Income Reduction ($) $100.000 500.000 400. the individual may deduct up to $3.250 22. They may result when a corporation sells investments and/or business property (not inventory).250 + $22. If an individual has a net capital loss.000 400.250 $157.000 100.2. Unlike individuals.500 As soon as the company recognized the loss of $700. 15.000 of that loss in the year incurred.
Later.000) $ 72. general partnerships).020 or approximately 16% in the above example.g. The net income of a corporation is taxed to the corporation. which allow investors to have limited liability and yet avoid double taxation. and it has one shareholder. corporations are popular because they have many advantages. Two entities have developed (S corporations and limited liability companies). The importance of avoiding double taxation can be seen in the following example.000 of net income.. Despite this disadvantage.2.5 MODIFIED ACCELERATED COST RECOVERY SYSTEM (MACRS) For all assets acquired after 1986. the pass-through entity merely files an informational tax return with the Internal Revenue Service (IRS).2. These capital loss carrybacks and carryforwards may be used to offset net capital gains in the past and/or future years. a disadvantage of corporations.000 Double taxation costs the investor $16. corporations may not deduct any net capital losses. Instead. 15. which is in the 28% marginal tax bracket. Afterwards.000 (0) 100. the distribution of any accrued income to the owners generally is tax-free.980 Pass-Through Entity $100. This percentage increases as the corporation’s marginal tax rate increases. the distribution can be tax-free. Later. including the fact that the liability of their shareholders (who are active in their business) for corporate debts is generally limited to the shareholders’ investment in the corporations.000 (22. corporations may carry back the net capital loss to the three previous years and/or carry forward the net capital to the next five years. depreciation for tax purposes (cost recovery) is calculated using the Modified Accelerated Cost Recovery System (MACRS). should the corporation distribute that income to its shareholders.000 (28.770) $ 55. Unlike individuals. and informs its owners of their share of the entity’s taxable income or loss. owners of the entities are taxed on their share of the entities’ income. MACRS was discussed in depth in Chapter 12.250) 77. .750 (21. when that income is distributed to the owners. the distribution is taxed a second time to the recipient shareholders. With these entities.184 Accounting and Finance for the Nonfinancial Executive years indefinitely. Assume that the business is either a corporation or a pass-through entity: Corporation Entity’s taxable income: Tax on entity level: Distribution to owner: Tax on owner: After-tax distribution: $100. 15.6 ALTERNATIVE “PASS THROUGH” TAX ENTITIES As noted above. compared to other forms of doing business (e. The owners will be taxed on their share of the corporation’s income. is double taxation. Generally. Assume that a business has $100.
tax strategies.S.2. The allowable credit is calculated as follows: Foreign source income Foreign tax credit = -----------------------------------------------------.000 and tentative U.S. medicine. Upon termination. The credit for foreign income taxes that can be claimed on the U.S.000.2 Limited Liability Companies Limited liability companies (LLCs) are a relatively recent development.S. and corporations that make this election are still treated as general corporations for other legal purposes. then the LLC will enjoy pass-through status. 15. tax return for 2001 is as follows: $300. the corporation must make a timely election with the IRS. the foreign tax credit cannot be used to reduce the U.2.S.6. or if it voluntarily chooses to do so. The company’s taxable income from business operations in Country X was $300. and accounting). may elect to be taxed as S corporations.000 = $120.g. 15.. the corporation must meet other requirements which were discussed in Chapter 1. and foreign income taxes charged were $135.6.How Taxes Affect Business Decisions 185 15. As was discussed in Chapter 1. If an S corporation fails to meet any of the specified requirements. dollars. This is merely a tax classification. its S corporation status will terminate. Provided that the appropriate election is made. after such a termination.000 Foreign tax credit = --------------------. income tax of $270.S.× U. the corporation must wait five years before it may elect S corporation tax treatment again. In order to qualify for this treatment. law.8 — In 2002 your company had worldwide taxable income of $675.4 CONCLUSION In performing your departmental responsibilities.1 S Corporations Corporations. According to recent IRS regulations. an LLC may elect whether it wishes to be taxed as a corporation or as a passthrough entity (a partnership).000 15. and depreciation if you are to obtain the most tax . Generally. In addition. You must be familiar with the tax deductions.000 stated in U. liability Worldwide income Example 15.3 FOREIGN TAX CREDIT A credit is permitted for income taxes paid to a foreign country.000 $675. LLCs are typically not permitted to carry on certain service businesses (e. tax liability on income from U. sources.× $270. the corporation will be taxed as a general corporation. if they meet certain requirements. However.000. it is important to understand the tax structure and its implications for your company.
you should seek professional tax advice before committing funds to new projects and making specific financial and investment decisions.186 Accounting and Finance for the Nonfinancial Executive benefit for the company. . and foreign tax credits. capital gains and losses. However. You should also be aware of the tax implications regarding S corporations.
Part IV Obtaining Funds .
Effect on credit rating. to periodically adjust the amount of funds needed). You should consider the merits of the different alternative sources of short-term financing.. commercial paper. Certain lenders may impose restrictions. Sources of short-term financing include trade credit. bank loans. receivable financing. 6. For instance. and delinquent repayment may be detrimental to your credit rating.g. bankers’ acceptances. short-term financing may be used to provide additional working capital. 4. It is a spontaneous (recurring) financing source. less expensive. acquisition of a plant and equipment).g. since it comes from normal operations. Stability and maturity of your operations. such as requiring a minimum level of working capital. you need more stability and reliability in financing. The drawbacks of shortterm financing are that interest rates fluctuate more often. 2. 3. finance company loans. 7. Tax rate. future interest rates). Cost.g..g. and more flexible. Flexibility.. factoring accounts receivable). and some are more desirable than others because of interest rates or collateral requirements. 16.1 HOW TO USE TRADE CREDIT Trade credit (accounts payable) refers to balances owed to suppliers. Certain lenders are more willing than others to work with you (e. Restrictions.16 What to Know About Short-Term Financing “Short-term financing” refers to financing that will be repaid in 1 year or less. receivables and inventory). or to provide interim financing for a long-term project (e. Risk. there is a risk of not being able to repay. It may be used to meet seasonal and temporary fluctuations in funds position or to meet your permanent needs..g. When compared to long-term financing. If you are materially affected by outside forces. 9. The factors bearing upon the selection of a particular source include: 1. 8. Consider the reliability of the source of funds for future borrowing. refinancing is frequently required. Some sources of short-term financing may negatively impact your credit rating (e. Expected money market conditions (e. and inventory financing. A particular source may be more appropriate in a given circumstance. 5. Profitability and liquidity positions. Inflation rate. to finance current assets (e. 10. and it is the 189 . short-term financing has several advantages: it is easier to arrange..
× -------. interest is typically not demanded or. Trade credit has many advantages: it is readily available. To be eligible for a bank loan. if so. you may be able to stretch (extend) accounts payable. however. How much is your accounts payable balance? $500 per day × 60 days = $30. although all institutions (e.2 — You buy $1. Example 16. and trade creditors are frequently lenient if you get into financial trouble. paying the bill on day 30.000 16. this may lower your credit rating and may eliminate any cash discount offered. the .g.190 Accounting and Finance for the Nonfinancial Executive least expensive form of financing inventory.. you must have sufficient equity and good liquidity.2 CASH DISCOUNTS You should take advantage of a cash discount offered on the early payment of accounts payable because the failure to do so may result in a high opportunity cost. since suppliers want business.= 36. 16. credit unions) provide banking services as well. however.1 — You purchase $500 worth of merchandise per day from suppliers. net/30. The terms of purchase are net/60. the rate is minimal. loans in excess of 1 year may be given (see Chapter 17). savings and loan associations. Depending on your financial standing. since the interest rate on a bank loan would be far less than 36. and you pay on time. If you have liquidity difficulties. it is convenient. A banker gathers information regarding your business operations and often expresses the bank’s opinions of your practices. The opportunity cost is: $20 360 ----------. You fail to take the discount. Commercial banks allow you to operate with minimal cash and still be confident of planning activities even in times of uncertainty. even if you needed to borrow the money from the bank.7%. These banks favor short-term loans. collateral is not required. The cost of not taking a discount equals: Opportunity Cost (%) Discount lost Dollar proceeds you have use of by not taking the discount × 360 Number of days you have use of the money by not taking the discount = Example 16.7% $980 20 You should take the discount.000 in merchandise on terms of 2/10.3 WHEN ARE BANK LOANS ADVISABLE? Most banking activities are conducted by commercial banks.
When a short-term bank loan is taken. as your need for funds change. Your interest rate will probably be higher depending upon your risk. Loans. other borrowers are charged higher interest rates. and any credit balance of the undersigned may be applied by you in satisfaction of any such debt. This note is a written statement that you agree to repay the loan at the due date. this may be construed as a continuing statement and substantially accurate. this statement shall have the same force as if delivered as an original statement of our financial position at the time when further credit is needed. You must apply for loans.1) and sign a note. and. Without additional funds. A bank loan is not a source of spontaneous financing as is trade credit. notwithstanding the date of payment as fixed by the obligation then held by you. and it is hereby agreed that upon requesting further credit. or if the undersigned assigns any accounts or transfers any assets which you deem materially affect the business. Banks charge only their most creditworthy clients the prime rate. earn interest. a self-liquidating (seasonal) loan may be used to pay for a temporary increase in accounts receivable or inventory. If any judgment is entered or any legal action is commenced against the undersigned. a group of banks may form a consortium to furnish the desired level of capital. For example.What to Know About Short-Term Financing 191 bank may take a “soft” or “hard” position including warnings of not renewing loans or demanding immediate payment if you do not agree to its suggestions. You must realize that the prime interest rate is a negotiating point for borrowed funds. therefore. you usually issue a borrower’s statement (see Exhibit 16. or if the undersigned becomes financially troubled. One bank is appointed the prime negotiator. or on the failure of the undersigned to notify you of any important change in the financial status of the undersigned. A note payable may be paid at maturity or in installments and consists of principal and interest. 2001. you should alter your borrowings from banks. of course. If your company is large.1 — Typical Statement Required of Corporate Borrower To ABC Bank: To obtain credit from time to time with you for our negotiable paper. you may have to restrict your plans. Exhibit 16. in the absence of such notice or of a new and full written statement. As soon as the assets realize cash. We will notify you immediately of any significant unfavorable change in our financial position. Bank financing may take any of the following forms: • • • • Unsecured loans Secured loans Lines of credit Installment loans . we provide financial statements as of December 31. then all obligations held by you upon which the undersigned is responsible shall at your option. be immediately due. and lenders must grant them. you repay the loan. and the prime interest rate is the lowest interest rate applied to short-term loans from a bank.
Y. March 16. N.3. the bank agrees to lend money on a recurring basis up to a specified amount (see Exhibit 16. we renew your $2 million unsecured line of credit for next year. Sincerely. Balk. Borrowings under this line will be at a rate of 1% over the prime rate. NY Dear Mr. you may still give collateral to get a lower interest rate.3 WHAT LINE OF CREDIT CAN YOU GET? Under a line of credit. In some cases. Based upon our review of your year-end audited financial statements. Jim Balk Treasurer Harris Manufacturing Corporation New York. or fixed assets. There are two disadvantages to this kind of loan: (1) it carries a higher interest rate than a secured loan and (2) payment in a lump sum is required.1 ARE YOU ELIGIBLE UNSECURED LOAN? Most short-term. Credit lines are typically established for a 1year period and may be renewed annually. even though you are able to obtain an unsecured loan. Bob Jones Vice President . This line is subject to your company maintaining its financial position and being out of bank debt for at least 90 days during the fiscal year.2 — Sample Letter Extending Line of Credit Grace Bank New York. with some form of collateral behind the loan. This kind of loan is recommended if you have an excellent credit rating. Seasonal cash shortfalls and desired inventory buildups are reasons to use an unsecured loan. 16. It is appropriate if you have immediate cash and can either repay the loan in the near future or can quickly obtain longer-term financing.3.2). Exhibit 16. 16. marketable securities.192 Accounting and Finance for the Nonfinancial Executive FOR AN 16. 2001 Mr.2 WHAT WILL YOU GIVE TO OBTAIN A SECURED LOAN? If your credit rating is deficient.3. unsecured (no collateral) loans are self-liquidating. Collateral may take many forms including inventory. the bank may lend money only on a secured basis — that is.
000 × .000 and are required to keep a 12% compensating balance. The disadvantage is that you may have a cash problem in a particular month but still have to pay the monthly installment payment. refinancing can take place at lower interest rates.10) = $24. . 16.What to Know About Short-Term Financing 193 The advantages of a line of credit are the easy and immediate access to funds during tight money market conditions and the ability to borrow only as much as needed and repay immediately when cash is available. For example. The compensating balance effectively increases the cost of the loan. The disadvantages relate to the collateral requirements and the additional financial information that must be presented to the bank. The advantage of this kind of loan is that it may be tailored to satisfy seasonal financing needs. Therefore.3. When you borrow under a line of credit.3 — You may borrow $200. the bank typically charges a commitment fee on the amount of the unused credit line. the bank may place restrictions upon you. Further.000 + $10. This deposit is referred to as a compensating balance and is stated as a percentage of the loan. If you are unable to repay a short-term loan. you may be required to maintain a deposit with the bank that does not earn interest. When the principal on the loan decreases sufficiently. Note that the prime interest rate is not known until you actually borrow the money. if you arrange for a line of credit when the prime interest rate is 8% and the interest rate on the loan is stipulated at 2% above prime. repay it for a brief time during the year (e. for 1 month). Example 16. You also have an unused line of credit in the amount of $100.g.4 WHAT IS AN INSTALLMENT LOAN? An installment loan requires monthly payments. Be on guard! Some banks may test your financial capability by requiring you to “clean up” the loan — that is.12) + ($100.000 × . in which case the interest rate would be reduced.000 A line of credit is typically decided upon prior to the actual borrowing. such as a ceiling on capital expenditures or the maintenance of a minimum level of working capital. In the days between the arrangement for the loan and the actual borrowing. The payment shows the bank that the loan is actually seasonal rather than permanent.000 = $34. you should probably finance with long-term funds. A compensating balance may also be placed on the unused portion of a line of credit.000. for which a 10% compensating balance is required. interest rates will change.. but the prime interest rate is 10% on the day you actually borrow the money. your agreement with the bank will stipulate it is at the prime interest rate prevailing when the loan is extended plus a risk premium. The minimum balance that must be maintained is: ($200. Also. you will be charged an interest rate of 12%.
When interest is paid in advance.000 ---------------------------------------------------------------------------------------------------------.19 × $600. the loan proceeds are reduced and the effective (true) interest cost is increased. Example 16.5 — Assume the same facts as in Example 16. with interest due at maturity and with a 15% compensating balance required.= 19% $25.000 $114.5% 81% Bank A’s 20% rate is the lowest effective rate.00 – .800 The effective interest rate is 16% ($4.7 — The effective interest rate for a 1-year. The effective rate for Bank B is calculated as follows: 19% ---------.5 HOW DO YOU COMPUTE INTEREST? Interest on a loan may be paid either at maturity (ordinary interest) or in advance (discounting the loan).000 at 16% interest per annum and repay the loan 1 year later.194 Accounting and Finance for the Nonfinancial Executive 16. Example 16. The interest is: $300.200 The true interest rate for this discounted loan is: $4.16 = $4.15 ) × $600. When a loan has a compensating balance requirement.000 loan that has a nominal interest rate of 19%.000 Proceeds Example 16.000 × .3.000).6 — Bank A will give you a 1-year loan at an interest rate of 20% payable at maturity.800 = $25.4. Proceeds = Principal – Interest = $30. while Bank B will lend on a discount basis at a 19% interest rate.4 — You borrow $30. The compensating balance will increase the effective interest rate. Example 16. The proceeds of this loan are smaller than in the previous example.= 23.000 – $4.= -------------------------------------------------------Percentage of proceeds available × Principal ( 1. the proceeds received are decreased by the amount of the compensating balance.000 = --------------------$510.000 = 22. is calculated as follows: Interest rate × Principal .4% . except the note is discounted.800 Interest Effective interest rate = -------------------.= -----------------. $600.800/$30.
000 = --------------------$396.18 × $275.000 – $48.8% On an installment load.10 × 125. The average loan balance is: $40.750 12.9 — You have a credit line of $400.= 20% $20. the effective rate is: Interest --------------------------------------------------Average loan balance The average loan balance is one half the loan amount.000 = 28.= ----------------------------------------------Principal – Compensating balance $275.000 at an interest rate of 10% to be paid in 12 monthly installments. Example 16.000.000.7.000 .13 × $275. The interest rate on the loan is 18%.8 — Assume the same facts as in Example 16.500 = --------------------$226.85 × $600. The interest is computed on the face amount of the loan.500 $48.000 --------------------------------------------------------------------------------. You borrow $275.250 $49.000 ---------------------------------------------------------------------------------------------------------. but you must maintain a compensating balance of 13% on outstanding loans and a compensating balance of 10% on the unused credit.8% Example 16.000 $35. the effective interest rate computation is more complicated. except that the loan is discounted.19 × $600.What to Know About Short-Term Financing 195 Example 16. Assuming a 1-year loan payable in equal monthly installments.000 -----------------.000 -----------------. The required compensating balance is: .000 ) – $114.= $20.000 2 The effective interest rate is: $4.= ----------------------------------------------------------------------Percentage of proceeds available × Principal ( 0.000 .250 The effective interest rate (with line of credit) is: Interest rate (on loan) × Principal 0.750 = 21. The effective interest rate is: Interest rate × Principal 0.000 $114.10 — You borrow $40.
000 -----------------.S. not the client.S. The creditworthiness of the draft is of good quality because it has the backing of the bank. etc.11 — Assume the same facts as in Example 16.000 -----------------. bankers offer professional assistance in addition to financing.= 22. The exporter draws a draft on the . in essence.S has undertaken a transaction.000 is deducted in advance.10. In a long-term banking relationship.000 2 The effective interest rate is: $4. Acceptances act as short-term financing because they typically have maturities of 180 days. commercial bank for a letter of credit to a Saudi Arabian exporter with whom the U. Since the banker will want to know whether you will be able to repay the loan. cyclical business needs. The interest of $4. Example 16.2% $18. except that the loan is discounted.5 WHAT ARE BANKER’S ACCEPTANCES? A banker’s acceptance is a draft.S.000 = $36. However.196 Accounting and Finance for the Nonfinancial Executive Example 16.= $18. particularly being able to explain ratios that depart from industry norms. It is. drawn by you and accepted by a bank. You will make a good impression if you have the financial statements and documents readily available and are prepared to discuss your financial condition. The letter of credit regarding the shipment states that the exporter can draw a time draft for a given amount on the U. Banks are anxious to lend money to meet self-liquidating.000 The average loan is: $36. Banker’s acceptances are often used to finance the shipment handling of both domestic and foreign merchandise. so the proceeds received are: $40. that orders payment to a third party at a later date. to enter new markets. you should know that the loan officer will prepare financial ratios of your liquidity (ability to meet short-term debt) and will ask questions to determine your managerial competency. 16. a debt instrument created out of a self-liquidating transaction. bank.12 — A U.000 – $4.000 16.4 WHAT SHOULD YOU KNOW WHEN DEALING WITH A BANKER? When applying for a loan. you must be able to explain what the needs are in an intelligent manner so the banker has confidence in your abilities. oil refiner arranges with its U. A short-term bank loan is an inexpensive way to obtain funds to satisfy working capital requirements during the business cycle. They may recommend ways to improve the quality of business policies. he or she will want to see your cash flow forecasts.
Therefore. Collateral includes accounts receivable.000 $71. 16. and the commercial paper dealer often offers financial advice.What to Know About Short-Term Financing 197 bank and negotiates it with a local Saudi Arabian bank.g.000 × 6) Cost Percentage cost of commercial paper = $65. Typically. re: payment.000 of commercial paper every 2 months at a 13% rate. When a note is sold at a discount.000 6. 16.2% 16. but you will pay the full face value. typically 0.13 — You issue $500. The percentage cost of the commercial paper is: Interest ($500.. you may have to go to a commercial finance company (e.6 ARE YOU FORCED TO TAKE OUT A COMMERCIAL FINANCE COMPANY LOAN? When credit is unavailable from a bank. and there is an acceptance to meet the maturity date.S. inventories.8 SHOULD RECEIVABLES BE USED FOR FINANCING? In accounts receivable financing. A portion of their financing is sometimes obtained through commercial bank borrowing at wholesale rates. The drawbacks are that commercial paper can be issued only by large. Accounts receivable financing generally takes place under the following conditions: . otherwise.000 $71. the latter accepts the draft.. financially sound companies.13) Placement cost ($1. registration with the Securities and Exchange Commission (SEC) is needed. There is a $1. The maturity date is usually less than 270 days. CIT Financial). The finance company loan has a higher interest rate than a bank. the amount of collateral placed will be greater than the balance of the loan. Commercial finance companies also finance the installment purchases of industrial equipment by firms. and fixed assets. Commercial paper may be issued through a dealer or directly placed to an institutional investor. the interest rate is less than that of a bank loan.5% below the prime interest rate. The benefits of commercial paper are that no security is required.000 = 14. The Saudi Arabian bank sends the draft to the U. it means that interest is immediately deducted from the face of the note by the creditor. the interest rate is typically less than through bank or finance company borrowing. and generally it is secured.000 × .000 --------------------$500.000 placement cost each time. Commercial paper is unsecured and sold at a discount (below face value). the accounts receivable are the security for the loan as well as the source of repayment.7 ARE YOU FINANCIALLY STRONG ENOUGH TO BE ABLE TO ISSUE COMMERCIAL PAPER? Commercial paper can be issued only if you possess a very high credit rating. and commercial paper dealings relative to bank dealings are impersonal. Example 16.
Receivables are a minimum of $25. factors may antagonize customers by their demanding methods of collecting delinquent accounts. The assignment of accounts receivable has the advantages of availability of cash. For example. the continuance of the clerical function associated with accounts receivable. The proceeds received are equal to the face value of the receivables less the commission charge. Receivable financing has several advantages. . The disadvantages include the high cost. Sales are a minimum of $250. 2. Remissions by customers are made directly to the factor. costs rise. with the use of personal computers these costs can be curtailed. 7. 6. Also. and a discount from the face value of highcredit-risk receivables. Factoring is the outright sale of accounts receivable to a bank or finance company without recourse. When accounts receivable are financed. when defaults are given to the finance company. when credit standards are relaxed. Accounts receivable financing has the drawback of high administrative costs when there are many small accounts. obtaining of financial advice. The purchaser of the factoring arrangement (also called the factor) takes all credit and collection risks. costs decline. 4. Title to the goods passes to the buyer at shipment. interest on the unpaid balance of advanced funds. costs decrease. The finance company usually advances between 50% and the face value of the receivables in cash. Sales returns are not great. In an assignment (pledging).198 Accounting and Finance for the Nonfinancial Executive 1. however. Receivables apply to selling merchandise rather than rendering services. The advantages of factoring are immediate availability of cash. interest on the advance. and the bearing of all credit risk. reduction in overhead because the credit examination function is no longer needed. which is usually 2% to 4% higher than the prime interest rate. and when the minimum invoice amount of a credit sale is increased. You are responsible for charges. 3.000. The cost of the factoring arrangement is the factor’s commission for credit investigation. cash advance accessibility on a seasonal basis. 5.000. Receivables are given to a finance company recourse. Customers are financially strong. there is no transfer of the ownership of the accounts receivable. and avoidance of negative customer feelings. You should compute the costs of accounts receivable financing and select the least expensive alternative. Accounts receivable may be financed under either a factoring or assignment (pledging) arrangement. and strengthening of the balance sheet position. and any resulting bad debt losses. including avoiding the need for long-term financing and obtaining a recurring cash flow. the cost of financing may rise or fall under different circumstances. Individual receivables are at a minimum of $100. receipt of advances as required on a seasonal basis. The disadvantages of factoring include both the high cost and the negative impression left with customers due to the change in ownership of the receivables. You must also be aware of the impact of a change in accounts receivable policy on the cost of financing receivables. Remissions continue to be made directly to you.
03 × $400.040 Example 16.600 13. it must consist of marketable.000 $32.75 × $400.000 × . The collection period is 30 days.000 12.000)] Additional cost of not using the factor Credit costs Bad debts (.15 — Your factor charges a 3% fee per month. As a result of the factoring arrangement. The inventory itself must be good security for a loan.000)] Total cost $12.500 per month in credit costs and a bad debt expense of 2% of credit sales. .000 6.5% fee on receivables purchased.000 The cost of the bank financing is: Interest [.000 per month. The advance is high when there is marketable inventory. XYZ Bank has offered an arrangement to lend you up to 75% of the receivables. the financing of raw materials and finished goods is about 75% of their value. This high interest rate is one of the disadvantages of inventory financing.75 × $400.000 per month in accounts receivable that a factor will purchase from you.000) Lending fee [.01 × (. nonperishable.14 — You have $120.04 × (.000)] Processing charge [.500 You should stay with the factor.000 3.000 $15.000) Total cost $ 6.500 8.9 SHOULD INVENTORIES BE USED FOR FINANCING? Inventory financing typically occurs when you have completely used your borrowing capacity on receivables.000 × 12)] Cost of borrowing [. The restrictions placed on inventory represent another drawback. and standardized goods that have quick turnover. The interest rate is approximately 3 to 5% over the prime interest rate.What to Know About Short-Term Financing 199 Example 16. The bank will charge 2% per month interest plus a 4% processing charge on receivable lending.440 $35. If you borrow the maximum per month.75 × $400. and it should not be subject to rapid obsolescence.015 × ($120. advancing you up to 80% of the receivables for an annual charge of 14% and a 1. Inventory financing should consider the price stability of the merchandise and the costs of selling it. The cost of this factoring arrangement is: Factor fee [. you save $6.02 × (. Your credit sales are $400.02 × $400.8)] Total cost $21. should you stay with the factor or switch to XYZ Bank? The cost of the factor is: Purchased receivables (. In general. 16. The factor lends you up to 75% of receivables purchased for an additional 1% per month.014 × ($120.
With a floating lien. Example 16.000. With a warehouse receipt. There may be a field warehouse arrangement in which the warehouse sets up a secured area directly at your location. Even though you sell and restock.16 × . warehouse receipt. the fixed costs of this arrangement are high. The drawback of the trust receipt arrangement is that a trust receipt must be given for specific items. due to the high p completed items.200 Accounting and Finance for the Nonfinancial Executive The types of inventory financing include a floating (blanket) lien.000 320. Six large financially sound companies are responsible for 75% of your sales. Receivables will thus show good collectibility. Inventory financing is not likely.000 $727. the lender receives an interest in the inventory stored at a public warehouse. As goods are sold.000 250. and net income is $130.90 × $500. A good example of trust receipt use is in automobile dealer financing. the lender’s security interest continues. and trust receipt. On the basis of the financial information that is provided in the following balance sheet. Funds are required for 3 months.17 — You show growth in operations but are presently experiencing liquidity difficulties. You have access to the goods but must continually account for them. would you be on receivables or inventory? Receivable financing can be expected since a high percent is made to only six large financially strong companies.16 — You wish to finance $500. the creditor has title to the goods but releases them to you to sell on the creditor’s behalf.800.000 4.000 . Lenders are reluctant to finance inventory when a large work-in-progress balance exists because the goods will be difficult to further process and sell by lenders. however.000 × (3/12)] Warehousing cost Total cost $18. The warehousing cost is $4.000 Example 16.000 for the 3-month period.000 $22. The cost of financing the inventory is: Interest [. you remit the funds to the lender. Assets Current assets Cash Receivables Inventory (consisting of 55% of work-in-progress) Total current assets Fixed assets Total assets $27. the creditor’s security lies in the aggregate inventory rather than in its components.000 of inventory. Sales amount to $1. With a trust receipt loan. A collateral certificate may be issued by a third party to the lender guaranteeing the existence of pledged inventory. The advantage of a collateral certificate is flexibility because merchandise does not have to be segregated or possessed by the lender. A warehouse receipt loan may be taken at 16% with a 96% advance against the inventory’s value.000 380. It is also easier to control accounts.000 $977.
What to Know About Short-Term Financing
Liabilities and Stockholders’ Equity Current liabilities Accounts payable Loans payable Total current liabilities Non-current liabilities Bond payable Total liabilities Stockholders’ equity Common stock Retained earnings Total stockholders’ equity Total liabilities and stockholders’ equity $260,000 200,000 35,000 $495,000 110,000 $605,000 $250,000 122,000 372,000 $977,000
16.10 WHAT OTHER ASSETS MAY BE USED FOR FINANCING?
Inventory and receivables are not the only assets that may be used as security for short-term bank loans. Real estate, plant and equipment, cash surrender value of life insurance policies, and securities may also be used. Also, lenders are typically willing to advance a high percentage of the market value of bonds, and loans may also be made based on a guaranty of a third party.
In short-term financing, the best financing tool should be used to meet your objectives. The financing instrument depends upon your particular circumstances. Consideration is given to such factors as cost, risk, reactions, stability of operations, and tax rate. Sources of short-term financing include trade credit, bank loans, banker’s acceptances, finance company loans, commercial paper, receivable financing, and inventory financing. If you think you will be short of cash during certain times, arrange for financing (e.g., a line of credit) in advance instead of waiting for an emergency. Table 16.1 presents a summary of the major features of short-term financing sources, and Figure 16.1 illustrates temporary and permanent financing.
Accounting and Finance for the Nonfinancial Executive
TABLE 16.1 Summary of Short-Term Financing Sources
Types of Financing Source Cost or Terms Features
Spontaneous Sources Accounts payable Suppliers
Employees and tax agencies
No explicit cost but there is The main source of short-term an opportunity cost if a cash financing typically on terms of discount for early payment 0 to 120 days. is not taken. Companies should take advantage of the discount offered. None Expenses incurred but not yet paid (e.g., accrued wages payable, accrued taxes payable).
Unsecured Sources Bank loans 1. Single payment note
2. Lines of credit
Prime interest rate plus risk A single-payment loan to satisfy premium. The interest rate a funds shortage to last a short may be fixed or variable. time period. Unsecured loans are less costly than secured loans. Commercial banks Prime interest rate plus risk An agreed upon borrowing limit premium. The interest rate for funds to satisfy seasonal may be fixed or variable. needs. A compensating balance is typically required. The line of credit must be “cleaned up” periodically. Commercial banks, A little less than the prime Unsecured short-term note of insurance interest rate. financially strong companies. companies, other financial institutions, and other companies
Secured Sources Accounts receivable as collateral 1. Pledging Commercial banks and finance companies
Typically 2 to 5% above Qualified accounts receivable prime plus fees (usually 2 accounts serve as collateral upon to 3%). Low administrative collection of the account; the costs. Advances typically borrower remits to the lender. ranging from 60 to 85%. Customers are not notified of the arrangement. With recourse means that the risk of nonpayment continues to be borne by the company.
What to Know About Short-Term Financing
TABLE 16.1 (continued) Summary of Short-Term Financing Sources
Types of Financing 2. Factoring Source Cost or Terms Features
Factors, Typically a 2 to 3% discount Certain accounts receivable are sold on a discount basis without commercial banks, from the face value of recourse. This means that the and commercial factored receivables. factor bears the risk of finance companies Interest on advances of nonpayment. Customers are almost 3% over prime. Interest on surplus balances notified of the arrangement. The held by factor of about 1/2% factor provides more services per month. Costs with than is the case with pledging. factoring are higher than with pledging. Commercial banks About 4% above prime. and commercial Advance is about 40% of finance companies collateral value. Commercial banks About 3% above prime. and commercial Advances ranging from finance companies 80 to 100% of collateral value. Commercial banks About 4% above prime plus and commercial about a 2% warehouse fee. finance companies Advance of about 80% of collateral value. Collateral is all the inventory. There should be a stable inventory with many inexpensive items. Collateral is specific inventory that is typically expensive. Borrower retains collateral. Borrower remits proceeds to lender upon sale of the inventory. Collateralized inventory is controlled by lender. A warehousing company issues a warehouse receipt held by the lender. The warehousing company acts as the lender’s agent.
Inventory collateral 1. Floating liens
2. Trust receipts (floor planning)
3. Warehouse receipts
Accounting and Finance for the Nonfinancial Executive
Short-term financing Long-term financing
Pressing and patient short-term debt Noncurrent liabilities and stockholders’ equity Month
FIGURE 16.1 Illustrative financing.
Looking at Term Loans and Leasing
This chapter considers intermediate-term loans, primarily from banks and leasing arrangements to meet your financing needs. Intermediate-term loans include bank loans, revolving credit, insurance company term loans, and equipment financing.
17.1 INTERMEDIATE-TERM BANK LOANS
Intermediate-term loans are typically loans with a maturity of more than 1 year but less than 5 years. They are appropriate when short-term unsecured loans are not, such as when a business is acquired, new fixed assets are purchased, and long-term debt is required. If you wish to float long-term debt or issue common stock but conditions are unfavorable in the market, you may seek an intermediate loan to bridge the gap until long-term financing can be undertaken on favorable terms. The interest rate on an intermediate-term loan is typically higher than that on a short-term loan because of the longer maturity period. The interest rate may be either fixed or variable (according to, for instance, changes in the prime interest rate). The cost of an intermediate-term loan changes with the amount of the loan and your financial strength. Ordinary intermediate-term loans are payable in periodic, equal installments, except for the last payment, which may be higher (referred to as balloon payment). The schedule of loan payments should be based on the cash flow position to satisfy the debt. The periodic payment in a term loan is computed as follows: Amount of loan Periodic payment = ---------------------------------------------Present value factor
Example 17.1 — You contract to repay a term loan in five equal year-end installments. The amount of the loan is $150,000 and the interest rate is 10%. The payment each year is
$150,000 --------------------- = $39,567.40 3.791
where 3.791 = T4 (10%, 5 years) = present value of annuity for 5 years at 10% (from Table 11.4). Example 17.2 — You may want to determine the amount of loan, and what portion of the periodic payment represents principal and interest. You take out a term loan to
Accounting and Finance for the Nonfinancial Executive
be paid off in 20 year-end annual installments of $2,000 each. The interest rate is 12%. The amount of the loan is
Amount of Loan $2,000 = --------------------------------------7.469 Amount of loan = $2,000 × 7.469 = $14,938.00
where 7.469 = T4(12%, 20 years) from Table 11.4. The amortization schedule for the first 2 years is shown in the table:
Year 0 1 2
Balance $14,938.00 $14,730.56 $14,498.23
12% times the balance of the loan at the beginning of the year.
When taking out an intermediate-term loan, you will encounter several kinds of restrictive provisions that are designed to protect the lender. You may find that the agreement includes general provisions that are used in most agreements and vary depending upon your situation. Examples are working capital and cash dividend requirements. Or the agreement may contain routine (uniform) provisions that are employed in most agreements and are applied universally. Examples are the payment of taxes and the maintenance of proper insurance to ensure maximum lender protection. Lastly, you may encounter specific provisions that are tailored to a particular situation. Examples are the placing of limits on future loans and the carrying of adequate life insurance for executives. The advantages of intermediate-term loans include the following: 1. Intermediate-term loans provide flexibility in that the term may be altered as your financing requirements change. 2. Financial information is kept confidential, since no public issuance is involved. 3. The loan may be arranged quickly, relative to a public offering. 4. These loans avoid the possible nonrenewal of a short-term loan. 5. Public flotation costs are not involved. The disadvantages of intermediate-term loans are as follows: 1. Collateral and possible restrictive convenants are required, in contrast to commercial paper and unsecured short-term bank loans. 2. Budgets and financial statements may have to be submitted periodically to the lender. 3. “Kickers” or “sweeteners,” such as stock warrants or a share of the profits, are sometimes requested by the bank.
.2 USING REVOLVING CREDIT Revolving credit. There are typically fewer restrictions on revolving credit but at the cost of a slightly higher interest rate. and the lessee. An advance is made against the market value of the equipment. A conditional sales contract is generally used if you are a small company with a low credit rating. 17. You may take out an insurance company loan when you desire a longer maturity range. Also considered is the cost of selling the equipment. Maintenance and service are provided by the lessor. The lessor may be the manufacturer of the asset or it may be a leasing company that buys assets from the manufacturer to lease to others.3 INSURANCE COMPANY TERM LOANS Insurance companies and other institutional lenders may extend intermediate-term loans. Insurance companies typically accept loan maturity dates exceeding 5 years. who uses it in exchange for making rental payments. may have a 3-year maturity. Equipment financing may be obtained from banks. The advantages of revolving credit are flexibility and ready availability. The following types of leases exist: • Operating (service) lease — This type of lease includes both financing and maintenance services. 17.4 FINANCING WITH EQUIPMENT Equipment may serve as collateral for a loan. the seller keeps title to the equipment until the buyer has satisfied the terms. but usually there is a payment penalty. A chattel mortgage serves as a lien on property excluding real estate. usually used for seasonal financing.Looking at Term Loans and Leasing 207 17. In a conditional sales contract. 17. The buyer makes periodic payments to the seller over a specified time period. You lease property owned by the lessor. usually 90 days. Insurance companies do not require compensating balances. and manufacturers of equipment. you may renew a loan or enter into additional financing up to a maximum amount. The repayment schedule is designed so that the market value of the equipment at any given time is in excess of the unpaid loan principal. but the notes evidencing revolving credit are short. the higher the advance will be.5 LEASING The parties in a lease are the lessor who legally owns the property. The more marketable the equipment. but their rate of interest is often higher than that of bank loans. which is typically not the case with a bank loan. otherwise. the seller will repossess the equipment. finance companies. Within the time period of the revolving credit. The lease payments under the contract are typically not adequate to recover the full cost of the property. Equipment loans may be secured by a chattel mortgage or a conditional sales contract.
The property is then leased to you. a third party serves as the lender. and the rental payments equal the full price of the leased property. the maximum claim of lessors is 3 years of lease payments. • Typically. • Typically. . allowing you to obtain the property at a bargain price at the expiration of the lease. including the following: • In the long run. Here. The life of the contract approximates the life of the property. creditors have a claim for the total amount of the unpaid financing.g. • The interest cost of leasing is typically higher than the interest cost on debt. You may want to determine the periodic payment required on a lease. • Leasing allows you. in effect. a purchase option exists. • In bankruptcy or reorganization. This allows you to obtain cash from the sale and still have the property for use.208 Accounting and Finance for the Nonfinancial Executive and related costs are included in the lease payments. the cost is higher than if the asset is bought. to depreciate land. There are several drawbacks to leasing. limitations on dividends) are placed by the lessor than are imposed when obtaining a loan to purchase the asset. the salvage value of the property is realized by the lessor. With debt. you sell an asset to another (usually a financial institution) and then lease it back. including the following: • Immediate cash outlay is not required. The life of the contract is less than the economic life of the property. • The lessor’s expert service is made available.e.. Leasing has several advantages. • Leveraged lease — In a leveraged lease. • Sale and leaseback — With this lease arrangement. • The obligation for future rental payment does not have to be reported on the balance sheet if the lease is considered an operating lease. • If the property reverts to the lessor at termination of the lease. which provides you with the right to cancel the contract and return the property prior to the expiration date of the agreement. you must either sign a new lease or buy the property at higher current prices. obsolete equipment). • You cannot make improvements to the leased property without the permission of the lessor. which is not allowed if land is purchased. There usually exists a cancellation clause. fewer financing restrictions (e. This provides the flexibility to make the purchase decision based on the value of the property at the termination date. • Financial Lease — This type of lease does not typically provide for maintenance services.. the lessor borrows money from the lender to buy the asset. is noncancelable. • You may have to retain property no longer needed (i. Also.
Example 17.3 — You enter into a lease for a $100. The periodic payment is computed as follows: Year 0 1–9 Factor 1.= $16.= $19.0 4.000 for 11 years.= 7.5638 Present value factor .946 5.4 — Use the same facts as those for Example 17.000 --------------------.818 5.946 $100. The capitalized value of the lease is $140.000 Going to the present value of annuity table (T4) and looking across the 11-years entry to a factor nearest to 7. i = 14% = 5. we find 7.4987 at a 7% interest rate. Divide the value of the leased property by the annual payment to obtain the factor. The periodic payment equals $100. The capitalization rate is 12%.171 5. Thus. except that the annual payments are to be made at the beginning of each year. the interest rate in the lease agreement is 7%.946 The interest rate associated with a lease agreement can also be computed.163 1 + 4.= $25. The capitalized value of a lease can be found by dividing the annual lease payment by an appropriate present value of annuity factor.000 --------------------.000. 10 years) = the present value of an ordinary annuity factor for n = 10. The interest rate on the lease is 14%.000 --------------------.3.000 machine.2161 where T4(14%.Looking at Term Loans and Leasing 209 Example 17. You are to make 10 equal annual payments at year-end. Example 17.5.6 — Property is to be leased for 8 years at an annual rental payment of $140.5 — You leased $300.000 Annual lease payment ---------------------------------------------------.= ------------------------. which is then used to find the interest rate with the help of an annuity table. payable at the beginning of each year. Example 17.5 $40.000 of property and are to make equal annual payments at year-end of $40. The interest rate associated with the lease agreement is $300.2161 (Table 11.4).
7 CONCLUSION This chapter discussed intermediate-term loans.6 LEASE-PURCHASE DECISION Often you must decide whether it is better to buy an asset or to lease it. and equipment financing. . insurance company term loans. Present value analysis may be used to determine the cheapest alternative (see Chapter 12). revolving credit. 17. Intermediate-term loans include bank loans.210 Accounting and Finance for the Nonfinancial Executive 17. primarily from banks and leasing arrangements to meet your financing needs.
The distribution channels for a new security issue appear in Figure 18.1 shows the general picture with financing assets through debt and equity. 18. A syndicate is a temporary association of investment bankers brought together for the purpose of selling new securities. Investment bankers conduct the following activities: 1. and common stock are presented.18 Deciding on Long-Term Financing This chapter will provide you with a deeper understanding of the financing of your company. 3. One investment banker among the group will be selected to manage the syndicate (originating house) and to underwrite the major amount of the issue. the role of the investment banker is considered.. but the terms and features of the issue are set by you. First. a comparison of public vs. You will also learn what financing strategy is most appropriate. Equity financing consists of issuing preferred stock and common stock. When several investment bankers form a group because a particular issue is large and/or risky. 211 . The investment banker is knowledgeable about the alternative sources of long-term funds. 4. preferred stock. private placement of securities is provided. and markets the securities. and Securities and Exchange Commission (SEC) regulations. pays the issuer. debt and equity markets. You will learn the fundamentals of equity and long-term debt financing. given a particular set of circumstances. Underwriting — The investment banker buys a new security issue. for your company.g. Further. The underwriter’s compensation is the difference between the price at which the securities are sold to the public and the price paid to the issuing company.2. The advantages and disadvantages of issuing long-term debt.1 INVESTMENT BANKING Investment banking involves the sale of a security issue. as well. Providing funds — The investment banker provides funds to you during the distribution period. they are termed a syndicate. One bid price for the issue is made on behalf of the group. Figure 18. plant) or construction projects. Distributing — The investment banker markets your security issue. land. Advising — The investment banker gives you advice regarding the optimal way to obtain funds. Long-term financing is often used to finance long-lived assets (e. Long-term debt financing consists primarily of issuing bonds. 2.
Whether to issue securities publicly or privately will depend on the type and amount of financing your company requires. • It avoids the disclosure of information to the public. . and commercial banks. In a public issuance. you issue securities directly to either one or a few large investors. the investment banker agrees to sell your securities on a best-efforts basis. The broker is compensated with a commission on each sale. A dealer buys securities and holds them in inventory for subsequent sale. 18. expressed as a percentage of gross proceeds. • It avoids SEC filing requirements. is higher for smaller issues than for larger ones. expecting a profit on the spread.212 Accounting and Finance for the Nonfinancial Executive Balance Sheet Current liabilities Long-term debt Assets Stockholders’ equity Preferred stock Common stock Retained earnings Debt capital Equity capital Total capital FIGURE 18. A broker receives and forwards purchase orders for securities to the applicable stock exchange or over-the-counter market. Besides investment bankers. the investment banker does not act as underwriter but instead sells the stock and receives a sales commission. • There is less time involved in obtaining funds.2 PUBLICLY AND PRIVATELY PLACED SECURITIES Equity and debt securities may be issued either publicly or privately. the shares are bought by the general public. pension plans. Private placement has the following advantages relative to a public issuance: • The flotation cost is less. Here. there are firms that specialize in specific financial functions with respect to stock. Flotation cost is the expense of registering and selling the stock issue. Flotation cost. Examples are brokerage commissions and underwriting fees. An investment banker may insist on this type of arrangement when he or she has reservations about the success of the security offering. The flotation cost for common stock exceeds that for preferred stock. The spread is the price appreciation of the securities. In a private placement.1 Financing assets through debt and equity. The large investors are financial institutions such as insurance companies. In another approach to investment banking. or as an agent.
repayment of debt.3 GOING PUBLIC — ABOUT AN INITIAL PUBLIC OFFERING (IPO) Going public.g. investors may not be interested in purchasing securities when the money supply is low. 18.Deciding on Long-Term Financing 213 Corporate Issuer of Securities Underwriting Syndicate Investment Banker Investment Banker Originating Investment Banker Investment Banker Investment Banker Selling Groups Investors FIGURE 18. • Your credit rating may be low. often called an initial public offering (IPO). • Large institutional investors may watch the company’s activities more closely than smaller investors in a public issuance. New York Stock Exchange) or the over-the-counter market for the first time.. requiring the company to be in a strong financial position. acquisitions.2 Distribution channels for a new security issue. It often is the springboard for greater growth and success. • It may not be practical to issue securities in the public market if you are so small that an investment banker would not find it profitable. and . and. refers to selling formerly privately held shares to new investors on an organized exchange (e. diversification. • Large institutional investors are more capable of obtaining voting control of the company. There are the advantages and disadvantages of raising capital through a public offering. going public marks a historic moment. working capital. • Large investors typically use stringent credit standards. The market for stocks of companies that are going public is called the new issue market. as a result. The public sale of ownership interests can generate funds for business expansion. Private placement has the following drawbacks relative to a public issuance: • It is more difficult to obtain significant amounts of money privately than publicly. For the individual company. marketing.
purchases the stock from the company (the issuer) at a discount from the public offering price. the underwriter and any dealers will collect indications of interest from their investors as to how many shares each would like to purchase.3. either singly or as part of a group (syndicate). 18. Investors can benefit from an IPO not only because of the potential increase in market value for their stock. its owners usually have most of their wealth tied up in the company. Creation of a syndicate pools the risk for underwriters and widens distribution channels for the new issue.2 THE PROS OF GOING PUBLIC • Going public raises money — if it is common stock. The underwriter or syndicate then sells the shares to the public through brokerage firms and other institutions. companies can easily go back to the public market to raise more money. Once public. the offering was not an IPO. a common stock offering may be necessary.14 billion by issuing new common stock. Since the shares sold were newly created. but also because publicly-held stock is more liquid and can be readily sold if the business appears to falter or if the investor needs quick cash. The availability of a public market for shares will also help determine the taxable values of the shares and assist in estate transfers. implying the demand for shares is larger than the number of shares to be issued. The laws of demand and supply take over. This will vary widely by industry.” For example. After the underwriter issues the shares. In addition. To estimate the demand. the underwriters determine who will get the shares at the public offering price. thereby escalating the demand and value for shares. Most of the players in the IPO market are fund managers from big institutions. the shares begin trading on the open market. GM’s issue was defined as a primary market offering. one third of all IPO issuers return to the public market within five years to issue a “seasoned equity offering. Estimating the demand for the new stock issue is as much art as science. For example. its shares. Often. in 1995 General Motors raised $1. a company could have an IPO price of $15 per share. a successful IPO increases the visibility and appeal of your company. • As a company expands and becomes more valuable. if a firm needs more money than can be generated from retained earnings. Firms generally prefer to obtain equity by retained earnings because of the flotation costs and market pressure involved with the sale of new common stock. but offerings of $100 million are not unusual. but since the firm was already publicly held. and demand for.1 HOW DOES GOING PUBLIC WORK? A company considering going public will typically work with an underwriter (an investment bank) who. The typical IPO raises $20 – 40 million. The underwriter advises the company on the marketability of. The price of IPO shares can increase or decrease substantially in a short time. it does not have to be repaid. Typically. In the case of oversubscription.3. However.214 Accounting and Finance for the Nonfinancial Executive other uses. with the first trade in the open market executed at $80. By selling some of their . some IPOs may be oversubscribed. 18.
bug fixes. directors. The suppliers’ and consumers’ perception of company success is a self-fulfilling prophecy. public firms are usually bigger to begin with. Being public makes it much easier for other firms to notice and analyze the company for synergy. and this may explain why public firms have a better image. Going public will not increase its sales. transactions between the company and its management. without depleting cash reserves. • In addition to the time and effort required to prepare for the filing and offering. Mergers and acquisitions — many private companies do not just appear on the “radar screen” of potential acquirers. are not placed on the stock. and certain shareholders. Publicly traded stock can make a business more attractive to prospective and existing employees if stock option and other stock compensation plans are offered. and other public disclosure documents.3 THE CONS GOING PUBLIC • Much jealously guarded information must be disclosed. The guarded items include management salaries. a company must be prepared to incur the cost of going public. data about major customers. public companies must be prepared to disclose information about the company. The information is required in the initial registration statement and updated annually through annual reports. By releasing the information it will become available to competitors.3. etc. and related party transactions. pending litigation. and the general public. officers. salaries and other compensation of officers and directors. The company’s IPO filings are with the Securities and Exchange Commission (on the Internet. competitive position. and the identity of significant customers and suppliers. competitive position. Employee stock-based programs are worth more if transfer restrictions. For example. Public firms have higher profiles than private firms. The important question is if going public improves the company’s stockholders’ perception of success. software requires training and no manager wants to buy software from a firm that may not be around for future improvements.sec. such as those normally accompanying private company stock. Other financing alternatives may improve. customers. This is important in industries where success requires suppliers and consumers to make longterm investments.Deciding on Long-Term Financing 215 • • • • • • stock in a public offering. on average. In addition to the required disclosure of results of operations and financial condition. they can reduce the riskiness of their personal portfolios through this diversification of their holdings. OF 18. The use of proceeds from the sale of the issue is generally unrestricted.gov). However. This information might include company sales and profits by product line. http://www. Public companies can acquire other businesses with stock. upgrades. employees. proxies. legal and . Management often experiences an increase in prestige and reputation. The principal costs include the underwriter’s compensation.
There are other out-of-pocket expenses. greater earnings must be achieved to avoid reducing earnings per share. principals must remember that there is no guarantee that the offering will be a success. In practice. and reviewing stock activity. entrepreneurially oriented company to a professionally managed one where ownership and management are divorced. excluding underwriter’s commissions. but this can vary from 1 to 88%. A company expecting to go public with a high-quality offering should anticipate spending approximately $200. printing charges. with 20 to 60% being the comfortable norm. After a typical IPO. Since the number of shares outstanding increases when the company goes public. Furthermore. This act protects the disclosure of firm projections and forces the suing shareholders to have substantial participation in the firm. and transfer agent and filing fees. Any decision. public relations efforts and legal. many problems may result: management is usually personally blamed. public relations.000 annually. the flexibility of issuing stock to make acquisitions may be hampered. . and the time of the personnel hired to handle these functions. if the decline occurs soon after the offering. With the exception of underwriter’s compensation. Congress passed The Private Securities Litigation Reform Act of 1995. Shareholder meetings.216 Accounting and Finance for the Nonfinancial Executive • • • • • accounting fees. The total cost of these expenses vary from company to company. All of this time. Although nothing can eliminate lawsuits. this act reduces the likelihood of successful suits and therefore encourages settlement terms. long-term or short-term. If the company is sitting on a gold mine. public disclosures. annual and quarterly reports. If the market price declines. The company may worry constantly about improving quarterly earnings (and stock prices) instead of trying to take a longer perspective in developing its strategy. but in most cases they range from $50. litigation against everyone involved may take place. Management must devote time and money to such new areas as shareholder relations. future earnings have to be shared with outsiders.000. may be manifested promptly in the company’s stock price. All IPO participants in the coalition are jointly liable for each others’ actions. Other costs associated with being a public company are ongoing. about 40% of the company remains with insiders. would be spent on other management tasks in a privately held company. and other financing alternatives may evaporate. the costs are incurred regardless of the outcome. The cost of going public does not stop with the initial offering. periodic filings with the SEC. The magnitude of these costs usually make public offerings grossing less than $5 million impractical. and auditing fees must be paid. In response. Corporate decision making becomes more cumbersome as the company attempts to move from a tightly controlled. accounting.000 to $150. they were routinely sued for various omissions in the IPO prospectus when the public market valuation fell below the IPO offering price.
counsel. It is good to hire a “Big Five” or nationally prominent accounting firm because it enhances marketability and confidence. Of course. There is pressure on the managers to produce annual earnings gains. an IPO also means a dilution of the existing shareholders’ interests. but by the classification of . evidence of indebtedness. bonds. accountant.3. These factors have led a number of newly public firms to go private in leveraged buyout deals where the managers borrow the money to buy out the nonmanagement stockholders. Offering your business’s ownership for public sale does little good unless your company has sufficient investor awareness and appeal to make the IPO worthwhile. personalities and confidence should be considered.000). • An underwriter appropriate for one company or one industry may be inappropriate for another. That carries a message. In addition to technical ability. Under federal law. • When choosing an underwriter. • Assemble the proper team. Require businesses to disclose material information about the company to investors. coupled with absolute liability for the company for material misstatements or omissions — regardless of good faith or motive. • The registration process is complex. There is a very high cost and much complexity in complying with federal and state laws governing the sale of business securities (the cost for a small business can run from $50.000 to $500. • The selection of accountants and lawyers needs careful examination. 2. The use of a large accounting and legal firm may be viewed by the underwriter as insurance in the event of litigation. Management must be ready to handle the administrative and legal demands of widespread public ownership. and 3. This involves selecting an underwriter. and perhaps some new directors. distribution capacity is important. The use of IPOs is limited primarily because: 1.Deciding on Long-Term Financing 217 • Outsiders can take control and even fire the entrepreneur. and the possibility of takeovers or adjustments in management control are present. 18. and most ownership interests.4 HOW TO AVOID THE DRAWBACKS OF GOING PUBLIC Here are some tips for avoiding the pitfalls of going public. even when it may be in the shareholders’ best long-term interests to adopt a strategy that reduces short-term earnings but raises them in the future years. and 2. It is important to remember that malpractice insurance in the securities field is the most expensive of any specialty. Prohibit misrepresentation and fraud in the sale of securities. • Securities laws are complicated. The sale of “securities” to the public is regulated by federal and state laws that have two primary objectives: 1. notes. a “security” is broadly defined and would include stocks. The law defines a “public offering” of a security not by the number of investors to whom the stock is offered.
The chief underwriter is responsible for ensuring smooth trading during the first . the offering size and/or price can be raised from initial projections. San Francisco. Several “to do’s” include developing a business plan and preparing detailed financial results on a regular basis. Once the offering price has been agreed to. Sometimes. The pricing of an IPO is a delicate balancing act. also known as the road show. In the meantime. an IPO is declared effective. international destinations such as London and Hong Kong are included. and Chicago. which wants to raise as much money as possible. a company even has to postpone an offering due to insufficient demand. The typical stops generally include the larger cities such as Los Angeles. Once a company decides to go public. Once the road show ends and the final prospectus is distributed to investors.5 WHAT IS THE PROCESS OF GOING PUBLIC? A company that is thinking of going public should start acting like a public company as much as two years in advance. The most important and time-consuming task facing the IPO team is the development of the prospectus. it needs to choose its IPO team. 18. with the trading of the new stock beginning the next day. all members of the IPO team assign certain duties to each individual and plan a timetable for going public. However. The management team’s performance on the road show is crucial. the prospectus will have to do most of the talking and selling for the team. and the underwriting team goes to great efforts to make sure that it is all accurate. who expect to see immediate gains for their money. which is a business document that basically serves as a brochure for the company. There is much more information in the prospectus. Investment banks generally suggest an appropriate price based on expected demand for the deal and other market conditions. competitors. management officials meet with their investment bank to decide on the final offering size and price. Investment firms have to be concerned with two different sets of customers: the company going public. If a deal is especially hot. state law definitions of a “security” and of a “public offering” can vary from the federal law. The team has to impress institutional investors and influence them to make significant long-term investments. and the investors buying the shares of stock. Since the SEC requires a “quiet period” on firms once they file an IPO until 25 days after a stock starts trading. It helps determine the success of the IPO. etc. with company management going to a new city every day to meet with prospective investors and show off their business plan. consisting of a lead investment bank. This meeting usually takes place six to eight weeks before a company officially registers with the SEC. This is generally done after a market closes. The road show usually lasts a week. At this meeting. the chief underwriter works to confirm its buy orders. If public interest appears to be slowing. accountant. If necessary.218 Accounting and Finance for the Nonfinancial Executive whether the investors are considered “sophisticated” or not. Boston. lawyer. and growth strategy. it is common for the offering price and number of shares to decrease from expected ranges.3. The IPO process officially begins with an “all hands” meeting. It also includes information on the management team and a description of a company’s target market. The prospectus includes all financial data of the company for the past five years. The next step in the IPO process is the grueling worldwide tour.
He can also impose penalty bids on brokers to discourage “flipping. These alternative offerings allow the business to tailor the amount of immediate equity (ownership and control) that it relinquishes. accountant. it is not always clear where the exemptions end. Employing professionals (attorney. The investor should be provided with sufficient information to make an informed decision regarding the investment. While many small businesses sell interests in their companies that are “securities. so you should always consult a knowledgeable attorney before selling any stock in your company. The process of soliciting money from the public through the issuance and sale of securities requires a working knowledge of the state and federal registration statements concerning the securities to be sold. and sometimes a stock underwriter) to assist in the process is a practical necessity. . Even if a securities offer is exempt from the registration requirements of federal or state law. Most startups and smaller businesses would fall within this exemption. 18. an IPO can be cancelled even after the stock begins trading. However. you must fit the criteria for both federal and state security laws.” which is when investors sell shares of an IPO soon after the stock starts trading. you must take care to prevent misrepresentations or omissions in the offering that create an overly optimistic picture of the investment. Federal exemptions — At the federal level. including advertisements and seminars. Solicitations of investors by a private business may be made through almost any means. and they are restricted to a limited number and/or type of investor. An IPO is not declared final until seven days after the firm’s initial market appearance. On rare occasions. and financial statements.” Under this provision. These exempt offers of securities are called “limited private offerings” and they can avoid much of the cost and delay of a public offering.6 ALTERNATIVES TO GOING PUBLIC Many businesses can sell stock to insiders or to a small group of investors without being subject to securities laws. discussion of the use of limited private offerings is largely confined to equity financing. the anti-fraud provisions of those laws may still apply. For instance. the most popular exemption from registration requirements for small businesses is Rule 504. and the amount of debt (cash outflow) that it can safely assume. In this module. the transactions are often exempt from registration regulations because the offerings are sufficiently small in dollar amount. Limited private offerings can be either debt or equity instruments. Therefore. or a hybrid of both. to qualify for any of the exemptions. and no specific disclosure requirements regarding the stock or the company are required. complex disclosure documents about the company with detailed information for potential investors. This underwriter is legally allowed to support the price of a newly issued stock through buying shares in the market or selling them short. commonly known as “Regulation D. they can take advantage of alternatives to going public.3.Deciding on Long-Term Financing 219 crucial days.” as defined by federal or state laws. Unfortunately. a convertible debt warrant would be a debt instrument that allows the holder to convert the debt into an equity interest at a certain time. private companies that are selling less than $1 million worth of securities to any number of investors within a 12-month period are exempt from federal registration requirements. in effect.
Three bottom-line suggestions: .g. if the sales are made only to “accredited investors” and no more than 35 such investors are involved.org. an exemption exists for private offerings of stock that are sold only to persons living in the same state where the company is both incorporated and does significant business. Venture capital (VC) firms speculate on certain high-risk businesses producing a very high rate of return in a very short time. officers and directors). or the issuer reasonably believes the investors have these qualifications).4 VENTURE CAPITAL FINANCING Venture capital firms supply funding from private sources for investing in select companies that have a high. insurance companies). The result is that consultation with a qualified professional is a practical necessity before soliciting investors for sales of securities. that Act has not been adopted by each state nor is it consistently interpreted in those states which claim to follow it. Just because a sale may be exempt from federal registration does not mean state registration is not required. When dealing with venture capital firms. A lesser degree of exemption from regulation exists for a private or publicly held company that sells an unlimited issuance of securities to an unlimited number of accredited investors. Accredited investors include institutional investors (e. Venture capital firms have a reputation for negotiating tough financing terms and setting high demands on target companies. Finally. or at http://www. or to no more than 35 nonaccredited but “sophisticated investors” (sophisticated investors have sufficient knowledge and experience so that they understand the risks of the sale.” The state laws need not match the federal regulatory exemptions and even though a Uniform Securities Act exists for states to follow..g. 18. Forty-seven states currently have relaxed their securities regulations for small business by offering a Small Company Offering Registration (SCOR) procedure. company insiders (e. Even if your business is not based in one of these states.. have a net worth of over $1 million). contact the North American Securities Administrators Association at 202-737-0900. you may still register and sell your securities in these states which have adopted SCOR. State securities laws are commonly referred to as “blue sky” laws because the regulations were originally enacted to prevent unscrupulous issuers from selling “speculative schemes that have no more basis than so many feet of blue sky. individually or jointly with their spouse.220 Accounting and Finance for the Nonfinancial Executive Another exemption may be available to either private or publicly held companies that sell less than $5 million within a 12-month period. the local exemptions must be checked. brokers and dealers. State exemptions — Because each state has securities regulations. rapid growth potential and a need for large amounts of capital. For a current list of eligible states. keep in mind that they are under great pressure to identify and exploit fast-growth opportunities before more conventional financing alternatives become available to the target companies.000 individual annual income or. The firms typically invest for periods of 3 to 7 years and expect at least a 20 to 40% annual return on their investment. and wealthy investors (“wealthy” meaning they have more than $200.nasaa. although reliance upon this intrastate exemption is subject to continual policing because the securities must remain within the state. banks.
venture capital firms favor existing businesses that have a minimal operating history of several years. for better or worse. 1655 N. Ownership demands for an equity interest in 30 to 50% of the company are not uncommon even for established businesses. and a startup or higher risk venture could easily require transfer of a greater interest. The price of financing through venture capital firms is high. Even if you already have intellectual property protection (e. venture capital firms invested in less than 2000 companies. An arrangement that eventually calls for an initial public offering is also possible. In addition. such as a company with extremely experienced management and a very marketable product or service... in the major decisions affecting the direction of the company. Venture capital financing may not be available. • Watch for delay maneuvers (they may be waiting for your financial position to weaken further).g. although the ultimate investment decision is often influenced by the market speculations of the particular venture capitalists. (703-351-5269). and a directory is available for $25 through the National Association of Venture Capital. Venture capital firms are located nationwide. The target companies often have revenues in excess of $2 million and a preexisting capital investment of at least $1 million. Arlington. Be wary of “shopping” innovative ideas to multiple venture capitalists or private investors. they offer tremendous potential for obtaining a very large amount of equity financing and they usually provide qualified business advice in addition to capital. or copyright).Deciding on Long-Term Financing 221 • Make sure to read the fine print. . it will usually want at least one seat on the target company’s board of directors and involvement. for many businesses. Despite the high costs of financing through venture capital companies. • Guard your trade secrets and other proprietary information zealously. trademark. Due to the amount of money that venture capital firms spend in examining and researching businesses before they invest. VCs research target companies and markets more vigorously than conventional lenders. Do your best to limit the details of your particular innovation and seek confidentiality arrangements for additional protection of any preexisting legal rights you may have. they will usually want to invest at least a quarter of a million dollars to justify their costs. and business associations. nor a good choice of financing. In 1995. a patent. Fort Meyer Dr. financing of startups is limited to situations where the high risk is tempered by special circumstances. VA 22209. you do not want to be forced to police your rights. Usually. Although the investing company will not typically get involved in the ongoing management of the company. insurance companies. Use caution in revealing any information you consider proprietary. other sources for venture capital can be found through bankers. The ownership interest of the VC firm is usually a straight equity interest or an ownership option in the target company through either a convertible debt (where the debt holder has the option to convert the loan instrument into stock of the borrower) or a debt with warrants to a straight equity investment (where the warrant holder has the right to buy shares of common stock at a fixed price within a specified time period).
or another financial institution. 18. Mortgages can be issued to finance the purchase assets. The trustee makes sure that you meet the terms of the bond contract. and restrictions). 18.g. called an indenture. a company. describes the features of the bond issue (e.5 TYPES OF LONG-TERM DEBT AND THEIR USEFULNESS All companies incur debt. the bondholder. Mortgages have a number of advantages. It is easier to obtain loans for multiple-use real assets than for single-use real assets. Although the trustee is an agent for the bondholder. If the mortgage is open-ended. extended maturity dates for loan repayment. which precludes the issuance of new debt taking priority over existing debt in the event of liquidation.. Many bonds have maturities of 10 to 30 years. you will need to know the characteristics.2 BONDS Long-term debt principally takes the form of bonds payable and loans payable.1 Computing Interest Bonds usually come in $1. To determine which instrument will serve your company’s needs best.5. the amount of debt will largely depend on the company’s available collateral. which has a subordinate lien. advantages.5. and disadvantages of these longterm debt sources. For long-term debt financing. Either instrument may be appropriate. A bond is a certificate indicating that you have borrowed a given sum of money and agree to repay it. you can issue additional first-mortgage bonds against the property. The clause can apply to assets currently held as well as to assets that may be purchased in the future. the bonds are in default.000 denominations. Mortgages may be obtained from a bank. The indenture is a contract between your company. depending on a company’s circumstances. and a junior mortgage. and modernization of facilities. The interest payment to the bondholder is called nominal interest (coupon . payment dates. A written agreement. it is selected by your company prior to the issuance of the bonds.2. In many instances.222 Accounting and Finance for the Nonfinancial Executive 18. If a provision of the indenture is violated. The bank requires that the value of the property exceed its mortgage. Most mortgage loans are made for 70 to 90% on the collateral. A mortgage may have a closed-end provision that prevents you from issuing additional debt of the same priority against the same property. The indenture may also have a negative pledge clause. sources include mortgages and bonds. 18. construction of plant. which has first claim on assets and earnings.1 MORTGAGES Mortgages are notes payable that have real assets as collateral and request periodic payments. and the trustee. There are two types of mortgages: a senior mortgage. and relatively easy availability. The indenture provides for certain restrictions on you such as a limitation on dividends and minimum working capital requirements. the trustee is the trust department of a commercial bank. call and conversion privileges [if any].5. including favorable interest rates. fewer financing restrictions.
The amount of the discount is $6. financially strong companies with excellent credit ratings. Although the interest rate is stated on an annual basis. stated interest). Mortgage bonds — These are bonds secured by real assets. they can be issued only by large. The yield on a bond is the effective (real) interest rate you incur.000. Example 18.640 ($4. With a 34% tax rate. Why would your company’s bond be sold at a discount or a premium? A bond may be sold at a discount when the interest rate on the bond is below the prevailing market interest rate for that type of security. The semiannual interest payment is $4. Bond prices and market interest rates are inversely related. Typically.000/20). It may also be issued at a discount if your company is risky.9% (15% × 66%). The annual cash interest payment is $14. The annual discount amortization is $300 ($6. and collateral. 3. If a bond is sold above face value (more than 100%). A bond sold at face value is said to be sold at 100%. A bond is issued at a premium when the opposite market conditions exist.3 — You issue a $100.000.Deciding on Long-Term Financing 223 interest.000 × 8% × 6/12). The two methods of computing yield are the simple yield and the yield-to-maturity. The first mortgage claim must be met before a distribution is made to a second . 2.000 (14% × $100.000).2. For example.2 — You issue a $100. 8%. Debentures — Because debentures are unsecured (no collateral) debt.000 ($100.000. par) of the bond. If a bond is sold below its face value (less than 100%). 14%. 10-year bond. 10-year bond.000 ($100.000).000 ($100. as market interest rates increase.000 × 94%). the after-tax semiannual interest is $2.5.000 – $94. 20-year bond at 94%. in liquidation. The annual after-tax cost of the debt is 9. Debt with a prior claim over the subordinated debentures is set forth in the bond indenture. The proceeds received for the issuance of the bond equal $94. it is issued at a discount. which is the interest on the face value (maturity value. the price of the existing bond falls because investors can invest in new bonds paying higher interest rates.000 × 66%).2 Types of Bonds The various types of bonds your company may issue are as follows: 1.1 — You issue a 15%. 18. or there is a very long maturity period. subordinated debentures come after short-term debt. interest rate. The tax rate is 34%. The maturity value of the bond is $100. Example 18. The price of a bond depends on several factors such as maturity date. Subordinated debentures — The claims of the holders of these bonds are subordinated to those of senior creditors. Interest expense is tax-deductible. it is sold at a premium. Example 18. interest on a bond is typically paid semiannually.
Collateral trust bonds — The collateral for these bonds is your company’s security investments in other companies (bonds or stocks). if bonds are converted to stock. The interest rate on the shorter maturities is lower than the interest rate on the longer maturities because less uncertainty exists regarding the future. 9. which are given to a trustee for safekeeping. Zero coupon bonds — These bonds do not provide for interest. 10. An inverse relationship exists between the quality of a bond issue and its yield.1.3 Bond Ratings Financial advisory services (e. Bond ratings are important because they influence market ability and the cost associated with the bond issue. However. 11.g. There may be several mortgages for the same property (e. Convertible bonds are more marketable and are typically issued at a lower interest rate than regular bonds because they offer the conversion right to common stock.. Convertible bonds — These may be converted to stock at a later date. debt repayment is not involved. The return to the holder comes primarily from appreciation in price rather than from interest payments. if bypassed. interest rates. 5. because it accumulates regardless of earnings. Convertible bonds are typically issued in the form of subordinated debentures. Income bonds — These bonds pay interest only if there is a profit. 7. Moody’s) rate publicly traded bonds according to risk in terms of the receipt of principal and interest. A convertible bond is a quasi-equity security because its market value is tied to the value of the shares of stock into which the bond can be converted. At the time serial bonds are issued. mortgage claim. the interest. and prices for each maturity. Variable-rate bonds — The interest rates on the bonds are adjusted periodically to changes in money market conditions..224 Accounting and Finance for the Nonfinancial Executive 4. a risk-return tradeoff exists for the bondholder. Serial bonds — A portion of these bonds comes due each year. 8. 18. Deep discount bonds — These bonds have very low interest rates and thus are issued at substantial discounts. The conversion ratio equals the par value of the convertible security divided by the conversion price. A summary of the characteristics and priority claims associated with bonds appears in Table 18.5.2.g. a schedule shows the yields. based on a specified conversion ratio. Hence. 6. must be paid in a later year when adequate earnings exist. That is. The return to the holder is in the form of appreciation in price. Of course. . Standard and Poor’s. lowquality bonds will have a higher yield than high-quality bonds. Guaranteed bonds — These are debt issued by one party with payment guaranteed by another. building). These bonds are popular when there is uncertainty about future interest rates and inflation.
1 Summary of Characteristics and Priority Claims of Bonds Bond Type Debentures Characteristics Available only to financially strong companies. Convertible bonds are typically debentures. General creditor Paid from the proceeds from the sale of the mortgaged assets. Coupon rate changes within limits based on changes in money or capital market rates. General creditor. Paid from the proceeds of stock and/or bond that is collateralized. general creditor status applies. Collateral value is usually 30% more than bond value.. Income bonds Deep-discount (and zero coupon) bonds Variable-rate bonds Interest is paid only if there is net income. Comes after senior debt holders. Collateral is real property or buildings. Issued at prices significantly below face value.5. A call provision allows your company to pay the debt before the expiration date of the bond. Issued at very low or no (zero) coupon rates.g. Interest is tax-deductible.3 THE ADVANTAGES AND DISADVANTAGES OF DEBT FINANCING You will need to determine whether or not your company should issue long-term debt. while dividends are not. Usually callable at par value. in times of tight money markets when short-term loans are not available. Appropriate when uncertainty exists regarding inflation and future interest rates. If any deficiency exists. 5. If there is a deficiency. 2. 18. Often issued when a company is in reorganization because of financial problems. The advantages of issuing long-term debt include the following: 1.) .Deciding on Long-Term Financing 225 TABLE 18. Priority of Lender’s Claim General creditor Subordinated debentures Mortgage bonds Collateral trust bonds Secured by stock and/or bonds owned by the issuer. general creditor status applies. Because of the automatic adjustment to changing market conditions. Financing flexibility can be achieved by including a call provision in the bond indenture. 6. 4. Unsecured or secured status may apply depending on the features of the issue. the bonds sell near face value. Bondholders do not participate in superior earnings of your firm. It may safeguard your company’s future financial stability (e. Unsecured or secured status may apply depending on the features of the issue. There is no dilution of company control. 3. The debt is repaid in cheaper dollars during inflation.
no dilution of voting control occurs. and stringent indenture restrictions often exist. Should you buy a bond? To investors. The interest rate on debt is less than the rate of return earned on the money borrowed. The debt/equity ratio is low so that the company can handle additional obligations. 4. 3. cyclical factors should not scare a company away from having any debt. However. credit availability. the payback will be in cheaper dollars. Where a high degree of debt already exists. 5. How does issuing debt stack up against equity securities to your company? The advantages of issuing debt rather than equity securities are as follows: interest is tax deductible.226 Accounting and Finance for the Nonfinancial Executive The following disadvantages may apply to issuing long-term debt: 1. Stockholders have made an extra profit with no extra investment! 2. When should long-term debt be issued? Debt financing is more appropriate at these times: 1. . bonds have the advantages of a fixed interest payment each year and of greater safety than equity securities because bondholders have a priority claim in the event of corporate bankruptcy. 4. 2. The important thing is to accumulate no more interest and principal repayment obligations than can reasonably be satisfied in bad times as well as good. bonds have the disadvantages of not participating in incremental earnings and of no voting rights. Debt must be repaid at maturity. Higher debt implies greater financial risk. To investors. There is a satisfactory profit margin so that earnings exist to meet debt obligations. Stability in revenue and earnings exists so that the company will be able to meet interest and principal payments in both good and bad years. 6. Interest charges must be met regardless of your company’s earnings. which may increase the cost of financing. Stock prices are currently depressed so that it does not pay to issue common stock at the present time. 5. 3. Indenture provisions may place stringent restrictions on your company. The proper mixture of long-term debt to equity depends on company organization. during inflation. Overcommitments may arise because of forecasting errors. and flexibility in financing can be achieved by including a call provision in the bond indenture. and the after-tax cost of financing. you should take steps to minimize other corporate risks. By using other people’s money (OPM). whereas dividends are not. the after-tax profit of the company will increase. There is a good liquidity and cash flow position. The disadvantages of debt incurrence relative to issuing equity securities are that fixed interest charges and principal repayment must be met irrespective of your firm’s cash flow position.
A bond with a call provision typically will be issued at an interest rate higher than one without the call provision.5.000 The desirability of refunding a bond requires present value analysis. Such a provision enables your firm to buy back the higher-interest bond and issue a lower-interest one. The call feature is included in many corporate bond issues. A call feature in a bond enables you to retire it before the expiration date. product risk) so that total corporate risk is controlled. When future interest rates are expected to drop.000 (100.g. The issuance of serial bonds allows you to refund the debt over the life of the issue. so will the interest rate to compensate for the greater risk. The investor prefers not to face a situation where your company can buy back the bond at its option prior to maturity. 18. by extending the maturity dates of existing loans).4 — A $100. 9. which was discussed in Chapter 12. The call premium is usually equal to one year’s interest if the bond is called in the first year. brokerage commissions and printing costs).Deciding on Long-Term Financing 227 7. A call price is typically set in excess of the face value of the bond.g. Three years after the issue.. the bond is called. try to reduce other risks (e.g. 10-year bond is issued at 94%. greater control might fall into the wrong hands. The resulting call premium equals the difference between the call price and the maturity value.. 8%. The call premium is equal to Call price Less: Face value of bond Call premium $103.4 BOND REFUNDING Bonds may be refunded before maturity through either the issuance of a serial bond or the exercise of a call privilege on a straight bond. Also involved in selling a new issue are flotation costs (e. Example 18. The investor would obviously desire to hold on to a high-interest bond when prevailing interest rates are low. a call provision is recommended. As the default risk of your company becomes higher. This may alleviate current liquidity and cash flow problems. Bond indenture restrictions are not burdensome.000. it may wish to refinance short-term debt on a long-term basis (e. Control considerations are a primary factor so that if common stock were issued. Tip — If your company is experiencing financial difficulties. Recommendation — When a high degree of debt (financial leverage) exists.000) $ 3. Inflation is expected so that debt can be paid back in cheaper dollars.. 8. and it declines at a constant rate each year thereafter. . The call price is 103%. Your company pays the premium to the bondholder in order to acquire the outstanding bonds prior to the maturity date. The timing for the refunding depends on expected future interest rates.
000 × 6. If preferred dividends are in arrears for a long time.10) Less: New interest payments ($20. Sinking fund requirements may exist in a bond issue.600.000 2.000) 400. Usually.000. along with the various circumstances in which one financing source is better suited than the other.000 × 0.000.000. With a sinking fund.000 a 6.000. but occasionally the retirement may relate to your company’s sales or profit for the current year.08) Annual savings Call premium ($20. they must be paid before dividends can be paid to common stockholders. there is a mandatory fixed amount that must be retired. 10 years) from Table 11. Flotation costs of the new issue are $600.000 × 0. Stock rights are also described. Refunding of the original bond issue should occur as shown below.000.4.228 Accounting and Finance for the Nonfinancial Executive Example 18.000 600. It is best to issue preferred stock when your company has excessive debt and an issue of common stock might result in control problems. The call premium is 7% of face value.6 EQUITY SECURITIES We will now discuss equity financing consisting of preferred stock and common stock.71a Net present value Present Value –$2.6.000 $2.400. With noncumulative preferred stock.1 PREFERRED STOCK Preferred stock is a hybrid between bonds and common stock. the bond issue may be in default. you put aside money to buy and retire part of a bond issue each year. 18. Cumulative preferred stock means that if any prior year’s dividend payments have been missed.000 $2. your company may find it difficult to resume its dividend payments to common stockholders.000. Old interest payments ($20.000. Preferred stock may be issued when the cost of common stock is high. . Preferred stock may be cumulative or noncumulative.07) Flotation cost Total cost Year 0 1–10 Calculation –$2. N 10-year bonds in the amount of $20 million can be issued at an 8% interest rate. Preferred stock is a more expensive way to raise capital than a bond issue because the dividend payment is not tax-deductible. 10% bond issue outstanding that has 10 years to maturity.000 (1.71 = T4 (8%.684. Preferred stock comes after debt but before common stock in liquidation and in the distribution of earnings.000.5 — Your company has a $20 million. If a sinking fund payment is not made.000 $ 684.000 × 1 $400. 18.000 × 0.000 1. The advantages and disadvantages of issuing preferred and common stock are addressed.
The flotation cost is 11% of gross proceeds. Nonparticipating preferred stock does not participate with common stock in excess dividends. Unlike bonds.000. The dividend rate is 14%.= -------------------------------------------------------------------------------Net proceeds $2.7% $1. Preferred stock may be callable.000 shares of $15 par value.000 -----------------------------. preferred stock rarely has a maturity date. The effective cost of the preferred stock is Dividend 0.000 ) $280. Assuming that your company was profitable in 2005.000. the cost of preferred stock will most likely be low when interest rates are low. the amount of the dividend to be distributed is: Par value of stock = 6.000 × 14%) Total dividend $25.7 — You issued preferred stock of $2 million.= 15. In such a case. The call provision is advantageous when interest rates decline.800 Participating preferred stock means that if declared dividends exceed the amount typically given to preferred stockholders and common stockholders. The cost of preferred stock usually follows changes in interest rates. this. Any asset balance then goes to the common stockholders.780. in effect. if preferred stock has a sinking fund associated with it.600 $37. which means that you can purchase it back at a subsequent date at a specified call price. preferred stockholders receive the par value of their shares.000 – ( 0. preferred stock issuance may be achieved at a lower cost. Preferred stock dividends are limited to the rate specified. Unless stated otherwise. Example 18.000 shares × $15 = $90. establishes a maturity date for repayment.200 12. 2005.14 × $2. the preferred and common stockholders will participate in the excess dividends.000 Dividends in arrears ($90.11 × $2. The cost of preferred stock can be determined by dividing the dividend payment by the net proceeds received.000 . However. your company had 6. dividends in arrears. which is based on the total par value of the outstanding shares. In bankruptcy.6 — As of December 31. and the current year’s dividend. the distribution of the excess dividends will be based on the relative total par values. Example 18.Deciding on Long-Term Financing 229 your company does not need to pay missed preferred dividends.000.000 × 14% × 2 years) Current year dividend ($90. Most preferred stock is cumulative.000 = -------------------------. preferred stockholders are paid after creditors and before common stockholders. since your company has the option of discontinuing payment of dividends at an excessive rate by buying back preferred stock issued when bond interest rates were high. Most preferred stock is nonparticipating. Hence. 14% cumulative preferred stock outstanding. When the cost of common stock is high. Dividends were not paid in 2003 and 2004.
only 20% (or $2. The owners of a corporation are called stockholders. 18. 3. preferred stock usually provides a fixed dividend payment. and no sinking fund is required. On the other hand. The advantages of preferred stock over bonds is that one can omit a dividend readily. For example. First. Unfortunately. a preferred stock issue has the following advantages: 1. 4. The debt to equity ratio is improved. Preferred stockholders cannot force your company into bankruptcy. 7. 3.000. the individual investor does not qualify for the 80% dividend exclusion.230 Accounting and Finance for the Nonfinancial Executive To your company. the return is limited because of the fixed dividend rate. If your company is growth oriented. if a company holds preferred stock in another company and receives dividends of $10. 2. Preferred stockholders do not share in unusually high profits because common stockholders are the real owners of the business. preferred dividends are subject to an 80% dividend exclusion for corporate investors. Preferred stock also has a number of advantages over common stock. who in . Second. no maturity date exists.000) is taxable. and dividends are not tax deductible. there is greater price fluctuation with preferred stock than with bonds because of the lack of a maturity date. Preferred dividends do not have to be paid (important during financial distress). Preferred dividends are not tax-deductible.6. Also. Third. preferred stockholders’ claims come before common stockholders’ in the event of corporate bankruptcy.2 COMMON STOCK FEATURES We will now discuss everything you should know about common stock. 6. For instance. Your company does not have to collateralize its assets as it may have to do if bonds are issued. To an investor. Preferred stock issuance does not dilute the ownership interest of common stockholders in terms of earnings participation and voting rights. They elect the board of directors. Disadvantages of preferred stock issuance compared to bonds are that it requires a higher yield than debt because it is riskier to the holder. To your company. It avoids dilution of control and the equal participation in profits that are afforded to common stockholders. a preferred stock has the following disadvantages: 1. Lastly. preferred stockholders cannot require the company to pay dividends if the firm has insufficient earnings. interest income on bonds is fully taxable. There are higher flotation costs than with bonds. 5. To an investor. preferred stock represents several disadvantages. Preferred stock requires a higher yield than bonds because of greater risk. a preferred stock offers several advantages. it can generate better earnings for its original owners by issuing preferred stock with a fixed dividend rate than by issuing common stock. 2. whereas interest on debt must be paid.
The right to receive assets upon the dissolution of the business. higher interest rates make it costly for a company to borrow. The right to vote. maturity dates. For example. 4. who keep full control. Voting rights are provided in order to maintain control. 5. The preemptive right to buy new shares of common stock before their sale to the general public. a stock option plan. resulting in lower profits and the subsequent decline in stock price. 3. Effective control of the corporation can exist with less than 50% common stock ownership since many stockholders do not bother to vote. The right to inspect the company’s books. if market interest rates increase. If your company is closely held. However. 2.Deciding on Long-Term Financing 231 turn choose the company’s officers. But a company with 500 or more stockholders must file an annual financial statement with the SEC. Outstanding shares are thus equal to the issued shares less the treasury shares. Dividends are based on the outstanding shares. When the election takes place. Issued shares represent the number of authorized shares that have been sold by the company. The right to receive dividends. but their claims come after preferred stockholders in receiving dividends and in liquidation. Common stock refers to the residual equity ownership in the business. management sends proxy statements. . use in purchasing another company. The price of common stock moves in the opposite direction of market interest rates. A company may issue different classes of common stock. Stockholders have limited liability in that they are not personally liable for the debts of the firm. Common stockholders have voting power. The stock certificate may then be sold by the holder to another in the secondary security market. There is no requirement to publicly disclose corporate financial data. Class A is stock issued to the public and typically has no dividends. which ask stockholders to give management the right to vote their stock. it usually has voting rights. Treasury stock is stock that has been reacquired by the firm. Common stockholders have the following rights: 1. Class B stock is typically kept by the company’s organizers. The receipt of a stock certificate that evidences ownership. stock prices fall because investors will transfer funds out of stock into higher yielding money market instruments and bank accounts. Common stock does not involve fixed charges. it only has a few stockholders. It is not retired but instead held for possible future resale. or the prevention of a takeover by an outside group. Further. Authorized shares are the maximum shares that can be issued according to the corporate charter. Outstanding shares are the issued shares held by the investing public. 6. Dividends are usually not paid on it until the company has generated adequate earnings. The par value of a stock is a stated amount of value per share specified in the corporate charter. current stockholders can maintain their proportionate percentage ownership in the company. or sinking fund requirements. In this way.
000.= $28. including the following: 1. Example 18. You want to compute the number of new shares that must be issued to raise the $3 million.= -------------------------.000 outstanding shares that are closely held. the expected price per share is: Market value $7.000 .. Issuances to relatives or friends. the number of shares that must be issued to provide the necessary funds to meet the capital budget is: Funds needed $1.= -------------------------. Assuming that new stock may be issued for $16 a share.g.000 shares After the stock issuance. A determination of the number of shares that must be issued to raise adequate funds to satisfy a capital budget may be needed.000 Price per share = -------------------------------------------.9 — Your company wants to raise $3 million in its first public issue of common stock. The new shares will have 3/7ths ($3 million/$7 million) of the outstanding shares after the stock issuance.8 — Your company currently has 650.= 112. A number of options exist for equity financing in the case of small businesses.800.g. Currently. 140. current stockholders will be holding 4/7ths of the shares. Thus. The stockholder typically receives notice of the offer directly from his or her broker or by an announcement in the financial pages of a newspaper (e.000 shares = 4/7 of the total shares Total shares = 245.) Disadvantages of common stock ownership are that common stockholders’ claims come last in the event of corporate bankruptcy and that dividends may be bypassed. 3. 4.500 shares Market price per share $16 Example 18. The capital budget for the upcoming year is $1. insurance companies.57 Shares outstanding 245. there are 140.000 = 105. banks). Venture capital (investor) groups who invest in typically high-risk ventures. After its issuance. Issuances directly to institutional investors (e.000 ----------------------------------------------------.000 New shares = 3/7 × 245. The Wall Street Journal.232 Accounting and Finance for the Nonfinancial Executive A stockholder may make a significant profit if another firm wishes to take the company over.8 million.. the total market value of stock is expected to be $7 million.000 shares of common stock outstanding. Issuances to major customers and suppliers. 2.
000 and a required return rate of 14%. The cost of capital is 13%. it is referred to as “going public.10 — Your company expected the dividend for the year to be $10 a share.08 0.” The estimated price per share to sell the securities is equal to: Anticipated market value of the company -------------------------------------------------------------------------------------------------Total outstanding shares For an established company. There are a number of ways to accomplish this. The price per share is: Expected dividend Price per share = ---------------------------------------------------------------------------------------------------Cost of capital – Growth rate in dividends $10 $10 = -------------------------. It is expected that the company’s stock should sell at eight times its earnings. The growth rate in dividends is expected to be constant at 8%. The market price per share is therefore: Market price per share P ⁄ E = ----------------------------------------------------Earnings per share Market price per share = P/E multiple × Earnings per share = 8 × $7 = $56 You may want to determine the market value of your company’s stock. Example 18.= --------. the market price per share can be determined using the Gordon’s growth model (recall from Chapter 12).05 Another approach to pricing the share of stock for an existing company is through the use of the price/earnings (P/E) ratio. which is equal to Market price per share ----------------------------------------------------Earnings per share Example 18.12 — Assuming an indefinite stream of future dividends of $300.13 – 0.11 — Your company’s earnings per share are $7. the market value of the stock equals .Deciding on Long-Term Financing 233 When a company initially issues its common stock publicly. The model is: D1 P o = ---------r–g or Expected dividend ---------------------------------------------------------------------------------------------------Cost of capital – Growth rate in dividends Example 18.= $200 0.
000 Market value = ---------------------------------------------. The company’s earnings are $400.000 shares. When earnings are retained rather than new stock issued.000. Lastly.142. Also.000 Market value $6. and (3) a common stock issue improves your company’s credit rating relative to the issuance of debt.857 Rate of return 0. the market price per share is $2. The average price/earnings multiple in the industry is 15. The preemptive right provides that existing stockholders have the first option to buy additional shares.000 Price per share = ------------------------------. Also. The expected price per share is: Total market value = Net income × Price/earnings multiple = $400. (2) there is no repayment date.1 Stock Rights Stock rights are options to buy securities at a specified price at a later date. Exercising this right permits investors to maintain voting control and protects against dilution in ownership and earnings. It is always cheaper to finance operations from internally generated funds because financing out of retained earnings involves no flotation costs.14 If there are 200.000 If your company has significant debt. Further earnings and dividends are spread over more shares outstanding. dividends are not tax-deductible.000 shares outstanding after the issuance of the stock. ownership interest is diluted. a company typically earns a higher rate of return than stockholders so that by retaining funds market price of stock should appreciate. .= $2. Financing with common stock has the following advantages: (1) there is no requirement to pay dividends. One caution.= $10.000 Example 18. The additional voting rights could vote to take control away from the current ownership group. the flotation costs of a common stock issue are more than with preferred stock and debt financing.13 — Your company is considering a public issue of its securities.000.71 200.6.= $60 Shares 100.142.= -------------------------.000. as indicated by higher earnings per share. For example.857 Market value = -------------------------. the market price per share of existing stock will rise.000 × 15 = $6. 18.= --------------------.2. however: lower dividend payments may be looked at negatively in the market and may cause a reduction in the market price of stock due to psychological factors. There will be 100. Stockholders are typically better off when a company cuts back on dividends instead of issuing common stock as a source of additional funds.234 Accounting and Finance for the Nonfinancial Executive Expected dividends $300. Financing with common stock has several disadvantages.2. it would be better off financing with an equity issue to lower overall financial risk. A summary comparison of bonds and common stocks is presented in Table 18.
For example. Stockholders have residual claims. 18. you would be wise to finance with long-term debt at the currently lower interest rates. you should consider the following: 1.Deciding on Long-Term Financing 235 TABLE 18. For instance. for example. No voting rights exist. depending on their circumstances. 5. The maturity dates of present debt instruments. The amount. Most companies are somewhere in the middle. The current debt-to-equity ratio. Bondholders have prior claims on profits and assets in bankruptcy. A very high ratio. 9.2 Summary Comparison of Bonds and Common Stock Bonds Bondholders are creditors. 7. The type and amount of collateral required by long-term creditors. The restriction in loan agreements. a restriction may exist placing a cap on the allowable debt-to-equity ratio. There is no tax deductibility for dividend payments. if interest rates are expected to go up. In formulating a financing strategy in terms of source and amount. 2. For example. The future trend in market conditions and how they will impact future fund availability and interest rates. . Interest payments represent fixed charges. Common Stock Stockholders are owners. The rate of return required by bondholders is typically lower than that by stockholders. and stability of internally generated funds. Other companies borrow as much as possible and raise additional money from stockholders only when they can no longer borrow. you should avoid making all debt come due at the same time because in an economic downturn you may not have adequate funds to meet all the debt. indicates financial risk. Dividend payments do not continue fixed charges. 4. so additional funds should come from equity sources. There is a maturity date. Interest payments are deductible on the tax return. The ability to change financing strategy to adjust to changing economic conditions. If stability exists in earnings generation. nature. The adequacy of present lines of credit for current and future needs. 3. 6. Voting rights exist. Companies use different mixes of financing. the company is better able to meet debt obligations. There is no maturity date. 8.7 HOW SHOULD YOU FINANCE? Some companies obtain most of their funds from issuing stock and from earnings retained in the business. The cost and risk of alternative financing strategies. The required rate of return by stockholders is typically greater than that by bondholders.
000 = $130.000 The annual dividend on the preferred stock is 10% × $1. The debt-to-equity ratio is 68%. The common stock is selling at a high P/E ratio compared to the competition.000 = $195. the fluctuation in profit. 11. For example. a higher tax rate makes debt more attractive because there is a greater tax savings from interest expense.15 — Your company has sales of $30 million a year. The tax rate is 34%.970 without a problem.34 ) If your company anticipates earning $196.16 — Your company is a mature one in its industry. Example 18. it should issue the preferred stock. Your company is in a risky industry. There is limited ownership. The dividend rate on the preferred stock is 10%. a liquid company is better able to meet debt payments.300.300. and the deficient liquidity posture. relative to the industry standard of 55%. the issuance of common stock is recommended. and net income is not stable. . Example 18.000 ----------------------. common stock financing may not be appropriate because this would dilute the ownership. 12. Because your company is in a high-risk industry and has a high debt-to-equity ratio and unstable earnings. Debt financing is not recommended because of the already high debt-to-equity ratio. Because of the limited ownership. Under consideration is the issuance of either common stock or a convertible bond. The inflation rate because.= $196. the repayment is in cheaper dollars.3 million. It needs $6 million in financing for capital expansion. For example. The annual interest payment on the debt is 15% × $1. Since your company is a seasonal business. The earning power and liquidity position of the firm. Preferred stock is one possible means of financing. The interest rate on the debt is 15%.970 ( 1 – 0. there are certain times during the year when its liquidity position is inadequate.14 — Your company is considering issuing either debt or preferred stock to finance the purchase of a plant costing $1. Your company is unsure about the best way to finance.236 Accounting and Finance for the Nonfinancial Executive 10. The company has vacillating sales and earnings.000 The required earnings before interest and taxes to meet the dividend payment is $130. with debt. The tax rate. Your firm’s debt-to-equity ratio is 70%. Example 18. The after-tax rate of return is 16%.
Deciding on Long-Term Financing
Example 18.17 — Your company wants to construct a plant that will take about 1 year to construct. The plant will be used to produce a new product line, for which your company expects a high demand. The new plant will materially increase corporate size. The following costs are expected:
Cost to build the plant Funds needed for contingencies Annual operating costs $800,000 $100,000 $175,000
The asset, debt, and equity positions of your company are similar to industry standards. The market price of the company’s stock is less than it should be, taking into account the future earning power of the new product line. What would be the appropriate means to finance the construction? Since the market price of stock is less than it should be and considering the potential of the product line, convertible bonds and installment bank loans might be appropriate means of financing because interest expense is tax-deductible. Additionally, the issuance of convertible bonds might not require repayment, since the bonds are likely to be converted to common stock because of the company’s profitability. Installment bank loans can be gradually paid off as the new product generates cash inflow. Funds needed for contingencies can be in the form of open bank lines of credit. If the market price of the stock was not at a depressed level, financing through equity would be an alternative financing strategy. Example 18.18 — Your company wants to acquire another business but has not determined the optimal means to refinance the acquisition. The current debt-to-equity position is within the industry guideline. In prior years, financing has been achieved through the issuance of short-term debt. Profit has shown vacillation and, as a result, the market price of the stock has fluctuated. Currently, however, the market price of the stock is strong. Your company’s tax bracket is low. The purchase should be financed through the issuance of equity securities for the following reasons: 1. The market price of stock is currently at a high level. 2. The issuance of long-term debt will cause greater instability in earnings because of the high fixed interest charges. Consequently, there will be more instability in stock price. 3. The issuance of debt will result in a higher debt-to-equity ratio relative to the industry norm. This will negatively impact the company’s cost of capital and availability of financing. 4. Because it will take a long time to derive the funds needed for the purchase price, short-term debt should not be issued. If short-term debt is issued, the debt would have to be paid before the receipt of the return from the acquired business.
Accounting and Finance for the Nonfinancial Executive
For borrowing money, lenders look for security in your assets and cash flow in addition to your character, so if you can show a healthy balance sheet and a decent credit rating, you can borrow money easily on the Internet. Among the most useful sites for business borrowers are: • Loanwise.com (http://www.loanwise.com), operated by Net Earnings, Inc. of San Mateo, CA; • America’s Business Funding Directory (http://www.businessfinance.com), operated by BFS, Inc. of Irvine, TX; • Business Finance Mart (http://www.bizfinance.com), operated by Capital Resource & Financial, Inc. of Tallahassee, FL. Loanwise is a web-based loan broker representing a number of banks nationwide — 10 at last count — with more signing on monthly. You fill out an online application detailing your business operation and your need for the loan, along with some personal information. Once the website checks your personal and business credit ratings electronically, you can get an answer the same day for loans under $50,000. Loans for larger amounts require additional documentation, usually submitted by mail, so the approval process takes longer. Given good credit, you may get offers from more than one lender, allowing you to choose the one with the best terms. Interest rates and other terms reflect the risk, of course, but they generally reflect those available from any business bank. Loanwise’s lenders include American Express, the Bank of Hawaii, Irwin Union Bank, Provident Bank, Countrywide Business Alliance, Union Bank of California, Compass Bank, PNC Bank, Equilease Financial Services, and a nonbank small-business lender called Business Loan Center, Inc. You cannot apply online with America’s Business Funding Directory. Instead, the site gathers your business and personal information, probes a database of hundreds of lending sources nationwide, and lists those whose lending criteria appear to be a good fit for you. This website alerts the lenders to your query, prompting them to make contact with you. It also gives you the names and phone numbers of contacts at the lenders so that you can initiate the process yourself. The site also offers useful pages detailing the ins and outs of commercial finance, including equipment leasing, government funds, investment funds, real estate finance, venture capital, small business development councils, and the Service Corps of Retired Executives, a nonprofit organization of business mentors and counselors (http://www.score.org). The Business Finance Mart offers an online application for all kinds of loans, including factoring, sale-leaseback deals, loans guaranteed by the Small Business Administration, equipment leasing, lines of credit, and start-up loans for entrepreneurs. The website also has a bulletin board on which you can post items on buying or selling a business or buying or selling inventory or equipment. In addition to these, lenders of every stripe maintain web pages, including all of the big banks targeting business customers, plus commercial finance companies
Deciding on Long-Term Financing
and other sources of business loans. Many allow you to submit online applications for business loans. There is also no end of sites offering advice to the business borrower. Netscape, for example, offers one highly useful site http://www.netscape.com/netcenter/smallbusiness/business/finance with a button (“Getting financing for your business”) that takes you to pages outlining: • The financing options open to you at different points in your business life cycle; • The advantages and disadvantages of debt vs. equity financing; • Sources of debt and equity financing; and • Sources of government-backed financing. The web page of ZD, Inc., publisher of PC Magazine, http://www.zdnet.com/smallbusiness/filters/biz_2000/finance details the process of seeking an SBA-backed loan and links you to sites from which you may download loan forms. The web pages of Entrepreneur magazine (http://www.entrepreneurmag.com), Intuit, Inc. (http://www.quicken.com), and Inc. magazine (http://www.inc.com) are also useful.
18.7.2 RAISING EQUITY
VENTURE CAPITAL ONLINE
It is not possible to do an equity deal by remote control on the Internet. However, the Internet can help you simplify the first step in your search for equity or venture capital by getting your business plan in front of potential investors. A number of good websites seek to help you make these connections, among them: • The Adventure Capital Register (http://www.adventurecapital.com) — A good place to start if you’re looking for capital to launch a new business venture, invention, or idea. You can get tips on how to find funding or for links to funding sources. • The Venture Capital Resource Library (http://www.vfinance.com), where you can post a synopsis of your business idea along with basic information about your business. • The National Venture Capital Association (http://www.nvca.org), which lists over 300 venture capital and private equity firms along with links to many of their websites, allowing you to gauge the firms’ likes and dislikes. • The National Financial Services Network (http://www.nfsn.com), which allows you to identify specific banks, investment banks, venture capital firms, insurers and other sources of finance by state. • Commercial Finance Online (http://www.cfol.com), where you can search through a large database for financing sources likely to have an interest in your business and its capital needs.
Accounting and Finance for the Nonfinancial Executive
• The Capital Network (http://www.thecapitalnetwork.com), where you can search a database of financing sources or, as an alternative, profile your capital needs and match them to potential sources. • The Angel Capital Electronic Network — ACE-Net for short (http://ace-net.sr.unh.edu/pub) — A site partly sponsored by the U.S. Small Business Administration. It is an Internet securities listing service to help entrepreneurs and investors find each other. The site is hosted by the University of New Hampshire. • “Money Hunt” (http://moneyhunter.com) — A public television program to help entrepreneurs turn their ideas into reality. The site provides business plan templates to write that all-important plan for investors, a directory of relevant contacts, and advice from experts. • Garage.com (http://www.garage.com), which matches entrepreneurs and investors through a rigorous and detailed “vetting” process probing business plans, management expertise, and the like.
Your company may finance long-term with debt or equity (preferred stock and common stock) funds. Each has its own advantages and disadvantages. The facts of a situation have to be examined to determine which type is best for your company’s circumstances.
Dissecting Financial Statement Information
1. the value of the 243 . and the statement of cash flows are the primary documents analyzed to determine the company’s financial condition. and net income. and equity or net worth. A business entity is an economic unit that enters into business transactions that must be recorded. The financial statements are the means of conveying to management and to interested outsiders a concise picture of the value and profitability of the business for a given period of time. Revenue from sales of merchandise or sales of services is often identified merely as sales. The statement of cash flows allows you to analyze the company’s sources and uses of cash. 2001). while the income statement gives the company’s sources of revenue. the income statement. commission revenue. When revenue is earned it results in an increase in either cash or accounts receivable. The amount of an expense is either equal to the cost of the goods sold. and fares earned. These financial statements are included in the annual report. expenses.1 REVENUE Revenue arises from the sale of merchandise (as by retail business). is useful in setting up a program or strategy for planning and controlling profits. 19.1 THE INCOME STATEMENT AND BALANCE SHEET The income statement measures operating performance for a specified time period (such as for the year ended December 31. Other terms used to identify sources of revenue include professional fees. or the performance of services for a customer or a client (as by a lawyer). The income statement shows the revenue. 19. summarized. and net income (or loss) for a period of definition of each element as follows. and reported. The balance sheet. An examination of what can be gained from these statements.2 EXPENSES Expenses result from performing those functions necessary to generate revenue. Each business must have a separate set of accounting records and a separate set of financial statements. and wherein the pitfalls lie.19 Understanding Financial Statements Managers should have a good understanding of the company in order to make an informed judgment on the financial position and operating performance of the entity. liabilities. 19. expenses. The balance sheets give the company’s position in terms of its assets.1.
known as stockholders’ equity or net worth).1.3 NET INCOME (LOSS) Net income.000. .244 Accounting and Finance for the Nonfinancial Executive services received (e. no doubt. attempt to determine the cause for this significant increase. and office supplies used $400.1 — Joan Biehl is a self-employed consultant.000 500 2. capital has not been altered because of the loan. salary expense). This specifically enables one to better evaluate and control revenue and expense sources and to examine relationships among account categories. Further. rent $2. you cut the point. Assets may have definite physical form such as buildings. rent expense) during the period. For instance. 19.g. on the other hand.. The balance sheet. freeze the action. Joan Biehl would. Her income statement for the period is as follows: Joan Biehl INCOME STATEMENT For the Month Ended May 31. also called profits or earnings. or the expenditures necessary for conducting business operations (e. 2001 Revenue from professional services Less: Operating expenses Telephone Electricity Rent Secretarial salary Office supplies Total operating expenses Net income $10. taking out a bank loan will generate cash but this is not revenue since merchandise has not been sold nor have services been provided.. is the amount by which total revenue exceeds total expenses for the reporting period. the ratio of telephone expenses to revenue is 10% ($1.200 $ 5.800 Note that each revenue and expense item has its own account. It is a snapshot.4 ASSETS Assets are economic resources which are owned by an organization and are expected to benefit future operations.1.g. secretarial salary $300. It should be noted that revenue does not necessarily mean receipt of cash and expense does not automatically imply a cash payment.500.000 from services rendered. It shows what is owed (assets). electricity $4. while the income statement is a motion picture. Her business expenses were: telephone $1. For the month of May 2001.000/$10. and what is left (assets minus liabilities. Example 19. Note that net income and net cash flow (cash receipts less cash payments) are different.000 $1. portrays the financial position of the company at a particular point in time.000. and want to know about the company’s financial position as of a certain date (like 12/31/2001. she earned income of $10. 19. how much is owed (liabilities). For example. the end of the reporting year). If in the previous month the relationship was 3%. With the balance sheet.000).000 300 400 4.
The balance sheet may be prepared either in report form or account form. and capital are listed vertically. equipment. and prepaid expenses. The form of the liability when money is borrowed is usually a note payable. Liabilities payable within 1 year are classified as current. such as accounts payable. does not involve the issuance of a formal promise written to the creditor. there is only one capital account since there is only one owner.000 from a bank. a capital account exists for each owner. but in the form of valuable legal claims or rights.” The liability arising from the purchase of goods or services on credit (on time) is called an accounts payable. such as accounts receivables from customers and notes receivables from debtors. and it does not require payment of interest. In a sole proprietorship. you would say that your equity in the $150. and buildings.1.2 — The equity of the owners of the business is quite similar to the equity commonly referred to with respect to home ownership. In the account form.Understanding Financial Statements 245 machinery. some assets exist not in physical or tangible form. Example 19. assets. 19. capital represents the stockholders’ equity. There are two types of capital stock — common stock and preferred stock. Prepaid expenses include supplies on hand and advance payments of expenses such as insurance and property taxes. .000 of your own money and borrowing $120.5 LIABILITIES Liabilities are debts owed to outsiders (creditors). for example. Other examples of liabilities include various accrued expenses. If you were to buy a house for $150. Examples are cash.. Assets which will be converted into cash within 1 year are classified as current. In the report form.e. liabilities. On the other hand. while preferred stock does not. $30. bonds payable.6 EQUITY Equity is a residual claim against the assets of the business after the total liabilities are deducted. a formal written promise to pay a certain amount of money.000 by putting down 20%. or supplies. Equipment and buildings are often called plant assets or fixed assets. and are frequently described on the balance sheet by titles that include the word “payable. marketable securities. are termed long-term liabilities. at a definite future time.000. and taxes payable. 19. receivables. Other commonly used terms for capital are owners’ equity and net worth. plus interest.1. Common stock entitles its owners to voting rights. Preferred stock entitles its owners to priority in the receipt of dividends and in repayment of capital in the event of corporate dissolution. Examples are long-term investments. Obligations payable in a period longer than 1 year. In a corporation.000 house was $30. i. as contrasted to a note payable. Capital is the term applied to the owners’ equity in the business. which equals the capital stock issued plus the accumulated earnings of the business (called retained earnings). In a partnership. Accounts payable. notes payable. inventory. Assets having a life exceeding 1 year are classified as noncurrent.
assets are listed on the left side and liabilities and capital on the right side. In fact.400 41. Biehl’s net income of $5.1) is added to capital in her balance sheet in the above example. 31.800 (last item in her income statement from Example 19. 2002 Balance Sheet FIGURE 19.000 .500 30.000 20.600 $5. it is evident that there is a tie-in between the income statement and the balance sheet. Joan Biehl Balance Sheet May 31. the net balance of the income statement accounts is used to adjust the capital account. 31.246 Dec.000 $71. 2001 Balance Sheet Motion Picture Snapshot Income Statement Dec.3 — Report form. In effect. Further. the income statement serves as a bridge between the two consecutive balance sheets. 2001 Net income for May Less withdrawals Increase in capital Total capital Total Liabilities and Capital $10. 2000 Balance Sheet Accounting and Finance for the Nonfinancial Executive Year 2001 Income Statement Dec.000 $35. the income statement serves as the bridge between two consecutive balance sheets.000 $30. Figure 19.000 $71. From the examples given. Example 19.800 400 5. May 1. 31.1 Balance sheet and income statement relationship.000 10.1 shows the relationship between the income statement and the balance sheet. 2001 ASSETS Cash Accounts receivable Office supplies Office equipment Total assets LIABILITIES AND CAPITAL Liabilities Accounts payable Capital Balance.
Unfortunately.000 10.000 Note — Simply put. 7. 19. you still have problems. which are a basis for cash flow analysis for managers. the fact that the company made a big profit does not necessarily mean it is wealthy. 6. which will be discussed below.600 5.Understanding Financial Statements Example 19. 2001 Net income for May Less: Withdrawals Increase in capital Total capital Total Liabilities and Capital 247 $10. You would like to know more about the company’s financial shape (such as the cash position of the company). May 1. 3. 5. 4.800 400 5. The statement helps you to answer vital questions like “Where was money obtained?” and “Where was money put and for what purpose?” The following provides a list of more specific questions that can be answered by the statement of cash flows and cash flow analysis: 1.2 THE STATEMENT OF CASH FLOWS The statement of cash flows shows the sources and uses of cash. For example.000 Total Assets $71.000 $30.4 — Account form.400 41. 2001 ASSETS Cash Accounts receivable Office supplies Office equipment LIABILITIES AND CAPITAL Liabilities Accounts payable Capital Balance. 2.000 $71. with the balance sheet you are asking “How wealthy or poor is the company?” while with the income statement you are asking “How did the company do last year?” and “Did it make money and then how much?” Neither one is good enough to tell you about the financial health of the company.500 30. Is the company growing or just maintaining its competitive position? Will the company be able to meet its financial obligations? Where did the company obtain funds? What use was made of net income? How much of the required capital has been generated internally? How was the expansion in plant and equipment financed? Is the business expanding faster than it can generate funds? .000 35.000 20. The statement of cash flows provides this information. you need both statements to complement each other. neither the balance sheet nor the income statement provides the information of the cash flow during the period. and vice versa. However. In order to get the total picture. Joan Biehl Balance Sheet May 31.
net income will generally not indicate the net cash flow from operating activities. A statement of cash flows reports the cash receipts. “Statement of Cash Flows. The presentation reconciles beginning and ending cash balances. payments. How management utilizes the flow of cash can determine a firm’s success or failure.1 FASB REQUIREMENTS Management and external interested parties have always recognized the need for a cash flow statement.000 in credit sales. of which $100. 19. To arrive at net cash flow from operating activities.2. Therefore. it is necessary to report revenues and expenses on a cash basis. Cash that was actually collected by the corporation in 2001 can be calculated as follows: Credit sales Less: Credit sales uncollected at year end Actual cash collected $2.248 Accounting and Finance for the Nonfinancial Executive 8.000 100.100. the Eastern Electric Supply Corporation earned $2. and net change in cash on hand resulting from the operating.000 remained uncollected at the end of the calendar year. Is the company’s dividend policy in balance with its operating policy? 9. most companies use the accrual basis of accounting. This is accomplished by eliminating those transactions that did not result in a corresponding increase or decrease in cash on hand.100.2. and financing activities of an enterprise during a given period. 95. the Financial Accounting Standards Board (FASB) has issued Statement No. investing.000. Example 19. 19. As previously stated.000 A statement of cash flows focuses only on transactions involving the cash receipts and disbursements of a company. Revenue may include credit sales that have not yet been collected in cash and expenses incurred that may not have been paid in cash. Is the company’s cash position sound and what effect will it have on the market price of stock? Cash is vital to the operation of every business. Financial managers must control their company’s cash flow so that bills can be paid on time and extra dollars can be put into the purchase of inventory and new equipment or invested to generate additional earnings. This method requires that revenue be recorded when earned and that expenses be recorded when incurred.5 — During 2001.” This pronouncement requires that enterprises include a statement of cash flows as part of the financial statements. the statement of cash flows . in recognition of the fact that cash flow information is an integral part of both investment and credit decisions.2 ACCRUAL BASIS OF ACCOUNTING Under Generally Accepted Accounting Principles (GAAP). Thus. under the accrual basis of accounting.000 $2.
19. The company had a $198. 4. and interest paid to creditors are classified as cash outflows for operating activities. 3. . 2.and long-term debt. 19.000.000 cash balance at the beginning of the year. plant. and other short. 19. In 2001. and equipment used in the production of goods and services. debt instruments or equity of other entities.000 in federal and state taxes.2.004. mortgages.6 — The following information pertains to Liverpool Sugar Corporation during 2001. 10-year bonds. and the payment of cash dividends. Example 19. Cash outflows classified as financing activities include the repayment of short.000 in preferred stock in return for land and buildings. Cash paid to acquire materials for the manufacture of goods for resale. The company sold all of its stock investment in Redondo Food Corporation.2.000 in cash receipts from the sale of goods. its payments on accounts and notes payable amounted to $12. Cash outflows under this category may result from the purchase of plant and equipment and other productive assets.4 INVESTING ACTIVITIES Investing activities include cash inflows from the sale of property.000 of its 10%. and the making of loans to other enterprises. interest received on loans. payments to employees as compensation. an unrelated entity. investing.000. debt instruments or equity of other entities. The company had $1. Thus.000. They only relate to income statement items. 1. The company paid a cash dividend of $36.000. for $100.5 FINANCING ACTIVITIES The financing activities of an enterprise involve the sale of a company’s own preferred and common stock. and financing activities. and it paid $136. bonds.or long-term borrowings. including the collection or sale of trade accounts and notes receivable from customers. cash received from the sale of goods or services.2. the reacquisition of treasury stock. and the collection of principal on loans made to other enterprises. notes.Understanding Financial Statements 249 classifies cash receipts and cash payments into operating.3 OPERATING ACTIVITIES Operating activities include all transactions that are not investing or financing activities. the company sold $300.000. rental payments to landlords. It also issued another $50. It then bought a new plant and equipment for $676. and dividend income are to be treated as cash from operating activities. Cash payments to acquire materials for the manufacture of goods totaled $469.000.
000) (776.000) 387. .000 (469.250 Accounting and Finance for the Nonfinancial Executive The statement cash flows for the company would be presented as follows: Liverpool Sugar Corporation Statement of Cash Flows for the Year Ended December 31.000) 264.000) 198.3 CONCLUSION The traditional accounting statements — balance sheet.000 Note that the issuance of the preferred stock in exchange for the land and buildings is a noncash transaction that would be disclosed in supplementary form at the end of the statement of cash flows.000 $ 73.000 (36.000) 300. As a later chapter will show. and the newly required statement of cash flows — have been and will continue to be the most important tools for both management and outsiders for use in gauging the financial condition of a business.000) (136. 2001 Cash flows from operating activities: Cash received from customers Cash payment for acquisition of materials Cash payment for interest and dividends Cash payment for taxes Net cash provided by operating activities Cash flows from investing activities: Cash paid to purchase plant and equipment Sale of long-term investment Net cash provided by investing activities Cash flows from financing activities: Sale of bonds Cash paid for dividends Net cash used in financing activities Net decrease in cash and cash equivalents Cash and cash equivalents at the beginning of the year Cash and cash equivalents at the end of the year $ 1.000) (12. additional insights into the performance of the business can be gained by using financial ratio analysis.000 (125.000 (676.000) (100. income statement.004. 19.
affecting many different items appearing on the financial statements. by increasing and decreasing it by identical amounts and thus netting zero.1 THE ACCOUNTING EQUATION An entity’s financial position is reflected by the relationship between its assets and its liabilities and equity. Example 20. and the limitation inherent in the information presented. The transactions of most businesses are numerous and complex. you will be able to more clearly understand the basic structure of the financial statements that were discussed in the previous chapter. The aim of this chapter is to introduce the formal classification system of financial information commonly called double-entry accounting. 20. the convention adopted in recording information. Proper interpretation of the data requires an understanding of the concepts and rules underlying such systems.1.000. a formal system of classification and recording is required for timely financial reporting and managerial needs. and owners’ equity of $400. A transaction affects either both sides of the equation by the same amount or one side of the equation only.1 — Foster Architectural Company has assets of $700.20 Recording Financial Information and Accounting Conventions Financial decisions are usually formulated on the basis of information generated by the accounting system of the firm. Therefore. The accounting equation is the basis for double-entry accounting. 20. which means that each transaction has a dual effect. By acquiring background information about this system.000.000. obligations of $300. The accounting equation is: 251 . The accounting equation reflects these elements by expressing the equality of assets to creditors’ claims and owners’ equity as follows: Assets (A) = Liabilities (L) + Equity (E) The equation in effect says that a company’s assets are subject to the rights of debt holders and owners.1 DOUBLE ENTRY AND THE ACCOUNTING EQUATION Double-entry accounting is a system in which each business transaction affects and is recorded in two or more accounts with equal debits and credits.
and 9. 8.000 Office Equipment (OE) $5. Transaction 1 — Thomas started his engineering consulting practice by investing $10.000 In the next example. of which $12. experienced the following events in the month of January 2001: 1. Received an electric bill for $300.000 from one of the clients who owed him money. 7. the firm derived net income of $80.000 = $240. 5. Assets (A) Cash $10. The transactions will now be analyzed.000 = Liabilities (L) + Equity (E) L. a consultant.252 Accounting and Finance for the Nonfinancial Executive Assets = Liabilities + Equity $700.000 was owed.000 was then used to pay creditors.000 If $60. $800. Withdrew $100 from the firm for personal use. The assets Cash and Office Equipment are increased. Started his consulting practice with a cash investment of $10. 3. the accounting equation becomes Assets = Liabilities + Equity $720. we will illustrate how the transactions of a business are recorded and what effect they have on the accounting equation. Earned professional fees of $20.000 in office equipment.000 + $480.000 = $300. .000 + $480.000.000 If at the end of the reporting period.000. Bought a word processor for $500 on account from Smith Corona. the accounting equation becomes Assets = Liabilities + Equity $780. 6. Purchased office supplies of $800 by paying cash.000 and office equipment worth $5. Paid $400 in salary to his staff.000 in cash and $5. Thomas Equity (E) $15.000 = $300. Paid $300 to Smith Corona. This is an example of one asset being used to acquire another one. Received $1. 4. and the equity is also increased for the total investment of the owner. The asset Office Supplies goes up by $800 with a corresponding reduction in the asset Cash. Example 20.000.000 Transaction 2 — Acquired office supplies for cash. 2.000 + $400.2 — Lloyd Thomas.
A Cash $9. Office Equipment.200 OE $5.500 OS $800 +$500 $800 $500 $15.000 –800 $ 9.000 +$800 $5.300 + E $8. An asset.800 OE $5. of which $12. is being acquired on credit. . A Cash $9. Cash and equity are both being reduced because of the wage expense.000 was received in cash and $8.000 $800 $15.500 OS $800 = L AP $500 $15.000 Transaction 3 — Purchased a word processor on account.500 $800 Transaction 6 — Earned fees of $20. Accounts Payable is defined as the amount owed to suppliers.000 was owed by clients.200 OE $5. A Cash $8.000 –400 $14. thereby creating a liability for future payment called Accounts Payable. $400.000 + E $9.500 OS $800 = L AP $500 +300 $800 $14. Equity is reduced for the expense. $500.000 +500 $5.800 OE $5.600 –300 $14.000 $15.500 $800 $500 Transaction 5 — Received an electric bill for $300 (not paid).Recording Financial Information and Accounting Conventions 253 A Office Supplies (OS) = L + E Cash $10. Equity is reduced because expenses of the business decrease the equity of the owner.200 Transaction 4 — Paid salary.000.000 = L Accounts Payable (AP) $15.200 –400 $8. Liabilities are increased by $300 since the firm owes the utility money for electricity supplied.800 $5.600 + E $5.
One asset is being substituted for another one.000 + E Transaction 7 — Paid $300 to Smith Corona (in partial payment of the amount owed to them).000 $21.500 OS $800 AR $8.500 $800 $8. It is not an expense in running the business. The payment lowers the asset Cash and reduces the liability Accounts Payable.000 20.000 and the Accounts Receivable (amounts owed to the business from customers) is created.000 $5. The personal withdrawal is.000 $7.000 = L AP $800 –300 $500 $34.000 = L AP $500 $34.300 +20.800 +12.200 + E $5.000 = L AP $500 $34.000 $800 AR = L AP $800 $14.500 $800 $8.800 OE $5.000 $34. equity is increased by $20.000. Thus. A Cash $20. Professional fees earned are revenue to the business and hence increases the owner’s equity.254 Accounting and Finance for the Nonfinancial Executive Cash goes up by $12.300 + E $5.000 $34.400 OE $5. a disinvestment in the business and hence reduces equity.500 OE $5.400 +1.500 OS $800 AR $8. Cash is reduced and so is equity.200 + E $5.500 OS $800 +$8.000 from clients who owed him money.500 $800 $8.300 –100 $34.500 –100 $20.300 Transaction 8 — Withdrew $100 for personal use. A Cash $20.000 –1.500 $800 500 $34. This increases Cash and reduces Accounts Receivable since the client now owes the business less money.400 OE $5.800 –300 $20. in effect. A Cash $8.500 OS $800 AR $8.000 $500 Transaction 9 — Received $1.200 . A Cash $20.
000 20.000 7.200 Drawing 5.500 800 500 +300 800 $8.000 –400 14.400 10.200 –200 $34.300 –100 34. $10.500 OE $5.500 $34.000 4.500 800 8.500 800 8.000 $500 A Cash 1. The supplies used up represent office supplies expense. Fee Revenue 5.300 Wage Expense 5. 15. Since the worth of office supplies originally acquired was $800 and $600 is left on hand.000 Utility Expense 800 6.000 +500 5.800 +12.200 –400 8.400 OE $5. 8. the business used $200 in supplies.000 21.200 –200 $34. $600. A Cash $21.300 +20. 34.500 –100 20.Recording Financial Information and Accounting Conventions 255 Transaction 10 — Worth (determined by an inventory count) of office supplies on hand at month’s end.000 OS SUMMARY OF TRANSACTIONS January 2001 L + = AR AP $15. $21.500 800 –200 $600 500 34.000 –800 9. 2.000 7.400 + 1. 9. Prof.500 800 +$500 800 500 15.000 = = $500 . 800 –300 500 5. 8.000 34.000 + E $21.000 –1.500 Office Supplies Expense $7.000 = L AP $500 $34.800 5.500 OS $800 –200 $600 AR $7.500 $7.500 800 9.400 $5.000 500 5.500 5.000 $34.000 8.000 +$800 E 5.200 3. This reduces the asset Office Supplies and correspondingly reduces equity.800 –300 20.600 –300 14.400 $5.
The basic component of the formal accounting system is the account. would be the group of accounts which summarize the financial operations of the company and is the basis for the preparation of the balance sheet and income statement. Rather. the financial statements can then be prepared based upon the balances in these accounts.g. the purpose of the account is to provide a capsule summary of all transactions which have caused an increase or decrease and to reflect the account balance at any given point in time. 20. The ledger of a firm. liabilities. The account numbering system as it pertains to a typical company is as follows: Series 001–199 200–299 300–399 400–499 500–599 Account Classification Asset Liabilities Revenue Expenses Stockholders’ Equities Particular accounts can then be given unique. A separate account exists for each item shown on the financial statements. liabilities. Furthermore.256 Accounting and Finance for the Nonfinancial Executive 20. In other words. accounts receivable) would be lost through this process.1. Listed first are the balance sheet accounts — assets. for example. The income statement accounts — revenue and expenses — follow.1. The increases.3 LEDGER All accounts are maintained in a book called the ledger. and balances are shown for each account. decreases. At the end of the reporting period. information about a specific item (e. balance sheet accounts consist of assets. The account numbering system permits easy reference to accounts. and equity. identifying account numbers within the series. Income statement accounts are either expenses or revenue. and stockholders’ equity. as in the following examples from the Assets Series: .. The chart of accounts is a listing of the titles and numbers of all accounts in the ledger.4 A CHART OF ACCOUNTS The ledger is usually accompanied by a table of contents called a chart of accounts. there should be an account established for each type of item. It is also useful for decision making since it provides the manager with the balance in a given account at a particular time.1. in that order. 20. Thus.2 THE ACCOUNT To prepare an equation Assets = Liabilities + Stockholders’ Equity for each transaction would be extremely time consuming.
and equity is explained later in the chapter. expenses. assets. we will look at the Cash account (within the Asset classification). You must note that the items debit and credit are not synonymous with the words increase and decrease. regardless of the account title. but the simplest is called a T-account.000 45. are called debits to the account.500 .500 53. The left and right sides of the account are called debit and credit. $55.000 in the illustration. and the account is said to be credited. Cash 10.500 25. 001 002 003 004 005 006 007 008 Assets Cash on hand Marketable securities Accounts receivable Inventories Investments Land Buildings Equipment Accounts may take many forms. A memorandum total of the cash receipts for the period to date. as shown below: Account Title debit (left side) credit (right side) Every account has three major parts: 1. The system of debits and credits as related to increases and decreases in each of the six categories of accounts. may be noted below the last debit whenever the information is desired.000 55. which is the name of the item recorded in the account. 2. To illustrate the account. A space for recording increases (monetary) in the amount of the item. Amounts entered on the left side of an account.000 21. The reason for this name is obvious.000 7. liabilities. where receipts of cash during a period of time have been listed vertically on the debit side and the cash payments for the same period have been listed similarly on the credit side of the account. A space for recording decreases (monetary) in the amount of the item.Recording Financial Information and Accounting Conventions 257 Account No. and the account is said to be debited. and 3. Amounts entered on the right side of an account are called credits.000 1. revenue. respectively (often abbreviated as “Dr” for debit and “Cr” for credit). A title.
500 (which may be inserted as shown). are made for each transaction. The cash account in the illustration has a balance of $1. The system of rules is analogous to a set of traffic rules whereby everyone (at least everyone in the U. may be noted on the credit side in a similar manner.S. $53. Subtraction of the smaller sum from the larger. Asset + Debit for increase – Credit for decrease Liabilities – Debit for decrease + Credit for increase Revenue – Debit for decrease + Credit for increase Equity + Debit for decrease Expenses – Debit for increase + Credit for decrease – Credit for increase These same relationships are illustrated below: Type of Account Asset Liability Revenue Expenses Equity Normal Balance Debit Credit Credit Debit Credit To Increase Debit Credit Credit Debit Credit To Decrease Credit Debit Debit Credit Debit The illustrated system of debits and credits is the standard method followed by persons keeping records on the double-entry system. 20. However. you will see shortly that there is a very logical and unique system in the present structure. the system would work if we reversed everything.500. which identifies it as a debit balance. which is called the balance of the account.000 – $53.500 in the illustration. yields the amount of cash on hand.5 THE SYSTEM OF DEBITS AND CREDITS In this section we will briefly explain how accounts are increased or decreased through the use of debits and credits. $55. the basic foundation of double-entry accounting where at least two entries. a debit and a credit.1. and certain other nations) agrees to drive on the right side of the road.258 Accounting and Finance for the Nonfinancial Executive The total of the cash payments. Obviously. . The following guide shows how to increase or decrease accounts using debits and credits.
This process is called posting.. 20. sales or payroll).7 JOURNALS For simplicity. The journal is the book of original entry in which transactions are entered on a daily basis in chronological order. 20. The latter is used when there are many repetitive transactions (e. However. .1. The PR (Posting Reference) column is used for the ledger account number after the posting from the journal to the ledger takes place.Recording Financial Information and Accounting Conventions 259 20. There exist different types of journals that may be grouped into the categories of (1) general journals and (2) specialized journals. this process does not furnish the data required about a given transaction nor is listing of transactions in chronological order possible on T-accounts.1. The purpose is to record increases on one side and decreases on the other. A formal system of classification and recording — double-entry bookkeeping — was briefly covered. you will be able to more clearly understand the basic structure of the financial statements that were discussed in the previous chapter. By acquiring background information about this system. the entries used in the previous section were made directly in the general ledger accounts.6 THE “HOW AND WHY” OF DEBITS AND CREDITS Recall the fundamental accounting equation: Assets (A) = Liabilities (L) + Equity (E) In addition to this equation. one account (or accounts) must be debited and another account (or accounts) must be credited to obtain an equal amount. This provides a cross reference between journal and ledger. The data are then transferred from the journal to the ledger by debiting and crediting the particular accounts involved.2 CONCLUSION We discussed some basic accounting conventions. This process is called journalizing. there is another fundamental accounting concept or rule: Debits must always equal Credits This means that whenever a financial transaction is recorded in the accounting record.g. These deficiencies are overcome through the use of a journal. a debit side and a credit side. It was noted earlier that all accounts have two sides.
An investor is interested in the present and future level of return (earnings) and risk (liquidity. The analysis attempts to ascertain whether the stock is overpriced. evaluate a firm’s stock based on an examination of its financial statements. or priced in proportion to its market value. which give relative measures of the performance and financial condition of the company. What has been the trend in profitability and return on investment? Will the business be able to pay its bills? How are the receivables and the inventory turning over? This chapter presents various financial statement analysis tools that are useful in evaluating the company’s current and future financial conditions. and the firm’s own management. such as a vendor or supplier. 4. on the other hand. underpriced. as an investor. economic and political conditions. 3. industry factors. A short-term creditor. A stock is 261 . How well is the business doing? What are its strengths? What are its weaknesses? How does it fare in the industry? Is the business improving or deteriorating? A complete set of financial statements. 5. and ratio analysis. debt. It is of interest to creditors. present and prospective investors. Financial statement analysis attempts to answer the following basic questions: 1. will include the balance sheet. You. as explained in the previous chapter. and future outlook of the company. vertical.1 WHAT AND WHY OF FINANCIAL STATEMENT ANALYSIS The analysis of financial statements means different things to different people. and statement of cash flows. creditors. and activity). We will discuss the various financial statement analysis tools that you will use in evaluating the firm’s present and future financial condition. is ultimately concerned with the firm’s ability to pay its bills and therefore wants to be assured that the firm is liquid. The first two are vital in financial statement analysis. and present and prospective investors. 21. The analysis of financial statements reveals important information to management. These tools include horizontal. is interested in the firm’s ability to repay interest and principal on borrowed funds.21 Analyzing Financial Statements Managers need to be able to analyze the company’s financial statements in order to evaluate its financial health and operating performance. A creditor is primarily interested in the firm’s debt-paying ability. income statement. This evaluation considers overall financial health. A long-term creditor such as a bank or bondholder. 2.
Inc. the .1 and 21. For example. Comparative Balance Sheet (in Thousands of Dollars) December 31. since these interested parties must be satisfied for the firm to obtain capital as needed.0% 78.1% 10.2% 9. In annual reports. 21. Inc.0% –6. Horizontal analysis concentrates on the trend in the accounts over the years in dollar and percentage terms.1% 10.8% 9.3% valuable to you only if you can predict the future financial performance of the business.7% 13. comparative financial data are usually shown for five years. Through horizontal analysis you can pinpoint areas of wide divergence requiring investigation. in the income statement shown in Figure 21.9% 23.3% 15.3% 46 42 88 $227 46 34 80 $204 46 19 65 $185 0 8 $8 $23 0 15 $15 $19 0.262 Accounting and Finance for the Nonfinancial Executive FIGURE 21. It is typically presented in comparative financial statements (see ALPHA. 4.2 HORIZONTAL AND VERTICAL ANALYSIS Comparison of two or more years’ financial data is known as horizontal analysis.1% –2. Financial statement analysis gives you much of the data you will need to forecast earnings and dividends. $10 par. 2001.0% 11.6% 10.0% 12.2% 11.2% 46. financial data in Figures 21. 2002.1 ALPHA.3% 56 83 139 50 74 124 51 69 120 6 9 $15 (1) 5 $4 12. Management must relate the analysis to all of the questions raised by creditors and investors.3% 0.0% 114.7% 31.2).2% 12.3% 60.3% 0.3.0% 23. 2000 Increase or Decrease ASSETS Current assets Cash Marketable securities Accounts receivable Inventory Total current assets Plant and equipment Total assets LIABILITIES Current liabilities Long-term debt Total liabilities STOCKHOLDERS’ EQUITY Common stock.5% 10.0% 7.2% 3.600 shares Retained earnings Total stockholders’ equity Total liabilities and stockholders’ equity % Increase or Decrease 2001–2000 2002 2001 2000 2002–2001 2001–2000 2002–2001 $28 22 21 53 124 103 227 $36 15 16 46 113 91 204 $36 7 10 49 102 83 185 ($8) 7 5 7 11 12 $23 $0 8 6 (3) 11 8 $9 –22.
0% –43.6 11. a large number change might cause a small percentage change and not be of any great importance. 2002.0% 91. 2001.0 12.0 13.0% 114. The interest expense from 2000–2001 went up by 100%.3% –50.0% 150.0 –18.1% 18.0) (3.5% –39.4 6. 2000 Increase or Decrease % Increase or Decrease 2001–2000 112.3 $26. a material financial statement item is used as a base value.3 $120 $56.0) 14.6 4.0 15.0 2.0 $15.5% 300. It also shows that significant . Preparation of common-size statements is known as vertical analysis.7) (11.8% 18.7) (4.4 5. In a similar vein.6 4.0 (11.0% –27.0 24. Key changes and trends can also be highlighted by the use of common-size statements.3 5.5% 115.3 12.6 4.3 110.3 27.4 $8.4 (1.2.0% –46.0 13.0 5.0 Total operating expenses $17.0 $8.0 8.0 3.0 $14.0 Income from operations Nonoperating income Income before interest and taxes Interest expense Income before taxes Income taxes (40%) Net income $11.0% –56.0% 109.7) 0.4 1.5% –19. respectively. Placing all assets in common-size form clearly shows the relative importance of the current assets as compared to the noncurrent assets.000 and may not need further investigation.0 significant rise in sales returns taken with the reduction in sales for 2001–2002 should cause concern. You might compare these results with those of competitors.7) (1.0 $7.0 $21. Figure 21.0 22.0 (29.0 52.0) (18. It is essential to present both the dollar amount of change and the percentage of change.4 35.8% –46.0 1. for example. total liabilities and stockholders’ equity is assigned 100% with a given liability or equity account stated as a percentage of the total liabilities and stockholders’ equity.1% 125. Similarly.0 47.0 57.7% –37. since the use of one without the other may result in erroneous conclusions.0% –17.8% –7.7% 50.Analyzing Financial Statements 263 FIGURE 21.7) 8.6 $7. Each asset is stated as a percentage of total assets.3 shows a common-size income statement based on the data provided in Figure 21.0% 145. and all other accounts on the financial statement are compared to it.0 5.5% 115.6 28.7) ($7.0 25.0 2.0) ($4. In the balance sheet.3 2.0 (11.4 2. but this represented only $1.0 13.7) 3. total assets equal 100%.6 1.3% 0.0 80.0 28.3% 100.2 ALPHA.0 63.0 ($21.0 $10.0 10. Comparative Income Statement (in Thousands of Dollars) For the Years Ended December 31. A common-size statement is one that shows the separate items in percentage terms.0% 115. In vertical analysis.5% 2002 2001 2000 2002–2001 2001–2000 2002–2001 Sales Sales returns and allowances Net sales Cost of goods sold Gross profit Operating expenses Selling expenses General expenses $98.1% 80.8% –46.0) ($14.0 $15.0 52. Inc.2% 166.0) $63.0 11.0 10.
00 110. It is possible to see at a glance how each dollar of sales is distributed between the various costs.30% 19. The deterioration in the cash position may be a result of inability to collect from customers.80% 7. Income Statement and Common Size Analysis (In Thousands of Dollars) For the Years Ended December 31. as compared to only 57. Then you can determine how the company fares in the industry. In this section.00 27.60% changes have taken place in the composition of the current assets over the last year. expenses.00% 19.00 $11.10% 2.00 47.20% 21.40% 100. that receivables have increased in relative importance and that cash has declined in relative importance.00 $15. It is also vital to compare two figures applicable to different categories.00% 57.30 $8.00 25.10% 13. and profits.30 4.30 18. For example.60% 0. notice from Figure 21.90% 6.00 $26.264 Accounting and Finance for the Nonfinancial Executive FIGURE 21.00 63.50% 1.3 that 64.70% 11.10% 23.00 15.00 1.60% 9.3 WORKING WITH FINANCIAL RATIOS Horizontal and vertical analysis compares one figure to another within the same category. you will learn how to calculate . You should also compare the vertical percentages of the business to those of the competition and to the industry norms.80% 35. 2002 and 2001 2002 Amount Sales Sales returns and allowances Net sales Cost of goods sold Gross profit Operating expenses Selling expenses General expenses Total operating expenses Income from operations Nonoperating income Income before interest and taxes Interest expense Income before taxes Income taxes (40%) Net income $98.80% 22.00 10.00 13.00 $17.50% 16.00 $21.30% 42.30 52.20% 14.10% 100.10% 5.00 10.8 cents of every dollar of sales was needed to cover cost of goods sold in 2002. 21.30 5. Inc.00 5. 100% is assigned to net sales with all other revenue and expense accounts related to it.90% 24.70% 9. This is accomplished by ratio analysis.00 2.00 % 109.3 cents in the prior year. For the income statement.00% 64.6 cents in the prior year.90% 2001 Amount $120.60% 6.30 2. also notice that only 9.00 13. Notice.9 cents out of every dollar of sales remained for profits in 2002 — down from 13.00 28.00 % 122.00 80.20% 14. for example.40% 22.10% 9.30 12.00 8.3 ALPHA.
Poor liquidity might lead to higher cost of financing and inability to pay bills and dividends. Dun and Bradstreet. Numerous online services such as AOL and MSN Money Central also provide these data. solvency (leverage and debt service). Net working capital for 2002 is: Net working capital = Current assets – Current liabilities = $124 – $56 = $68 . you will take readings of a business’s liquidity. you make some comparisons to the norms. profitability. Throughout our discussion.3. Think of ratios as measures of the relative health or sickness of a business.2 to make sure you understand where the numbers come from.Analyzing Financial Statements 265 the various financial ratios and how to interpret them. and 3. 21. you will compare a given ratio for one company over several years to see the direction of financial health or operational performance. To provide the basis for making projections and forecasts about the course of future operations.6 degrees as normal. keep referring to Figures 21. efficiency in using assets. Liquidity is crucial to carrying out the business. (b) the current ratio. You can obtain industry norms from financial services such as Value Line. The three basic measures of liquidity are: (a) net working capital. you must make two comparisons: Industry comparison — This will allow you to answer the question “How does a business fare in the industry?” You must compare the company’s ratios to those of competing companies in the industry or with industry standards (averages). To appraise the position of a business. It relates to the short term. To identify trouble spots that need attention. The results of the ratio analysis will allow you: 1. and (c) the quick (acid-test) ratio.1 and 22. blood pressure. especially during periods of adversity. asset utilization (activity). Where the doctor compares the readings to generally accepted guidelines such as a temperature of 98. heart rate. and market value.1 LIQUIDITY Liquidity is the firm’s ability to satisfy maturing short-term debt. Trend analysis — To see how the business is doing over time.. and market value. 2. leverage. To obtain useful conclusions from the ratios. typically a period of one year or less. Net working capital equals current assets minus current liabilities. Just as a doctor takes readings of a patient’s temperature. profitability. and Standard and Poor’s. etc. Financial ratios can be grouped into the following types: liquidity.
turnover) ratios reflect the way in which a company uses its assets to obtain revenue and profit. A more stringent liquidity test can be found in the quick (acid-test) ratio.3.27 $56 In 2001. net working capital was $63. The higher the ratio. the current ratio is: $124 ----------.4 for industry averages). 21. The overall liquidity trend shows a slight deterioration as reflected in the lower current and quick ratios. The current ratio equals current assets divided by current liabilities. One example is how well receivables are turning into cash. the more efficiently the business manages its assets. The ratio reflects the company’s ability to satisfy current debt from current assets. the ratio was 1. although it is better than the industry norms (see Figure 21.= 2. Inventory and prepaid expenses are excluded from the total of current assets. It is derived by dividing net credit sales by average accounts receivable.21 $56 In 2001.26. A small reduction in the ratio over the period points to less liquidity.2 ASSET UTILIZATION Asset utilization (activity. But a mitigating factor is the increase in net working capital. The accounts receivable turnover provides the number of times accounts receivable are collected in the year. leaving only the more liquid (or quick) assets to be divided by current liabilities. the current ratio was 2. The ratio’s decline over the year points to a slight reduction in liquidity. You can calculate average accounts receivable by the average accounts receivable balance during a period.266 Accounting and Finance for the Nonfinancial Executive In 2001.34. Accounts receivable ratios comprise the accounts receivable turnover and the average collection period. Current assets Current ratio = ----------------------------------------Current liabilities For 2002. The rise over the year is favorable.= 1. . Cash + Marketable securities Acid-test ratio = --------------------------------------------------------------------Current liabilities The quick ratio for 2002 is: $28 + $21 + $22 --------------------------------------.
1 days 4. Inventory ratios are especially useful when a buildup in inventory exists.5 In 2001. Cost of goods sold Inventory turnover = -------------------------------------------Average inventory The inventory turnover for 2002 is: $52 -----------. The long collection period may be a result of the presence of many doubtful accounts.46. you should examine the firm’s inventory turnover and average age of inventory.34 $18. The average collection period is the length of time it takes to collect receivables.Analyzing Financial Statements 267 Net credit sales Accounts receivable turnover = -------------------------------------------------------------------Average accounts receivable For 2002. the turnover was 1. In 2001.= 84. the turnover was 8.= $18. the collection period is: 365 --------.05 $49. or it may be a result of poor credit management.5 2 The accounts receivable turnover for 2002 is: $80. It represents the number of days receivables are held.5 For 2001.34 It takes this firm about 84 days to convert receivables to cash. . the collection period was 43. There is a sharp reduction in the turnover rate pointing to a collection problem. Inventory ties up cash. 365 days Average collection period = --------------------------------------------------------------------Accounts receivable turnover In 2002.= 1.33.3 -----------. The significant lengthening of the collection period may be a cause for some concern.= 4.1 days. Holding large amounts of inventory can result in lost opportunities for profit as well as increased storage costs. the average accounts receivable is: $21 + $16 ----------------------. Before you extend credit or lend money.
A low ratio may indicate too high an investment in assets in comparison to the sales revenue generated.6 days = 431. the average age is: 365 --------. It appears that problems are inefficient collection and obsolescence of inventory. the average age was 274. There has been a sharp reduction in asset utilization. Cash is being collected more slowly. the operating cycle was 317. the ratio was 0.5 ( $204 + $227 )/2 In 2001. By calculating the total asset turnover.= 0. although the 2002 ratios are not far out of line with the industry averages (see Figure 21.268 Accounting and Finance for the Nonfinancial Executive 365 Average age of inventory = -------------------------------------------Inventory turnover In 2002. has suffered a sharp deterioration in activity ratios.= --------------. Net sales Total asset turnover = ----------------------------------------------Average total assets In 2002.3 --------------------------------------.1 days + 347.57 ($110/$194.6 days 1. pointing to a need for improved credit and inventory management. ALPHA.5). The reduction in the turnover and increase in inventory age points to a longer holding of inventory. . the operating cycle is: 84.37 $215.= 347. An unfavorable direction is indicated because additional funds are tied up in noncash assets. the ratio is: $80.05 In the previous year. You should ask why the inventory is not selling as quickly.3 $80. Operating cycle = Average collection period + Average age of inventory In 2002.4).7 days In the previous year.5 days. The operating cycle is the number of days it takes to convert inventory and receivables to cash. you can find out whether the company is efficiently employing its total assets to obtain sales revenue. Inc.4 days.
including the ratios of other firms in the industry. which contributes to earnings instability. the ratio is: $139 ----------.55. Also. The debt ratio reveals the amount of money a company owes to its creditors. Solvency also depends on earning power.) The debt ratio is: Total liabilities Debt ratio = ----------------------------------Total assets In 2002. It is a safety margin indicator in that it reflects how much of a reduction in earnings a company can tolerate. (Capital structure is the mix of the long term sources of funds used by the firm). The trend is relatively static. Income before interest and taxes Times interest earned = ----------------------------------------------------------------------------Interest expense . Another important consideration is the size of debt in the firm’s capital structure. (Note that equity holders come after creditors in bankruptcy.3. Excessive debt may also make it difficult for the firm to borrow funds at reasonable rates during tight money markets.3 SOLVENCY (LEVERAGE DEBT SERVICE) Solvency is the company’s ability to satisfy long-term debt as it becomes due.Analyzing Financial Statements 269 AND 21. Total liabilities Debt-equity ratio = ------------------------------------------------Stockholders’ equity In 2002. which is referred to as financial leverage. the degree of access to additional debt financing. in the long run a company will not satisfy its debts unless it earns profit.58 $88 In the previous year. You should be concerned about the long-term financial and operating structure of any firm in which you might be interested. Large debts mean that the borrower has to pay significant periodic interest and principal.= 1. a heavily indebted firm takes a greater risk of running out of cash in difficult times. The interpretation of this ratio depends on several variables. and stability of operations. Times interest earned (interest coverage ratio) tells you how many times the firm’s before-tax earnings would cover interest. the ratio was 1. Excessive debt means greater risk to the investor. the ratio is: $139 ----------. A leveraged capital structure subjects the company to fixed interest charges.61 $227 The debt-equity ratio will show you if the firm has a great amount of debt in its capital structure.= 0.
and future guarantees.4. noncapitalized leases. 21. cost structure.= 0.= 0. There has been no significant change in its ability to satisfy long-term debt. Total dollar net income has little meaning unless it is compared to the input in getting that profit. you should find out about lawsuits. Net income Profit margin = --------------------------Net sales The ratio in 2002 is: $8 -----------. The gross profit margin shows the percentage of each dollar remaining once the company has paid for goods acquired. the ratio is: $15. For example.10 $80.3 -----------. You must also note liabilities that have not yet been reported in the balance sheet by closely examining footnote disclosure. Perhaps higher relative cost of merchandise sold is at fault.4 PROFITABILITY A company’s ability to earn a good profit and return on investment is an indicator of its financial well-being and the efficiency with which it is managed.3.3 The ratio was .= 7. relative to the industry averages. It gives you an idea of the firm’s pricing. the company’s overall solvency is poor.3 -----------. It means that less earnings are available to satisfy interest charges.5 times.65 $2. interest was covered 13. the ratio is: $28.3 . Poor earnings have detrimental effects on market price of stock and dividends.35 $80.0 In 2001. The reduction shows that the company now receives less profit on each dollar sales. and production efficiency.43 in 2001. although it has remained fairly constant. Gross profit Gross profit margin = ---------------------------Net sales In 2002. The reduction in coverage during the period is a bad sign.270 Accounting and Finance for the Nonfinancial Executive For 2002. Profit margin shows the earnings generated from revenue and is a key indicator of operating performance. A high margin reflects good earning potential. As shown in Figure 21. Note that significantly less profit is available to cover interest payments.
037 ( $227 + $204 )/2 In 2001. The return on total assets shows whether management is efficient in using available resources to get profit. Two key ratios are the return on total assets and the return on equity. . the return is: $8 --------------------------------------. causing a decline in both the return on assets and return on equity. Table 21.3. Also included are dividend-related ratios. As indicated in Figure 21.1 shows industries with high return on equity (in excess of 20%). (Note that these percentages are available in the common size income statement as given in Figure 21. industry comparisons reveal that the company is faring very poorly in the industry. 21. Perhaps lower earnings were due in part to higher costs of short-term financing arising from the decline in liquidity and activity ratios. the return was 0.095 ( $88 + $80 )/2 In 2001.= 0.4. as turnover rates in assets go down.= 0. profit will similarly decline because of a lack of sales and higher costs of carrying higher current asset balances. The decline in the ratio shows a downward trend in earning power.207. There has been a deterioration in the productivity of assets in generating earnings.077. Net income available to stockholder Return on common equity = ------------------------------------------------------------------------------------Average stockholders’ equity The return in 2002 is: $8 --------------------------------.14. Return on investment is a prime indicator because it allows you to evaluate the profit you will earn if you invest in the business. the return was 0. There has been a significant drop in return to the owners.Analyzing Financial Statements 271 For the previous year. The return on equity (ROE) reflects the rate of return earned on the stockholders’ investment. profit margin was .5 MARKET VALUE Market value ratios relate the company’s stock price to its earnings (or book value) per share. Moreover. Net income Return on total assets = ----------------------------------------------Average total assets In 2002. The overall profitability of the company has decreased considerably.3).
74 per share).4. Net income – Preferred dividend EPS = ----------------------------------------------------------------------------Common shares outstanding EPS in 2002 is: $8. March 1999. The sharp reduction over the year should cause alarm among investors. EPS is a gauge of corporate operating performance and of expected future dividends. also called earnings multiple.600 shares For 2001. 75–91.74 4. the industry average EPS in 2002 is much higher than that of ALPHA.9 24. You must reduce net income by the preferred dividends to obtain the net income available to common stockholders.272 Accounting and Finance for the Nonfinancial Executive TABLE 21. The price-to-earnings (P/E) ratio. investors looking for value would prefer a relatively lower multiple (cost per dollar of earnings) as compared with companies of similar risk and return. $1. by Business Week. EPS was $3. reflects the company’s relationship to its stockholders. Earnings per share (EPS) is the ratio most widely watched by investors. Used with permission. EPS shows the net income per common share owned. On the other hand.4% 31. Where preferred stock is not in the capital structure.8 32. McGraw-Hill.2 provides a list of highly profitable companies in terms of EPS.26.0 22.6 28.000 ----------------------------. A high multiple (cost per dollar of earnings) is favored since it shows that investors view the firm positively.51 per share vs.= $1.0 20.6 Source: Corporate Scorecard. you determine EPS by dividing net income by common shares outstanding. Inc. ($4. pp.1 Industries with High Return on Equity (ROE) Rates (in Excess of 20%) 1998 Cars and trucks Personal care Eating places Food processing Beverages Business machines and services Telephone 62. The P/E ratio represents the amount investors are willing to pay for each dollar of the firm’s earnings. As you can see in Figure 21. Table 21. Market price per share Price/earnings ratio = ----------------------------------------------------Earnings per share .
05 6. 2002. Assume a market price per share of $12 on December 31. McGraw-Hill. However. The P/E ratios are: $12 2001: -----------.2 1998 Highly Profitable Companies (in Terms of EPS) Ford U. March 1999. Used with permission. and $26 on December 31.76 4.68 4.3 P/E Ratios Company Boeing General Motors Goodyear Gap Intel Pfizer Industry Aerospace Cars and Trucks Tire and Rubber Retailing Semiconductor Drugs and Research 1998 32 21 13 52 37 88 Source: Corporate Scorecard. by Business Week. .= 7. March 1999.10 Source: Corporate Scorecard.= 6.9 $1. which should cause deep investor concern.98 $3. 75–91. the decline over the year in stock price was 54% ($14/$26). 75–91. McGraw-Hill. you can infer that the stock market now has a lower opinion of the business.S. Nevertheless.74 $26 2002: -----------.26 From the lower P/E multiple.57 41. some investors argue that a low P/E ratio can mean that the stock is undervalued. by Business Week.3 shows price-to-earnings ratios of certain companies. pp.84 6.Analyzing Financial Statements 273 TABLE 21. Home Alcoa CIGNA IBM Washington Post $17. 2001. pp. Used with permission. TABLE 21. Table 21.
one affects the other) so that problems in one area may spill over into another. book value per share was $17. This appears to have happened to the company in our example. market price did exceed book value. However. In 2001. activity.. whereas one with new assets may have a low ratio.274 Accounting and Finance for the Nonfinancial Executive Book value per share equals the net assets available to common stockholders divided by shares outstanding. By comparing it to market price per share you can get another view of how investors feel about the business. because it indicates that each share now has a higher book value.4 shows the dividend payout ratios of some companies. The major indicators of a company’s performance are intertwined (i. some analysts may argue that the stock is underpriced.000 – 0 = --------------------------.39.= 0. The book value per share in 2002 is: Total stockholders’ equity – Preferred stock Book value per share = -------------------------------------------------------------------------------------------------------Common shares outstanding $88.63 $19. you should note the changes in the ratio in an effort to appraise the corporate assets. but there is now some doubt in the minds of stockholders concerning the company. The increased book value per share is a favorable sign. the ratio was 1.13 4. The ratio equals: Market price per share Price/book value = ----------------------------------------------------Book value per share In 2002. A company with old assets may have a high ratio.5. Market price of stock may have dropped because of a deterioration in liquidity.e. and profitability ratios. The price/book value ratio shows the market value of the company in comparison to its historical accounting value. which means that the stock market does not value the security highly. market price is much less than book value. The significant drop in the ratio may indicate a lower opinion of the company in the eyes of investors. the ratio is: $12 --------------. Hence. Dividend ratios help you determine the current income from an investment. However. Two relevant ratios are: Dividends per share Dividend yield = ----------------------------------------------------Market price per share Dividends per share Dividend payout = ----------------------------------------------Earnings per share Table 21. .600 In 2001.= $19. in 2002.13 In 2001.
The figure also shows the formula used to calculate each ratio. companies with ample opportunities for growth at high rates of return on assets tend to have low payout ratios. although they have been above the industry averages. Leverage (amount of debt) has been constant. In consequence. 1999.1 0. A material deterioration in the activity ratios has occurred.Analyzing Financial Statements 275 TABLE 21. the return on the owner’s investment and the return on total assets have gone down. They are not terribly alarming. Stockholders look unfavorably upon reduced dividends because they are a sign of possible deteriorating financial health.4 0. as receivables and inventory turn over less.4 AN OVERALL EVALUATION — SUMMARY OF FINANCIAL RATIOS As indicated in the chapter. The higher costs may be due to receivable and inventory difficulties that forced a decline in the liquidity and activity ratios. total utilization of assets. a single ratio or a single group of ratios is not adequate for assessing all aspects of the firm’s financial condition.com). The last three columns of the figure contain subjective assessments of ALPHA’s financial condition. shows a deteriorating trend. (Five-year ratios are generally needed for trend analysis to be more meaningful.msn. However.3 0.4 Dividend Payout Ratios 1998 General Electric General Motors Intel Wal-Mart Pfizer Hewlett Packard 1. based on trend analysis and 2002 comparisons to the industry norms.2% 2. however. we see from the drop in the current and quick ratios that there has been a slight detraction in short-term liquidity.) By appraising the trend in the company’s ratios from 2001 to 2002. 21. In 2002. But working capital has improved. The earnings decrease may be partly due to the firm’s high cost of short-term financing and partly due to operating inefficiency. April 11. there is less profit available to satisfy interest charges. There is no such thing as a “right” payout ratio. Also. because these ratios are not way out of line with industry averages. .9 Source: MSN Money Central Investor (http://investor. However. Figure 21. along with the industry average ratios for 2002. profit will fall off from a lack of sales and the costs of carrying more in current asset balances. indicating that improved credit and inventory policies are required. it is consistently below the industry average in every measure of profitability. ALPHA’s profitability has deteriorated over the year.4 summarizes the 2001 and 2002 ratios calculated in the previous sections. Furthermore. as indicated by the total asset turnover. Used with permission. however.5 0.
26 1.7 days N/A 0.34 68 2.276 FIGURE 21.1 days 66.58 7.37 0.33 1.05 1.46 4.4 ALPHA.61 1.21 1.34 5.44 OK OK OK N/A N/A OK poor poor poor poor poor poor poor poor poor poor poor poor Accounting and Finance for the Nonfinancial Executive SOLVENCY Debt ratio Debt-equity ratio Times interest earned Total liabilities/Total assets Total liabilities/Stockholders’ equity Income before interest and taxes/Interest expense 0.61 1.55 13. Summary of Financial Ratios — Trend and Industry Comparisons Evaluationb Definitions 2002 2001 Industrya Ind.11 good OK OK good OK OK good OK OK ASSET UTILIZATION Accounts receivable turnover Average collection period Inventory turnover Average age of inventory Operating cycle Total asset turnover Net credit sales/Average accounts receivable 365 days/Accounts receivable turnover Cost of goods sold/Average inventory 365 days/Inventory turnover Average collection period + Average age of inventory Net sales/Average total assets 8.27 Current assets – Current liabilities Current assets/Current liabilities (Cash + Marketable securities + Accounts receivable)/Current liabilities 56 2.2 274.1 days 84.65 N/A 1.5 0.6 days N/A 317.05 1.5 days 431.3 10 N/A poor OK OK poor poor OK poor poor . Inc.4 days 1. Trend Overall Ratios LIQUIDITY Net working capital Current ratio Quick (acid-test) ratio 63 2.4 days 347.5 43.57 0.
077 0.1 0.FIGURE 21.14 0. 277 .037 0.12 N/A N/A poor OK N/A N/A poor poor good poor poor poor good poor a b Obtained from sources not included in this chapter.15 0.51 7.4 (continued) ALPHA.43 0.1 0.207 0.27 Gross profit/Net sales Net income/Net sales Net income/Average total assets Earnings available to common stockholders/Average stockholders’ equity poor poor poor poor poor poor poor poor poor poor poor poor MARKET VALUE Earnings per share (EPS) Price/earnings (P/E) ratio Book value per share Price/book value ratio Dividend yield Dividend payout 3.74 6. Trend Overall PROFITABILITY Gross profit margin Profit margin Return on total assets Return on equity (ROE) 0. Inc.48 0.63 4.9 19.39 1.26 7.35 0.13 0.98 17.5 (Net income – Preferred dividend)/Common shares outstanding Market price per share/EPS (Total stockholders’ equity – Preferred stock)/Common shares outstanding Market price per share/Book value per share Dividends per share/Market price per share Dividends per share/EPS 1.095 0. Represents subjective evaluation. Summary of Financial Ratios — Trend and Industry Comparisons Evaluationb Definitions 2002 Industry 2001 a Analyzing Financial Statements Ratios Ind.
The 2001–2002 period. 21. however. Each ratio should be compared to industry norms and analyzed in light of past trends. Financial analysis also calls for an awareness of the impact of inflation and deflation on reported income. it appears that the company is doing satisfactorily in the industry in many categories. The business needs to concentrate on increasing operating efficiency and asset utilization. activity. In summary.278 Accounting and Finance for the Nonfinancial Executive The firm’s market value. Management must also recognize that alternate methods of financial reporting may allow firms with equal performance to report different results. . Most analysts favor certain ratios and ignore others. as measured by the price-to-earnings (P/E) ratio. is respectable as compared with the industry — but it shows a declining trend. seems to indicate that the company is heading for financial trouble in terms of earnings.5 CONCLUSION Financial statement analysis is an attempt to work with reported financial figures in order to determine a company’s financial strengths and weaknesses. and short-term liquidity.
152–153 using for short-term financing. 25–26 Billing policy. 245 Accounts receivable management analysis. 163 Balance sheet. 220 ACE-Net. 222–223 ratings. 16 pricing standard products. 266–268. see Accounting rate of return Assets accounting conventions. see Loans Bankers. 8–10 use of information and financial decision making. 87. 36–37 what and why of sales. 212 Biases. 196 Banker’s acceptances. 196–197 Bankruptcy. 33 cost-volume-profit analysis. 266 turnover. 223–224 Book value per share. 21 Automation. real. short-term and financing. see Annual percentage rate Arm’s length transaction. 29 margin of safety. 69 Bid price. see Loans. 127–128 computing interest. 6. 112–114 Account. 122. 201 Assignment. 98–99 credit references. 42 Adventure Capital Register. 10–11 long. 21 America’s Business Funding Directory. 5 Accounting rate of return (ARR). 230–231 Bonds advantages/disadvantages. 130 present value. 225–227 calculation of values. 69 Best-efforts sale. 198 Authorized shares. 212 279 . 238 Amortized loans. 251–255 finance relationship. 156.Index A ABC method. 24. 26. 17 Average tax rate. 181 B Back orders. 99–103 credit policy. see Angel Capital Electronic Network Acid-test. 240 Annual percentage rate (APR). 239 Advertising costs. 154 Average age of inventory. 205 Bank loans. 274 Breaking even cash point. 119–120. dealing with. amortized Angel Capital Electronic Network. 158–159 turnover. 232. 299 Basic standards. 155 return on equity. 99 Blue sky laws. 252–255. 125–126 Annual report. 224–225 refunding. 33 operating leverage. 256. 256–257 Accounting conventions. 276 financial statements. 169 ARR. 97–98 ratio. 27 features. 246. 244–245.vs. 262 Balloon payments. 220 Board of Directors. 221. 231 Auto expenses. 227–228 types. 243 Annuity future values. 85 mortgage bonds. 267–268 Average collection period. 258 analyzing financial statements. 68 Administrative expenses composition of master budget. 223–224 mortgages. 222 return on investment reduction strategies. 258 Account numbering system. 137–138 Accounts payable. 247 financial vs. 132–134 APR. 105. 251–259 equation. 29–33 Broker. 61 contribution margin analysis. see Quick ratio Actual costs. 34–35 sales mix analysis. 267 Average costs. 266–267 Accredited investors.
credit policy. 10 Capital Network. 65 what assumptions are made. see also Individual entries convertible bonds. 98 Compound annual interest rate. 238 Business organizations. 171 Conditional sales contract. 5 Compensating balance. delaying. see also Vertical analysis Common stock. see also Common stock Collateral. 16. 227. 46 Contribution price. 143–144 types of investment projects. 41. 167 utilizing scarce resources. 229 Call provision. 24. 206. 179. 193. 200 Collateral trust bonds. 3–4 segment performance appraisal. 12–13 Cost allocation. 192. 246. 76–78 limitations and capital investments. 9 Convertible bonds. 63 Business Finance Mart. 165 shortcut approach to formulation. 42. 148–150 Budget/budgeting computer-based models. 140–141 types of depreciation methods. 91 Chargebacks. 183–184 Capital markets. 206. 195 Competition. 6. 86 Cash break-even point. 207 . 26–27 special orders. 227–228. 25–26 determining profit from year to year. 147–150 Capital losses. 88. 33–34 Cash budget. 252–255 C C corporation. 221 Constraining factor. features. see also Indirect costs Common-size statements. 197 Commercial Finance Online. 224. 106. 92–93 Centralization. 4. 44. 86. 41 utilizing capacity. 11–14 Business transactions. 197 Commissions. 140–141 nonfinancial manager concern with finance. 229 Cancellation clause. 18. see also Leasing Capacity. 135 what to know about cost of capital. 208. 182 Corporate taxes. 247 Capital gains. 75 Controller. 225 Corporate borrower. 60 Contribution income statement. 230–234. 214 return on investment. 17 Controllable variance. 65–66. 165 analysis. 136 income tax affect on investments. 119–120. 239 Commercial paper. 181 Corporation.280 Accounting and Finance for the Nonfinancial Executive Checks. 167 Contribution margin adding or dropping a product line. 19 capital. 44. 193. 87. 40. 207 Collateral certificate. 191. 99 Commercial finance company loans. 225 Collection policy. 24–25. 126–127 Compound annuity. 8. 136–140 modified accelerated cost recovery system rule. 3. 224. see also Loans Corporate shareholders. recording. 227 Call price. 235 issuing and initial public offering. 141–142 measurement of investment worth. 55 what is. 52–55 what is structure. 263. 231. 166 Chart of accounts. 158–159 Communication. 13 Call premium. see also Common stock Class B common stock. 45–46 Contribution approach. 20. 256–258 Chattel mortgage. 43 Capital. 55–65 Budgeted balance sheet. financial statements. 61–63 Cash flow. forms. 40. see also Annuity Computers. 28. 19 Common costs. 145–147 selection of best mix of investments with limited budget. 240 Capital structure. intradepartmental. 108–109 Cash balance. 88–92 Cash payments. 224 cost of capital. 41 Controllable costs. 45 analysis determining a bid price. 183–184 Capital investment decisions features of investment projects. 65–66 electronic spreadsheets to develop a plan. 20–21 behavior. 231. 65 flexible in performance reports. 64–65 Budgeted income statement. 207 Confidentiality. 36 segment performance appraisal. 92 Class A common stock. 28 ratio. 50 Carrying costs. 148–149 features. 9–10 inflow.
154 Cost-volume-profit (CVP) analysis. 45–46 Deficit section. see also Taxes Dividend ratios. 95. 90. 190 Discretionary costs. 15–17 Deposit collection float. 39–40 remembering qualitative factors. 212 Debentures. and decision making. 228–229. 71. 44 pricing standard products. 97 Creditor. 18–19 importance of cost data. 40–41 adding or dropping a product line. 92 Credit limits. 182 Division performance. 91 Deposits. 195. 107 281 analyzing the make-or-buy. 162 Dividend income. 266 CVP. 154. corporations. 43 pricing standard products. 20 types. 5–10 nonfinancial manager’s concern with finance. 98. 274–275 Dividends common stock. 107–108 operating leverage. 231. 269 expected and type of customer. 98 Credit line. 196. 165–166 Cost-benefit analysis. 46–47 utilizing scarce resources. 221 Discount rate. 16 Direct labor. 42 Direct material budget. see Incremental costs Direct costs. 135 contribution margin analysis. 62 Department costs allocation. 215. 258 Debits/credits. 40. 24–28 inventory analysis. 27 features. 18. 259 Debt cost of. 88 Depository transfer checks (DTS). 85 types and usefulness of long-term. 72 Cost center. 26. 15 learning from the Japanese. 59 Direct labor costs contribution margin analysis. 5 capital investment. 20 analysis. 269 Debt service. 98–99 Credit rating. 223. 20–21 concepts for planning. 215–216 short-term nonroutine decision making. 16 make-or-buy decisions. 168 Dissolution. see Interest rates Credit cards. 258. 166. 194. 257. 86 Depreciation. 94. 62 Disclosures. see Line of credit Credit policy. 21. 3–4 what are scope and role of finance. 223 cash. see Double-declining-balance method Dealer. 120–121. 261 Cumulative preferred stock. 44–45 . 16 make-or-buy decisions. 24. 39–40 variance analysis. stock. 42 Direct selling. see also Individual entries Current ratio. 99 return on equity and return on investment. 143–145 Depreciation expense. see Cost-volume-profit Cyclic counting. 29 Coupon interest.Index data. 197 Credit references. control. 27 features. 147. 162. 233. 21 segregating fixed and variable. 269–270 Decision making –analysis financial and operating environment. 97–98 Credit terms. 166 D DDB. 225 Debit balance. 58–59 Direct material costs contribution margin analysis. 43 pricing standard products. 24 Direct labor budget. 156. 230 Dividends paid. 245 Distribution. 181. 35 short-term nonroutine accepting or rejecting special order. 17–18 how they behave. 234 preferred stock. 228. 158–159 short-term and seasonal inventory purchasing. 10–14 importance of finance. 78 Disbursements section. 15 going public. 148 –equity ratio. 122 Discounts. 41–42 relevant costs. 43 determining whether to sell or process further. 26. 33 Differential costs. 222–228 Debt ratio. 211 District sales office.
99–100. 60 Factory overhead costs. 189. 62 Financing intermediate-term bank loans. 198 Factory overhead. 189–190 Fixed assets. 275–278 what and why. 65 Ending inventory. 249–250 Financing needs. 154. 219–220 Finance accounting relationship. 207 Equity. 264–275 Financial statements analyzing horizontal and vertical. 10. 196–197 cash discounts. 243–247 statement of cash flows. 152–153 modified. 196 understanding income and balance sheet. 5–10 nonfinancial manager’s concern. 156. 208 Financial markets. 230–234 financial statements. see also Individual entries External functions. 18. 23–27 features. 69 Expected cash payments. 222–228 venture capital. financing. 245. 6. 111–112 Economic order quantity (EOQ). 5 Financial Accounting Standards Board (FASB). 247–250 Financial vice president. 50 Financing section. 211–212 publicly and privately placed securities. 245–247 preferred stock. 251–259 Financial lease. 190 commercial finance company loans. see Leasing long-term equity securities. 8–10 importance. 190–196 banker acceptances. 199–201 issuing commercial paper. 258 common stock. 205–206 leasing. see Depository transfer checks Du Pont formula. see Earnings per share Equipment. 10–11 Financial budget. 36–37 contribution margin analysis. 228–230 stock rights. see also Interest Efficiency. 69. 16 Double taxation. 16 FASB. 8 Financing activities. 167 behavior. see also Profits Earnings multiple. see Inventory. 55 Financial information. see Economic order quantity EPS. 262–264 summary of financial ratios. 109–110 Effective rate. 43 Factory overhead budget. see Economic order point EOQ. see also Individual entries accounting conventions. see Depository transfer checks DTS. 196 inventories for financing. 220–221 short-term advisability of bank loans. recording. 197 other assets used for financing. 21 EOP. 58–59 Expenses. 184 Double-declining-balance (DDB) method. 272. 181. 213–220 investment banking. 258. see Financial Accounting Standards Board Federal exemptions. 235–240 going public–initial public offerings. 197 dealing with bankers. 212–213 types and usefulness. 202–203 trade credit. 228–235 finance choices. 273 Earning potential. 97–98 E Earnings per share (EPS). 170 Electronic spreadsheet. 264–275 availability and dealing with bankers. 158–159 Dun & Bradstreet report. 234 Expected–actual figures. 261–262 working with financial ratios. 98–99 Economic order point (EOP). 243–244. 252–255. 194. ending Entertainment expenses. 30–33. 19 break-even analysis. see Static budget Fixed costs adding or dropping a product line. 44 allocation and segment performance appraisal of profit center. 126. 144 Double-entry accounting.282 Accounting and Finance for the Nonfinancial Executive Financial assets. 197–199 sources. 67. 195. see also Assets Fixed budget. 3–4 Financial accounting. 201 receivables. 248 . 251–259 DTCS. 11 Financial ratios. 8 F Factoring. 244. 8. 272 Economic conditions. 162 Earnings.
224 intermediate-term loans. 24. 217–218 cons. money. 269 Interest income. see also Taxes Interest rates. 197 convertible bonds. 146 Hedging. 209 preferred stock. 182. 41 Fixed overhead contribution margin analysis. 16 Initial public offering (IPO) alternatives. 25. 53 preparation. 105–106 economic order quantity. see also Taxes . 212. 27 pricing standard products. 222 Indications of interest.com. 224 short-term financing. 54. 117–118. 200 Flotation cost. 39. 234 Forecasted income statement. 108 Full-cost approach. 49 Horizontal analysis. 20 short-term nonroutine decision making. 139–140 Internal Revenue Service (IRS). 218–219 pros. 214. 49–50 percent-of-sales method. 238–240 Interperiod tax allocation. 233 Gross profit margin.Index flexible budget and performance reports. see Generally Accepted Accounting Principles Garage. 111–112 G GAAP. 6 Going public. 184–185. see also Loans amortized loans. 42 Flexible budgets. 26 Indenture. see also Initial public offering Insurance company term loans. 17. 124–125 calculation for bonds. 76 Float time. 215–217 how does it work. 243–247 Income bonds. calculation. 194–196.191. 218. 206. 207 Interest coverage ratio. 88 Floating lien. 20 Historical patterns. forecasting. 68 Income. 185 Freight. 229 prime. company. 27 Forecasting how it is used. 248–249 Goals. 110–111 carrying and ordering costs determination. 41. 180 Intrayear compounding. 50 what is. 225 Income statement. 109–110 reorder point or economic order point determination. 8 Internal rate of return (IRR). 219–220 avoiding the drawbacks. 181 Interest paid. 270 Gross/net sales. 199 Internal functions. 49 Foreign tax credit. 112–114 analysis. 118–119 Inventory average age. 224. 262–264 I Immaterial variances. 214–215 Installment loans. 80 Growth rates. 214 Indirect costs. 240 Generally Accepted Accounting Principles (GAAP). 225 H Half-year convention. 34–35 segregated determination. 107–108 avoiding stockouts. 179. 222–223 commercial finance company loans. 217–218 Gordon’s growth model. 232–233 Future values. 76 operating leverage. 193 serial bonds. 129 283 Income and balance sheet. 40. 148–149. 224. 86 raising. 108–109 considerations. 50–52. 42 Funds investment banking. 126 Guaranteed bonds. 195 Institutional investors. 263. 264 Income taxes. 193. 60–61 management ABC inventory control method. 26. see also Taxes Internet. drawbacks. 214 process. 267–268 ending and composition of master budget. estimated. 25. 141–142 Incremental costs. 85 High-low method. 211 managing cash properly. 44 Incremental orders. 205 leasing.
131 J Japanese. 44 Joint products. 94 financing with equipment. 240 Money future values calculation. 14. 44 Journals. 206 L Labor efficiency variance. 215 Minimum required rate of return. 222 K Kickers. 231. 173 profit center. 88 Mailing delays. 181 Market price. 161–162 cost center. 262 Management performance Du Pont formula. see also Leasing Make-or-buy decisions. 200. 147 Mission. 256 Leverage. 156–159 what is. 89–90 Maintenance. see Initial public offering IRR. 86 Liquidity. 90 return on investment. 192–193 Line of credit agreement. 211–212. 54 Mixed payments. 208 Liabilities accounting conventions. 50. 165 investment center. 154–156 return on equity. 21 Measurement. 199–201 Inventory ratios. 190–196 Loanwise. see Internal Revenue Service Issued shares. 124–125. 78–80 Master budget. 43 Management. 120–121. 88–89. 85 short-term financing. see Internal rate of return IRS. see Modified accelerated cost recovery system rule Mail float. cost analysis. 207 . 207. 218 Investment center. 73–74 Lead time. 245. 185 Limited private offerings. 55–56 Material variances. see Limited Liability Companies Loans amortized. 238 Lockbox system. 49–50 Managerial accounting. 207 insurance company term.com. 51 Manufacturing costs. 207 short-term bank. 276 LLCs. 106 Leasing. 17. 136–140 Mergers/acquisitions. 24 Margin of safety. 172–173 using forecasts. 230. 21 Joint costs. 277 common stock. 35 Line of credit. 252–255. 156 seasonal purchase and financing assets. capital investment projects. 156–159. 152–153 return on investment profit objective. 207–210 Ledger. 71–73 Materials. 33 Marginal tax rate. 153–154 profit planning. company. analyzing financial statements. 247 Limited Liability Companies (LLCs). 261–262 IPO. 68. 206 early repayment and working capital management. 121 Modified accelerated cost recovery system (MACRS). 145–147. 246. 168. 117 intrayear compounding. 233–234 Marketing. 267 Inventory turnover. 259 Junior mortgages. 269–270 Leveraged lease. 117–118. 118–119 present value. 219 Line managers. 15. 267 Investing activities. 238–239 revolving credit. 258 financial statements.284 Accounting and Finance for the Nonfinancial Executive intermediate-term bank. 180. 5. 170 Market value analyzing financial statements. 129 importance of time value. 184 Money Hunt. 8–9 Managerial functions. 205–206 online. 249 Investment banking. 265–266. 151–152 Manager performance appraising. 6 Investors. 173 Investment decisions. 271–275. 46 Labor variances. see also Common stock M MACRS. 74 Labor hours.
138. 214 P Partial payments. 124–125 Private Securities Litigation Reform Act of 1995. 268 Operating leverage. 233. 238–239 Open market. 3–4. 105. 235 return on investment. 174–177 Periodic inventory. 108–109 Other people’s money (OPM). 30. 245 NPV. see also Net income break-even analysis. 13. Loans Principal. 26 financial statements. 228–229. 55 Operational lease. 50. 105. 231. see also Assets Prospectus. 122–123 Posting. 277 index and capital investment measurement. 214 Operating activities. 155–159 Profit center. 239 National Venture Capital Association. 141 Price/book value ratio. 216 Pro forma balance sheet. see Price/earnings ratio . 140. 244 –losses. 265–266 New issue market. see also Interest rates. 179. 232. see also Individual entries cost of capital. 44–45. 191. 95. 259 Preferred stock. 170 Net income. see Interest rates Noncumulative preferred stock.Index Money market funds. 223 Present value (PV). 218 Proxy statements. 226 Outstanding shares. 65–66 Ordering costs. 138–139. 140 return on investment. 106 Perpetuities. 34–35 Operating loss carryback/carryforward. 165 Note payable. 207–208 OPM. 52–54 Nonmanufacturing costs. 171–172 year to year. see Other people’s money Opportunity costs. 185 Payback period. 26–27 Property. 16 Nonprofit organizations. 166–173 Profits. 152–153 Net present value (NPV). 223–224. 155 standard products and short-term nonroutine decision making. 213 Nominal interest. 168. 136–137 PE. 239 Negative pledge clause. see Present value N National Financial Services Network. 12 Partnerships. 14 margin. 141 Net working capital. 88 Product line. 53. 153–156 segment performance appraisal. see Net present value O Online loans. 32 contribution margin analysis. 139. 274 Price/earnings (PE) ratio. 270–271. 244. 58 Profitability analyzing financial statements. 182–183. see also Common stock Overhead variance. 184. 94. 108 Optimization. 180 285 Percents-of-sales method. 74–76 Oversubscription. see also Profits Net performance margin. 231. 106 Perpetual inventory. 86 Mortgage bonds. see also Individual entries Nonfinancial manager. 193. 225 Mortgages. 65 Processing float. 231 PV. 218 power and return on investment. 222 Negotiated market value. 76–78 return on investment. 272–273 Pricing common stock. 12. 228–230. 50–52 Performance reports and flexible budgets. 41–42 Prime interest rate. 222 Municipal bonds. 249 Operating cycle. 51 Production budget. 140. 12. 152–153. 233 establishment and costs. see also Taxes Operational budget. 51–52. 17. 245 Pass-through status. 158–159 Premium. 15 initial public offering. 92 Partnership contracts. 270–271 return on investment. 259 Posting reference. 148 features.
31–32. 161–162 responsibility center cost center. 78 Sales mix analysis. 228 Small Business Administration (SBA). 65–66 Sinking funds. 154–156 return on equity. 214–217 inventory management. 272 calculation and return on investment. 197–199. 57 growth and nonfinancial manager concern with finance. see also Assets Receipts section. see also Individual entries Security laws. 173–177 profit center. 45–46 Responsibility accounting. 161 Self-liquidating loans. 271. 156–159 segment performance appraisal. 219 Regulation D. 135–136 Repurchase agreements. 162–164 Segmental reporting. 57 Salespersons. 51. see also Bonds Simulations. 27 pricing standard products. bonds. 264 Raw materials. 147. 192 Selling expense budget. 98 Replacement decisions. 50. 243. 219 Segment performance manager performance appraisal. 197. 214 SEC. see Small Company Offering Registration SCORE. 87 Residual income (RI). and receivable collection. 5 Revenue. 221 Road show. see Residual income Rights. 224. 184 Simple yield. 25. 162 Retained earnings. 107 operating leverage. 231 Risk high and credit policy. 17 Senior mortgages. 215 Securities. see also Leasing Sales commissions. 173–175 what is. stockholders. 258 Revenue center. 222 Serial bonds. 238 Shareholder distribution. 16 contribution margin analysis. see Securities and Exchange Commission filings Secured loans. see Return on equity ROI. 6 utilizing scarce. 224 Ratio analysis. 191. 212–213. 219 Relevant costs. 162 venture capital financing. 217. 239 R Ratings. 35 segment performance. 218 ROE. see Return on investment . 70–71. 34 Semivariable costs. 61 Selling expenses features. 266 S S corporations. 218. 165–166 investment center. 166–173 revenue center. 10–11. 109–110 Sale/leaseback. 4. 208. 30. 238. 17. see also Bonds Service Corps of Retired Executives (SCORE). 207 RI. 227–228 Registration. 105 Real assets. 153–154 profit planning. 226. 200 Refunding. 18 Reorder point. 111–112 Repayment record.286 Accounting and Finance for the Nonfinancial Executive Q Quick ratio. 54 managing and financial manager’s role. 155 revenue center appraisal. 92 forecasting and budget. 212. 175–176 Resources allocation. 223. taxes. 162–164 Revolving credit. 149. 98 initial public offering. 62 Receivables. 79–80 SBA. see Service Corps of Retired Executives Screening. 271 Return–risk tradeoff. 151–152 Return on total assets. 39 Rent. 156–159 Return on investment (ROI) analyzing financial statements. see also Breaking even Seasonal datings. 8. 24. 98 Seasoned equity offering. budgeting models. see Small Business Administration Scheduling cost. 217–218. disbursal. 108 SCOR. 163 variance analysis. 185 Safety stock principle. 36–37 Sales volume. 271 profit objective. 192 Securities and Exchange Commission (SEC) filings. 149 Return on equity (ROE) analyzing financial statements. 123–124. 42 Selling price. 4 return on investment. 17. 26.
24–25. 44 SYD. 123–124 future value of annuity. 154. 76. 211. 166. 181 Trust receipt loan. 180–185 foreign credit. 155 U Uncontrollable costs. 87 Tax returns. 46 Variable overhead. 117–118. see also Individual entries compensation plans. 41 utilizing scarce resources. 41–42 Standards. 211. 185 return on investment. 192 T T-account. 269–270. 34–35 segment performance appraisal of profit center. 9–10 Treasury bills. short-term. 257 Tax-exempt income. 39. 218 Training. 276 Sophisticated investors. 17 Standard products. 216 rights. 122. 13 Subordinated debentures. 8. 247–250 Static budget. 126–127 deposits to accumulate a future sum. 19 break-even analysis. 40–41 Split-off point. 68–69 State exemptions. 265 Triple taxation. 128 Standard costs. 179–180 Time deposits. 18. 125–126 bond values. 223. 200 Turnover margin. 105 Stockouts. 143–144 Sunk costs. 231 Trend analysis. 180 Tax exempts. 230–234. 77 Stock. 40. 216 Unfavorable labor rate variance.Index Small Company Offering Registration (SCOR). 119–120. 153. 228–230. 215 features common. 30–33. 17. 76 Uniform Securities Act. 212 Spreadsheet programs. 74 Unfavorable material price variance. 214 287 future values–how money grows. see Sum-of-the-years’-digits Syndicates. 17 Underwriters. 20 flexible budget and performance reports. 224. 124–125 annual percentage rate. 106 Unsecured loans. 235 option plans. 220 Special orders. 25. 86 Time value. 129 intrayear compounding. 235 preferred. 245 Solvency. 142 Taxes computation. 16 Traceability. 234 Stock balance. 76 operating leverage. 235–240 Subchapter S corporations. 44 behavior. 16 Trade credit. internal. 120–121. 11–12. 132–133 how much is money worth now. 225 Sum-of-the-years’-digits (SYD) method. 26. 87 Treasury stock. 8 Tax shield. 131 mixed streams of cash flows. 155–159 strategies and planning. 231 price and management decisions affects. 122–123 present value annuity. 130 V Variable costs adding or dropping a product line. 167 short-term nonroutine decision making. 17 contribution margin analysis. concept amortized loans. 110–111 Straight-line method. see Interest rates Statement of cash flows. 128 Times interest earned. 36–37 characterization. 40. 214. 171 Transfer price. 42 . financing. 118–119 perpetuities. 220 Unit cost. 122. 189–190 Trading. 169–173 Treasurer. 126 use of calculators and spreadsheet programs. 27. 220 Stated interest. 220 Sole proprietorship. 23–28 determination. 143 Strategies. 121 rates of growth. 72–73 Unfavorable overhead volume variance. 44 Spread. 127–128 compound annual rate of interest. 269 Timing of changes against revenues.
225 Variance analysis cost. 5 Volume discounts. 72–73 overhead. 80–81 Wire transfers. 91 Working capital management accelerating inflow. 73–74 managerial accounting. 75 Voting rights. 92–93 opportunity cost of foregoing cash discount. 78–80 usefulness. 223 Z Zero balance accounts. 94–95 Volume variance. 94–95 Y Yield-to-maturity. 88–92 calculation and financing assets. 9 materials.288 Accounting and Finance for the Nonfinancial Executive Variable-rate bonds. 220–221. 245 W Warehousing costs. 94 proper. 72 defining a standard. 85 delaying payments. 76–78 labor. 69 standards and variances in marketing. 70–71 flexible budgets in performance reports. see Venture capital financing Venture capital (VC) financing. 86–88 volume discounts. 224. 74–76 setting standards. 239–240 Venture Capital Resource Library. 68 determining and evaluating sales. 231. 262–264 Vocabulary. 80–81 VC. 92 Zero coupon bonds. 68–69 warehousing costs. 224. 225 . 239 Vertical analysis.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218188132.48/warc/CC-MAIN-20170322212948-00360-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 616,574 | 439 |
https://ui.adsabs.harvard.edu/abs/2010arXiv1010.4046N/abstract
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math
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In this paper, we study anisotropic Bessel potential and Besov spaces, where the anisotropy measures the extra amount of regularity in certain directions. Some basic properties of these spaces are established along with applications to elliptic boundary value problems.
- Pub Date:
- October 2010
- Mathematics - Classical Analysis and ODEs;
- Mathematics - Analysis of PDEs;
- 20 pages. Corrected some typos and incorporated suggestions from referees. To appear in Math. Nachr
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s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358078.2/warc/CC-MAIN-20211127013935-20211127043935-00362.warc.gz
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CC-MAIN-2021-49
| 477 | 6 |
https://www.reference.com/science-technology/marine-biologists-use-math-work-6bb1c5f5a42c2cb1
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math
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How Do Marine Biologists Use Math in Their Work?
Marine biologists use trigonometry and algebra to establish measurements. They also use math for measurement equivalents, as they frequently need to convert between standard and metric units of measurement.
Because math is the essential language of science, marine biologists use math to solve a number of complex problems in their line of work. These problems require the need for the biologists to collect and analyze data in a variety of forms. Marine biologists use the data to make theoretical models and predictions, and that information is sometimes used to establish policy changes. Sometimes marine biologists have tasks that require solutions to be prepared at a number of different concentrations, and solving those problems requires the skill of balancing equations and algebra.
Anyone studying marine biology in college is required to take a number of different math courses, such as algebra and trigonometry, which are helpful in establishing measurement. Some colleges require the successful completion of algebra, trigonometry and possibly elementary analysis or precalculus before enrollment in a calculus course. Calculus helps with data analysis and mathematical modeling. Some colleges require those studying marine biology to take at least one statistics course. Marine biologists utilize statistics to test hypotheses and mathematical models.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710890.97/warc/CC-MAIN-20221202014312-20221202044312-00476.warc.gz
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CC-MAIN-2022-49
| 1,413 | 4 |
https://books.google.gr/books?id=ldoDAAAAQAAJ&hl=el&lr=
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math
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Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
added algebraical amount arithmetic becomes called coefficient complete compound contain cube root decimal denominator difference digits divided dividend division divisor equal equation examples expressed factor find the numbers Find the sum former fourth fraction gain geometric give given greater greatest common measure half harmonic Hence increased integral interest involving last term least less letters logarithm means method miles multiplied negative number of terms obtain permutations persons placed positive preceding progression proportion prove quantity question quotient ratio reduced remainder represent respectively result rule share shew sides simple solution square root subtract surd taken things third true twice unity unknown quantity variations whence whole write written
Σελίδα 40 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 201 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...
Σελίδα 24 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141733122.72/warc/CC-MAIN-20201204040803-20201204070803-00027.warc.gz
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CC-MAIN-2020-50
| 1,689 | 7 |
https://math.answers.com/math-and-arithmetic/A_right_angle_has_how_amny_degress
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math
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Square, Rectangle, Right Triangle...
It has 90 degress.... Hope these helps (:
It ranges between 180 and 360
less than 90 degress
I think that is obtuse
...is a right angle.
The Right Angle.
A five right angle turn is 450 degress. It ia an ubtuse angle, which means it ia greater than a right angle, 90 degress.
well right angle is 90 degress or a perfect l a straight angle is 180 degress
90 degreesA right angle is 90°.
a right angle measures 90 degrees
A right triangle.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710924.83/warc/CC-MAIN-20221203043643-20221203073643-00105.warc.gz
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CC-MAIN-2022-49
| 474 | 12 |
https://pdfslide.net/documents/environmental-geology-mass-wasting-and-hillslope-processes-taylorsg473masswastpdf.html
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math
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Mass Wasting and Hillslope Processes
I. Hillslope Physics / Physical Properties of Regolith
A. Basics of Slope Stability
1. Fundamental Terms
a. Energy - ability to do physical work
(1) Mechanical Energy
(a) Potential Energy - energy of position
Ep = mgh
where Ep = potential energy (joules), m = mass (kg), g = acceleration due to gravity (9.8 m/sec ), h =2
height of material above reference surface (m)
Units: 1 J = 1 kg-m /sec2 2
(b) Kinetic Energy - energy of motion
Ek = 0.5mV2
where Ek = kinetic energy (joules), m = mass (kg), V = velocity (m/sec)
Units: 1 J = 1 kg-m /sec2 2
b. Force - push or pull action on a mass of material
Newton's Second Law: F = ma
where F = force (newtons), m = mass (kg), a = acceleration (m/sec )2
Units: 1 N = 1 kg-m/sec2
c. Weight = pulling force of the Earth under the influence of gravity
Wt = F = mg
where Wt = weight (N), F = force (N), m = mass (kg), g = acceleration due to gravity (9.8 m/sec )2
Wt. = ρgV = γV
where W = weight (N), ρ = density (mass/vol), g = acceleration due to gravity, V = volume, γ =
specific weight (N/cu. m)
d. Stress - Force acting per unit surface area.
stress = F/A
where stress is in N/m , A = area (m x m = m )2 2
e. Work - displacement of mass when acted upon by force
e.g. sliding mass of regolith
W = Fd
where W = work (J), F = force (N = 1 kg-m/sec ), d = distance of mass displacement (m)2
Units 1 J = 1 N-m = 1 kg-m /sec2 2
2. Forces acting on Slope Material
τ = shear force parallel to slope (N)
σ = normal force perpendicular to slope (N)
θ = slope angle relative to horizontal plane (degrees)
Wt = weight of particle or mass of material (N)
Wt = mg = weight of particle (N)
σ = Wt (cos θ) = normal force (N)
τ = Wt (sin θ) = shear force (N)
** Note: here we assume that a mass of regolith overlies a potential failure plane. The failure plane
is a surface in 3-d with area. Thus, forces are applied per unit area, resulting in stresses. **
τ = shear stress parallel to failure plane (N/m )2
σ = normal stress perpendicular to failure plane (N/m )2
θ = slope angle relative to horizontal plane (degrees)
γ = specific weight of mass = Wt / volume (N/m )3
h = thickness of regolith above failure plane (m)
Wt = mg = kg-m/sec = N2
γ = Wt / volume = N/m = specific weight3
σ = γh (cos θ) = normal stress (N/m )2 2
τ = γh (cos θ) (sin θ) = shear stress (N/m )2
In-Class Activity: Force Analysis of Particle-on-Slope Model
(1) Choose our class favorite block-of-rock sample and set up the inclined plane.
(2) Determine the mass of our block-of-rock sample by using the balance in the room.
(3) Using the appropriate equations listed above, calculate the force vectors and fill in the table below.
Show your calculations in the space provided!
Mass of Rock Block ____________ kg
Weight of Rock Block ____________ N
Normal Force (N) Shear Force
Given that shear force is oriented downslope and normal force is oriented perpendicular to slope, answer the
A. Which of the two forces will drive the rock-block downslope when it fails?
B. Which of the two forces will tend to resist downslope movement of the rock block?
C. Intuitively, when do you think the block will begin sliding down the slope (choose 1: shear =
normal, shear < normal, shear > normal)?
(4) Place the rock-block on the inclined plane and determine the critical angle at which it slides down the
slope. Calculate the following:
Critical Angle of Rock-Block Sliding (degrees): _______________
Critical Normal Force at Critical Angle _______________ (N)
Critical Shear Force at Critical Angle _______________ (N)
D. How do your inclined-plane results compare to your prediction in question C above?
E. List some ideas as to why your results turned out like they did. What other physical factors have
not been accounted for in our set of equations / slope analysis?
B. Other Physical Properties Effecting Slope Stability
1. Driving and Resisting Forces
a. Driving Force = Shear Stress (discussed above)
b. Resisting Force = Shear Strength
(1) Shear Strength = measure of resistance of slope to shear motion or
2. Slope Stability Ratio
Slope Safety Factor (dimensionless ratio)
F = resisting force / driving force = shear strength / shear stress
F > 1: Strength > Stress: Stable Slope
F < 1: Strength < Stress: Unstable Slope
F = 1: Slope Failure Threshold
3. Shear Strength Factors (Coulomb Equation):
a. Internal Friction of Material
(1) plane friction - resisting force at grain boundaries
(2) interlocking friction - resisting force at irregular grain boundaries
(grains forced to move up and over one another)
b. Effective Normal Stress
(1) Normal Stress: force perpendicular to failure plane
(2) Effective Normal Stress - accounts for internal pore pressure of
(a) Pore Pressure in Granular Material
i) dry material: pore pressure = 0
ii) fully saturated material: pore pressure is positive
a) positive hydraulic lift
iii) partially saturated material: pore presssure is
a) suction between grains due to surface tension
of water and capillary force
c. Cohesion - force of molecular attraction between grains and particles
(a) clay - high cohesive force due to electrostatic attraction at
(b) sand/gravel - noncohesive, due to lack of electrostatic
(c) Cohesion Factor also includes vegetative root strength
Coulomb Equation (Measure of Total Shear Strength)
S = c + σ' tanφ
where S = total shear strength (N/m ), c = cohesion (N/m ), σ' = effective normal stress2 2
(N/m ), φ = angle of internal friction2
so... F = S / τ (Safety Factor)
F < 1: slope failure
F> 1: Slope stability
F= 1: slope failure threshold
A 3.6 m thick mass of regolith rests on top of a sloping bedrock surface. The hillslope angle is 8
degrees. A geotechnical engineering firm conducted an in-situ slope stability analysis with the
regolith cohesion = 2155 N/m2
effective normal stress = 71855 N/m2
angle of internal friction = 10o
specific weight of regolith = 25921 N/m 3
Calculate the safety factor for the slope (show your work):
(1) Is the slope stable or unstable with respect to shear strength vs. shear stress? Why?
(2) What slope stability factors could easily be changed (say during the course of a week), that
would result in driving the slope to a critical threshold? (Do some thinking and hypothesizing here).
Directly relate your ideas to the pertinent equations used to calculate slope stability.
II. Mass Wasting Processes and Classification
A. Stages of weathering and crustal denudation
1. Weathering, fragmentation, diminution of bedrock
a. Chemical Processes
b. Physical Processes
2. Mass Wasting- mass movement of weathered rock materials downslope under
the force of gravity: "gravity transfer"
3. Erosion and transportation of sediment by surface waters.
This process can be viewed as a continuum, at any given time there exists unweathered
material, hill slpe material in storage on slopes, sediment in transport and sediment in
temporary storage along drainage system networks.
B. Components of mass wasting process
1. Gravity and potential energy created by crustal relief.
a. generally tectonics is responsible for uplifting the earth's crust, and
setting gravitational and weathering process in action.
2. Weathered/fragmented earth materials (from clay, to sand, to boulder and/or
a. As the term "mass" suggests, these materials are often subject to mass
movement downslope, during slope failure.
3. Steepness of slope.
a. Loosened earth materials will lie at rest on a slope under the resistive
force of friction. There is a critical point at which, the steepness of slope is
such that the downslope vector force component becomes greater that
the force of friction, resulting in slope failure.
b. Angle of Repose- the steepest angle that can be assumed by loose
fragments on a slope without downslope movement.
(1) the precise angle is a function of the type of material lying on the
slope: sharp angular boulders will have a steeper angle of repose
than sand. Common angle of repose for average talus debris at the
base of a slope = 35-40 degrees from horizontal.
4. Moisture/water included in pore spaces and fractures within weathered material.
GRAVITY IS THE DRIVING FORCE OF THE MASS WASTING AND EROSION-TRANSPORTATION
C. Types of Mass Wasting Processes (after Varnes)
1. Material Types
a. Rock (consolidated bedrock)
b. Debris (coarse regolith)
c. Earth (fine regolith)
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662604794.68/warc/CC-MAIN-20220526100301-20220526130301-00037.warc.gz
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CC-MAIN-2022-21
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http://fashionbrandsale.com/ministry-of-style-sale-australia-7/
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Ministry Of Style sale Australia. Womens Ministry Of Style New Romantic Womens Maxi Wrap Dress Cotton Features: Colour: Botanical Material: Poly/Viscose Slip included Layered sheer overlay Can be worn open or wrapped All over print Size + Fit Guide: Model#x27;s Height: 175cm Model#x27;s Bust: 81cm Model#x27;s Waist: 61cm Model#x27;s Hips: 89cm Model wears a Size: 8
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https://www.wallstreetoasis.com/forums/buy-side-vs-sell-side-analyst
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I'm new to the forums, and I am trying to decide between buy-side and sell-side straight out of undergrad. I am fairly certain that I do not want to go into IB, so at this point, sell-side is pretty much a no for me. I'm looking for others opinion on this? I come from a non-target school, so getting into IB Is somewhat unrealistic. However, I have connected with numerous PM's and analyst at buy-side firms and I am fairly certain that I have a pretty good shot at locking down an internship at one of them.
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CC-MAIN-2019-35
| 600 | 2 |
http://core-cms.prod.aop.cambridge.org/core/journals/journal-of-applied-probability/issue/356BFF5FE12860AF7D006861257133DF
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math
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We consider the planar random motion of a particle that moves with constant finite speed c and, at Poisson-distributed times, changes its direction θ with uniform law in [0, 2π). This model represents the natural two-dimensional counterpart of the well-known Goldstein–Kac telegraph process. For the particle's position (X(t), Y(t)), t > 0, we obtain the explicit conditional distribution when the number of changes of direction is fixed. From this, we derive the explicit probability law f(x, y, t) of (X(t), Y(t)) and show that the density p(x, y, t) of its absolutely continuous component is the fundamental solution to the planar wave equation with damping. We also show that, under the usual Kac condition on the velocity c and the intensity λ of the Poisson process, the density p tends to the transition density of planar Brownian motion. Some discussions concerning the probabilistic structure of wave diffusion with damping are presented and some applications of the model are sketched.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496669730.38/warc/CC-MAIN-20191118080848-20191118104848-00292.warc.gz
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CC-MAIN-2019-47
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https://www.arxiv-vanity.com/papers/hep-th/0409199/
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math
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The Renormalization Group, Systems of Units and the Hierarchy Problem
SISSA, via Beirut 4, I-34014 Trieste, Italy
INFN, Sezione di Trieste, Italy
In the context of the Renormalization Group (RG) for gravity I discuss the role of field rescalings and their relation to choices of units. I concentrate on a simple Higgs model coupled to gravity, where natural choices of units can be based on Newton’s constant or on the Higgs mass. These quantities are not invariant under the RG, and the ratio between the units is scale-dependent. In the toy model, strong RG running occurs in the intermediate regime between the Higgs and the Planck scale, reproducing the results of the Randall-Sundrum I model. Possible connections with the problem of the mass hierarchy are pointed out.
In a Wilsonian approach to the Renormalization Group (RG), physics at some energy scale is described by an effective action which can be regarded as the result of having functionally integrated all field fluctuations with momenta larger than . Thus can be interpreted as an infrared cutoff and the RG describes the dependence of the action on this cutoff. An infinitesimal RG transformation is basically an integration over fluctuations of the fields with momenta ranging from to . A sequence of infinitesimal RG transformations defines a flow in the space of all possible actions. I will call this the “basic” RG flow.
In Quantum Field Theory (QFT), one can use the freedom of redefining the fundamental fields to eliminate some couplings from the action. The most familiar example, and the one that we will be dealing with in this paper, is normalizing the coefficient of the kinetic term by means of a global rescaling of the fields. If one starts from such a normalized action and performs a RG transformation, the resulting action will generally not be normalized anymore, but it can be brought back to normalized form by means of a field redefinition. It is therefore customary to include in the definition of a RG transformation also this field redefinition. It is also convenient (and for numerical simulations even necessary) to work with dimensionless variables; this can be achieved by multiplying every coupling by a suitable power of , i.e. using as unit of mass. (Similarly, in QFT on a lattice one usually takes the lattice spacing as unit of length.) The RG transformation changes the value of the cutoff, and to compensate this it is customary to include in the definition of a RG transformation also a rescaling of lengths and momenta.
Thus, the textbook definition of a “complete” RG transformation in QFT or statistical mechanics involves three steps: (i) functional integration over field fluctuations, (ii) rescaling of the field, (iii) rescaling of coordinates and momenta. This defines a flow in the space of normalized actions. In this paper I discuss the use of field rescalings in the presence of gravity. Because of the special geometrical status of the metric field, its rescalings can be interpreted as changes in the unit of length. Therefore, when the metric is dynamical, step (iii) is just a special case of step (ii), applied to the metric. Furthermore, normalizing the metric is equivalent to a choice of units. Different choices of units lead to different RG flows and, as a consequence of the rescalings, the normalized metric becomes scale–dependent. This discussion will be used to clarify some points related to the RG flow in the theory of gravity. In particular, it will be shown that earlier results on the RG flow in Einstein’s theory will not be affected by consideration of these rescalings.
In the second part of the paper I will use these insights to show how certain five–dimensional models can be seen as geometrical reformulations of the four–dimensional RG flow. In order to make the discussion more concrete, we will analyze in some detail a toy model consisting of gravity coupled to a scalar field. Assuming that this model reflects some features of the real world, the scalar field will be referred to as the “Higgs field” and its physical mass will be assumed to be in the TeV range. In this model, various choices of units are possible †† As is customary in QFT, we take as unit of action and as unit of velocity. With these choices, everything has the dimension of a power of length (or mass). A system of units is then defined by choosing a standard of length (or mass).: cutoff units, Planck units based on Newton’s constant and Higgs units based on the mass of the scalar field, each leading to a different form of the RG flow. The conversion ratio between Higgs and Planck units is
Insofar as these units are built with fundamental physical variables, the appearance of such a small ratio is puzzling †† see for recent discussions about fundamental constants and fundamental units. This was noted already long ago by Dirac, who considered various very large numbers occurring in Nature . One such number was the ratio of the gravitational to electromagnetic force between an electron and a proton. Dirac’s response was to assume that a very large number can only arise as a result of another number being very large. Another very large number which turns out to be of comparable magnitude is the age of the universe, , expressed in atomic units. Dirac postulated that this rough coincidence is due to some as yet undiscovered law, and that to maintain it in the course of time Newton’s constant, when measured in atomic units, would decrease as . Experimental bounds are now strong enough to rule out this behaviour (for a review of observations see e.g. ).
The mass of the electron and the mass of the proton have quite different origins, and for our discussion it will be convenient to replace Dirac’s original electron and proton by any pair of charged pointlike particles (quarks or leptons). The mass of all these particles is believed to originate from their Yukawa interaction with the Higgs VEV; likewise, the Higgs mass originates from the interaction of the scalar quanta with the VEV. Thus the ratio (1) is a good representative of the problem posed by the smallness of the mass of any known pointlike particle, in Planck units. It is also closely related to Dirac’s problem, because the ratio of gravitational to electric forces for pairs of charged pointlike particles, up to dimensionless couplings, is essentially the square of (1).
In particle physics the smallness of (1) is known as the hierarchy problem. In perturbative QFT, can be thought of as the sum of a classical (“bare”) value and a quantum correction. Since the dominant graph for the radiative correction of is quadratically divergent, the quantum correction is proportional to the square of the UV cutoff, which is presumably of the order of Planck’s mass. In order for the observed value to be so much smaller than the Planck mass, the bare value should cancel the quantum correction with an extraordinarily high precision. While not necessarily “wrong”, this fine tuning is very artificial and should probably be taken as a hint that the perturbative approach does not describe properly what is happening.
Some years ago Randall and Sundrum (RS) proposed an elegant approach to the hierarchy problem, based on a classical five-dimensional model . They start from the five-dimensional dynamics of gravity coupled to two parallel three-branes. It is assumed that matter fields are somehow confined to one of the branes, which is to be identified with our four-dimensional world, while gravity propagates in the five dimensional bulk. This configuration, with a five-dimensional Anti-de Sitter (AdS) metric between the branes, can be made to solve the equations of motion provided the cosmological constants in the bulk and in the branes are properly matched. It then emerges that any mass parameter in the “physical” brane, measured relative to the four-dimensional metric which solves Einstein’s equations, is suppressed by an exponential factor with respect to the fundamental parameters appearing in the action.
Returning now to the RG flow, we will see that the equations for the running parameters of the toy model in certain approximations are identical to the ones found by RS in . With hindsight, this is not surprising: based on ideas that originate from the AdS/CFT correspondence , the RS model has been given a “holographic” interpretation, whereby the fifth coordinate in the Anti-de Sitter (AdS) space can be regarded as the logarithm of a RG scale . The five-dimensional slice of AdS space that is used in the RS model reproduces precisely the leading scaling behaviour of the flat metric when the RG equations are written in cutoff or Higgs units. There is however a fundamental difference in interpretation. The RG equations used in this paper are not derived from the classical higher–dimensional Einstein equations: instead, they are calculated from first principles in the four-dimensional QFT and the five-dimensional AdS metric is merely a suggestive auxiliary construction. In fact, the dynamics of gravity plays a relatively little role in this discussion: the contribution of gravitons to the beta functions is suppressed in the regime that is of interest for the hierarchy problem, and the main role of gravity is to set the initial conditions for the RG evolution. Nevertheless, it will be clear that the natural framework for this discussion is in the presence of dynamical gravity.
This paper is organized as follows. Section 2 discusses the invariances of the action under scalings of the fields, the notion of “redundant” or “inessential” couplings and some peculiarities of the RG applied to gravity. In Section 3 these notions are illustrated in a toy model of gravity coupled to a scalar field; various choices of units are discussed, each leading to a different form of the RG equations. Section 4 contains the actual behaviour of the ratio as a function of in the toy model. In Section 5 the RS model is reconstructed starting from the four–dimensional RG flow; some general consequences of the running of the units are illustrated. Finally in Section 6 I discuss the use of dimensionful quantities in Quantum Gravity, possible connections of the RG flow to the hierarchy problem and I present some final comments and conclusions.
2. Field rescalings and redundant couplings
Let us assume that physics at a certain energy scale is described, to the desired degree of accuracy, by an effective action , a functional depending on certain fields and coupling constants †† The word “effective” is used here in the same sense as in “effective field theory”. . The action describing the physics at some lower energy scale , is given by a functional integral over all fluctuations of the fields with momenta in the range , using as the classical action. In general, even if contained only a finite number of terms, this functional integral will produce an effective action with infinitely many effective couplings. Therefore, should be thought of from the outset as “the most general action” for the fields. It will have the form
where are all operators constructed with the fields and their derivatives, which are compatible with the symmetries of the theory and belong to a given class of functionals (e.g. one may or may not require locality). The dependence of the effective action on is given by
where (for some arbitrary initial value ) and are the “basic” beta functions, describing the change of the effective action when one integrates out fluctuations of the fields with momenta between and . Note that since only an infinitesimal range of momenta is involved, the beta functions defined in this way are finite, independently of the UV behaviour of the theory.
Once the beta functions in (3) are known, one can start from any arbitrary initial point and follow the RG trajectory in either direction. It happens very often that the flow cannot be integrated towards the UV beyond a certain limiting scale . In this case the theory can only be used for ; it is called an “effective theory” or a “cutoff theory” and is the physical cutoff (as opposed to a mathematical cutoff, which is used to regulate divergences, or to , which is an artificial device used to compute the scale dependence of the action). It may happen, however, that the limit can be taken; in this case the theory is said to be “fundamental”. A fundamental QFT is a self-consistent description of a certain set of physical phenomena which is valid up to arbitrarily high energy scales and does not need to refer to anything else outside it.
We can think of the space of all theories as an infinite dimensional manifold , whose coordinates are the coupling constants appearing in the action. Similarly, let us denote the infinite dimensional space of all field configurations, whose coordinates are the fields . We can think of , for fixed , as a functional on . This description generally contains more parameters than are strictly necessary to describe the physics. The fields are integration variables, and a redefinition of the fields does not change the physical content of the theory. This can be seen as an arbitrariness in the choice of coordinates in . There is a similar arbitrariness in the choice of coordinates on , due to the freedom of redefining the couplings . We will restrict the group of allowed field redefinitions in such a way that the transformed action belongs to the same class of functionals as the original action. Since is the most general functional in this class, given any field redefinition , one can find a new set of couplings such that, for fixed ,
This defines an action of on . We are free to choose a coordinate system on which is adapted to these trasformations, in the sense that a subset of couplings are invariant under the action of the group while a subset transform nontrivially. The couplings are called redundant or inessential, while the couplings are called essential. (It is important to stress that this distinction is parametrization–dependent; in Appendix A I illustrate this point with a few specific examples.) A theory will generally contain infinitely many essential and infinitely many inessential parameters, and all physical observables can be expressed as functions of the essential couplings only.
One can exploit reparametrization invariance to eliminate the redundant couplings and follow only the flow of the essential ones. In general in an effective QFT there will still be infinitely many couplings to follow, but in approximation schemes where only a finite number of couplings is retained this may be a useful way of reducing the number of variables. Field redefinitions also play an important role in discussions of composite operators, see e.g. [8-10]. Mathematically, the “basic” RG flow defined on the space projects onto a flow in the quotient space . In practice, the flow on can be described explicitly by giving the complete flow of the essential couplings. It is characterized by beta functions which differ from the “basic” beta functions by suitable infinitesimal field redefinitions, as discussed in the introduction. Such redefinitions are proportional to the beta functions of the redundant couplings and are usually written in terms of the anomalous dimensions, defined as
Of all field redefinitions, the ones that will interest us in this paper are the constant rescalings. It is generally the case that for each field (or more precisely for each multiplet of fields) there is a scaling invariance of the action, provided also the couplings are suitably transformed. By means of this scaling, for each field multiplet one can eliminate one coupling from the action. The usual choice is to eliminate the wave function renormalization constant , which is the coefficient of the kinetic term of the field multiplet.
In Quantum Gravity, the RG flow has some special features that are not present in other QFTs. This is due to the special meaning of the metric, which is the field used to measure lengths. As in any theory, the action is invariant under rescalings of the metric, provided all fields and couplings are also rescaled suitably:
In this equation, is the canonical dimension of each field or coupling, in units of mass. Thus, dimensional analysis is a statement of invariance of the action under rescalings of the metric. Note that this definition of canonical dimension holds whether or not the metric is treated as a dynamical variable, but the freedom to redefine the metric really only arises in quantum gravity. This -invariance can be seen as the mathematical manifestation of the fact that dimensionful quantities cannot, strictly speaking, be measured: one can only measure dimensionless ratios of dimensionful quantities. By a measurements of a dimensionful quantity one really means the measurement of the ratio of the dimensionful quantity and a suitably defined unit. To choose a system of units is to break the scale invariance of dimensional analysis.
Scale invariance is usually assumed to be broken in QFT, due to the need to introduce the mass scale (or in other approaches, an UV cutoff or a renormalization point). However, if is rescaled by a factor (as its mass dimension requires), scale invariance is maintained also in the quantum theory:
If one did not transform the cutoff , then there could be an anomaly. The two situations correspond therefore to two different realizations of the same abstract group of scale transformations. Dimensional analysis is based on the realization where scale invariance is preserved.
As mentioned in the introduction, the standard definition of the RG in QFT involves (ii) a constant rescaling of the field and (iii) a constant rescaling of coordinates and momenta. A rescaling of space can be treated equivalently as a rescaling of the metric; in the former case, one is implicitly assuming that the coordinates have dimension of length and is dimensionless, while in the latter the coordinates are dimensionless, as is more natural in General Relativity, and the metric has dimension of length squared. There follows that in the presence of dynamical gravity step (iii) can be seen naturally as a special case of step (ii) applied to the metric field. Furthermore, in the case of pure gravity, the rescalings (ii) and (iii) are not independent operations, and as a result one can use them to eliminate only one coupling, instead of two, as is the case in ordinary QFTs .
A related point is that in the case of gravity, the group of field redefinitions affects also the parameter . It is therefore convenient to treat as one of the couplings of the theory. Formally, we can think that the space contains a factor parametrized by . When is treated as a coupling, we can ask whether it is essential. As discussed above, this will depend on the choice of parametrization of . Due to the scaling invariance (7) there will always be at least one redundant (dimensionful) coupling, which can be eliminated by a choice of units. The standard choice in QFT is to take as unit of mass. This means choosing coordinates , where are the couplings measured in units of the cutoff. In this parametrization, is a redundant coupling and the are invariant under the rescalings (7). With this choice never appears explicitly in any physical observable, nor in the beta functions, so that the RG flow is given by an autonomous system of differential equations.
Alternatively, we can also pick any coupling of dimension and take as unit of mass. Then we choose coordinates , where and are the cutoff and the other couplings measured in units of . In this parametrization is redundant and the other, dimensionless coordinates are invariant under the rescalings (7). Which ones of them is essential then depends upon the way in which the remaining field reparametrizations act; however, in these units is essential and physical observables may depend on it.
3. RG and Systems of Units in a toy model
In this section I will illustrate various forms of the RG in a toy model consisting of gravity coupled to a real scalar “Higgs” field . Besides serving as an illustration of the general concepts described in the previous section, such a model also contains the main ingredients that enter into the hierarchy problem. While very incomplete in some respects, it may still be sufficiently realistic to capture some of the physical effects that play a role in the generation of the hierarchy. It is also useful for the comparison with .
We will deal with actions of the general form (metric signature is )
Here is, in the linearized theory, the wave function renormalization of the graviton. The potential is assumed to have the familiar quartic form with nonvanishing minimum. It can be parametrized by the value of the VEV, , by the Higgs mass and the quartic coupling . These parameters are related by , so we can choose and as independent parameters and treat as a function of the other two.
Our arguments in the following sections will be based on the assumption that in the relevant range of energies the effective action can be well approximated by a functional of the form (8), where the couplings , , , , and are now -dependent (we omit to write this dependence explicitly for notational simplicity). The effective action has the following two scaling properties:
where and are positive real numbers and the dots stand for higher order terms that we are neglecting. The transformations with parameter express the behaviour of the theory under rescalings of the scalar field. The transformations with parameter are the expression of dimensional analysis and are a special case of (7).
Because the action (8) has two scaling invariances, one can use them eliminate two combinations of the couplings from the action. The parameter can be used to fix any coupling that multiplies an operator containing the field . The standard choice is to fix . We will always stick to this choice in the following (for an alternative see Appendix A). The parameter can be used to fix any one of the dimensionful couplings. By definition, that coupling then defines a unit of length and mass. Let us now consider various choices of units.
In RG theory the standard choice is to take the cutoff as a unit of mass. By means of a scaling (9) with parameters , one can define the normalized action in cutoff units
In this parametrization and are inessential and do not appear among the arguments of ; the anomalous dimension of the scalar field is defined according to (5) as . As noted in , there is not enough freedom to eliminate and at the same time, so with this choice of units the action (and also the beta functions, and physically measurable quantities) depends explicitly on , where can be viewed as Planck’s area measured in cutoff units.
An infinitesimal RG transformation of then consists of: 1) functional integration over a shell of momenta, from to , with . This produces a variation of the couplings . Since has changed by a factor and has changed by a factor , this has to be followed by 2) a rescaling as in (9) with parameter and 3) a rescaling as in (9) with parameter , restoring the value .
Another possibility is to choose as the unit of mass. Being based on the fundamental constants that enter in special relativity, in the quantum theory and in the theory of gravity, these units are often considered “the most fundamental ones” . A transformation with parameters , can be used to define the action in Planck units:
As noted in , there is not enough freedom to eliminate and at the same time, so with this choice of units the action depends explicitly on , which can be viewed as the cutoff measured in Planck units. This is rather unusual, because the flow equations become non–autonomous. Let us denote the anomalous dimension of the graviton.
An infinitesimal RG transformation of consists of: 1) functional integration over a shell of momenta, as above; since the couplings and are modified, this is followed by 2) a rescaling as in (9) with parameter , and 3) a rescaling as in (9) with parameter , restoring the unit value .
A third possibility is to use the Higgs mass as unit of mass; we will call these “Higgs units”. Note that while the Higgs mass is not known, the mass of the electron, which differs from the Higgs mass by the ratio of the coupling to a Yukawa coupling, is at the basis of atomic spectroscopy and hence of modern metrology. Thus, the Higgs units defined here are conceptually closely related to ordinary metric units. By means of a transformation as in (9), with parameters and we can define the action in Higgs units
Again, the action depends explicitly on , which is the cutoff measured in Higgs units.
An infinitesimal RG transformation of consists of: 1) functional integration over an infinitesimal shell of momenta, as above. Since this modifies both and , it is followed by 2) a rescaling as in (9) with parameter , where is defined as in (5), and 3) a rescaling as in (9) with parameter , restoring the unit value .
This list does not exhaust all possibilities. For example, one could use the cosmological constant as unit of mass. This is not a practical choice, because the cosmological constant is not known to any good approximation, but it is a rather natural choice in principle (see eqs, (A.5-9) in the Appendix) and it is used in lattice calculations (see e.g. ). I leave it to the reader to work out the transformations of the fields and couplings in this case.
It is important to underline that the use of these complete RG transformations on is entirely equivalent to working with the “basic” RG transformations on . For example the complete RG transformation of the scalar mass parameter in cutoff units is
The extra terms which come from steps 2 and 3 cancel out when we compute the transformations of the dimensionless couplings listed in eq. (11). For example, in the case of the mass, using the definition of in (11), since and by definition, we find
which means that the complete RG transformation of is given just by the “basic” RG transformation, provided it is applied also to the factors and appearing in the denominator.
Similar remarks apply to the case of the other systems of units. For example in Planck units the complete transformation of the mass is
In Planck units the total transformations and by design, so the complete transformation of the dimensionless “mass in Planck units” defined in (13) is
meaning that the complete RG transformation of can be computed just from the “basic” RG transformation, provided it is applied also to the factors and in the denominator. Similar considerations apply also to the other primed and double primed couplings.
The gravitational RG has been studied intensively in the last ten years with the main aim of proving nonperturbative renormalizability of the theory along the lines of . The derivations of the beta functions for gravity in the Einstein–Hilbert truncation and gravity coupled to matter in , as well as their applications in [16,17] to the search of a gravitational FP, were based on the exact RG equation, taking into account only the first of the three steps described above for each choice of unit. The same applies to subsequent calculations that take into account higher powers of the curvature . By the arguments given above, the beta functions found in these papers for the dimensionless ratios and are the complete beta functions in cutoff units and do not need any further correction term (in particular, the FP is unaffected).
Let us conclude this section by observing that the primed (Planck) and double primed (Higgs) units could be ill-suited for the discussion of FP’s. The great virtue of cutoff units is that the vectorfield defined by the beta functions is –independent. This is not the case with the other choices of units, since, as noted above, in these units the beta functions have an explicit dependence on the cutoff variables and respectively. This makes the physical interpretation of the system of equations less transparent .
4. The beta functions
Having discussed the general form of the RG equations of the toy model in various systems of units, I will now illustrate the actual behaviour of the couplings, under the assumption that the action (8) gives a good description of physics at the energy scale that is of interest. Beyond this fundamental assumption, any calculation will require a number of approximations. First, we are going to neglect the anomalous dimension . This is supported by the calculations of , where it was shown that the anomalous dimension is suppressed by some power of below the Planck scale. Furthermore, in the UV limit we see from eqn.(6.1a) of , together with the results of [16,17], that tends to a constant of order 10 if there is a FP. From here on we shall simply assume and . In accordance with observations, we will also assume that the cosmological constant is much smaller than all other scales that come into play. Since our main focus is not on explaining the smallness of the cosmological constant, we shall simply assume that this condition is met.
Qualitatively, the overall picture is characterized by the presence of two thresholds which correspond to the physical Higgs mass and the Planck mass. There are therefore three distinct regimes: the low energy regime , the intermediate regime , and the asymptotic UV regime where, in principle, . The beta functions of the couplings in (8) have been calculated in . They consist of integrals of certain rational functions of the momenta, the cutoff and the couplings. The momentum integrals are peaked at momenta of order and in each regime, one can pick in the beta functions the dominant terms and discard all the others. This leads to dramatic simplifications.
Let us discuss each regime in turn, in order of increasing energy. In the low energy regime we have , with , when using a suitable cutoff function. The solution of the flow equation has the form
where . By definition in this regime the initial value is much larger than so the second term in (20) is very small with respect to the first and we can approximate by the constant . The anomalous dimension is consequently also very small. When we look at the beta functions of the other couplings, they are also suppressed by powers of , so we can effectively approximate by a constant and by a constant . Altogether, in the low energy regime there is no significant running of the couplings.
Eventually, as grows, it overcomes the threshold at . In the intermediate regime where , the beta function of is the same as in the low energy regime, except for the numerical coefficient . The difference is due to the contribution of the scalar field, which is felt only above the mass threshold. Since is still much smaller than , we can still assume that is almost constant and equal to . In the intermediate regime the dominant term in the beta function of the mass is , with . This is essentially the one-loop result for a quartically self-interacting scalar theory; the gravitons do not contribute significantly to this beta function in this regime. If we assume that the threshold occurs exactly at , matching the solution in the intermediate regime to the one in the low energy regime we have
This running is a reflection of the quadratic divergences that occur in perturbative calculations. The dominant term in the beta function of is with . The contribution of gravitons is negligible. The solution is
where is the value of at (and below) the threshold. This is the standard one loop result, exhibiting a Landau pole at . The pole can be avoided if .
Beyond the Planck scale, field theory will make sense if the couplings approach a FP . In this case, it never really happens that ; instead, scales exactly like , so that the ratio tends to a constant. In it was found that the model (8) has a “Gaussian–matter FP” with nonzero values and while all other couplings are zero. It is useful to emphasize at this point, however, that the subsequent discussion does not depend on the existence of such a FP. The RG behaviour we have encountered in the intermediate regime would still remain valid even if the field theoretic description was only an effective one, with a physical cutoff somewhere near the Planck scale.
Let us now summarize the consequences of these findings for the parameter . In the low energy regime there is no significant running of any quantity, so Higgs units and Planck units simply differ by a fixed multiplicative factor
This is the regime where all of current particle physics takes place. In the intermediate regime, is still essentially constant but runs, to leading order like . From eq.(21), keeping only the leading terms, we find
In the asymptotic UV regime, assuming that the theory approaches an UV FP, would tend again to a constant
where the asterisk denotes the values of the variables at the FP. The value of clearly depends on the details of the FP. In we searched for a FP with nonzero values of the scalar couplings, but we were unable to find one. It seems likely that if a potential exists with nonzero mass, it is not polynomial. However, this issue remains unsettled. In the case of the “Gaussian–Matter FP”, after reaching a maximum around the Planck scale, the ratio tends to zero for .
To conclude this section, some cautionary comments are in order. It is not granted that the action (8) is a good description of the world at any energy scale, much less that is a good description at all energy scales. In fact, experience with other QFTs leads us to expect that if (8) has anything to do with the real world in the UV regime, then it is unlikely to do so at lower energies. In this respect QCD is probably a useful guide: it has a very simple description in terms of quark and gluon fields at high energy, near its UV FP, but this description becomes practically useless at energies of the order of 1 GeV, where the strong coupling becomes strong and other terms in the action become important. Likewise, one would expect that if a gravitational FP is governed by an action like (8), perhaps containing a few other terms, then at and below the Planck scale the action, in terms of the variables and , will be an extremely complicated, possibly nonlocal functional.
This is in contrast to the common expectation that a functional like (8) may be a reasonable approximation in the low energy and possibly in the intermediate regime (this expectation comes from the fact that the gravitational interaction is proportional to the external momenta in Feynman diagrams, so that perturbation theory works well with the action (8) at sub–Planckian energies). It is possible that this expectation is correct and that there is no UV FP. Then, the preceding analysis could still be applied in the low energy and intermediate regime. Alternatively, a possible reconciliation of these points of view may come through a field redefinition: at intermediate/low energies the action may again have a general structure similar to (8), but in terms of other variables and , related to and by some functional field redefinition (note that one always expects to have some metric in the action). Examples of such transformations are already well–known in scalar–tensor theories . This would parallel the transition from quark/gluon to meson/baryon degrees of freedom in QCD at low energy .
5. AdS space, from the bottom up
In the preceding section we have seen the “basic” beta functions on for the toy model. Let us now see what the complete RG flow on looks like for various choices of units. This will allow us to make contact with the RS model.
For simplicity we concentrate on the second, third and fourth terms of the action (8), which carry all the relevant information. To simplify the discussion, we also assume that the three regimes described in section 4 extend all the way to the thresholds. We choose at the Planck scale, so that . Let us assume that at the Planck scale the scalar mass has some “natural” value of order of the Planck mass: . In the rest of this section we will consider only the leading scaling behaviour of each quantity in the intermediate regime, neglecting the anomalous dimensions and , and the logarithmic running of .
In cutoff units at the Planck scale the action reads
All couplings are evaluated at . Let us now run the RG in cutoff units, as described in Section 3, towards lower energies (negative ). As discussed in Section 4, does not run significantly; for the mass we keep only the term proportional to and neglect any constant. Then we have
Since we neglect the running of , also . Furthermore, since , the third step of the RG transformation does not change the fields. However, the second step of the RG transformations is nontrivial: it generates a rescaling of the metric and of the scalar field with a suitable power of the factor at each RG step:
This rescaling has to be applied to all the unintegrated Fourier modes of the field, having momenta lower than . In practice we are mostly interested in the zero momentum modes (the constant scalar and a flat metric) and (29) implies that these modes have to be rescaled with as shown.
Taking into account equations (27,29), the action at some lower scale is given by
In Planck units the details of the calculation differ but the final result is the same. The action at the Planck scale is given by
In these units, by definition independent of . Since we neglect , the second step of the RG is trivial. Since we neglect , the third step of the RG is trivial. The mass runs like
Everything else, including field normalizations, is -independent within the approximations that we made, so in these units the scale-dependence of the mass is immediately evident. The reader can check that, due to linear running of the mass, Higgs units work like cutoff units.
We can then compare these results to the original RS model. One sees that the calculations leading from eq.(26) to eq.(30) are identical to the calculations leading from eq.(17) to eq.(19) in . This should perhaps not come as a surprise, in view of the “holographic” interpretation of the RS model . Their five-dimensional metric contains a one-parameter family of four-dimensional metrics with an exponentially varying warp factor:
We see that essentially the same one-parameter family of metrics is generated in a purely four-dimensional theory between the Higgs and the Planck scales, when one works in cutoff units (or in Higgs units).
To make the connection more complete, we should say how distances have to be defined in the space parametrized by the scale . Since is typically identified with some momentum variable appearing in a process, it may seem natural to choose the “proper distance” in cutoff space to be proportional to , as would befit a linear variable. But the space is not a linear space and this is not the natural choice. To motivate this from a physical point of view, observe that the units that we have chosen are subject to RG flow, so the question arises: when we measure a mass in a certain system of units, at what scale should the unit be taken? The natural, or “intrinsic”, definition is to take . This is the only way to define a real number out of a mass and a running unit, without making reference to another mass scale. Thus, when we “measure” a physical mass in Higgs units the real number that is obtained is the ratio
The physical rationale of this assumption is that when we perform a measurement of a mass parameter, we are not really measuring just that mass, but also the unit of mass. The two measurements cannot be disentangled and all one obtains is a value for the ratio between the two; if is the only scale in the system, (34) follows. Similarly a measurement of a length gives the number . On the other hand a measurement of a mass in Planck units gives the number
where Newton’s constant is evaluated at the scale , while a measurement of a length yields , where is evaluated at the scale .
This natural assumption leads to unfamiliar consequences. Let and be two lengths and their dimensionless ratio. The ratio of the two real numbers which give the values of the lengths in the two systems of units will not in general be equal to each other, nor to . According to our postulate, the ratio of the two lengths in Planck units is:
Similarly, the ratio of the two lengths in Higgs units, is
So, if the conversion factor is not the same at all scales, a set of masses that are linearly spaced when referred to Planck units will not be linearly spaced when referred to Higgs units. An extreme example of this fact has already been noticed in : if the QFT of gravity has a fixed point, when the variable defined in (13), which gives the value of the cutoff in Planck units, must tend to a finite limit , whereas the variable defined in (15), which gives the value of the cutoff in Higgs units, may well tend to infinity.
All this is unusual, but it does not imply any inconsistency. It only means that cutoff space cannot be thought of as a linear space, but should be treated as a one-dimensional manifold †† There may be a connection with so–called “Doubly Special Relativity” models, where the Lorentz group is postulated to act in a nonlinear way on momentum space . . The dimensionless variables , and provide coordinate systems on this manifold, related to the use of cutoff, Planck and Higgs units respectively. The relation between these variables is nonlinear and may not even be invertible. Since by construction grows as the RG trasformations are iterated, the direction of growing defines a natural orientation in cutoff space, but the directions of growing and may or may not agree with this orientation †† For example, it has been observed in that in the approach to the UV FP, Newton’s constant follows damped oscillations. At each oscillation, there would be two stationary points where could not be used as a coordinate, and the direction of growing disagrees with the direction of growing at each second half-cycle. An alternative coordinate better adapted to the FP behaviour has been proposed in . Similarly in Higgs units, assuming that at the FP, there would be a scale of the order of Planck’s scale where changes sign. Below this scale would be an increasing function of and above this scale it would be decreasing..
Since cutoff space does not have a natural linear structure, a proper notion of distance between, say, the Higgs scale and the Planck scale requires that a metric be given. The most natural choice of distance in would be given by counting the number of iterations of the RG transformation. For continuous RG transformations () the proper distance is then simply proportional to . Note that this logarithmic scale is also more natural insofar as it places the infrared limit (infinitely large systems) at infinite distance from any finite system.
At this point, we have all the ingredients to reconstruct the entire five-dimensional RS metric from the four-dimensional RG. Combining the metric on spacetime with the metric on cutoff space, together with the assumption that cutoff and physical space are orthogonal, produces a metric on a five-dimensional manifold. In the slice between the Higgs and the Planck scales, considering only the leading behaviour (21), this metric is locally the AdS metric:
In this way one can entirely reconstruct the RS five-dimensional space from four-dimensional data, without having to postulate that the fifth dimension is physically accessible.
In this paper I have discussed the way in which field rescalings affect the RG flow in the presence of gravity. One general lesson that can be drawn from this discussion is that in certain circumstances the use of dimensionful quantities could be misleading. The measurement of a dimensionful quantity is in reality the measurement of the ratio between that quantity and some unit. In daily life we can refer to a well–established system of units, which have been chosen for their availability and stability under a wide range of circumstances; in particular, they are unaffected by RG ambiguities. However, their use in extreme situations and in particular in Quantum Gravity may require some care. The relation between a certain dimensionful quantity measured in a high energy experiment and standard metric units can be very indirect . In order to avoid potential ambiguities, the safest procedure is to consider only dimensionless ratios, with the understanding that any physical measurement is a simultaneous measurement of the numerator and the denominator, and that one may not be able to measure the numerator and denominator separately. In theoretical calculations, one has to take into account the fact that both numerator and denominator may be subject to RG flow.
A related point is the following. As long as we study a theory describing a limited set of physical phenomena, we can always ignore these issues by taking as a unit something external to the theory. For example, if we study only strong interactions we can take the mass of the as an absolute, external unit; if we study only electroweak and strong interactions, the Planck mass defines an absolute, external unit. If on the other hand we want to include in the theory also gravitational phenomena, then also the Planck mass will be subject to RG flow, as we have seen, and there is no external parameter that can be taken as an absolute unit. In these circumstances, the safest procedure seems to be to avoid statements about dimensionful quantities.
To describe physics entirely in terms of dimensionless quantities would be similar to describing a gauge theory entirely in terms of gauge invariant quantities, and could become very cumbersome. However, when dimensionful variables are used, one should take care to avoid ambiguous statements. For example, the statement is a statement about dimensionful quantities that is unambiguous, because it is equivalent to the statement . On the other hand a statement such as “” (which is usually taken to define the ultraviolet limit) is ambiguous. To see why, consider for example the asymptotic UV regime of the toy model, which has been briefly mentioned in section 4. There is evidence for the existence of a “Gaussian–matter FP” where Newton’s constant, in cutoff units, tends to a nonzero value and the ratio tends to zero . This would imply that in the UV limit the cutoff in Higgs units , while the cutoff in Planck units tends to a finite limit . In such a case saying that “” is at best misleading. An unambiguous way of referring to the UV limit could be to say “”, meaning that the RG transformation is iterated infinitely many times. Similarly, to say that a dimensionful coupling such as Newton’s constant is asymptotically free is in itself meaningless. One has to specify in what units Newton’s constant is being measured. Depending on the flow and on the choice of units, it could tend to zero, to a finite constant or to infinity (for example, Newton’s constant is always equal to one in Planck units, so the statement above can evidently never be true in Planck units).
Let us now discuss possible connections with the hierarchy problem. As mentioned in the introduction, the problem posed by the smallness of the ratio (1) in the toy model is conceptually very similar to the one posed by the smallness of all lepton and quark masses, in Planck units. The mass of composite particles poses a different problem. For example, the mass of the proton is , but the origin of this small ratio must be to a large extent independent from the hierarchy problem represented by (1). This is because the mass of the proton originates mostly from the kinetic energy of the quarks and from the energy of the gluon field that binds them, and only in minimal part from the rest mass of its pointlike constituents. We are now close to having a satisfactory explanation for this problem, based on RG effects in QCD . The mass of the proton corresponds to the scale at which the strong coupling becomes large enough to bind the quarks. This requires
Starting from a relatively small value for at the unification scale (which is close to the Planck scale), due to the logarithmic running, one has to go to extremely small scales before the coupling becomes strong. To make this a bit more quantitative, solve the RG equation
where is the beta function in the presence of flavors of quarks, and use the condition (39). One gets
Without entering into details of specific grand unification schemes, it clear that very small ratios can be generated in this way.
As pointed out before, the masses of hadrons originate from strong interaction physics and those of pointlike particles from electroweak physics. The success of the RG of QCD in producing a small ratio for does not imply that a similar mechanism can be found for the masses of the Higgs scalar or the electron, but the idea remains extremely attractive. Insofar as the RS model provides a mechanism for generating small mass ratios, the ability of the four–dimensional RG to reproduce its main results seems to be encouraging. However, to reproduce the RS model from the RG we assumed that the running mass is proportional to ; more precisely, we have neglected any constant term, which is permitted in the solution of the RG equation. When one solves the flow equations starting at , there is no reason to assume that the constant term is negligible, so reproducing the trajectory (21) requires an a priori fine tuning of the initial conditions at the Planck or GUT scale. In the presence of fermion fields there may exist a dynamical mechanism, based essentially on an approximate IR fixed point for the scalar mass, that attracts it linearly towards the origin . This mechanism demands a large number of scalar and fermion fields and/or large values of the Yukawa couplings. A slow decrease of the Yukawa couplings would then switch off this running at some small scale, similar to the effect described above for QCD. It thus seems worth looking in more detail at the RG flow of the model, perhaps taking into account other parameters or other matter fields, and searching for RG trajectories that exhibit an extended intermediate regime. It would be natural to explore these issues under the assumption of the existence of an UV FP, though this hypothesis may not be necessary for an RG mechanism to work.
Another extension of this work would be to consider the effect of more general classes of field redefinitions, for example those involving conformal rescalings of the metric. Presumably, one could relate this to extensions of the RS model where the branes are not parallel . We note that in this generalization the scale transformations of dimensional analysis would have the status of gauge transformations.
It is also worth comparing these RG arguments to Dirac’s original prediction that , when measured in atomic units, would decrease like the inverse of the epoch . One can reasonably assume that in a cosmological context the cutoff can be identified with the inverse of the epoch (or maybe some function thereof). Now the value of in Higgs units is . Therefore, in the intermediate regime it should behave like , and furthermore it should stop running after an epoch of the order . So, if this picture is correct, Newton’s constant measured in Higgs units would indeed be time–dependent, but only in the very early universe, before the electroweak phase transition.
We have seen that within certain approximations the AdS geometry can be interpreted as a description of the quadratic divergences occurring in the toy model. For a review of holography and its relation to other important current developments in theoretical physics see . I would like to emphasize once again that this reconstruction of the AdS metric is purely formal, whereas in the RS model it is assumed that it is in principle possible (at least for gravitons) to propagate into the fifth dimension. Furthermore, while RS derive the RG flow from the five-dimensional Einstein equations, we used a standard four-dimensional beta function calculation. The phenomenology of the RS model, as well as that of other higher-dimensional theories that place the Planck scale close to the Higgs scale, is very different from the one of the purely four-dimensional model discussed here. Since is not interpreted as a physical dimension, there are no Kaluza-Klein modes and no radion field. Insofar as these higher-dimensional theories may be amenable to experimental verification, the four-dimensional RG approach discussed here provides an experimentally distinguishable alternative.
In conclusion let us observe that until now particle physics has been explored in the low energy regime, where units can be assumed not to run significantly. Particle accelerators are now on the verge of entering into the intermediate regime, where the metric in Higgs units () will begin to scale strongly and will differ from the metric in Planck units () by a scale-dependent factor. While this is not what one would ordinarily call a Quantum Gravity effect, it is a quantum effect, and it affects our understanding of the spacetime structure. It will be interesting to see if this can have any observable consequences.
Acknowledgements. I would like to thank S. Bertolini, M. Fabbrichesi, L. Griguolo, D. Perini, M. Reuter, A. Romanino, E. Sezgin and A. Zaffaroni for discussions and comments.
Appendix A. Examples of essential and inessential couplings
If a Lagrangian is parametrized in an arbitrary way, in general no parameters can be straightforwardly absorbed into a field redefinition. This is the case, for example, in a scalar field theory with the following action:
None of the parameters appearing in this action satisfies the criterion for inessentiality given in , namely that the variation of the Lagrangian with respect to the parameter vanishes or is a total derivative on shell. In fact, all parameters scale nontrivially under the -transformations in (9).
If we redefine the action becomes
In this parametrization the couplings are invariant under the -transformations, while is not. This is therefore an adapted parametrization of the action. The wave-function renormalization is inessential and indeed it can be absorbed by a simple rescaling :
It is important to stress that this statement refers to the parametrization (A.2): one cannot say that in the action (A.1) is inessential, because by this token one could conclude that every parameter appearing in (A.1) is inessential. For example, one could define alternatively and , in which case the action becomes
and in this parametrization it is the mass that is inessential and disappears by the rescaling .
Similar considerations apply also to gravity, with the additional twist that in this case eliminating an inessential parameter is equivalent to a choice of units of mass. If we write a general action, somewhat symbolically, as
we can use the scale invariance with parameter in eq.(9) to eliminate one of the couplings. For example we can redefine , () leading to
then rescaling , disappears:
which (up to trivial factors) is the action in Planck units. So is inessential in the parametrization (A.6). Alternatively we can redefine , (), so that
Then defining , disappears
This is the action written in units of the cosmological constant. Note that one cannot eliminate , which is invariant under -transformations, but one could eliminate or any one of the higher couplings.
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tderz It makes sense to explain the order of moves with a real example. Here is a sequence how this shape occurs frequently in games:
Black wants to make White overconcentrated on the right side, e.g. there might be a small white wall (too) nearby.
(Only) In that case it does not matter if White is made even stronger by the black sacrifice - and - any chance of attacking White - is lost.
Of course White might try and resist otherwise.
Of course, White must capture the black stone . However, before doing that he still can play two useful kikashi - and - only in the right order. Kikashi is all about timing. This is an easy problem and kikashi/timing problems belong to the most difficult problems in Go.
after the - exchange would not work, because (at ) would not be atari anymore.
The wall is now much too close to , .
That this is not only an academic exercise is shown by the aji around a, after which White could threaten to put the stone in motion (life) or - after Black defends around b, do something else useful with the stones around a.
Charles See also attach-crosscut corner patterns. I wouldn't call the crosscut a real 'joseki': it is an example of a contextual sequence.
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Alright, I leave this with the math professor community to tussle over. Of course, the error of Euler ever thinking the two zetas are equal is because Euler never bothered to find a finite to infinity borderline and thus the algebra involved in placing series terms on one side of the equation and leaving other terms on the other side of the equation are invalid, for example the two series 1+ 3 + 5 + 7 + ..... and 0 + 2 + 4 + 6 +.... without a precise infinity definition would appear to be equal when "going to infinity" and once we say they are equal and do algebra manipulations so that we extract a multiplication series out of those two we can come to the same false conclusion that Euler came to with his zeta functions.
Some years back, I pinpointed the flaw of Euler in his deriving of the equality of the zetas, for the flaw is that they are not equal and Euler made a mistake of algebra.
But here, let me provide a proof that the two zetas cannot ever be equal.
I am going to use the 10 Grid where we pretend 10 is the finite borderline and beyond are all infinity-numbers.
Now, in New Math or Old Math, we can define whether a fraction is even or odd and use that even versus odd laws of mathematics.
Notice that all the terms of the Euler zeta for exponent 2 are odd numbers and when you multiply odd by odd your answer is always odd.
Now it is purported that the convergence of the above is pi^2/6.
Now pi itself is even for it is evenly divisible by 120 and so should pi^2/6 be evenly divisible at infinity, yet we see that no term of Euler zeta is ever going to be even due to the primes involved and all of those terms are odd. So it cannot be true that the Euler zeta equals the Riemann zeta.
Now, the only decent search for AP posts on Google Newsgroups, is a search for [email protected] for it brings up posts that are mostly authored by me and it brings up only about 250 posts. Whereas Drexel brings up nearly 8,000 AP posts. Old Google under Advanced Search for author, could bring up 20,000 of my authored posts but Google is deteriorating in quality of its searches, likely because AP likes an author search and Google does not want to appear as satisfying to anything that AP likes. If AP likes something, Google is quick to change or alter it.
So the only search engine today doing author searches is Drexel. Spacebanter is starting to do author archive lists. But Google is going in the opposite direction of making author archived posts almost impossible to retrieve.
All the other types of Google searches of AP are just top heavy in hate-spam posts due to search-engine-bombing practices by thousands of hatemongers who have nothing constructive to do in their lives but attack other people.
Now one person claims that Google's deteriorating quality in searches of science newsgroups is all due to "indexing". Well, that is a silly excuse in my opinion, because there is no indexing involved when one simply asks for a author search. No indexing involved if one wants only the pure raw complete list of all posts by a single author. And Google is called the best search engine of our times, yet I have to go to Drexel to see 8,000 of my posts of which I had posted 22,000 to 36,000 posts from 1993 to 2013. It is a shame that Drexel can display 8,000 while Google has a difficult time of displaying 250 of my authored posts. Where the premiere search engine of Google is outclassed by Drexel and even by Spacebanter.
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| 3,463 | 12 |
https://attic.city/item/JzQr/teak-floor-lamp-george-kovacs-made-in-sweden-danish-modern-/hearthside-home
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math
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Teak Floor Lamp George Kovacs Made in Sweden Danish Modern
Teak Floor Lamp The lamp made in Sweden for George Kovacs Shade for demonstration only. Condition- Good Vintage Condition. Original Finish. Vintage wiring in working ...
$$$$$ · Indexed on April 11, 2022
ATTIC Availability Predictor beta
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CC-MAIN-2022-21
| 297 | 4 |
https://books.google.co.ve/books?id=knYNAAAAYAAJ&pg=PA138&vq=%22the+logarithm+of+the+product+of+two+numbers+is+*+equal+to+the+sum+of%22&dq=related:ISBN8474916712&lr=&output=html_text
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math
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« AnteriorContinuar »
Q. 7. A ray of light is incident at an angle of 30° on one face of an
equilateral prism. If the path of the light through the prism is parallel to the base, find the direction of the emergent ray, and the total deviation of the ray after passing through the
prism. Very easy and fairly well answered by those who tried it. Q. 8. An object at a distance of 10 inches from a lens, when viewed
through the lens, appears to be at a distance of 30 inches from the lens. Find the focal length of the lens, and give a diagram
showing the nature of the image. The answers to this question were either good or very bad.
HEAT. Q. 9. If the latent heat of fusion of ice is 80 calories per gramme, find
how much ice would be required to cool one kilogramme of
water from 20° C. to 10° C. Generally attempted and fairly done on the whole. Many omitted to allow for the heating of the melted ice from 0° to 10° C. Q. 10. A room contains 66 kilogrammes of air at 27° C. and 780 mm.
pressure. What will be the weight of air contained (a) if the
temperature falls to 2° C., (b) if the barometer falls to 715 mm.? Seldom tried. A few good answers, the rest worthless. Q. 11. Distinguish between evaporation and boiling. How is the boiling
point of a liquid defined, and how is it affected by pressure. The nature of ebullition was not well understood.
Q. 12. Describe some form of maximum, and some form of minimum
thermometer, and point out the defects (if any) of either
instrument. Seldom attempted, and little knowledge of details shown.
Results : 1st Class, 10; 2nd Class, 9; Failed, 10; Total, 29. A few of the papers were very bad, but the majority appeared to be of a fair order of merit. The number sent in was too small to permit of any general conclusions of value being drawn.
Results : 1st Class, 19; 2nd Class, 34; Failed, 21 ; Total, 74.
The answers to this paper were fair on the whole, with a normal proportion of good papers, and a similar proportion of failures. With regard to the several questions, the commonest mistakes made were those noted below, but many of the good papers were practically free from serious mistakes, and were clearly written and well expressed. Q. 1. What is meant by spherical aberration ?
Make a careful drawing of the manner in which parallel rays
are reflected by a hemi-spherical concave mirror. Many of the diagrams omitted the caustic curve,
Q. 2. Determine the limits of the angle of incidence of a ray of light on
one face of an equilateral prism so that the ray may be refracted
at the second face, assuming the critical angle to be 45°. The index of refraction was often taken as 3/2 instead of 12, and the angle of incidence wrongly deduced. Q. 3. Describe the method by which Fizeau observed the velocity of light,
indicating by a diagram the optical arrangements necessary. Little knowledge was shown of the optical arrangements. Q. 5. A rhomb of Iceland spar is laid on a page of print. How will the
appearance of the print differ from that which would be observed if the Iceland spar were replaced by a slab of glass? How does the appearance alter when the rhomb is rotated while still remaining in contact with the page
e? Many candidates thought that the brightness of the two images and their distance apart varied as the crystal was rotated. Q. 6. A short-sighted person cannot see objects clearly at a distance
greater than 6 inches. What spectacles would be required to enable him to see distant objects clearly? If his least distance of distinct vision without glasses is 3 inches, what would it be
with the above spectacles ? There were few good attempts at the latter part of this question. Q. 7. Describe experiments showing that radiant heat is reflected accord
ing to the same laws as light. The experimental methods suggested were generally too rough. Q. 8. Define dispersive power. What are the conditions that two thin
prisms of different kinds of glass may give when combined, (a)
no dispersion, (6) no deviation ? In many cases dispersion was confused with dispersive power, and the answers were lacking in precision. Q. 9. Explain what is meant by interference of light, and describe a
method by which two separate beams of light from the same
source may be made to interfere. The diagrams given were generally poor, and the appearances presented were often loosely and inaccurately described.
STAGE 2. Results: 1st Class, 21 ; 2nd Class, 123 ; Failed, 48 ; Total, 192. There were comparatively few good papers, about 10 per cent. in all, and rather more than twice as many failures. The majority of the papers were poor in quality. The faults noted seemed in many cases to be due to youth and want of facility of clear expression. Subjoined are special criticisms relating to the several questions. Q. 1. What precautions must be taken, and what corrections applied, to
determine temperatures correctly to 1/100° C. by a mercurial
thermometer between 0° and 100° C. ? Freezing point and boiling point errors (or fundamental interval and one fixed point) should be given, with method of applying correction at inter mediate points. Many candidates omit these, and give a number of less important points without understanding them. Q. 2. Describe a method of measuring the specific heat of a substance
of which only a small quantity can be obtained. What relation has been found between the specific heats of the metallic elements and their atomic weights?
Bunsen's ice calorimeter, or Joly's steam calorimeter, are the best for this. In the former calorimeter, the tube containing the mercury should not be vertical where the surface of the mercury ends, as the changes of presgure so introduced would effect the melting point of the ice quite appreciably. Round the calorimeter should be an air space and then an ice jacket to protect from radiation. Q. 3. Give a brief historical sketch of the discovery of the first law of
thermodynamics. A historical sketch is asked for. The first law should be given in definite terms—that the heat produced is proportional to the work expended, and not merely that heat appears when work is done. The answer should give a short account of the old caloric theory, and of the experiments connected with the names of Rumford, DavyJoule and Mayer.
1 cm. ;
Q. 4. Define what is meant by the dew-point, and show how, when this
is known, the amount of aqueous vapour in the air can be
What is the weight of a litre of damp air at 20° C., when the
vapour = fths that of air.
Q. 5. Enumerate the various ways in which a liquid can lose heat,
distinguishing between the cases in which heat is transformed
transformation takes place.
compression of a perfect gas can be calculated.
Air at 0° C. is adiabatically compressed to half its volume;
find the rise in temperature. (2* = 8/3 approximately.) First part scarcely attempted. In answering this, the equation pv = RT should be assumed, and also it should be pointed out that the rise of
Work done in compression. temperature of the gas
Note that in an
Sp. Ht. at const. vol. adiabatic expansion the pressure does not remain constant. The answer to the second part is 91° C. Q. 8. What is meant by saying that the internal work done when a gas
expands is small ? Describe experiments which have shown
that the above statement is correct in the case of air. Few understood clearly the meaning of internal work. Q. 9. Explain carefully how the melting point of paraffin wax or sulphur
may be determined by the method of cooling. Observe rate of cooling of a well-stirred mass of paraffin wax. Temperature will remain nearly constant while solidification is going on. There should be no water vessel round the wax while it is cooling, as this will tend to swamp the effect, owing to the increased area of cooling, and increased thermal capacity.
Report on the Examinations in Magnetism and
Results : 1st Class, 709; 2nd Class, 708 ; Failed, 793 ; Total, 2,210. This paper was, on the whole, rather better done than the corresponding paper last year, and this remark applies to each of the three divisions of the paper. Comments on the answers to individual questions are given below.
Magnetism. Q. 1. A wooden ball contains a bar magnet imbedded so that the axis of
the magnet lies along a diameter, but the ends do not reach the surface. Explain carefully how you would mark on the surface of the ball the points where the axis of the magnet prolonged
would cut the surface. Few of the answers were more than partially correct. It was a comnion mistake to float the ball in water, and then to assume the magnet to lie N. and S., and to be horizontal. Various tests (by compass, dip needle, bar magnet, etc.) were suggested, which would only give correct results if the earth's field could be neglected.
Q. 2. What is meant by the statement that the declination at a place is
18° west? At such a place how must a boat be steered by com
pass so that its course may be due east ? Well done on the whole. A curious and not infrequent blunder was to direct the helmsman to steer so that the compass pointed 18° S. of E. Q. 3. A horse-shoe magnet is brought due south of a small compass
needle, the line joining the poles of the magnet being east and west, with the north pole to the west. Describe the manner in which the compass is deflected.
Describe and explain what will happen if the keeper is placed
on the magnet. The drawings were very bad as regards proportions. In the first part the influence of the earth's field was generally ignored. In the second part all the lines of force due to the magnet were regarded as passing through the keeper. Q. 4. How would you hold a rod of soft iron so that the influence of the
earth's magnetic field upon it may be (1) as great as possible, (2)
as small as possible! Frequently well done. For the least magnetic effect almost all placed the rod horizontal, E. and W. Extremely few gave the more general answer, viz., that the rod might be placed anywhere in a plane at right angles to the line of dip.
Having charged the instrument positively, how would you test the sign of the charge on the inner coating of a Leyden jar
without discharging or moving either the jar or the electroscope ? Answers to the first part were usually reasonable ; there were scarcely any correct answers to the second. Nearly all the candidates adopted a method by which the jar was partially discharged.
Q. 6. What is meant by the statement that a given body is at a higher
potential than the earth ? Illustrate your answer by means of
analogous phenomena in heat and hydrostatics. The main part was badly answered. There were two types of answer ; the first omitted to state that it is a flow of positive electricity from a body to the earth that is a test of higher pictential in the former ; the second, whether expressed in terms of two fluids, one fluid or Faraday tubes, merely amounted to saying that a body has higher potential than the earth if it is positively electrified. Q. 7. A hollow metal can is placed on an insulated stand and electrified
Describe the distribution of the electrification on the can and
explain how you would examine the distribution experimentally. Many knew that there is no electrification inside ; not so many stated that the density is greatest at the edges, etc. The statement that the absence of electrification can be proved by connecting the inside to an electroscope was made a good many times ; but a fair proportion knew all about the question. Q. 8. A metal plate A, thickly varnished on the top, is insulated and
connected to a gold-leaf electroscope, the whole being charged with positive electricity until the leaves diverge widely. When another insulated plate B (for instance, the cover of an electrophorus) is placed on the top of A, the divergence of the leaves is very little altered, but if B is touched the leaves fall nearly
vertical. How do you explain these effects ? There was a greater number of unsatisfactory answers to this than to any other question in the paper. The usual mistake was to assume that the touching of B connected the whole apparatus to earth, and allowed the electricity to escape. The common explanation in terms of " free and " bound" electricity was sometimes given, but the number of incorrect explanations in terms of capacity and potential changes was great. Q. 9. Describe and explain the action of a plate-glass frictional machine
How would you use it to charge a Leyden jar? The machine was well described, but the action of the collecting combg seemed to be imperfectly understood. Some attempted to describe the Wimshurst machine, and knew very little about it.
Voltaic Electricity. Q. 10. Describe the Daniell cell, and explain the functions of each part
of the cell and the action that takes place when the poles are connected by a conducting wire.
What advantages does this form of cell possess over a simple voltaic cell consisting of plates of copper and zinc immersed in
dilute acid ? Answered by nearly all, and the best answers were very good.
A large number knew nearly all about the Daniell cell. The function of the porous pot was seldom stated explicitly ; a good many stated that bubbles of hydrogen passed through, and then interacted with the sulphate. Some had very vague notions of polarisation. A few had apparently been taught that copper coated with hydrogen is more electropositive than zirc. Local action was frequently stated to be absent from the Daniell cell, without any mention of amalgamation of the zinc. Q. 11. State Ohm's law, and explain the terms used.
An incandescent electric lamp takes a current of :5 ampère when connected to a circuit of 100 volts. What is the resistance
of the lamp? The answers to this question were too indefinite Nearly ali the candidates stated that current equalled electromotive force divided by resistance, but did not explain themselves by considering any particular case of the
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CC-MAIN-2021-49
| 13,941 | 86 |
https://www.coursehero.com/file/6288680/rpp2010-rev-monte-carlo-techniques/
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math
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This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: 34. Monte Carlo techniques 1 34. MONTE CARLO TECHNIQUES Revised September 2009 by G. Cowan (RHUL). Monte Carlo techniques are often the only practical way to evaluate difficult integrals or to sample random variables governed by complicated probability density functions. Here we describe an assortment of methods for sampling some commonly occurring probability density functions. 34.1. Sampling the uniform distribution Most Monte Carlo sampling or integration techniques assume a “random number generator,” which generates uniform statistically independent values on the half open interval [0 , 1); for reviews see, e.g. ,[1, 2]. Uniform random number generators are available in software libraries such as CERNLIB , CLHEP , and ROOT . For example, in addition to a basic congruential generator TRandom (see below), ROOT provides three more sophisticated routines: TRandom1 implements the RANLUX generator based on the method by L¨uscher, and allows the user to select different quality levels, trading off quality with speed; TRandom2 is based on the maximally equidistributed combined Tausworthe generator by L’Ecuyer ; the TRandom3 generator implements the Mersenne twister algorithm of Matsumoto and Nishimura . All of the algorithms produce a periodic sequence of numbers, and to obtain effectively random values, one must not use more than a small subset of a single period. The Mersenne twister algorithm has an extremely long period of 2 19937 − 1. The performance of the generators can be investigated with tests such as DIEHARD or TestU01 . Many commonly available congruential generators fail these tests and often have sequences (typically with periods less than 2 32 ), which can be easily exhausted on modern computers. A short period is a problem for the TRandom generator in ROOT, which, however, has the advantage that its state is stored in a single 32-bit word. The generators TRandom1 , TRandom2 , or TRandom3 have much longer periods, with TRandom3 being recommended by the ROOT authors as providing the best combination of speed and good random properties. 34.2. Inverse transform method If the desired probability density function is f ( x ) on the range −∞ < x < ∞ , its cumulative distribution function (expressing the probability that x ≤ a ) is given by Eq. (32 . 6). If a is chosen with probability density f ( a ), then the integrated probability up to point a , F ( a ), is itself a random variable which will occur with uniform probability density on [0 , 1]. If x can take on any value, and ignoring the endpoints, we can then find a unique x chosen from the p.d.f. f ( s ) for a given u if we set u = F ( x ) , (34 . 1) provided we can find an inverse of F , defined by x = F − 1 ( u ) . (34 . 2) K. Nakamura et al. , JPG 37 , 075021 (2010) (http://pdg.lbl.gov) July 30, 2010 14:36 2 34. Monte Carlo techniques This method is shown in Fig. 34.1a. It is most convenient when one can calculate by hand the inverse function of the indefinite integral of...
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- Spring '11
- Normal Distribution, Probability theory, probability density function, Cumulative distribution function, Monte Carlo techniques
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| 3,299 | 5 |
https://avesis.gazi.edu.tr/yayin/751bdf4c-07a7-4978-b3ff-735205abd547/the-big-fish-little-pond-effect-on-affective-factors-based-on-pisa-2012-mathematics-achievement
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math
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In this study, the 2012 PISA Turkey student questionnaire data is considered to determine the big fish-little pond effect. The mathematics self-efficacy, self-concept and anxiety affective factors are examined to explain the relation of each of them with the school type, gender, socioeconomic status, student's mathematics achievement and school's mathematics achievement covariates. A total number of 771 students from 88 high schools are in the sample. Factor analyses' results support the construct validity of the Student Questionnaire's mathematics self-efficacy, anxiety and self-concept items. Data set is analyzed with Multiple Indicator Multiple Cause Model and the patterns of association with covariates and affective factors were tested simultaneously. According to the results, Anatolian high school students have a higher mathematics self-efficacy and lower mathematics anxiety than do the general high school students. However, when the student mathematics achievement and school mathematics achievement variables were inserted to the model, school type was not associated with mathematics self-efficacy. Moreover, Anatolian high school student's mathematics anxiety was higher than that of the general high school students. Student's mathematics achievement was the most significant predictor of the mathematics self-efficacy, anxiety and self-concept factors. Finally, school's mathematics achievement was a significant predictor of only mathematics self-concept. The identification of increase in school's mathematics achievement yields a decrease in the student's mathematics self-concept may be considered as the most important result of this study. These results provide evidence about the Anatolian high schools' students experience big fish-little pond effect.
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CC-MAIN-2021-25
| 1,784 | 1 |
https://www.accidentaltalmudist.org/atdaily/shekalim/at-daily-448-the-holiness-of-a-50-cent-piece-by-purim-shekalim-6/
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math
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Chapter 2, Misha 3, 4
If one sets aside more money than he needs to pay his annual half-shekel obligation, what should be done with the surplus? Is it consecrated, or is it his? Why do we get a different result if he saves up one coin at a time vs. grabbing a stack of coins? Why is the result different if the money is set aside to purchase a sin-offering? Why does the Torah specify a half-shekel as the annual obligation when the Temple is standing? Can money set aside for one kind of offering be used for a different kind?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100674.56/warc/CC-MAIN-20231207121942-20231207151942-00812.warc.gz
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CC-MAIN-2023-50
| 527 | 2 |
http://www.anujvarma.com/some-cool-proofs-in-math/
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math
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If you are looking for some of the most important, yet elegant math proofs, look no further than these two books.
- The first one – Proofs from the book – The book is dedicated to the mathematician Paul Erdős, who often referred to “The Book” in which God keeps the most elegant proof of each mathematical theorem.
- The second one – 100 great problems of Elementary Math – This interesting book covers 100 of the most famous historical problems of elementary mathematics. The book provides insight into the extraordinary ingenuity of some of the greatest mathematical minds of history — Archimedes, Isaac Newton, Leonhard Euler, Augustin Cauchy, Pierre Fermat, Carl Friedrich Gauss, Gaspard Monge, Jakob Steiner, and many others…
If you have any other books or online resources you would like to contribute to this list (book containing elegant proofs only), feel free to comment.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813571.24/warc/CC-MAIN-20180221063956-20180221083956-00391.warc.gz
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CC-MAIN-2018-09
| 898 | 4 |
http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA019800
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math
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Accession Number : ADA019800
Title : A LIFO Implicit Enumeration Algorithm for the Asymmetric Traveling Salesman Problem Using a One-Arborescence Relaxation.
Descriptive Note : Technical rept.,
Corporate Author : CARNEGIE-MELLON UNIV PITTSBURGH PA MANAGEMENT SCIENCES RESEARCH GROUP
Personal Author(s) : Smith,Theunis H. C.
Report Date : OCT 1975
Pagination or Media Count : 22
Abstract : The author proposes a LIFO implicit enumeration algorithm for the asymmetric traveling salesman problem in which the one-arborescence relaxation of the traveling salesman problem (originally suggested by Held and Karp) is employed as a fathoming device. The efficient Edmonds-Fulkerson algorithm is used to construct minimum-cost arborescences. Computational exerpience with the algorithm is also presented.
Descriptors : *Integer programming, Mathematical models, Algorithms, Computations, FORTRAN
Subject Categories : Operations Research
Distribution Statement : APPROVED FOR PUBLIC RELEASE
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s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812327.1/warc/CC-MAIN-20180219032249-20180219052249-00779.warc.gz
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CC-MAIN-2018-09
| 981 | 11 |
https://electronics.stackexchange.com/questions/192894/a-questions-about-negative-resistance
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math
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I would like to look at negative resistance from a practical point of view, not just theory. Would you answer my questions,please?
The op-amp, R1, R2, and R3 behave as a negative resistance: Rn = - 100 ohms.
R4 is in series with the negative resistance.
1- If I constructed this circuit on a breadboard, Will the negative resistor work as a generator and injects current through AA batteries and damage them? Or the current just stops?
2- If the supply was a transformer with bridge rectifier, Would the bridge rectifier prevent the current form interning the supply?
3- If the op-amp IC is supplied with 12 volts or any value that is different from input voltage, Will that affect any parts of the circuit ?
4- If I changed the value of R4 to be 150 ohms, The current will be:
V = I*R
I = 0.1 A , Is that right ?
Rn is the equivalent negative resistance, on of its terminals appears at the non inverting input of the op-amp and the other terminal appears at the ground.
What I mean by AA batter or transformer is we remove the 5 volts supply and put an AA battery or a transformer instead.
I think the output terminal is also the non inverting input because the circuit behave just like a resistance.
For more information about negative impedance converter :https://en.wikipedia.org/wiki/Negative_impedance_converter
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| 1,317 | 13 |
http://www.idealessaywriters.com/using-the-concept-of-dependent-probabilities-determine-the-odds-that-you-would-draw-these-hands-card-combinations-directly-from-a-deck-of-cards/
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math
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In the lecture of this module, you were introduced to determining probable outcomes related to drawing cards from a 52-card deck. Using cards to demonstrate probability concepts is a classic approach to learning about dependent probability events. In this assignment, you are going to calculate the probabilities related to drawing cards from a standard deck.
Select three different five-card combinations or five-card hands from your favorite card game that utilizes a standard 52-card deck containing four suits (clubs, hearts, diamonds, and spades), with each suit containing 13 cards with numbers 2–10 and face cards ace, king, queen, and jack. Then, do the following:
- Using the concept of dependent probabilities, determine the odds that you would draw these hands (card combinations) directly from a deck of cards.
- Determine the probability that you would not draw these hands (card combinations) directly from a deck of cards.
- Think of another activity in life, besides playing cards, where the concepts of probability would be useful to the decision-making process and share it with the group.
Write your initial response in a minimum of 200 words. Apply APA standards to citation of sources.
By Saturday, November 21, 2015, post your response to the appropriateDiscussion Area. Through Wednesday, November 25, 2015, review the postings of your peers and respond to at least two of them. Consider commenting on the following:
- How do your peers’ card probabilities compare to the probabilities that you determined for your card combinations?
- Do you think that knowledge of how to calculate probability would be useful for playing games of chance or for making decisions in other areas of life? Explain.
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| 1,723 | 9 |
http://cafe-drome.com/index.php/epub/differential-geometry-part-1
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math
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By Chern S., Osserman R. (eds.)
Read or Download Differential Geometry, Part 1 PDF
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The instruction manual provides an outline of so much points of contemporary Banach house thought and its functions. The updated surveys, authored via top study employees within the sector, are written to be available to a large viewers. as well as proposing the state-of-the-art of Banach area concept, the surveys talk about the relation of the topic with such components as harmonic research, advanced research, classical convexity, likelihood thought, operator thought, combinatorics, good judgment, geometric degree idea, and partial differential equations.
The booklet encompasses a survey of study on non-regular Riemannian geome try out, conducted commonly by means of Soviet authors. the start of this course oc curred within the works of A. D. Aleksandrov at the intrinsic geometry of convex surfaces. For an arbitrary floor F, as is understood, all these suggestions that may be outlined and proof that may be demonstrated via measuring the lengths of curves at the floor relate to intrinsic geometry.
In accordance with the Simons Symposia held in 2015, the court cases during this quantity specialize in rational curves on higher-dimensional algebraic kinds and functions of the speculation of curves to mathematics difficulties. there was major growth during this box with significant new effects, that have given new impetus to the learn of rational curves and areas of rational curves on K3 surfaces and their higher-dimensional generalizations.
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Additional info for Differential Geometry, Part 1
There are both mathematical and cultural accounts of the convention. The overlap and ramification of those accounts makes a convention appear all but inevitable, just the way the world is. And, in time, in the matter of course, a new convention might arise, and it, too, will be inevitable. How is that air of inevitability maintained? It might be useful to think of ourselves as anthropologists trying to understand the practices of a culture—here, a culture of randomness as practiced in probability, statistics, and decision theory.
Larry Yangster has become a physicist doing statistical mechanics. When Bernie asks Larry to tell him about his current work, Larry mentions that he is working on a statistical counting problem that has three main methods of calculating its partition function, the physicists' way of packaging counting information about a system. The natural logarithm of the partition function is proportional to the thermodynamic free energy that the chemists so value. Bernie remarks that it is amazing that the packaging function could be so related to something a chemist would be interested in.
Now if one were to take, say, Fredrick Mosteller and John Tukey’s 1977 text on statistics as the current gospel, then the alternatives hinted at here and by Huber are in fact fully in place. ”13 Means and variances and Gaussians are seen to be an idiosyncratic and parochial case. 15 Moreover, probability distributions much broader than the Gaussian do play an important role in the natural and the economic sciences. And computation allows for empirical estimates of variation (bootstrap, resampling).
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CC-MAIN-2022-33
| 3,565 | 15 |
https://eng.kakprosto.ru/how-896025-how-to-solve-a-system-of-equations-for-grade-7
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math
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The method of substitution
To understand the essence of this method is easiest on the example of solving a typical system includes two equations and requires finding the values of the two unknowns. So, this may be the following system consisting of the equations x + 2y = 6 and x - 3y = -18. In order to solve it by the method of substitution is required in any of the equations to Express one member through another. For example, this can be done using the first equation: x = 6 - 2y.
You must then substitute the resulting expression into the second equation instead of x. The result of this lookup will be the equality of 6 - 2y - 3y = -18. By performing simple arithmetic calculations, this equation is easy to lead to standard view 5y = 24 where y = 4,8. Then the value obtained should be substituted in the expression used for the lookup. Hence x = 6 - 2*4,8 = -3,6.
Then it is advisable to verify the obtained results, substituting them in both equations of the original system. This will give the following equations: -3,6 + 2*4,8 = 6 and -3,6 - 3*4,8 = -18. Both of these equality are true, so you can conclude that the system is solved correctly.
Method of addition
The second method of solving such systems of equations is called the method of addition, which can be illustrated on the basis of the same example. To use, all members of one of the equations is multiplied by a certain factor, with the result that one of them will be the opposite to another. The choice of this ratio is the method of selection, and the same system it is possible to decide using different factors.
In this case, it is advisable to perform a multiplication of the second equation by the coefficient -1. Thus, the first equation retains its original form x + 2y = 6, and the second will take the form -x + 3y = 18. Then you must combine the resulting equations: x + 2y - x + 3y = 6 + 18.
Having made simple calculations, we can obtain an equation of the form 5y = 24, which is similar to the equation resulting from the solution of the system by method of substitution. Accordingly, the roots of such equation will be the same values: x = -3,6, y = 4,8. This clearly demonstrates that both methods are equally applicable for the solution of such systems, and both give the same correct results.
The choice of a particular method may depend on the personal preferences of the student or from a particular expression in which it is easier to Express one through another member or to choose a ratio that will make the members of the two equations are opposite.
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http://www.chegg.com/homework-help/questions-and-answers/200-kg-cannon-ball-fired-cannon-muzzle-speed-of1000-m-s-angle-370-degrees-horizontal-secon-q378860
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math
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A 20.0 kg cannon ball is fired from a cannon with a muzzle speed of1000 m/s at an angle of 37.0 degrees with the horizontal. A secondball is fired at angle of 90 degrees. Use the conservation ofenergy principle to find (a) the maximum height reached by eachball and (b) the total mechanical energy at the maximum height foreach ball. Let y = 0 at the cannon.
Please clearly explain and show all steps.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982925602.40/warc/CC-MAIN-20160823200845-00281-ip-10-153-172-175.ec2.internal.warc.gz
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CC-MAIN-2016-36
| 401 | 2 |
https://sellfy.com/p/gchR/
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math
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Managerial Accounting: E5-11 Mackenzie Chemicals has developed a new window
Managerial Accounting E5-11 Preparing a direct materials purchases budget Mackenzie Chemicals has developed a new window cleaner that requires two ingredients, AM972 and CA38. Based on forecasted sales, Mackenzie has developed the following budgeted production for the coming year. 1st Quarter 2nd Quarter 3rd Quarter 4th Quarter 1st Quarter Next Year Forecasted production (gallons) 5,000 7,500 9,000 12,000 6,000
Each gallon of window cleaner requires 100 ounces of AM972 and 28 ounces of CA38. An ounce of AM972 costs Mackenzie $0.15. An ounce of CA38 costs the company $0.25. Mackenzie’s inventory policy requires ending inventory equal to 20 percent of the next quarter’s production needs. At the beginning of the year, Mackenzie expects to have 80,000 ounces of AM972 and 30,000 ounces of CA38 on hand.
Required Prepare Mackenzie’s AM972 purchases budget for the coming year.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125949036.99/warc/CC-MAIN-20180427041028-20180427061028-00195.warc.gz
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CC-MAIN-2018-17
| 963 | 4 |
https://research.chalmers.se/publication/501368
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math
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Regularity of Plurisubharmonic Upper Envelopes in Big Cohomology Classes
Paper i proceeding, 2012
The goal of this work is to prove the regularity of certain quasiplurisubharmonic upper envelopes. Such envelopes appear in a natural way in the construction of Hermitian metrics with minimal singularities on a big line bundle over a compact complex manifold. We prove that the complex Hessian forms of these envelopes are locally bounded outside an analytic set of singularities. It is furthermore shown that a parametrized version of this result yields a priori inequalities for the solution of the Dirichlet problem for a degenerate Monge-Ampere operator; applications to geodesics in the space of Kahler metrics are discussed. A similar technique provides a logarithmic modulus of continuity for Tsuji's "supercanonical" metrics, that generalize a well-known construction of Narasimhan and Simha.
Hermitian line bundle
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CC-MAIN-2019-47
| 920 | 4 |
https://wallsneedlove.zendesk.com/hc/en-us/articles/229151808-How-do-I-figure-out-how-much-wallpaper-I-will-need-
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math
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To figure out how much wallpaper you will need, you will need to figure out the square footage of your wall. Try using this calculator from Better Homes and Gardens: http://www.bhg.com/home-improvement/advice/measuring-materials/square-footage-calculator/. The square footage of the wallpaper is as follows:
20" X 8' - 13.36 sq ft
20" X 16' - 26.72 sq ft
20" X 25' - 41.75 sq ft
20" X 48' - 80.16 sq ft
20" X 96' - 160. 32 sq ft
Finally, match your square footage to the next highest wallpaper square footage and go!
Not sure this will work for you? Think about it this way:
The wallpaper is 20" (1.67 feet) wide (across) so you need to figure out the length of your wall, say for example it is 100 inches (8.3 ft) long. Then you need to divide the length of the wallpaper (20") into the length of your wall (in this example it's 100") to see how many times you will need the pattern to repeat across the top. In this example you will need 5 strips of wall paper (100" divided by 20"). If your wall is 6 feet tall, then you will need 5 sets of wall paper that are 6 feet in length. This means that you will need a total of 30 feet of wall paper. So you should order the 20" x 48' option so that you can cover the entire wall. You can check this by figuring out the square footage. Plug your dimensions into the calculator 8.3 ft x 6 ft. which gives you 49.8 sq ft. More than 41.75 and less than 80.16 means you have selected the correct option. Easy as Pi, right?
Want to see it on paper? Try this:
Please note that wallpaper cannot be returned or exchanged as it is all made to order and therefore considered a custom item.
Give us a call at 8778078897 if you still have questions!
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CC-MAIN-2020-10
| 1,682 | 12 |
https://kasmana.people.cofc.edu/MATHFICT/mfview.php?callnumber=mf884
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math
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a list compiled by Alex Kasman (College of Charleston)
|An unusual and intimate novel that follows three women: a widowed sheep-farmer, a mathematician who studies quasicrystals, and a taxidermist (whose included blog entries explain the title of the book). Each of them is an unusual character, both in the sense that they are somewhat odd people and in that they are not like most fictional characters. The sheep-farmer has a growth on her face that leaves her anti-social and the taxidermist poses squirrels as athletes (an old tradition I have always thought strange). Refreshingly, the mathematician Lisa Wallace is in many ways the most normal of the three.
Quite a bit of the book is about biology. There is a lot of interesting factual biological information entertainingly provided within its pages, primarily provided by the taxidermist. However, as this is a Website about mathematics in fiction, I will be spending most of the rest of this essay discussing the mathematical aspects of the story involving Lisa Wallace.
The most unusual thing about Lisa is that she is achondroplasic. Although she has some insecurities due to her dwarfism, she is much more outgoing and confident than either of the two other women. In an opening chapter we see her as a little girl, being humiliated by her sister and promising to grow up to be a "rocket scientist". Presumably, she was already thinking that in a field like math (or rocket science) your physical body is not as important as what your mind can achieve. [To some degree, I think that is true, and it is something that I personally appreciate about this discipline. Of course, there are some individuals in math who are beautiful and/or physically fit, but it is difficult to think of a field in which those things matter less than they do in math.]
The book includes just a tiny bit of discussion of what quasicrystals are and why they are studied both by scientists and by mathematicians. For instance, it says:
Penrose tilings are casually mentioned much later, but it is probably not clear to the uninformed reader that this is connected to the lack of symmetry in quasi-crystals described above. All together, there is not enough of a discussion of the mathematics of quasi-crystals to truly inform someone who was not previous familiar with them, but it may be enough to spark their interest and get them to look it up elsewhere. [If you're someone who is reading this seeking such information, let me just explain the basic idea, hopefully in easy to understand terms. If you could look at the atoms in a crystal like salt, they are arranged in a very neat regular pattern, like the squares on an empty chess board. The chess board has a lot of symmetries. If the chess board was infinite rather than having edges, you could shift it around so that a black square ends up where another black square had been and it would look exactly the same. Similarly, rotating the board around the center of any square by 90 degrees also leaves it looking exactly as before. That is what we call a "symmetry", and it had been assumed that all crystals were symmetric in that way. But, just as you can "tile" an infinite plane with black and white squares to make a symmetric infinite chess board pattern, you can tile it with "dart" and "kite" shapes invented by mathematician Roger Penrose, and the odd thing about that tessellation is that it does not have any symmetries. You cannot shift or rotate it so that it comes out looking the same. It is a non-periodic tiling. Completely independently of Penrose's theoretical discovery, scientists were discovering that some physical solids that they thought were crystals also had no actual symmetries. The field of quasicrystals combines these two into a single subject of research.]
The readers are invited into the minds of the three principle characters; we learn something about the way they think. I believe we are supposed to recognize that Lisa thinks geometrically. Frequently she has an image of "pale spheres" and has to try to figure out why she is thinking about it, running through memories of baby dolls with hair made of metal shavings from her father's workshop and a photo of (glass) eyeballs in the taxidermist's house. Consider also this passage:
This way of thinking is presumably intended to tie in with her math research. This seems improbable to me, both because none of the geometers I know seem to think so geometrically, and because the study of quasicrystals is actually much more algebraic than it is geometric. (I wonder if the reference to arrows of different lengths radiating from a common point that Lisa imagines at some point was a reference to root systems, one of those very algebraic things utilized by crystallographers.)
Perhaps you're now wondering about the plot and how the three women's lives are intertwined. Lisa and a physicist colleague (who works on the more scientific aspects of quasicrystals) visit a farm in the UK's Cumbria Lake District to see the physicists former lover. The farm belongs to the widow and the former lover who lives in a house on her property is the taxidermist. We see each of the characters in romantic/sexual relationships, and we see them interacting together as friends. However, I think focusing on the plot would be a mistake. This is a book of interesting moments -- like the way people react to Lisa's dwarfism -- and big ideas (eugenics, the Foot & Mouth epidemic, and love).
The author has a few brief comments on her Website concerning her selection of the area of research for the mathematician. Click here to read it (and scroll down to the beautiful picture of Dutch tulip fields).
|More information about this work can be found at www.amazon.co.uk.
|(Note: This is just one work of mathematical fiction from the list. To see the entire list or to see more works of mathematical fiction, return to the Homepage.)
Exciting News: The 1,600th entry was recently added to this database of mathematical fiction! Also, for those of you interested in non-fictional math books
let me (shamelessly) plug the recent release of the second edition of my soliton theory textbook.
(Maintained by Alex Kasman,
College of Charleston)
(Maintained by Alex Kasman, College of Charleston)
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CC-MAIN-2024-10
| 6,260 | 17 |
https://sihivubefavoqe.unavocenorthernalabama.com/symbolic-algebra-online-16592gj.html
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math
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In this universe the matrix is important to be rank deficient. Child Algebra, 2nd Edition. Use it most of the argentinian in KS3. The Balanced Study Companion makes teaching from it very personal for homeschoolers or strengths.
Perhaps more notable is the country between even and odd starting states. Also, another permanent question remains.
Well done an idea you very much for information my maths lessons more interesting and fun.
Materialism of the language of thesis can be learned from the impression of functions. There are so many students of functions today that can be able at the substantial levels.
Executing this program consists in defeating the expression for next values of a and b; if they do not have any tangible—that is they are indeterminates—, the result of the college is simply its input.
Professor Lisa won a Summary Prize in Chemistry in because of his young with radiocarbons. One way to see the rank of a thesis is to consider the row expand form. If this sentence is zero and any nonzero effects are in the best beneath, the rows are exchanged and the very is repeated.
Fantastic way to sleep the pupils at the research of a lesson. Then, when faced enough, hailstones mere out of the benefits and tumble to make. Understanding the graphs of words relates to the ability to use other peoples in other subjects concerning kittens between knowns or unknowns.
Gottfried Leibniz rambling the term to complicated aspects of a glowing in Refund my review of these two conflicting algebra companions. Bitter is, as yet, no different understanding of the apparently chaotic tree of the directions produced by this straightforward procedure. Some larger examples may show red variation attained in reverse number sequences.
Diacritics have application in all walks of descriptive such as homophobia, science, mathematics, homemaking, sports, and symbolic algebra online, just to name a few. The final sections are reputed to have been assigned by Menaechmus c. Mathematica, Maple, and similar software packages provide programs that carry out sophisticated mathematical operations.
Applying the ideas introduced in Computer Algebra and Symbolic Computation: Elementary Algorithms, this book explores the application of algorithms to such methods as automatic simplification, polynomial decomposition, and polynomial factorization.
The following tables provide a comparison of computer algebra systems (CAS). A CAS is a package comprising a set of algorithms for performing symbolic manipulations on algebraic objects, a language to implement them.
unavocenorthernalabama.com Online Algebra Calculator. Many of users do not use powerful Maxima computer algebra system for systematic work, but for ad hoc algebraic calculations – equations, functions, matrixes, etc. only. To do this job, it is not useful to download the whole application from a web site.
Read the latest articles of Journal of Pure and Applied Algebra at unavocenorthernalabama.com, Elsevier’s leading platform of peer-reviewed scholarly literature. Jul 29, · Symbolic Expressions and Algebra The sym function can be used to create “symbolic objects” in MATLAB.
If the input argument to sym is a string, the result is a symbolic number or variable. Maxima, a Computer Algebra System. Maxima is a system for the manipulation of symbolic and numerical expressions, including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, polynomials, sets, lists, vectors, matrices and tensors.Symbolic algebra online
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057504.60/warc/CC-MAIN-20210924050055-20210924080055-00492.warc.gz
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CC-MAIN-2021-39
| 3,581 | 14 |
https://www.skoolie.net/forums/f9/skoolie-leveling-2280.html
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math
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Correct me if I'm wrong, but a little trignometry using 100 feet as the base length and 35 degrees as the angle nets an opposite side length of 70. So that's a 70 foot vertical change over 100 feet or a 70% grade. Something about that just doesn't jive with me. Another way to look at it would be this. The maximum length for a bus is 40 feet. With a 40 foot bus on a 35* hill there would be a 28 foot difference in altitude between the front and the rear. I don't think 2x8's are going to make up that difference. If you park across the side hill and the bus is 8 feet long there will be a 5.6 foot difference between the height of the uphill and downhill sides.
Are we sure that wasn't a typo?
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588257.34/warc/CC-MAIN-20211028034828-20211028064828-00629.warc.gz
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CC-MAIN-2021-43
| 695 | 2 |
https://www.physicsforums.com/threads/can-a-reaction-be-exothermic-due-to-increased-kinetic-energy.725655/
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math
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1. The problem statement, all variables and given/known data Examkrackers Lecture question - MCAT Prep book 116. A student holds a beaker of pure liquid A in one hand and pure liquid B in the other. Liquid A has a higher boiling point than liquid B. When the student pours a small amount of liquid B into liquid A, the temperature of the solution increases. Which of the following statements is true? Tempting answer choices: B. The boiling point of the solutions is higher than either pure liquid A or B. C. The freezing point of the solution is higher than either pure liquid A or B. 2. Relevant equations None were supplied. 3. The attempt at a solution I can argue for either answer B or answer C. C: By mixing the solutions together, any lattice which would form upon freezing must have been disrupted, producing a higher melting point. Is this thinking correct? Why or why not? B: Maybe not because isn't it possible that mixing two solutions would increase the kinetic energy of the particles? If it is possible that kinetic energy is responsible for the increase in temperature, then, B is not necessarily correct. Could that be the case? Why or why not? (The obvious other possibility is that stronger bonds formed releasing energy and increasing the boiling point.) Thanks for your help!
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591596.64/warc/CC-MAIN-20180720115631-20180720135631-00321.warc.gz
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CC-MAIN-2018-30
| 1,297 | 1 |
https://www.chemicalforums.com/index.php?topic=34251.0
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math
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Hydrogen sulfide gas is a poisonous gas with the odor of rotten eggs. It occurs in natural gas and is produced during the decay of organic matter, which contains sulfur. The gas burns in oxygen as follow:
Calculate the standard enthalpy change for this reaction using standard enthalpies of formation.
Okay so here is my work after using the standard enthalpy chart to determine the ∆Hf˚
I put them into the reaction ΔH° = Σ(ΔHf°products) - Σ(ΔHf°reactants) which looked like this
/1)- (2molH2S×-20.5/1)+(3molO2×0/1) =19kJ/mol
But the answer is supposed to be -1124.2kJ, can anyone tell me what I did wrong here?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571284.54/warc/CC-MAIN-20220811103305-20220811133305-00493.warc.gz
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CC-MAIN-2022-33
| 625 | 6 |
https://pdfslide.us/documents/activity-graphing-absolute-value-2018-10-13-graphing-absolute-value-functions.html
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math
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Activity: Graphing Absolute Value Functions
With a partner, complete the 2.8 Graphing Absolute Value
You will need:• A partner• Activity sheet• Pencil• Graphing
using the following table of values
using the following table of values:
Graphing Absolute Value functions on a TI83: You can find the absolute value function by accessing the Math key. Arrow to the right to find the NUM menu. On this screen you will find: #1 abs( the absolute value function:
using your calculator and leave the equation in y
for the rest of the activity.
3. THE EFFECT OF K:Graph the following functions and identify the vertex
Describe the effect of k on the graph:
4. THE EFFECT OF h:Graph the following functions and identifya.
Describe the effect of h on the graph:
5. THE EFFECT OF a:Graph the following functions and identify the vertex:
Describe the two effects of a on the graph:
6. Putting it all together…graph the following functions and identify the vertex.
7. WITHOUT graphing, can you figure out the vertex of the following function?
2.8 Graphing Absolute Value Functions
The graph is a piecewise function that consists of two rays and
It opens up.
The corner point of the graph is called the vertex. In this
case, it occurs at the origin.
Notice that the graph of is symmetric in the y-axis because for
every point (x,y) on the graph, the point (-x,y) is also on the
General form of an absolute value function is y = a |x - h| +
• The graph has vertex (h,k) and is symmetric in the line x =
• The graph is V-shaped
• If a < 0, the graph opens down (a is negative)• If a >
0, the graph opens up (a is positive)
• The graph is wider than the graph of y = |x| if |a| < 1•
The graph is narrower than the graph of y = |x| if |a| > 1
Note: When graphing, "a" is the slope to the RIGHT of the
For examples 1 & 2 tell if the graph opens up or down, and
if it is narrower or wider. State the vertex.
Example 1: y = 6 |x - 7| Example 2: y = |x| + 9
To graph y = a |x - h| + k
1. Plot the vertex (h,k)
2. Use the slope (a) to plot another point to the RIGHT of the
3. Use symmetry to plot a 3rd point
4. Complete the graph
Graph y = - |x + 2| + 3
Graph y = 2 |x - 1| + 1
Example 3: Write the equation for
Example 4: Write the equation for
Take out your student handbook and write downthe homework
pg. 125-126 #12-17, 19-25 odd, 34-39
Page 1: Sep 21-12:39 PMPage 2: Sep 21-12:47 PMPage 3: Sep
21-12:49 PMPage 4: Sep 21-12:50 PMPage 5: Sep 21-12:51 PMPage 6:
Sep 21-12:52 PMPage 7: Sep 21-12:53 PMPage 8: Sep 21-12:54 PMPage
9: Sep 21-10:32 AMPage 10: Sep 21-10:57 AMPage 11: Sep 21-11:09
AMPage 12: Sep 21-11:12 AMPage 13: Sep 21-11:13 AMPage 14: Sep
21-11:14 AMPage 15: Sep 21-11:15 AMPage 16: Sep 21-11:16 AMPage 17:
Sep 21-12:42 PM
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CC-MAIN-2022-40
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https://fructaroma.ru/how-to-solve-math-problems-fast-3797.html
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math
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“If you want to know how fast computers can solve certain mathematical problems, then integer multiplication pops up as some kind of basic building brick with respect to which you can express those kinds of speeds.” Most everyone learns to multiply the same way.
We stack two numbers, multiply every digit in the bottom number by every digit in the top number, and do addition at the end.
Mental math works great for four of the six operations of math: addition (4 4=8), subtraction (8-4=4), multiplication (4x2=8), and division (8/4=2). To solve this problem first we identify all the numbers and the operations that will be used.
These four operations can be used to solve any math problem. Let's imagine you and your best friend are heading on a road trip. While on the highway, there are a total of seven cars in your lane. We know that we start with seven cars and three leave. Our problem is this: 7 cars in the lane - 3 cars that leave= 4 cars left in the lane Now we have to add the seven cars to our lane, because they joined us.
If you’re multiplying two two-digit numbers, you end up performing four smaller multiplications to produce a final product.
The grade school or “carrying” method requires about is the number of digits of each of the numbers you’re multiplying.So three-digit numbers require nine multiplications, while 100-digit numbers require 10,000 multiplications.The carrying method works well for numbers with just a few digits, but it bogs down when we’re multiplying numbers with millions or billions of digits (which is what computers do to accurately calculate pi or as part of the worldwide search for large primes).You also have to share the costs of gas with your friend. You can visualize what the problem is asking you when you use mental math.The four operations used in math are addition, subtraction, multiplication, and division.The word joined indicates addition: 4 cars in the lane 7 cars that joined= 11 cars in total To solve this problem, first we subtracted the cars that left and then added the cars that joined.We can also solve the problem this way: 7 cars in the lane 7 cars that joined= 14 cars 14 cars - 3 cars that left= 11 cars in total The answer is the same even though we solved the problem two different ways.“Everybody thinks basically that the method you learn in school is the best one, but in fact it’s an active area of research,” said Joris van der Hoeven, a mathematician at the French National Center for Scientific Research and one of the co-authors.The complexity of many computational problems, from calculating new digits of pi to finding large prime numbers, boils down to the speed of multiplication., or If I eat four slices of pizza tonight, will I have enough for lunch tomorrow?Using mental math to solve two-step word problems can be easy and very useful in everyday life, and you might not even know it.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587659.72/warc/CC-MAIN-20211025092203-20211025122203-00647.warc.gz
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CC-MAIN-2021-43
| 2,902 | 6 |
https://acot-centr.ru/mathematics-trivia-math/math-symbols-bold-latex-font.php
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math
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- speech laboratory description job duties manager
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- math symbols bold latex font
Subscribe to RSS math symbols bold latex font
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Feb 26 '19 at And none of these bold across an alignment character. Community and Moderator guidelines for escalating issues via new response….
math symbols bold latex sheets
Konrad Swanepoel Konrad Swanepoel 5 5 silver badges 12 12 bronze badges. Like italic x as a variable, but bold x as a vector.
math symbols bold latex and makeup
It could be very hard to change all the formatting later if a style should be changed. Javier E. Just as a sidenote: bold letters in math usually have a distinct meaning from non-bold letters.
math symbols bold latex and yellow
Sign up to join this community. Linked
math symbols bold latex white
Just as a sidenote: bold letters in math usually have a laex meaning from non-bold letters. Stefan Kottwitz. There are several ways to tweak this behavior.
Active Oldest Votes. See tex. Szczypawka Most universal
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- A practical guide to writing technical specs.
- Cragfelt 3, 3 3 gold badges 12 12 silver tont 31 31 bronze badges.
- Viewed 1.
- Ask Question.
- Oh well.
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https://math.answers.com/Q/What_is_the_Equation_for_volume_of_o-ring
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math
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Volume = 0.
No equation is possible, lung volume is measured by a machine in to which you breath.
Nicole Oring was born on January 19, 1977, in Seoul, South Korea.
Circles don't have volume, but they do have area.
You have to know the density of the material, and the density equation, Density = mass/volume. Manipulate the equation to Mass = density x volume.
Use the equation for the volume of a cone, replace the known height and volume, and solve the resulting equation for the radius.
ring volume formula ring volume formula
Oring noun is superlative
density = mass / volume mass = density * volume volume = mass / density
Density = mass/volume.
Since a triangle is two-dimensional, it cannot have volume.
Mass = Density x Volume Density = Mass/Volume Volume = Mass/Density
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https://www.qfak.com/education_reference/homework_help/?id=2886120
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math
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It's a binomial, not a trinomial.
The way I approach these is, to reduce this to (x+a)(x+b), I need to find a and b such that
a*b = 16
a+b = 8
Since a*b is positive, either both a and b are positive, or both a and b are negative.
Since a+b is positive, a and b must both be positive.
What are the factors of 16? 1 and 16, 2 and 8, 4 and 4. A quick glance reveals which two add up to 8.
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https://www.crackap.com/ap/physics-1/question-191-answer-and-explanation.html
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math
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AP Physics 1 Question 191: Answer and Explanation
Use your browser's back button to return to your test results.
1. In section 5 of the velocity-versus-time graph, the object is
- A. speeding up moving in the positive direction
- B. slowing down moving in the positive direction
- C. speeding up moving in the negative direction
- D. slowing down moving in the negative direction
Correct Answer: D
Section 1 represents a constant positive speed. Section 2 shows an object slowing down, moving in the positive direction. Section 3 represents an object speeding up in the negative direction. Section 4 demonstrates a constant negative speed, and section 5 represents the correct answer: slowing down moving in the negative direction. Though the slope is positive, this corresponds to acceleration, indicating that the direction of acceleration is opposite to the direction of velocity and thus is slowing down. However, the section remains in the negative quadrant, and the velocity becomes slower but is still negative.
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http://www.brightstorm.com/math/algebra-2/roots-and-radicals/introduction-to-imaginary-numbers-problem-6/
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math
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Like what you saw?
Create FREE Account and:
Introduction to Imaginary Numbers - Problem 6
By definition, a complex number is written as a + bi where "a" is a real number, and "b" is a coefficient in front of the imaginary number, i. Recall that i is defined as the square root of negative one, so i squared is negative one. We are often asked to write square roots of negative numbers as complex numbers, and we do so by first simplifying any negative roots.
Transcript Coming Soon!
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http://www.jiskha.com/display.cgi?id=1292619539
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math
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September 30, 2016
Post a New Question
Friday, December 17, 2010
find three rational numbers between the negtive square root of 26 and the negtive square root of 15 and explain how you got the answer
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- I am supposed to "write each expression with a rational denominator" 1...
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7th grade math Ms. Sue please
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http://www.hatrack.com/cgi-bin/ubbmain/ultimatebb.cgi?ubb=print_topic;f=2;t=056717
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math
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Which I imagine if you factor it probably equals to (x+2)^2 if you solve for c
Which seems a little wierd, is the answer good enough at the polynomial x^2+4x+C or do I have to get it back to (x+2)^2?
Next if I have (x+2)^2, do I find its integral? Foil it out and do f(x)= x^2+4x+4 (dx)?
In which case it should be (1/3)(x^3) + 2x^2 + 4x + C?
Or is there a reverse chain rule I can use?
//one third times x+2 cubed times the intergral of the inside plus a constant?
Posted by Phanto (Member # 5897) on :
Your question doesn't really make sense to me.
quote: is the answer good enough at the polynomial x^2+4x+C or do I have to get it back to (x+2)^2?
The integral of 2x + 4 is x^2 + 4x + C... where are you getting the whole weird (x+2)^2 stuff from?
The fact that you can rewrite an equation in another way doesn't mean you should, and unless you know what C is for some reason then it is unknown.
Posted by Blayne Bradley (Member # 8565) on :
The point is say I have f(x) = (x+2)^2
The idea is figuring out how to integrate it and how to integrate back from its derivative.
Posted by fugu13 (Member # 2859) on :
You can't, perfectly. Information is lost. Taking the derivative of any constant is 0, so it is impossible to integrate and work out any constant terms that were part of the original.
(x+2)^2 has a constant term -- writing it another way, as x^2 + 4x + 4, you can see that clearly. After taking the derivative, all information about that constant term is lost. It was a 4, but from the derivative you can't tell if it was a 23 or a 7 or 2.1 billion. So no, you can't get back to (x+2)^2 from knowing the derivative is 2x + 4. Because it could have been x^2 + 4x + 3.14159 instead of x^2 + 4x + 4.
Now, if you have additional information, you can compute the constant factor. For instance, sometimes you are given the intercept or somesuch.
Posted by The Rabbit (Member # 671) on :
quote:Originally posted by Blayne Bradley: okay so if I have f(x)=(x+2)^2
then f'(x) = 2*(x+2)* (dx/dy) x+2 which is 1
so f'(x) = 2x+4
You've lost me completely.
What is y? What variable are you differentiating with respect to?
what is 1?
Aside from that, the answer fugu and Phanto have given you is accurate.
You loose information when you take a derivative, that's why you have to add in an arbitrary constant when you integrate. In order to recover the original function by integrating a derivative, you have to have more information. Typically, you have to know the value of the initial function at some point.
Posted by The White Whale (Member # 6594) on :
I think he means f'(x) = 2*(x+2)*d/dx(x+2), and that d/dx(x+2) = 1.
Posted by Mike (Member # 55) on :
quote:You loose information...
Speaking of which, I can't wait 'til my information bow arrives in the mail.
Posted by willthesane (Member # 11754) on :
the integral from a to b of f(g(x))*g'(x) is the same as the integral from g(a) to g(b) of f(x).
so, the integral of f(x)=(x+2)^2 dx from 0 to 2 is the same as the integral of f(u)=u^2 from 2 to 4.
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| 3,009 | 35 |
https://dominicantoday.com/dr/economy/2018/08/24/gasoline-gases-stay-put-other-fuels-mixed/
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math
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Gasoline, gases stay put, other fuels mixed
Santo Domingo.- The Industry and Commerce Ministry on Fri. posted the fuel prices for the week from August 25 to 31, when premium gasoline will still cost RD$241.30, regular gasoline RD$228.20 and optimum diesel stays at RD$198.60 per gallon.
Regular diesel will cost RD$188.50, and avtur RD$148.90, both RD$1.00 higher, while kerosene will cost RD$175.70, or RD$1.60 lower per gallon.
Fuel oil will continue at RD$120.85; propane at RD$122.30 per gallon and natural gas at RD$28.97 per cubic meter.
The Dominican Republic Central Bank’s posted average exchange rate of RD$49.79 per dollar was used to calculate all fuel prices.
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http://tpk-ast.com/solutions-to-math-problems.html
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math
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Solutions to math problems are explained step-by-step.
Related Pictures solutions to math problems amor s personal website
Communication activities become more elaborate in third andfourth grade, as students become more comfortable with symbolic andwritten representations of ideas. Students should communicate witheach other about mathematics on a daily basis, exploring problemsituations and justifying their solutions. Different types of writingassignments may be used: keeping journals, explaining solutions tomath problems, explaining mathematical ideas, and writing about thereasoning involved in solving a problem. Students continue to usemanipulatives to explore new ideas and learn to relate differentrepresentations of an idea to each other. For example, after usingbase ten blocks to solve x , students might providea pictorial representation of these blocks (at left below) followed bya written explanation of what they did to get x . Linking the use of concrete manipulatives to the pictorialand symbolic representations is critical to understanding themathematical procedures.
found a solution to the math problem using the elephant! Hilarious
Writing is an integral part of conveying both mathematical concepts and solutions. Often K-12 educators are not provided with an adequate means of teaching writing in the math curriculum without delving into the English curriculum. By teaching the students to construct heuristics and algorithms (HAL) to derive solutions to mathematical problems, then the student is learning an effective means of problem solving to the extent that they must list the givens, concepts learned, and learn to think sequentially. The construction of algorithms and heuristics stands on its own merits in the area of problem solving and critical thinking. By teaching students not only how to construct algorithms and heuristics, but also a few transitional words and phrases then the HAL can then be used by the student to write an English translation of any given problem and its solution. Obviously, HAL is a form of pseudo code.
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http://asrjetsjournal.org/index.php/American_Scientific_Journal/article/view/4050
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math
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Implicit Second Derivative Hybrid Linear Multistep Method with Nested Predictors for Ordinary Differential Equations
In this paper, we considered an implicit hybrid linear multistep method with nested hybrid predictors for solving first order initial value problems in ordinary differential equations. The derivation of the methods is based on interpolation and collocation approach using polynomial basis function. The region of absolute stability of the method is investigated using the boundary locus approach and the methods have been found to be stable for step-length
Brugnano, L & Trigiante, D.; Solving Differential Problems by Multistep Initial and Boundary Value Methods, Amsterdan: Gordon and Breach Science Publishers, 1998.
Butcher, J.C; A modified multistep method of numerical integration of ordinary Differential equations, J Ass. comput. Math; 1965, vol;12, pp.124-135.
Butcher, J.C; A Transformed implicit Runge-Kutta Method, J. Ass. comput. Math., 1979, Vol.26, pp.731-738.
Dahlquist, G. A; special stability problems for linear multistep methods, BIT. 1963, vol.3, pp. 27
Donelson, J. & Hansen, E.; Cyclic Composite Multistep Predictor-Correctors Methods, SIAM, J. Num. Anal.,1971, Vol.8,pp.137-157.
Enright,W.H., Second Derivative Multistep Methods for stiff ODE’s, SAIM. J. Num.Anal., 1974, vol.11, ISS.2 pp. 321-331.
Enright, W.H., continuous numerical methods for ODE’s with defect control, J. computational. Appl. math., Vol.25, (2000), pp. 159-170.
Esuabana I. M & Ekoro S. E.; Hybrid Linear Multistep Methods with Nested Hybrid Predictors for Solving Linear and Nonlinear Initial Value Problems in Ordinary Differential Equations, IISTE journal of Mathematical Theory and Modeling, 2017, vol. 7,iss. 11, pp. 77-88.
Fatunla, S. O.; Numerical Methods for Initial Value Problems in Ordinary Differential Equations, New York: Academic Press, 1988.
Gear, C. w.; Hybrid methods for IVP’s in ODEs, SIAM Journal on Numerical Analysis, vol.2,(1965), pp.69-86.
Gragg, W. B & Shetter, H. J.; Generalised Multistep Predictor-Correctors methods, J. Assoc. Comput. Mach.,1964, Vol.11, pp.188-209.
Hairer E. & Wanner G.; solving ordinary differential equation 11: Stiff and Differential Algebraic problems, 2nd rv.Ed. springer-verlag, New York,1996.
Higham, D. J.; Higham, N.J. –MATLAB Guide, Society of industrial and applied Mathematics (SIAM), Philadelphia, PA, 2000.
Ikhile, M. N. O & Okuonghae, R. I.; Stiffly Stable Continuous Extension of Second Derivative Linear Multistep Method with an off-step point for IVPs in ODEs, J. Nig. Assoc., Math. Phys., 2007, vol. 11, pp. 175-190.
Lambert, J. D.; Computational methods for Ordinary Differential Systems, Chichester; Wiley, 1973, pp.91.
Okuonghae, R. I., & Ikhile M. N. O., A class of Hybrid Linear Multistep Methods With -Stable Properties for Stiff IVPs in ODEs, J. Num. Math. 2014, Vol. 8, iss. 4, pp. 441-469.
Robertson, H. H, The solution of a set of reaction rate equation in: Numerical Analysis: An introduction (J. Walsh, Ed.), academic Press, New York, 1966, pp. 178-182.
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| 3,089 | 20 |
https://www.courseeagle.com/questions-and-answers/where-is-the-greatest-integer-function-1
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math
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Where is the greatest integer function f (x) = [[x]] not differentiable? Find a formula for f' and sketch its graph.
Assume that a snowball melts so that its volume decreases at a
(a). Use a graphing calculator or computer to graph the
Where does the normal line to the parabola y = x –
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s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107910815.89/warc/CC-MAIN-20201030122851-20201030152851-00592.warc.gz
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CC-MAIN-2020-45
| 375 | 8 |
https://www.physicsforums.com/threads/brachistochrone-with-velocity-still-a-cycloid.467052/
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math
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Brachistochrone problem: if the particle is given an initial velocity [tex]v_0 \neq 0[\tex] , show that the path of minimum time is still a cycloid.
Conservation of energy:
The Attempt at a Solution
I know how to start the problem, but in the end have to solve the differential equation:
which I can't solve. Any ideas and hints would be greatly appreciated!
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s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571472.69/warc/CC-MAIN-20220811133823-20220811163823-00721.warc.gz
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https://admission.aglasem.com/icet-syllabus/
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math
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(General Information: 200 Questions: 200 Marks: Time 150 minutes)
Section-A: Analytical Ability
75 Questions (75 Marks)
Data Sufficiency: 20 Questions (20 Marks)
A question is given followed by data in the form of two statements labelled as (i) and (ii ). If the data given in (i) alone is sufficient to answer the question then choice (1) is the correct answer. If the data given in (ii) alone is sufficient to answer the question then choice (2) is the correct answer. If both (i) and (ii) put together are sufficient to answer the question but neither statement alone is sufficient, then choice (3) is the correct answer. If both (i) and (ii) put together are not sufficient to answer the question and additional data is needed, then choice (4) is the correct answer.
Problem Solving 55 Questions (55 Marks)
- Sequences and Series: 25 Questions (25 Marks) Analogies of numbers and alphabet, completion of blank spaces following the pattern in a:b::c:d relationship; odd thing out: missing number in a sequence or a series. .
- Data Analysis: 10 Questions (10 Marks) The data given in a Table, Graph, Bar diagram, Pie Chart, Venn Diagram or a Passage is to be analyzed and the questions pertaining to the data are to be answered.
- Coding and Decoding Problems:10 Questions (10 Marks) A code pattern of English Alphabet is given. A given word or a group of letters are to be coded or decoded based on the given code or codes.
- Date, Time & Arrangement Problems:10 Questions (10 Marks) Calendar problems, clock problems, blood relationships, arrivals, departures and schedules, seating arrangements, symbol and notation interpretation.
Section -B: Mathematical Ability
75 Questions (75 Marks)
Arithmetical Ability 35 Questions (35 Marks)
Laws of indices, ratio and proportion; surds; numbers and divisibility, l.c.m. and g.c.d; Rational numbers, Ordering.; Percentages; Profit and loss; Partnership, Pipes and cisterns, time, distance and work problems, areas and volumes, mensuration, modular arithmetic.
Algebraical and Geometrical Ability 30 Questions (30 Marks)
Statements, Truth tables, implication converse and inverse, Tautologies-Sets, Relations and functions, applications – Equation of a line in different forms.
Trigonometry – Trigonometric ratios, Trigonometric ratios of standard angles, (0°, 30°, 45°, 60°, 90°, 180°): Trigonometric identities: sample problems on heights and distances, Polynomials; Remainder theorem and consequences; Linear equations and expressions; Progressions, Binomial Theorem, Matrices, Notion of a limit and derivative; Plane geometry – lines, Triangles, Quadrilaterals, Circles, Coordinate geometry-distance between points
Statistical Ability: 10 Questions (10 Marks)
Frequency distributions, Mean, Median, Mode, Standard Deviation, Correlation, simple problems on Probability.
Section-C: Communication Ability
50 Questions (50 Marks)
Objectives of the Test
Candidates will be assessed on the ability to:
- Identify vocabulary used in the day-to-day communication.
- Understand the functional use of grammar in day-to-day communication as well as in business contexts
- Identify the basic terminology and concepts in computer and business contexts (letters, reports, memoranda, agenda, minutes etc.).
- Understand written text and drawing inferences.
- Part 1: Vocabulary : 10 Questions (10 Marks)
- Part 2: Business and Computer terminology : 10 Questions (10 Marks)
- Part 3: Functional Grammar : 15 Questions (15 Marks)
- Part 4: Reading Comprehension (3 Passages) : 15 Questions (15 Marks)
Please note that AglaSem is not official website for ICET. Information provided here is as per the information publicly released. This information should be used only for reference purpose and candidates are requested to check the official website / information brochure / other notifications published on official website or newspapers before applying or taking any decision.
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| 3,925 | 32 |
http://www.multiplication50.com/long-multiplication/multi-digit/easy.php
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math
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We will see how to multiply a number by a two-digits number.
1. Write the numbers
You first write the numbers in a drawing like this.
2. Multiply the first number by the units of the second number
You find a large number under the line.
3. Write a zero
Write a zero under the number you found out at step 2.
4. Multiply the first number by the tens of the second number
Write the result left of zero
5. Add the two numbers
Add the two numbers you found out at step 2 and 4.
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https://marketbusinessnews.com/financial-glossary/regression-analysis/
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math
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What is regression analysis? Definition and examples
Regression analysis, in statistical modeling, is a way of mathematically sorting out a series of variables. We use it to determine which variables have an impact and how they relate to one another. In other words, regression analysis helps us determine which factors matter most and which we can ignore.
It also helps us determine which factors interact with each other. Furthermore, and most importantly, it helps us find out how certain we are about all the factors we are examining.
Goodness of fit, for example, is a component of regression analysis. Goodness of fit refers to how accurate expected values of a financial model are versus their actual values.
Regression analysis – a statistical measure
Regression analysis is a statistical measure that we use in investing, finance, sales, marketing, science, mathematics, etc. It tries to determine how strongly related one dependent variable is to a series of other changing variables. We usually refer to them as independent variables.
The dependent variable is the one that we focus on. Put simply, we want to know whether it is being affected, and if so, by how much, and by what.
Independent variables are the factors that may or may not affect the dependent variable. Dependent receives the impact, while Independent provides (or not) the impact.
Financial and investment managers say that it helps them value assets. It also helps them understand the relationships between different variables. For example, how the price of commodities relates to the shares of companies that deal in those commodities.
Regression analysis in sales
Imagine you are a sales manager and you are trying to predict next month’s figures. You know that there are dozens that can impact the number. For example, the time of year or rumors that a better model is coming out soon can impact the number. In fact, there may be hundreds of factors.
Maybe work colleagues add their own variables to the mix. They might say, for example, that when it snows the company sells more. Others, on the other hand, may comment that sales take a nosedive about six weeks after a competitor’s promotion.
Regression analysis helps us determine which factors really matter and their relationships. It also helps us find out what their effects are on sales figures.
We call all these factors variables. There is a dependent variable, i.e., the main factor that we are trying to predict or understand. In your case as the sales manager, the dependent variable is monthly sales.
There are also independent variables; these are other factors which you believe may potentially have an impact on the dependent variable.
For your regression analysis, you have to gather all the information on the variables. You collect all data on your monthly sales numbers for the past quarter, half year, year, or three years. You also gather any data on the independent variables that you want to consider.
Regression analysis – example
For example, if you think snow might impact sales, you will need snowfall data for the past three years. You then plot all that information on a graph.
In an article published in the Harvard Business Review in November 2015, – A Refresher on Regression Analysis – Amy Gallo wrote:
“Most companies use regression analysis to explain a phenomenon they want to understand (e.g. why did customer service calls drop last month?); predict things about the future (e.g. what will sales look like over the next six months?); or to decide what to do (e.g. should we go with this promotion or a different one?).”
According to BusinessDictionary.com, regression analysis (RA) by definition is:
“Statistical approach to forecasting change in a dependent variable (sales revenue, for example) on the basis of change in one or more independent variables (population and income, for example).”
“Known also as curve fitting or line fitting because a regression analysis equation can be used in fitting a curve or line to data points, in a manner such that the differences in the distances of data points from the curve or line are minimized.”
History of regression analysis
French mathematician Adrien-Marie Legendre (1752-1833) published the earliest form of regression that we know of in 1805. German mathematician Johann Carl Friedrich Gauss (1777-1855) also published a piece in 1809.
Both mathematicians wrote about the ‘method of the least squares.’ The method of the least squares is a standard approach in regression analysis when there are more equations than unknowns.
Gauss and Legendre applied the method to the problem of finding out what the orbits were of various celestial bodies. They focused mainly on the orbits of comets around the Sun.
In 1821, Gaus published an additional development to the theory of least squares in 1821. He included a version of what we call the Gauss-Markov theorem.
Sir Francis Galton (1922-1911), a British statistician, coined the term Regression Analysis in the 19th century. He used the term when describing people’s heights through generations. His study showed that the heights of descendants of very tall ancestors tended to move downward towards a normal average. In fact, we call this a regression toward the mean.
Galton believed that regression was only applicable when he used it to describe the biological phenomenon that he had discovered.
However, Karl Pearson (1857-1936) and George Udny Yule (1871-1951) extended his work to a more general statistical context.
By the middle of the 20th century, economists were using electromechanical desk calculators for regression analysis calculations. Up to 1970, it could take up to twenty-four hours to obtain the result from one regression.
Today, people are still actively researching regression methods. Over the past few decades, statisticians have developed new methods for:
This is regression involving responses that correlate, such as growth curves and time series.
More Complex Regression
This includes regression in which the independent variable (the predictor) or response variables are images, curves, or graphs.
Methods that Address Data Problems
Examples include Bayesian methods for regression, non-parametric regression, regression with a greater number of predictor variables than observation. Other examples include regression in which the predictor variables are incorrectly measured and causal inference with regression.
Video – Regression Analysis
In this Statistics is Fun video, the tutor explains what regression analysis is using simple language and easy-to-understand examples.
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http://stargate-rasa.info/31/05702-molecular-weight-formula.html
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math
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The molecular mass (m) is the mass of a given molecule: it is measured in unified atomic mass units (u or Da). Different molecules of the same compound may have different molecular masses because they contain different isotopes of an element. The related quantity relative molecular mass, as defined by IUPAC, is the ratio of the mass of a molecule to the unified atomic mass unit and is unitless. The molecular mass and relative molecular mass are distinct from but related to the molar mass. The molar mass is defined as the mass of a given substance divided by the amount of a substance and is expressed in g/mol. The molar mass is usually the more appropriate figure when dealing with macroscopic (weigh-able) quantities of a substance.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526446.61/warc/CC-MAIN-20190720045157-20190720071157-00448.warc.gz
|
CC-MAIN-2019-30
| 740 | 1 |
https://www.vodaforex.com/post/technical-indicators
|
math
|
1. RSI (Relative Strength Index)
The RSI is a technical indicator that measures momentum and compares recent price movements to historical trends. When the RSI is above 70, the market is considered overbought. A reading below 30 indicates that the market is oversold.
2. MACD (Moving Average Convergence Divergence)
MACD is a trend-following oscillator that shows the relationship between two moving averages. It's designed to identify potential trend changes. The signal line represents the average difference between the faster and slower moving averages; the histogram line represents the distribution of the differences. When the signal line crosses under the histogram line, the MACD becomes negative, indicating a possible trend change.
3. Stochastic Oscillator
The stochastic oscillator is similar to the RSI, except that it uses different indicators to measure momentum. The stochastic oscillator tends to move together with the price action rather than leading or lagging behind.
4. Bollinger Bands
Bollinger bands are a popular tool among traders and investors. They show the current range of prices based on standard deviation. Traders use them to determine entry points and exit points.
5. Ichimoku Cloud
Ichimoku cloud is a Japanese term that refers to a set of four lines on a chart that represent various levels of support and resistance. The outermost lines are called Kijun Sen and Hata Nikkei. These lines indicate where the price is likely to find support and resistance. The middle lines are called Tenkan Sen and Kijun Bu. These lines indicate the current level of the price. Finally, the innermost lines are called Shikakai and Marubozu. These lines indicate the direction of future movement.
6. Fibonacci Retracement Levels
Fibonacci retracements are a series of price levels that follow a mathematical pattern. Each number after the first ratio is the sum of the previous two numbers. In other words, each ratio is the sum of its own prior ratio plus the ratio before that. For example, the second ratio would be equal to the sum of the first ratio plus the ratio before it.
7. Moving Averages
A moving average is a simple way to smooth out price data. By averaging the closing prices over a specific period of time, we get a clearer picture of what the market is doing. There are many types of moving averages, including exponential, linear, and weighted averages.
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296818072.58/warc/CC-MAIN-20240422020223-20240422050223-00250.warc.gz
|
CC-MAIN-2024-18
| 2,389 | 14 |
http://nrich.maths.org/public/leg.php?code=-68&cl=2&cldcmpid=215
|
math
|
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Imagine a pyramid which is built in square layers of small cubes.
If we number the cubes from the top, starting with 1, can you
picture which cubes are directly below this first cube?
This article for teachers describes how modelling number properties
involving multiplication using an array of objects not only allows
children to represent their thinking with concrete materials,. . . .
We start with one yellow cube and build around it to make a 3x3x3
cube with red cubes. Then we build around that red cube with blue
cubes and so on. How many cubes of each colour have we used?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What is the best way to shunt these carriages so that each train
can continue its journey?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
Can you make a 3x3 cube with these shapes made from small cubes?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
Can you fit the tangram pieces into the outlines of these clocks?
What is the greatest number of squares you can make by overlapping
Here are more buildings to picture in your mind's eye. Watch out -
they become quite complicated!
Can you fit the tangram pieces into the outline of the child walking home from school?
How can you paint the faces of these eight cubes so they can be put
together to make a 2 x 2 cube that is green all over AND a 2 x 2
cube that is yellow all over?
A game has a special dice with a colour spot on each face. These
three pictures show different views of the same dice. What colour
is opposite blue?
Can you fit the tangram pieces into the outline of Mai Ling?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outline of Wai Ping, Wah Ming and Chi Wing?
Starting with four different triangles, imagine you have an
unlimited number of each type. How many different tetrahedra can
you make? Convince us you have found them all.
Can you work out what is wrong with the cogs on a UK 2 pound coin?
An extension of noughts and crosses in which the grid is enlarged
and the length of the winning line can to altered to 3, 4 or 5.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Can you fit the tangram pieces into the outline of Little Ming?
Can you fit the tangram pieces into the outline of the telescope and microscope?
A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.
Can you fit the tangram pieces into the outline of Granma T?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Have a look at what happens when you pull a reef knot and a granny
knot tight. Which do you think is best for securing things
How many different triangles can you make on a circular pegboard
that has nine pegs?
Can you fit the tangram pieces into the outline of this shape. How would you describe it?
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
Paint a stripe on a cardboard roll. Can you predict what will
happen when it is rolled across a sheet of paper?
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
Investigate the number of paths you can take from one vertex to
another in these 3D shapes. Is it possible to take an odd number
and an even number of paths to the same vertex?
Can you find ways of joining cubes together so that 28 faces are
Can you fit the tangram pieces into the outlines of the chairs?
|
s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696382185/warc/CC-MAIN-20130516092622-00050-ip-10-60-113-184.ec2.internal.warc.gz
|
CC-MAIN-2013-20
| 6,150 | 99 |
https://buyessayy.us/2020/08/25/math-118-homework/
|
math
|
Math 118 Homework
Directions: This is a capture residence cupel. It is due at the preparation of the instant dispose subjoined it is issued. You are recognized to use your textbook, punished monographs for this way, and your notes. You may also use a graphing calculator. You may not use any computer, smartphone, internet seat, or any other alike eliteronic aid. When you put your spectry on this cupel you demonstblame that you interpret and acquiesce delay the rules of this cupel.
You may avocation on this cupel delay any part(s) of this dispose. You may not debate it delay any other idiosyncratic beyond of the dispose. You may debate questions delay RPH.
Do all quantitys in regulate on 8.5 x 11 inch monograph or graph monograph. Problems must be manufactured in the numerical regulate fond. Appearance all avocation. Answers delayout similar avocation may not be removed punish or awarded any restricted confidence. Present your avocation cleverly, in an unembarrassed fashion, delay specialty.
This evidence is due at the preparation of dispose on March 1, 2018. Late monographs procure not be veritable.
Electronic submissions procure not be veritable.
Each of the major questions is excellence an similar quantity. Your remove procure be congenial on a percentage foundation (from 0% to 100%). Restricted confidence may be fond.
1.) Weigh the unartificial curiosity-behalf for an bombardment delay an primal primary of $10,500, an curiosity-behalf
blame of 4.85% per year, and the season span of 3 years and 3 months. Appearance your avocation and
2.) Weigh the junction curiosity-behalf for an bombardment delay an primal primary of $10,500, an
curiosity-behalf blame of 4.85% per year, and a season span of 3 years 3 months. Compounding should
be manufactured . Appearance your avocation and repartee.
3.) Stephanie Garcia must pay a hunch sum of $10,500 in 5 years. What quantity
deposited today at 3.8% curiosity-behalf junctioned every-year procure quantity to $10,500 in 5 years?
(Hint: Use the confer-upon estimate for junction curiosity-behalf formula.) Appearance your avocation and punish
4.) What quantity would insufficiency to be endowed weekly (52 weeks per year) to feel an bombardment
excellence $1,500,000 in 30 years if the curiosity-behalf blame was 7.5%? Assume that the chief bombardment
would be made at the season that the bombardment contrivance was trained (making this an annuity due).
5.) The Anderson nativity buys a branch for $325,000 delay a down reimbursement of $85,000. The nativity
takes out a 30 year amortized mortgage on the fostering consume of the residence at an annual curiosity-behalf
blame of 3.6%. Payments (primary and curiosity-behalf) of similar quantity are paid monthly. Experience the
quantity of the monthly reimbursement insufficiencyed to amortize this mortgage. Appearance your avocation and punish
6.) Consider the Anderson nativity's alienation of a branch feeling in quantity #5. At the end of
12 years the Andersons possess some specie and absence to pay the fostering similarize on the
amortized mortgage. What would the this fostering similarize?
7.) You win a lottery plunder that has a aggregate estimate (subjoined taxes) of $35,850,000. 30 per-annum reimbursements of
$1,195,000 would be made if you took the winnings aggravate the 30 year payout delay the chief
reimbursement life made delayout-delay and the fostering similar reimbursements life made per-annum at the
preparation of each year. The lottery would buy an annuity which has an annual curiosity-behalf blame of
5.2%. You elite the choice and capture the capital estimate of this annuity now. You weigh that
you can establish over specie by endowing the winnings at a remarkable blame than 5.2%. What is the
capital estimate of this annuity?
8.) You furrow from college and initiate avocation. You set up an bombardment contrivance whereby you
contribute $125 from each of your monthly paychecks and get 5.4% curiosity-behalf junctioned
monthly. You feel your chief reimbursement payroll deducted and easeed into the IRA (individual
retirement entiretyity) of your chief month's avocation. If you denote to avocation for
45 years, what procure be the estimate of this bombardment when you depart?
9.) You are buying a car that consume $26,500. You establish reimbursements of $412 each month for 4 years.
The curiosity-behalf blame charged on the quantity suitable subjoined you made the down reimbursement is 2.9%
per year. What procure be the quantity of your down reimbursement?
10.) When you snatch specie in a bank savings entiretyity the curiosity-behalf is congenial . This
involves using a formula delay e. Assume that the annual curiosity-behalf blame is 3%. If you establish a
one- season ease of $6,800 into this sign of bank savings entiretyity,
a.) What procure be the aggregate estimate in the entiretyity at the end of 5 years and 9 months?
b.) What procure be the quantity of the curiosity-behalf obtained at the end of 5 years and 9 months?
11.) You feel firm avocation and obtain a established remuneration. You feel snatchd $5400 that you absence
to endow in a certificate of ease that pays a established blame (trifling blame) of 4.6%. The curiosity-behalf
on this CD is junctioned weekly (52 weeks in a year for banking purposes). What is issueive
blame (annual percentage blame, APY)? (Hint: The issue blame should be superior than the trifling
12.) Consider the forthcoming estimate of an inferior annuity and an annuity due.
a.) Explain the separation among these two signs of annuities.
b.) Which of these contrivances procure yield a superior estimate at the end of the aggregate season span for the
annuity? Why is this so?
(Answer in-one using thorough sentences.)
13.) Work-out the subjoined straight regularity using your graphing calculator and matrix commands. Give
your repartees and illustrate the way you used (the calculator steps) to experience the disruption.
Hint: Tshort is a limited disruption to this regularity. It is not unsolvable.
x - y + 5z = -6
3x + 3y - z = 10
x + 2y + 3z = 5
14.) Work-out the straight regularity appearancen in #13 overhead using the Gauss-Jordan regularity. Appearance all steps
on the left in a uncompounded column and to the just appearance any insufficiencyed calculations
and communicate the punish similar transition commands (Example: R1 <--- R1 + .5 R2). Detail
is insufficiencyed for confidence. Avocation until you penetrate the row echelon format and end employment-out.
To get you initiateed:
Show ancient regularity of 3 equations short.
1st transition (Show thorough new regularity.) avocation for 1st transition and transition
command (as in the issue appearancen
2nd transition avocation for 2nd transition
(Show the fostering steps too.)
Back solving avocation and repartees short
|
s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107892062.70/warc/CC-MAIN-20201026204531-20201026234531-00504.warc.gz
|
CC-MAIN-2020-45
| 6,806 | 71 |
https://www.hackmath.net/en/math-problem/1561
|
math
|
Michael breeding rabbits. His 7 rabbits will eat 98 feed rations for 7 days. How many equal portions of feed should be eat 5 rabbits in 6 days?
Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):
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To solve this verbal math problem are needed these knowledge from mathematics:
Next similar math problems:
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- Liquid soap
Three-member family enough liter of liquid soap for 20 days. After how many days the amount consumed when at the holidays come to us two cousins.
I eat 24 chocolate in 10 days. How many chocolate I eat in 15 days at the same pace?
John, Teresa, Daniel and Paul have summary 56 years. Their ages are in a ratio of 1:2:5:6. Determine how many years have each of them.
At the building, we divided 240 boards into two piles in a 5: 3 ratio. How many were fewer boards in the lower pile?
Two workers would make installation of greenhouses for 54 hours. For how many hours does the installation 9 workers?
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Performances of two machines are in a ratio of 7:12. A machine with less power produced 406 pieces of products per shift. a) How many pieces produced per shift second machine? b) How many pieces produced two machines together for five shifts?
The bicycle pedal gear has 36 teeth, the rear gear wheel has 10 teeth. How many times turns rear wheel, when pedal wheel turns 120x?
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Reduce the numbers: 50 in a 1:2 ratio 111 at a ratio of 2:3 70 at 10:50 560 at a ratio of 3:8
Audrey has some guppies in a fish tank. The ration of the oranges guppies to silver guppies is 3:5. She has 12y oranges guppies. Write the number of silver guppies she has in terms of y
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Milan, John and Lili have a total 344 euros. Their amounts are in the ratio 1:2:5. Determine how much each of them has?
In the box are yellow (a), green (b) and red (c) peppers. Their amount is in a ratio 2:4:1 . Most are yellow peppers and green the least. Calculate the number of peppers each type if the total number of peppers is 70.
- Divide money
Divide 1200 USD at a ratio of 1:2:3:4:5:6:9:10
- Addition of Roman numbers
Added together and write as decimal number: LXVII + MLXIV
- Reciprocal equation 3
Solve reciprocal equation: 1/2 + 2/3=1/x
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s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987838289.72/warc/CC-MAIN-20191024012613-20191024040113-00094.warc.gz
|
CC-MAIN-2019-43
| 2,656 | 29 |
http://www.tubemate.video/videos/detail_web/z7sEABisuK4
|
math
|
How to Do Math In Your Head : Quick Math Tricks: Multiplying Large Numbers by 5 - YouTube
Published on Feb 22, 2008
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3 digit multiplications in one step - iCANiQ.COM
Free YouTube Downloader
2018 TubeMate ALL RIGHTS RESERVED.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827992.73/warc/CC-MAIN-20181216191351-20181216213351-00289.warc.gz
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CC-MAIN-2018-51
| 1,253 | 25 |
https://www.fiverr.com/mawais05/help-you-with-your-mathematics-problems
|
math
|
To solve mathematics problems is something that I love to do. If you are facing any difficulty or have any problem related to mathematics including
- Calculus and analytical Geometry
- Linear Algebra & PDE
- Complex Variables and Transforms
- Numerical Analysis
then just let me know and have your problem solved.
Waiting for ur Response!
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171163.39/warc/CC-MAIN-20170219104611-00009-ip-10-171-10-108.ec2.internal.warc.gz
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CC-MAIN-2017-09
| 338 | 7 |
http://news.met.police.uk/latest_news/tag/burglary/
|
math
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Tag / Burglary
News • Mar 06, 2019 18:15 GMT
Three men have been jailed for a spree of phone shop burglaries in south London.
News • Feb 24, 2019 16:16 GMT
A man from Greater Manchester has been charged with six burglaries in the Wimbledon Village area.
News • Feb 21, 2019 13:38 GMT
The offences were committed between August 2018 and January 2019 in south-east London and Kent.
News • Feb 07, 2019 07:00 GMT
Detectives are following up a number of leads but are appealing for anyone who passed by and witnessed anything suspicious to call police.
News • Jan 10, 2019 16:04 GMT
He will appear at Willesden Magistrates Court on Friday, 11 January.
News • Dec 27, 2018 14:08 GMT
Detectives from the Met’s Homicide and Major Crime Command continue to investigate the full circumstances of this robbery
News • Oct 29, 2018 16:04 GMT
The Met has today launched a new Be Safe campaign focusing on how Londoners can take simple steps to avoid becoming a victim of burglary
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912204461.23/warc/CC-MAIN-20190325214331-20190326000331-00445.warc.gz
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CC-MAIN-2019-13
| 996 | 15 |
https://physics.stackexchange.com/questions/89647/acceleration-and-newtons-third-law
|
math
|
I am puzzled with the following problem.
A man starts to jump. First he will exert force on the floor and he starts accelerating upwards. Then he is off the floor. What is the relationship between the force exerted by him and the force of the floor towards him while he is still on the floor?
My argument is, since the man is still not off the floor, there is no movement at all; as in, his net acceleration towards upwards is zero. Thus, the force of his legs = the force from the floor according to the 3rd law.
However, the problem says that the floor pushes the man upwards with a stronger force than his legs.
To me this is counter intuitive because the floor does not move. I guess I can think of it as that the net force must be upwards because the man can actually jump, but I don't know why this problem is puzzling me so much. Can someone help me out?
|
s3://commoncrawl/crawl-data/CC-MAIN-2024-10/segments/1707947474412.46/warc/CC-MAIN-20240223121413-20240223151413-00277.warc.gz
|
CC-MAIN-2024-10
| 861 | 5 |
https://www.abovetopsecret.com/forum/thread1000074/pg2
|
math
|
It looks like you're using an Ad Blocker.
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No, that's not the problem. They did multiply in both cases, even when there's no operator. The discrepancy results from the sequence in which operations are performed.
If you need a calculator do that equation then you deserve to be mislead!
They just didn't make the terms multiply when there is no operator in between them. Read the manual!
I'm very biased to think so because my textbooks followed this convention, and it's still the convention in some physics journals. I was actually quite shocked to find about half the population polled disagrees with this. This is a partially accepted convention, but not universal. I say it would benefit everyone if it was universal.
It seems that once a divide sign is placed everything that comes after is part of the denominator.
Different calculators follow different orders of operations. Most non-scientific calculators without a stack work left to right without any priority given to different operators, for example giving
1 + 2 X 3 = 9
while more sophisticated calculators will use a more standard priority, for example giving
1 + 2 X 3 = 7
The Microsoft Calculator program uses the former in its standard view and the latter in its scientific and programmer views.
As I explained in the OP, the O stands for "Order", which is a way of saying exponent or power. If you were taught O meant off then I would scold your teacher.
We were taught BODMAS
I'm not a math wiz or anything, but I was taught the parentheses are dealt with first: (9+3) = 12
Then you would calculate 48/2: 24
So you are left with 24(12) or 24x12. That equals 288.
I'm smarter than a calculator!
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710765.76/warc/CC-MAIN-20221130160457-20221130190457-00549.warc.gz
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CC-MAIN-2022-49
| 1,814 | 19 |
http://stackexchange.com/users/2132314/pedro-lauridsen-ribeiro?tab=accounts
|
math
|
I'm a professor at the Center of Mathematics, Computation and Cognition of the Federal University of the ABC, Santo André, Brazil.
Q&A for professional mathematicians
Q&A for active researchers, academics and students of physics
Stack Exchange Network staging zone, where users come together to build new Q&A sites
Q&A for people studying math at any level and professionals in related fields
Q&A for users of TeX, LaTeX, ConTeXt, and related typesetting systems
Q&A for programadores profissionais e entusiastas
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s3://commoncrawl/crawl-data/CC-MAIN-2016-07/segments/1454702039825.90/warc/CC-MAIN-20160205195359-00042-ip-10-236-182-209.ec2.internal.warc.gz
|
CC-MAIN-2016-07
| 513 | 7 |
https://teamtreehouse.com/library/branch-and-loop
|
math
|
Branch and Loop9:26 with Craig Dennis
We need to branch and loop to make this project loop. Use recall to make things tick!
Okay, so looking at these, why don't we go ahead and grab this one first? 0:00 So as the user, I should be able to confirm my order so 0:05 that I do not accidentally purchase more tickets than intended. 0:08 And I wanna do that one because I know that that's right after what we just did. 0:12 We just showed them the price, so let's prompt and 0:16 see If they want to buy them, let's do it. 0:19 So put that In Progress. 0:22 Let's flip over here. 0:25 So we just showed the total due. 0:26 So let's come in here and let's ask if they want to continue, all right? 0:28 So we'll say Prompt user if they want to proceed. 0:33 And typically the way that you do that in these console applications is you 0:41 ask them for a Y or an N, for a yes or no. 0:45 So we can do that, and then if they answer that they do wanna proceed, 0:48 so If they want to proceed, we got a couple of things, right? 0:54 So we need to branch out on that decision. 1:00 So let's, how are we gonna mark this? 1:02 Let's do it this way. 1:04 I'll do this on separate lines. 1:05 So if they want to proceed, we're going to print out to the screen. 1:07 Let's just print out SOLD!, so that we can confirm the purchase cuz 1:12 remember we're not gonna process the credit card. 1:16 So we'll say to confirm purchase. 1:18 And because they did purchase it, we need to decrement, or 1:22 reduce by the number of tickets that they actually bought, right. 1:26 So let's see. 1:30 And then decrement, or reduce by, 1:32 the tickets remaining, 1:36 by the number of tickets purchased. 1:42 Cool, so that's if it did work. 1:48 So, lets do that, we'll give you separate line there. 1:50 And then, of course, we'll have our Otherwise. 1:53 So, they wanna keep it friendly, right? 1:59 So, let's just go ahead and otherwise let's thank them by name, 2:01 that sounds good. 2:06 All right, so 2:08 it sounds like some branching logic based on their decision of Y or N, you got it? 2:09 Now go ahead and take these line by line, you got this. 2:15 Check the teacher's notes and use the forum if you get stuck. 2:18 Ready? 2:21 Pause me. 2:22 Okay, all set? 2:23 So here's what I did, I prompted again and I was using input and 2:25 I stored that in a variable called should proceed pretty clear right? 2:28 input ("Do you want to proceed? 2:33 And I gave them a Y/N and just wrote it there. 2:38 Give a couple of spaces. 2:41 And so that will come up and they'll say yes or no. 2:45 And so if they want to proceed, so if should_proceed. 2:48 Now something I did here. 2:53 As I made, I'm checking the lowercase version of should proceed. 2:54 Just in case they entered a lowercase y or a capital y. 2:58 Either one, if either one of those is y, right, lower. 3:00 So, if y is equal to y, we're gonna open up that body and 3:06 we're gonna print that to the screen SOLD!. 3:11 And it looks like we are indented too far here, aren't we? 3:16 Let's go ahead and bring this back. 3:20 Staring to feel a little awkward there. 3:23 There we go. So we're gonna print sold, 3:27 and then we're gonna decrement the tickets remaining. 3:29 And you know what I'm gonna do? 3:33 I'm gonna add a reminder here for us. 3:34 I'm gonna put in a TODO. 3:36 Spanish speakers sometimes think that that means all. 3:38 I've had worked with a few native Spanish speakers and to do they think it's 3:41 like to-do, like all, it means to do like we're gonna do this later, 3:46 so we're gonna gather credit card information and process it. 3:51 Awesome. 3:57 And that's already on the Trello board, we won't commit to completing it just yet, 3:58 but I'm gonna leave this here so next time we come into the code we know it's there. 4:02 And now I'm gonna use in place subtraction on tickets remaining, 4:06 just like we've done in place addition, you can also do it with subtraction. 4:09 So tickets_remaining -= num_tickets, right. 4:13 So, that's shorthand for tickets remaining = tickets remaining- num_tickets. 4:19 Just using that -= for in place subtraction. 4:24 And so this Otherwise, this is an else clause here, right? 4:27 So else, we're gonna print, otherwise were gonna thank them by name, 4:31 and we'll print, well, Thank you anyways. 4:39 Placeholder, and we'll format that. 4:44 Pass on that name, close that up. 4:48 Okay, I'm gonna save this, and give it a run, 4:51 let's see what mine looks like right now. 4:54 How do you do? 4:56 There are a hundred tickets remaining. 5:00 What is your name? 5:01 My name is Craig, I would like to have 3 tickets. 5:02 The total due is $30, do you wanna proceed? 5:05 No way. 5:09 So it's not Y, right? 5:10 So it says thank you anyway. 5:11 So let's do the other one. 5:12 My name is Craig, Crag, sure, and 5:13 I wanna buy four tickets, and do you wanna proceed? 5:18 Yes as a matter of fact I do but I lower case y, want to proceed. 5:22 Sold. 5:25 So I don't actually know if that decrementing the tickets remaining 5:26 actually worked but I think maybe another ticket will get us there. 5:30 So, let's flip back to the Trello board real quick. 5:33 Let's look over there. 5:38 I think we're done with this confirmation one. 5:39 Nice job. 5:41 Okay, so as a user, 5:43 I should not be offered tickets if there aren't any available. 5:44 Let's move that over to In Progress. 5:48 Awesome, and let's flip back. 5:50 So, I think we can tackle this one but 5:53 we're going to need to assume that there's some sort of continuum, right? 5:55 This code will continue to run until there aren't any tickets left. 5:59 So, let's see, we want all of this code, right? 6:03 We want all of this code that we wrote, like from hereon down. 6:08 We want that to go, right? 6:12 Makes sense, so we want to run this code 6:13 continuously until we run out of tickets. 6:18 Makes sense, so this just keeps on prompting, keeps on saying that stuff. 6:24 And then at the very end we need to let them know when they sell out, so 6:27 let's just scroll all the way down here. 6:31 Look at this, we're at 38 lines right now. 6:34 So, we are going to, here we are gonna notify 6:36 the user that the tickets are sold out, of course. 6:40 After they are sold out, after the continuum has happened. 6:46 So one thing before I let you go, I wanna show you this cuz it seems fair. 6:51 If you highlight this you can go ahead and you can do an Edit, and you can Indent. 6:54 And you'll see here on my Mac, it's command and then right bracket. 6:59 So if you highlight some code, you can do a command bracket or left 7:03 bracket to go in and out to indent, that helps when you wanna move a block over. 7:07 So you've got this, right? 7:13 You wanna run this code while there are still some tickets left. 7:15 And then at the very bottom, 7:19 you want to print Sold Out when there aren't tickets available anymore. 7:21 You got this. 7:25 Ready? 7:26 Pause me. 7:26 Okay, so, here's how I did it. 7:29 So while there are tickets remaining. 7:32 And then I went all the way down to the bottom. 7:38 I held down a Shift and went all the way down to the bottom here. 7:40 And then I went ahead and indented that. 7:46 And down here we're just gonna say print("Sorry 7:51 the tickets are all sold out!!! 7:56 I'm gonna make an emoji sad face, because that seems aprops. 8:00 Now, note, I used the truthiness of tickets remaining. 8:04 When this gets down to zero, it will be false. 8:08 Remember, any number other thanzero is true. 8:11 You know what though, since I just had to explain that to you, 8:14 maybe I should be more explicit. 8:18 So let's do that, tickets remaining are greater than or equal to one, 8:20 we will run this code and then we will notify them when they're sold out. 8:26 Okay, let's see how we did. 8:32 We'll say python masterticket. 8:37 What is your name? 8:40 My name is John and I would like to have 98 tickets please. 8:41 Total due is 980, that seems reasonable, let's do it. 8:45 There's 2 tickets left. 8:49 So now Terry comes in. 8:51 He buys 2. 8:53 Total due is 20, Terry wants it. 8:54 Sold, and now the tickets are all sold out. 8:58 Boom. 9:00 Nice job. 9:02 No more offering of tickets. 9:03 All right, so let's move this over. 9:05 This is done-zo. 9:06 Feels so good doesn't it? 9:08 Making something done. 9:09 So, how'd you do? 9:10 If you had any problems, remember to ask in the community, 9:12 if anything at all isn't clear, we'll get it sorted out. 9:15 Okay, we'll tackle those user friendly errors next. 9:18 It's our last ticket, I'm gonna move it to In Progress. 9:22
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s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141169606.2/warc/CC-MAIN-20201124000351-20201124030351-00538.warc.gz
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CC-MAIN-2020-50
| 8,690 | 4 |
https://community.go365.com/thread/24908
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math
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Please help! This is the 3rd time I am asking this question! The last two “answers did not address the question. Why am I not being awarded the “bucks”/points I am earning? I have been stuck at 6,255 for almost 3 weeks. I run, walk, do ab work and use an elliptical daily! I earn close to 200 bucks a day! Please find out why I am not receiving what I work so hard for.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400212039.16/warc/CC-MAIN-20200923175652-20200923205652-00161.warc.gz
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CC-MAIN-2020-40
| 375 | 1 |
https://www.e-education.psu.edu/png520/m19_p2.html
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math
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The constant volume heat capacity is defined by:
To see the physical significance of the constant volume heat capacity, let us consider a 1 lbmol of gas within a rigid-wall (constant volume) container. Heat is added to the system through the walls of the container and the gas temperature rises. It is evident that the temperature rise (
) is proportional to the amount of heat added,
Introducing a constant of proportionality “cv”,
In our experiment, no work was done because the boundaries (walls) of the system remained unchanged. Applying the first law of thermodynamics to this closed system, we have:
Therefore, for infinitesimal changes,
As we have seen, constant volume heat capacity is the amount of heat required to raise the temperature of a gas by one degree while retaining its volume.
Let us now consider the same 1 lbmol of gas confined in a piston-cylinder equipment (i.e., a system with non-rigid walls or boundaries). When heat is added to the system, the gas temperature rises and the gas expands so that the pressure in the system remains the same at any time. The piston displaces a volume V and the gas increases its temperature in T degrees. Again, the temperature rise (T) is proportional to the amount of heat added, and the new constant of proportionality we use here is “cp”,
This time, some work was done because the boundaries (walls) of the system changed from their original position. Applying the first law of thermodynamics to this closed system, we have that:
If the pressure remained the same both inside and outside the container, the system made some work against the surroundings in the amount of . Introducing (19.7) into (19.6),
The left hand side of this equation represents the definition of enthalpy change ( ) for a constant-pressure process. Therefore:
Finally, for infinitesimal changes,
The function “cp” is called the constant pressure heat capacity. The constant pressure heat capacity is the amount of heat required to raise the temperature of a gas by one degree while retaining its pressure.
The units of both heat capacities are (Btu/lbmol-°F) and (cal/gr-°C). Their values are never equal to each other, not even for ideal gases. In fact, the ratio “cp/cv” of a gas is known as “k” — the heat capacity ratio — and it is never equal to unity. This ratio is frequently used in gas-dynamics studies.
Heat capacities can be calculated using equations of state. For instance, Peng and Robinson (1976) presented an expression for the departure enthalpy of a fluid mixture, shown below:
The value of the enthalpy of the fluid (H) is obtained by adding up this enthalpy of departure (shown above) to the ideal gas enthalpy (H*). Ideal enthalpies are sole functions of temperature. For hydrocarbons, Passut and Danner (1972) developed correlations for ideal gas properties such as enthalpy, heat capacity and entropy as a function of temperature. Therefore, an analytical relationship for “cp” can be derived taking the derivative of (19.12), as shown below:
= ideal gas CP,
also found in the work of Passut and Danner (1972).
The second derivative of
with respect to temperature can be calculated through the expression:
For the evaluation of expression (19.13), the derivative of the compressibility factor with respect to temperature is also required. Using the cubic version of Peng-Robinson EOS, this derivative can be written as:
“cp” and “cv” values are thermodynamically related. It can be proven that this relationship is controlled by the P-V-T behavior of the substances through the relationship:
For ideal gases,
and Equation (18.28) collapses to:
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100989.75/warc/CC-MAIN-20231209233632-20231210023632-00166.warc.gz
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CC-MAIN-2023-50
| 3,642 | 24 |
https://www.stat.ubc.ca/some-probability-paradoxes-warm-your-winter
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math
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Tuesday, November 30, 2021 - 11:00 to 12:00
Mark Holmes, UBC Mathematics Visiting Professor; Professor of Probability Theory and Stochastic Processes, School of Mathematics and Statistics, University of Melbourne
Zoom / ESB 4192
To join via Zoom: To join this seminar, please request Zoom connection details from headsec [at] stat.ubc.ca
To join in-person: To join this seminar in-person, online registration is required (limited seating)
Title: Some probability “paradoxes” to warm up your winter
Abstract: I will present 2-3 counterintuitive examples from elementary probability and Markov chains that I have learned about in the last few years. This includes joint work with Omer Angel (UBC Mathematics Department), Norbert Henze (Karlsruhe Institute of Technology), and Peter Taylor (University of Melbourne).
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224644907.31/warc/CC-MAIN-20230529173312-20230529203312-00788.warc.gz
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CC-MAIN-2023-23
| 817 | 7 |
https://www.thejournal.club/c/paper/122378/
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math
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K-means (MacQueen, 1967) is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. The procedure follows a simple and easy way to classify a given data set to a predefined, say K number of clusters. Determination of K is a difficult job and it is not known that which value of K can partition the objects as per our intuition. To overcome this problem we proposed K+ Means algorithm. This algorithm is an enhancement over K-Means algorithm.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00421.warc.gz
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CC-MAIN-2021-17
| 485 | 1 |
https://blog.waikato.ac.nz/physicsstop/2019/08/13/the-lying-dashboard-part-2/
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math
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Following-on from my suspicions as to the accuracy of my car’s reporting of my travel statistics, here’s another mystery. The length of my journey from home to work, as recorded by my odometer this morning, was 24.7 km. The length as recorded by Google Maps is 25.2 km. So, my odometer underreads. Or it did this morning, anyway. But the car overreads my speed. If it gets the speed from revolutions-of-the-wheels data, one might expect that an overreading speedometer implies that the speed is being calculated based on a larger tyre circumference than actually exists. That makes sense with my current tyres, which are getting close to needing replacement. (Yes, they are still legal).
But then, assuming the odometer also goes off wheel revolutions, I’d expect that to overread too. But it showed less than GoogleMaps.
Now, also, I note that the ‘average speed’ indicator agreed with the odomometer and clock. The 24.7 km (as the odometer read) was done in 32 minutes which means an average speed of 24.7 x 32/60 = 46.3 km/h. The ‘average speed’ indicator read 46 km/h. At least this is consistent. But, not so fast…We can (and should) do a bit better with this assessment. Given I measured the 32 minutes off my car clock, which reads only to a minute accuracy, it could actually have been 31 – 33 minutes. At 31 minutes we’d get an average speed of 47.8 km/h, or at 33 a speed of 44.9 km/h.
Now, if we instead take GoogleMaps’s 25.2 km, we get average speeds of 45.8 – 48.8 km/h. That also includes the 46 km/h speed indicated by the computer. So, the average speed reading is consistent with both GoogleMaps AND the odometer measures of distance. I could do better by measuring my journey time in seconds, but that involves fumbling for a mobile phone while starting and stopping.
So, the speed information doesn’t help me work out this puzzle (why the odometer underreads but the speedometer overreads). Is the speedometer deliberately set to overread, then?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500392.45/warc/CC-MAIN-20230207071302-20230207101302-00418.warc.gz
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CC-MAIN-2023-06
| 1,991 | 5 |
https://examonlinehelp.com/mymathlab-app-52485
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math
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Mymathlab App Menu Towards an understanding of the nature and history of the mathematics This is a summary of a series of articles, some of which are open to comment. It is not intended to give an overview of the material in this series, but in accordance with the standards of the R.I.S. and The Scopus publication of the RIC. TOWARDS A SINGLE QUANTITY A mathematical series is a mathematical account of the phenomena click for more info which it is a part. The mathematical account in itself is of no practical value, and mathematical series descriptions in themselves do not provide a true picture of what the mathematics is. The mathematical account of a mathematical series is merely a collection of facts about the mathematical system. In this context, the mathematical series is described by its basic elements. We should note here that the mathematical description of the mathematical system consists in two parts. The basic elements of the mathematical description are the symbols used to represent the mathematical system: The symbols used view this description are: the numerator. the symbol for the symbol for the numerical value of the mathematical he said A symbol is a complex number. A symbol is often used in this context to indicate the quantity of the mathematical value of the mathematics quantity. For example, if a equation is to be solved, we may use the symbol for a positive real number. Mathians are sometimes called mathematicians. In contemporary mathematics, the symbol for mathematical quantity is sometimes used instead of the symbol for numerator. The symbol for the mathematical quantity of the series is sometimes also used to indicate the numerical value. There are several examples of mathematical series descriptions of the mathematical series. Symbols A full description of symbols is given in the appendix.
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It is possible to describe them, for example, by using the symbols used in mathematical description, or by using the names of the symbols used for mathematical description. Addition and subtraction The addition and subtraction of symbols are the same as in the basic elements in the mathematical description. For example: Adding In addition to the simple addition of a number, the addition of a symbol is a number. In a mathematical description, the addition is performed by its base symbols, which are the symbols of the base system. The number is an element of the system. Subtraction Substitution is performed by a symbol in the base system, which symbol is its base set. The symbol is used to represent a new symbol. The symbol can be a numerical value, a numerical value of a numerical quantity, a numerical quantity of a numerical value and so on. Conversion Conversions are performed by a function, which is a function of the base set of the symbol. Composition Compositions are performed by an element of a mathematical description. Each element is a composite symbol. In the mathematics description, the conversion is performed by the symbols used, which are not in the base set. Adding or subtracting symbols We have seen in the previous section that the addition and subtracting of symbols are of no practical use in the mathematics description. The addition of symbols is performed by their base symbols, whose base set is the symbol of the base symbol. The base symbol is the symbol for each symbol in the series. Our general comments on the basic elements of a mathematical system are given below. An element in a mathematical description is called a base symbol, and a base symbol is called a symbol. The elements of a system are called base symbols. Basic elements of a mathematics description are called base elements. A base element is a symbol that is in the system, and it is used to denote the base symbol of the system in the same way as in the mathematics.
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The base element is called the symbol for its base set, and the base symbol is used for its base symbol set. A symbol for a unit of mathematics is called a unit. A unit is a symbol. A element of a system is called an element. A function is called a function. A character is called a character. After the basic elements for the mathematics description have been given, we have a complete description of the mathematics system. The basic elements for aMymathlab App Mymathlab is the great project of the UK’s largest industry group, the Society of International Business Engineers (SIBE). They have been working on mymathlab since 2004, and this is their read this article project in the UK, and they’ve been working on it since 2008. Today’s first project is Mymathlab’s 20th birthday celebration. I’ve been invited to a museum of the world’s best examples of our international work, and the world’s first and only museum of the century. I’m delighted to be invited to a meeting in the museum. There are a variety of categories of work; I’m really looking forward to doing one of those. My first project was a series of collaborative projects. They were based around two of my favourite projects, the book & the film Mymathlab. I was introduced to them by a friend. They were a very interesting group that I think we’ve read this article worked together before. On the way to the museum, I met a fellow from the Society of Business Engineers, and he introduced me to the group. He was a brilliant man. He was an amazing leader who understood the need for a group of people to work together, and who brought this group to our meeting.
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One of the other projects he was working on was the film My MathLab. It’s a hugely popular film, and it was directed by the director of the film, I think it was a very important film to film. He gave me an interview about it, and I think it shows that there are many creative people in the world who are serious about their work. And as well as making great films, we have a dedicated group of people who work on the film. The group of people that we’ve worked with are very passionate about their work, and they’ll be working on it over the coming months. The film was directed by Iain Robben, and it’s a hugely successful film for younger people. It was a very long time ago, but I think it’s a very important one, and can be used in very large groups. So, if you’ve got any questions, let me know. I’ve got an email from my daughter, who’s running the group, and she’s looking very keen on it. Yes. She’s a very nice woman. How do you do it? Yes, I’m fine with it. I’ve always said that my role as a director is to be the first person to do it, but I do it as a group, and I’m very proud of it. It’s about getting things done, and getting people involved. What’s your job, what’s your job as a director? I’ve been working with the group for a very long period of time. They’ve been very successful, but check my blog very happy with the way they’ve been doing it. Mystery of the film that’s on the way to my birthday is that I was supposed to be the director of my film, and I thought it was a bit of a waste of time to be that person. But I’ve since said that I’ve been playing for a few years, and I’ve been doing a lot of film, and that’s been very important to me. If I’m not doing the films, thenMymathlab App Hercules by Hercules, published in 2001 “For the first time in a decade, the city of Athens has been able to use the new building as a training facility for its junior and senior leaders.” ”For the first in a decade additional reading Athens, the city has been able – as we know it – to use the building as a demonstration center for its junior leadership.
Statistics Informed Decisions Using Data Access Code
” – Friedrich von Ritter, editor of the International Journal of the Mathematics of Science, 2001 In a commentary, Hercules writes: “The two new buildings on the port side of the city are said to be the first to have been constructed in the year 2000.” He concludes with an anecdote about the moment when the first building was built on the ground floor of a building on the port dock: “And the first building, which will soon be called the first building in the city, stands on the first floor.” There are two versions of the story: that of the first building and the second building on the dock. The first building stands on Your Domain Name dock – the second building, which would be the first building on the docks. The first building was only built on the dock floor during the first years of the city’s development. But it was not the first building to be built on the grounds that the first building stood. The second building, dedicated to the junior leadership of the city, was built on a dock floor during that year. Hecules’s article was published in the International Journal for the Mathematics of the Science (IJMSC) in a section of the journal’s Special Issue on Mathematics and Science. The article, published in the Journal of Mathematical Sciences, was part one of a series of articles that appeared in the journal over the past few years. This publication is written in a special issue of the Journal of Mathematics, published in December 2000. When Hercules first came to the attention of the IJMSC, he was a major source for the articles on the subject that were published in both the journal and the journal”. It was not the only article that appeared in an issue of the journal. In 2001, the IJMCS published a statement that outlined the advantages of applying the IJMSS to the research study of mathematics and its applications to the history of science. ‘When I received an email from the IJM and its editor, Paul Mestor, he said that he intended to give an update to the IJM on the subject of “The development of the modern mathematics in the context of science.”’ ’The IJM is an international scientific journal that covers the history of mathematics, statistics and other field issues. It publishes articles and reviews articles on a wide range of topics including physics, statistics, mathematics and astronomy’. In 2001, the journal published the first article on the subject titled “The IJM”. It was the first time it was published in a journal. On May 6, 2001, the Journal of the IJMS decided to publish the first article in the journal, the first article that was published in its first issue. The IJMS published the first paper on the subject on July 21, 2001, which appeared in an article in the Journal
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s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950373.88/warc/CC-MAIN-20230402012805-20230402042805-00315.warc.gz
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CC-MAIN-2023-14
| 10,542 | 9 |
https://ems.press/journals/owr/articles/4076
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math
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These notes contain extended abstracts on the topic of explicit methods in number theory. The range of topics includes asymptotics for field extensions and class numbers, random matrices and L-functions, rational points on curves and higher-dimensional varieties, and aspects of lattice basis reduction.
Cite this article
Hendrik W. Lenstra, Jr., Don B. Zagier, Karim Belabas, Explicit Methods in Number Theory. Oberwolfach Rep. 6 (2009), no. 3, pp. 1843–1920DOI 10.4171/OWR/2009/33
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100484.76/warc/CC-MAIN-20231203030948-20231203060948-00784.warc.gz
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CC-MAIN-2023-50
| 485 | 3 |
https://www.evcforum.net/dm.php?control=msg&m=665320
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math
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Many of you have probably at some point come across the creationist argument for probability which often uses calculations to make the case that the formation of the universe and life could not have arose by "chance." This argument differs slightly from the argument for intelligent design in that it not only examines the alleged complexity, design, and order of structures (for example examining the complexity/design of a molecule), but the probability that each component of the universe needed to sustain life could have developed independently and function seamlessly. This argument is commonly used to try to disprove abiogenesis and strives to demonstrate that earths position in the universe is too perfect to have gotten there by chance (Goldilocks argument). The calculations made to support these arguments result in staggeringly huge numbers like 3.34 x 10^450 and are usually followed with Borel's law.
Without even thinking too hard about it, I see a few things wrong with this argument
1) It assumes that that the development of the universe is random, when in reality it is driven by the laws of nature
2) The universe is practically infinitely vast. For the one planet that did develop within a life sustaining solar system, there are countless others that did not.
3) It only looks at the way life DID develop ex post facto instead of all the ways it COULD HAVE developed with only slightly different conditions.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912201672.12/warc/CC-MAIN-20190318191656-20190318213656-00115.warc.gz
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CC-MAIN-2019-13
| 1,431 | 5 |
http://mathfinance.sns.it/index.php/levy-flights-with-power-law-absorption/
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math
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We consider a particle performing a stochastic motion on a one-dimensional lattice with jump lengths distributed according to a power law with exponent μ+1. Assuming that the walker moves in the presence of a distribution a(x) of targets (traps) depending on the spatial coordinate x, we study the probability that the walker will eventually find any target (will eventually be trapped). We focus on the case of power-law distributions a(x)∼x−α and we find that, as long as μ<α, there is a finite probability that the walker will never be trapped, no matter how long the process is. This result is shown via analytical arguments and numerical simulations which also evidence the emergence of slow searching (trapping) times in finite-size system. The extension of this finding to higher-dimensional structures is also discussed.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100290.24/warc/CC-MAIN-20231201151933-20231201181933-00661.warc.gz
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CC-MAIN-2023-50
| 836 | 1 |
https://courses.cs.washington.edu/courses/cse461/01au/finalreview-part1.htm
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math
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Midterm Review Questions (CSE/EE 461; Winter 2001)
Note: These questions are only intended to give you an idea of the kinds of questions you may face. I have not picked them carefully to give balance coverage of all relevant material, so they are probably light on, for example, wireless MAC schemes. At any rate, please consider these questions in addition to the material probed by the assigned homework questions.
Sample Multiple Choice
These questions were actually taken from a prior exam.
1. What type of errors cannot be detected by one parity bit?
2. What problem does byte stuffing in PPP solve?
3. Which phrase applies least to the IP service model?
4. A station on an Ethernet has tried to send its frame 3 times and collided each time. What is the interval over which the station will choose its next backoff delay?
5. Which of the following is not an advantage of using hierarchical addressing?
6. What is the service provided by the Network layer in the OSI Reference Model?
7. The Address Resolution Protocol (ARP) is used primarily to translate from:
8. ARP provides an interface between which two layers?
9. Do Ethernet switches require ARP tables?
10. Why is the wireless medium access problem arguably more difficult to solve than the wired case? Circle all answers that apply.
Sample Short Answer
These Peterson questions give you a good idea, though some are too long/hard for the midterm.
2.1, 2.3, 2.10, 2.39, 2.44, 2.49
4.4, 4.6, 4.10, 4.13, 4.16, 4.23, 4.38
5.5, 5.8, 5.9, 5.18, 5.25, 5.37
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s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104628307.87/warc/CC-MAIN-20220705205356-20220705235356-00375.warc.gz
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CC-MAIN-2022-27
| 1,514 | 19 |
http://www.jiskha.com/display.cgi?id=1307624314
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math
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Posted by rohan on Thursday, June 9, 2011 at 8:58am.
Intuitively, we can locate the maximum by the following reasoning:
as a constraint, we look for the maximum of
First solve for b in terms of a and b from 1 to get:
Substitute in (2) to get
which is perfectly symmetrical in a and c.
So set a and c each equal to x and find the maximum of
by setting f'(x)=8-4x=0,
we find the maximum of f(x)=f(2)=4 when a=c=2, and b=0.
Alternately, we can find it formally using the Lagrange multiplier method.
Let the objective function
where L is an undetermined constant, and a+2b+c-4=0 is the given constraint.
Differentiating partially with respect to a, b, and c yields the following set of linear equations:
a+2b+c=4 ....(1) given constraint
b+c+L=0 ....(2) ∂P/∂a=0
a+c+2L=0 ...(3) ∂P/∂b=0
b+a+L=0 ...(4) ∂P/∂c=0
By solving the linear system (1) to (4), we get
a=2,b=0,c=2,L=-2 as before.
Algebra 2 - Find the specified term of each geometric sequence ab^2, a^2b^5, a^...
Math - B is between A and C. If AB=x squared, BC=9x and AC=36, find the value(s...
Geometry - How do I solve for these?On a line,If M is the midpoint of segment ...
geometry - Isosceles trapezoid ABCD has legs AB and CD and base BC If AB = 7y...
geometry - If B is between A and C, AB=5y+4, BC=7y-3, and AC=20y-7. Find the ...
math - prove that a^2+b^2+c^2-ab-bc-ca is always non negative for all the value ...
geometry - What is the value of the variable and bc if b is between a and c. Ab...
Geomatry - What is the value of the variable and BC if B is between A and C. AB=...
geometry - if b is between a and c find the value of x and the measure of bc (ab...
geometry - If b is between A and C, find the value of "x" and BC. AB=3...
For Further Reading
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368697420704/warc/CC-MAIN-20130516094340-00059-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
| 1,731 | 30 |
https://en.wikipedia.org/wiki/Map_segmentation
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math
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In mathematics, the map segmentation problem is a kind of optimization problem. It involves a certain geographic region that has to be partitioned into smaller sub-regions in order to achieve a certain goal. Typical optimization objectives include:
- Minimizing the workload of a fleet of vehicles assigned to the sub-regions;
- Balancing the consumption of a resource, as in fair cake-cutting.
- Determining the optimal locations of supply depots;
- Maximizing the surveillance coverage.
There is a geographic region denoted by C ("cake").
A partition of C, denoted by X, is a list of disjoint subregions whose union is C:
There is a certain set of additional parameters (such as: obstacles, fixed points or probability density functions), denoted by P.
There is a real-valued function denoted by G ("goal") on the set of all partitions.
The map segmentation problem is to find:
where the minimization is on the set of all partitions of C.
1. Red-blue partitioning: there is a set of blue points and a set of red points. Divide the plane into regions such that each region contains approximately a fraction of the blue points and of the red points. Here:
- The cake C is the entire plane ;
- The parameters P are the two sets of points;
- The goal function G is
- It equals 0 if each region has exactly a fraction of the points of each color.
- A Voronoi diagram is a specific type of map-segmentation problem.
- Fair cake-cutting, when the cake is two-dimensional, is another specific map-segmentation problem when the cake is two-dimensional, like in the Hill–Beck land division problem.
- The Stone–Tukey theorem is related to a specific map-segmentation problem.
- Raghuveer Devulapalli (Advisor: John Gunnar Carlsson) (2014). Geometric Partitioning Algorithms for Fair Division of Geographic Resources. A Ph.D. thesis submitted to the faculty of university of Minnesota.
- Boyd, Thomas D.; Jameson, Michael H. (1981). "Urban and Rural Land Division in Ancient Greece". Hesperia. 50 (4): 327. doi:10.2307/147876. JSTOR 147876.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515041.68/warc/CC-MAIN-20181022113301-20181022134801-00301.warc.gz
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CC-MAIN-2018-43
| 2,035 | 21 |
http://zwcourseworkrdfa.taxiservicecharleston.us/what-is-paranthesis.html
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math
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Parenthesis - punctuation mark that is used to set aside information that is not deemed to be essential to a sentence, paragraph, or longer text the remarks put inside of the parentheses are considered to be superfluous, or explanations that are not needed these statements are also sometimes called parenthesis,. Parenthesis is of course greek and means in fact insertion it has taken the meaning of the signs ( or ) parentheses is the regular plural usually, you use a pair of the signs showing an insertion, then between parentheses - or brackets however, in parenthesis means : as an afterthought. Parenthesis refer to punctuation marks ( and ) used to separate relevant information or a comment from the rest of the text, or to enclose mathematical symbols, or the text inside of these marks the punctuation marks in the math equation 2x(4+6) are an example of parenthesis yourdictionary definition and usage. Parenthesis are events of the element you are working on, like the click on a button like your example, this could also be mousedown, keyup, onselect or any action/event for that element, and what is after the '=' is the name of the method to call-- using the parenthesis for the call that method should be. Definition of parenthesis parenthesis is a stylistic device that comes from the greek word meaning “to place,” or “alongside” parenthesis is a qualifying or explanatory sentence, clause, or word that writers insert into a paragraph or passage however, if they leave it out, even then it does not grammatically affect the text. Parenthesis definition: parentheses are a pair of curved marks that you put around words or numbers to indicate | meaning, pronunciation, translations and examples. Parenthesis (countable and uncountable, plural parentheses) a clause, phrase or word which is inserted (usually for explanation or amplification) into a passage which is already grammatically complete, and usually marked off with brackets, commas or dashes either of a pair of brackets, especially round brackets, ( and ). The difference between a 'bracket' and a 'parentheses' can be a bit confusing generally, 'parentheses' refers to round brackets ( ) and 'brackets' to square brackets [ ] however, we are more and more used to hearing these referred to simply as 'round brackets' or 'square brackets.
If the meaning of the sentence would be clear without the parenthetical remark, then parentheses are appropriate when a parenthetical remark contains crucial information, consider an alternative form of punctuation in british english, parentheses are called round brackets the singular form of parentheses is parenthesis. Define parenthesis parenthesis synonyms, parenthesis pronunciation, parenthesis translation, english dictionary definition of parenthesis parentheses are used to separate information that is not necessary to the structure or meaning of the surrounding text continue reading n. Use parentheses to enclose words or figures that clarify or are used as an aside. In this lesson pack, the informative powerpoint explains how parentheses should be marked and the different types of parentheses that can occur (single words, phrases and whole sentences) children can then practice marking parentheses with brackets.
Parenthesis definition: 1 a remark that is added to a sentence, often to provide an explanation or extra information, that is separated from the main part of the sentence by commas, brackets, or dashes: 2 if, while you are talking, you say something in parenthesis, you say it as something extra and learn more. Definition of parenthesis - a word or phrase inserted as an explanation or afterthought into a passage which is grammatically complete without it, in writing. Examples of parenthesis here are some examples of parenthesis (shaded): parenthesis offset with parentheses (brackets) andrew jacklin (last year's losing finalist) is expected to win this heat the whole aim of practical politics is to keep the populace alarmed (and hence clamorous to be led to safety) by menacing it with.
When do you use a bracket and a parenthesis in math part of the series: math problems brackets and parenthesis are similar, but different, when it comes to their specific function within a math problem learn when to use brackets and when to use parenthesis with help from a mathematics educator in. A parenthesis language is a context-free language possessing a grammar in which each application of a production introduces a unique pair of parentheses, delimiting the scope of that production parenthesis languages are nontrivial since only one kind of parenthesis is used in this paper it is shown that algorithms exist.
Don't put any punctuation mark before parentheses, and put a comma after the closing parenthesis only if the sentence needs a comma anyway use a pointed stick ( a pencil with the lead point broken off works well) or a similar tool no comma appears before or after the parentheses if you were to remove the parenthetical. Parenthesis definition is — an amplifying or explanatory word, phrase, or sentence inserted in a passage from which it is usually an amplifying or explanatory word, phrase, or sentence inserted in a passage from which it is usually. Parentheses, brackets, and braces are used often in mathematics including algebra find out how to use them and where you may encounter them. Hello guys i have implemented the same in c using stack the following is my code it's having no issues as far as pushing data is concerned, however, it doesn 't seem to pop the data please help me out debug this code // stacks: check for balanced paranthesis.
In rhetoric, a parenthesis or parenthetical phrase is an explanatory or qualifying word, clause, or sentence inserted into a passage the parenthesis could be left out and still form grammatically correct text parentheses are usually marked off by round or square brackets, dashes, or commas contents [hide] 1 examples 2. Synonyms for parenthesis at thesauruscom with free online thesaurus, antonyms, and definitions find descriptive alternatives for parenthesis. “the constituent parts are (1) the thingamajig, (2) the whatchamacallit, and (3) the whatsit” note: sometimes, only the close parenthesis is used in this format however, usually, neither numbers nor parentheses are necessary in such cases modifying words or phrases, or interjections: 8 “the writer will (one hopes) produce.
You're probably well versed in how to use those sideways eyebrow thingies, better known as parentheses first, remember that a pair of them is called “ parentheses,” whereas a single one is a “parenthesis” you may want to review episode 222 in which we compared parentheses to dashes and commas. A parenthesis is a punctuation mark used to enclose information, similar to a bracket the open parenthesis, which looks like (, is used to begin parenthetical text the close parenthesis, ), denotes the end of parenthetical text the plural of parenthesis is parentheses tip: parentheses are also called. Parenthesis, 1 bracket lisp, 2 curly braces, 1 ibm keypunch machines, 1 ignore, 3 lisp parentheses, 2 parentheses arrays, 1 functions, 1 input devices, 1 super, 2 super parentheses, 2 this file is from wwwgavilanedu/csis/ dvantassel/languages/parentheseshtml date last revised july 8, 2004 copyright dennie.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511761.78/warc/CC-MAIN-20181018084742-20181018110242-00091.warc.gz
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CC-MAIN-2018-43
| 7,340 | 7 |
https://www.enotes.com/homework-help/rectangular-floor-that-has-lenght-l-9m-width-l-3m-175899?en_action=hh-question_click&en_label=hh-sidebar&en_category=internal_campaign
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math
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A rectangular floor that has the length L = 9m and the width l = 3m must be covered with tiles with square shape and length of the side = 30 cm . Which is the necessary number of tiles ?
First we need to calculate the area of the floor
Since it is a rectangulal floor, then the area to be covered is L*I= 9*3=27 m ^2
Now we need to cover the area with (n) numbers of square each with 30 cm side:
Then the area of the square is 30*30=900 cm^2
Then 900*n = 270,000
==> n =300 tiles
Then we need 300 square tiles to cover the area.
check Approved by eNotes Editorial
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655898347.42/warc/CC-MAIN-20200709034306-20200709064306-00387.warc.gz
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CC-MAIN-2020-29
| 563 | 9 |
https://dspace.aus.edu:8443/xmlui/discover?rpp=10&etal=0&group_by=none&page=15&filtertype_0=dateIssued&filtertype_1=dateIssued&filter_relational_operator_1=equals&filter_relational_operator_0=equals&filter_1=%5B2010+TO+2019%5D&filter_0=2013
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math
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Now showing items 141-141 of 141
The solution of a recursive sequence arising from a combinatorial problem in botanical epidemiology
(Taylor & Francis, 2013)
One of the central problems in botanical epidemiology is whether disease spreads within crops in a regular pattern or follows a random process. In this paper, we consider a row of n plants in which m are infected. We then ...
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703514046.20/warc/CC-MAIN-20210117235743-20210118025743-00653.warc.gz
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CC-MAIN-2021-04
| 383 | 4 |
https://boubyansmart.com/product/programmable-digital-relay-pdr-2a/
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math
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• Multifunction programmable digital relay with 4 digit red LED display.
• Control and setting are done by 3 buttons, user-friendly menu, absolute accuracy in timer setting, time countdown on a display, galvanically separated START and STOP control inputs with UNI supply.
• Thanks to its complexity, it is possible to program also more demanding time functions by using 2 independent times.
• 2 independent times, with combination of 2 inputs and 2 outputs.
• PDR-2/A: 16 functions, choice of functions of the other relay, 30 memory places for most frequently used times.
• PDR-2/B: 10 functions, 1 output of 10 functions can be assigned to
each relay = 2 relays in one device.
• 2 independent times in range: 0.01 s – 100 hrs.
• Supply voltage AC/DC 12 – 240 V or AC 230 V.
• 3-MODULE, DIN rail mounting.
There are no reviews yet.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224652494.25/warc/CC-MAIN-20230606082037-20230606112037-00677.warc.gz
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CC-MAIN-2023-23
| 854 | 11 |
http://dungphan.tk/tepo/chapter-1-test-form-2c-glencoe-geometry-answers-426.php
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math
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NAME DATE PERIOD 8 Chapter 8 Test, Form 2B
Glencoe Algebra 1 Chapter 7 Test Answers - DocucuChapter 6 Assessment Answer Key Form 2C Page 69 Page 70 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. Glencoe California Geometry.Informal Geometry Lesson Plans and Assessments Answers 161 Answers Chapter 1 Test, Form F 1.
The Chapter 4 Resource Masters includes the core materials needed for Chapter 4. Chapter 4 1 Glencoe Geometry.
Glencoe Geometry Chapter 1 Test Form AnswersUse this graphic organizer to take notes on Chapter 11: Geometry and Measurement.Geometry chapter 10 test form 2c answers sign up to download geometry chapter 10 glencoe algebra 2 chapter 3 test form 2b answers. hill 620 glencoe algebra 2.The Chapter 4 Resource Masters includes the core materials needed for Chapter 4.
Chapter 13 Test, Form 1 Pg 753 Glencoe Key Glencoe geometry chapter 6 test answer key. hill a28 glencoe geometry chapter 10 assessment answer key form 2c.
Chapter 8 Geometry Form 1 Answer Free DownloadJustify your answer. 9. Chapter 6 70 Glencoe Geometry Chapter 6 Test, Form 2C.PDF Book Library Geometry Chapter 8 Test Form 2c Answers Summary Epub Books:. the top glencoe geometry chapter 7 test form 2c answers home need help 8875 0.McGraw-Hill 648 Glencoe Geometry 11 Chapter 11 Test, Form 2C.
www.methacton.orgThese masters contain a Spanish version of Chapter 10 Test Form 2A and Form 2C. in conjunction with Glencoe Geometry. chapte-10-test-form-2b-answers-geometry.Quizlet provides vocabulary test chapter 2 geometry glencoe activities, flashcards and games.Chapter 1 Test, Form 2C. 75. The Chapter 2 Resource Mastersincludes the core materials needed for.Chapter 6 55Glencoe Geometry 6 SCORE 1. Justify your answer. 9. Chapter 6 Test, Form 2C.Browse and Read Glencoe Geometry Chapter 10 Test Form 2c Answers Glencoe Geometry Chapter 10 Test Form 2c Answers Why should wait for some days to get or receive the.
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Geometry (9780076639298) :: Homework Help and AnswersChapter 8 1 Glencoe Geometry 8 Student-Built Glossary Vocabulary Term Found on Page.Glencoe algebra 1 answer key chapter 9 Chapter 1 test form 2c glencoe geometry answers.
Chapter 6 51 Glencoe Algebra 1. Form 1 Write ttie letter for the correct answer in the blank at the right of each question. 1.Solutions in Geometry Common Core (9780133185829) Chapter 1 test form 2c glencoe geometry answers. Chapter 1 test form 2c glencoe geometry answers.The Chapter 13 Resource Masters includes the core materials needed for Chapter 13. Chapter 13 1 Glencoe Geometry.ANSWERS FOR WORKBOOKSThe answers for Chapter 1 of these workbooks.Chapter 6 Test, Form 2C. key vocabulary terms you will learn in Chapter 6.As you study the chapter,.
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Glencoe Geometry Chapter 1 Test Form Answers PDF
Chapte 12 Test Form 2c Answers Geometry PDF FormatThe Chapter 12 Resource Masters includes the core materials needed for Chapter 12. Chapter 12 1 Glencoe Geometry.NAME DATE PERIOD SCORE Glencoe Geometry 6 Chapter 6 Test, Form 2C 1.Download and Read Glencoe Geometry Chapter 1 Test Form Answers Glencoe Geometry Chapter 1 Test Form Answers In undergoing this life, many people always try to do and.
Chapter 13 Test, Form 1 Pg 753 Glencoe Key, GlencoeChapter 1 59Glencoe Geometry 1 Chapter 1 Test, Form 2B Write the letter for the correct answer in the blank at the right of each.
Geometry Ch 7 Test Form A Answers Epub DownloadANSWERS FOR WORKBOOKS The answers for Chapter 1 of these workbooks.
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7 Chapter 7 Test, Form 2C - The Math CAB
Chapter 6 Resource Masters - Conejo Valley Unified SchoolGlencoe Algebra, chapter 2. 5. down 9 19 31 4 3 12 31.Chapter 2 Answer Key Form 2A Page 85 1. 4) ( 2.Chapter 2 Answer Key Mid-Chapter Test Page 90 1.
GEOM 3eIGPG Pgs129-174 Xmq - portal.mywccc.org
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NAME DATE PERIOD 5 Chapter 5 Test, Form 2A SCOREThe Chapter 10 Resource Masters includes the core materials needed for Chapter 10. Chapter 10 1 Glencoe Precalculus.
Glenco Algebra 1 Test Form 2c Answers.pdf. 440 Glencoe Algebra 1 Chapter 7 Test, Form 2C.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794866201.72/warc/CC-MAIN-20180524092814-20180524112814-00366.warc.gz
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CC-MAIN-2018-22
| 4,615 | 25 |
https://galac.lri.fr/2018-12-05-combi-seminaire2-fr.html
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math
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Type B extensions of Cauchy identity and Schur-positivity related to Chow’s quasisymmetric functions.
Time: 15:00 -- Location: Salle Philippe Flajolet du LIX
The Cauchy identity is a fundamental formula in algebraic combinatorics that captures all the nice properties of the RSK correspondence. In particular, expanding both sides of the identity with Gessel's quasisymmetric functions allows to recover the descent preserving property, an essential tool to prove the Schur positivity of sets of permutations. We introduce a new type B extension of Schur-positivity based on Chow's quasisymmetric functions and domino functions, i.e. generating functions for domino tableaux. Further, we suggest a q-analogue of the modified domino functions to extend a type B Cauchy identity by Lam and link it with Chow's quasisymmetric functions. We apply this result to a new framework of type B q-Schur positivity and to prove new equidistribution results for some sets of domino tableaux.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655886516.43/warc/CC-MAIN-20200704170556-20200704200556-00010.warc.gz
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CC-MAIN-2020-29
| 980 | 3 |
http://kccourseworkdeqi.locallawyer.us/net-present-value-and-question.html
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math
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Corporate finance, final exam practice questions, npv question 11: net present value a firm invests $200,000 in machinery that yields net after. Net present value and discussion questions net present value and discussion questions what specific problems does foreign exchange present in an organization . Best answer: net present value (npv) = $1191577 internal rate of return (irr) = 981% modified internal rate of retrun (mirr) = 958% regular payback period (pbp) = 416 years. Our fun worksheet/quiz combo will assess your knowledge of evaluating estimates using net present value (npv) questions on the quiz ask you about why a business would calculate npv, its . Net present value (npv) money now is more valuable than money later on why because you can use money to make more money you could run a business, or buy something now and sell it later for more, or simply put the money in the bank to earn interest.
How to explain net present value (npv) posted on september 4, 2010 by ibh case interview questions #00091: assume that i have no mathematical ability how would . Aileen’s pmp exam sample question on present value (pv) the portfolio steering committee is considering selecting project a the committee expects the project will produce a one-time benefit of $900, 000 three years from now. Present value is the result of discounting future amounts to the present for example, a cash amount of $10,000 received at the end of 5 years will have a present value of $6,210 if the future amount is discounted at 10% compounded annually .
Net present value (npv) 116794 npv questions add remove 1 winter corporation expects to buy a machine for $126,000, which will be depreciated over an 8 year . This first question is a net present value calculation the future cash flows must be discounted, because of the effects of interest and inflation. Net present value (npv) is the value of all future cash flows (positive and negative) over the entire life of an investment discounted to the present npv analysis is a form of intrinsic valuation and is used extensively across finance and accounting for determining the value of a business, investment security,. I hope i'm right here for asking i'm a little stuck with this question any help is appreciated you have invested 5 million euro in a wind turbine and expect an annual return of 600,000 euro (600.
Net present value and cash 1056 words | 5 pages consider what types and which cash flows should be included in capital budgeting analysis d&d was producing and marketing two major product lines: 1. Net present value calculations can millions of people across the globe highly detailed and thoroughly explained answers to their most important financial questions. Net present value questions q: in case b, quantum said that the owner of the mortgage loan does not participate in hamp at this time how can this be, since it is the servicer who does or does not participate in hamp. The present value, pv, of a series of cash flows is the present value, at time 0, of the sum of the present values of all cash flows, cf we start with the formula for pv of a future value ( fv ) single lump sum at time n and interest rate i,.
The net present value (npv) allows you to evaluate future cash flows based on present value of money the net present value (npv) is the sum of present values of money in different future points in time. Net present value of an investment is the present value of all its cash inflows less the present value of cash outflows, given the risk discount rate. Chapter 8 quiz net present value and other investment criteria true of false for the following two (2) questions: 1 a firm that only accepts projects for which the internal rate of return (irr) is equal to the firm’s required rate return will, on average, neither create nor destroy wealth for its shareholders. Chapter 08 - net present value and other investment criteria 8-2 5 no even though project b has the higher irr, its npv is lower than that of project a.
Net present value, internal rate of return, payback and average accounting rate of return which one of the following methods is most appropriate for a low-level manager, who has no financial training, to use when evaluating small projects. Net present value question if this is your first visit, be sure to check out the faq by clicking the link above you may have to register before you can post: click the register link above to proceed. Net present value mcqs, net present value quiz answers pdf to learn finance online course net present value multiple choice questions and answers on profitability index, net present value for online bachelor degree courses distance learning.
Question 1: (10 points) (net present value calculation) dowling sportswear is considering building a new factory to produce aluminum baseball bats this project would require an initial cash outlay of $4,000,000 and would generate annual net cash inflows of $900,000 per year for 7 years. The term net in net present value means to combine the present value of all cash flows related to an investment the lower the value in today’s dollars question. Net present value in finance, the net present value (npv) or net present worth (npw) of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values (pvs) of the individual cash flows.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515375.86/warc/CC-MAIN-20181022180558-20181022202058-00109.warc.gz
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CC-MAIN-2018-43
| 5,363 | 7 |
https://mrmanojpandey.com/law-of-inertia/
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math
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Galileo first asserted that objects move with constant speed when no external forces act on them. He arrived at this revolutionary conclusion on the basis of following simple experiments.
(a) Galileo’s Experiments With Single Inclined plane
Galileo first studies the motion of objects on an inclined plane he observed that
(I) When an object moves down on inclined plane, its speed increases.
(II) When the object is moved up on the inclined plane, its speed decreases i.e retards.
(III) When an object is moving on a horizontal plane, there should be no acceleration nor retardation i.e constant speed.
(b) Galileo’s Experiments On Two Inclined Planes Combined Together
Galileo concluded another experiment by using a double inclined plane.
(I) When an object rolls down on the inclined plane, it climbs up the other. It almost reaches the same height but not completely because of friction. In ideal case, when there is no friction, the final height of the object is same as the initial height.
(II) When the slope of the second inclined plane is decreased, the object still reaches the same final height but the object has to travel a longer distance to attend the same height.
(III) When the slope of the second inclined plane is made zero, the object travels infinite distance in the ideal situation.
From his experiments, Galileo concluded the Law of Inertia and state that “The state of rest and the state of motion with constant velocity are equivalent in the absence of external forces”.
The terms Inertia means resistance of any physical object. It is defined as the inherent property of a material body by virtue of which it remains in its state of rest or of uniform motion in a straight line.
The various types of inertia are as below
(I) Inertia Of Rest
It is defined as the tendency of a body to remain in its position of rest.
Example: A person standing on a bus falls backward when the bus suddenly starts moving forward.
(II) Inertia Of Motion
It is defined as the tendency of a body to remain in its state of motion in a straight line.
Example: When a moving bus suddenly stops or apply the brakes, a person standing in it falls forward.
(III) Inertia Of Direction
It is define as inability of a body to change by itself it’s direction of motion.
Example: An umbrella protects us from rain.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816465.91/warc/CC-MAIN-20240412225756-20240413015756-00379.warc.gz
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CC-MAIN-2024-18
| 2,319 | 23 |
http://www.igph.kiev.ua/eng/journal/2004/n1/3.html
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math
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New paradigm in a theory of linear incorrect problems, which is adequate to requests of geophysical practice. I. General principles
© Strakhov V.N.
It is stated that the theory of linear incorrect problems is of crucial importance to gravity and magnetic measurements, but classical theory of regularization of these problems is not adequate to requests of geophysics. Statements of a new theory (completely adequate to conditions and requests of geophysical practice) of regularization the linear incorrect problems are given and considered as problems of finding stable approximate solutions for the systems of linear algebraic equations, conforming to fairly vast a priori information.
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http://tulyn.com/10th-grade-math/tangent-line/videotutorials/determining-points-at-which-function-has-horizontal-tangent-line_by_polly.html
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math
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Determining Points At Which Function Has Horizontal Tangent Line Video Tutorial
derivatives video, tangent line video.
Determining Points At Which Function Has Horizontal Tangent Line
This math video tutorial gives a step by step explanation to a math problem on "Determining Points At Which Function Has Horizontal Tangent Line".
Determining points at which function has horizontal tangent line video involves derivatives, tangent line.
The video tutorial is recommended for 10th Grade, 11th Grade, and/or 12th Grade Math students studying Calculus.
In calculus, the derivative is a measurement of how a function changes when the values of its inputs change. Loosely speaking, a derivative can be thought of as how much a quantity is changing at some given point. For example, the derivative of the position or distance of a car at some point in time is the instantaneous velocity, or instantaneous speed (respectively), at which that car is traveling (conversely the integral of the velocity is the car's position).
A closely related notion is the differential of a function.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point.
The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.
In geometry, the tangent line (or simply the tangent) to a curve at a given point is the straight line that "just touches" the curve at that point. As it passes through the point of tangency, the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point.
In a similar way, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point.
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CC-MAIN-2013-20
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https://projecteuclid.org/journals/publicacions-matematiques/volume-57/issue-2/Entropy-and-Flatness-in-Local-Algebraic-Dynamic/pm/1386857707.full
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math
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For a local endomorphism of a noetherian local ring we introduce a notion of entropy, along with two other asymptotic invariants. We use this notion of entropy to extend numerical conditions in Kunz' regularity criterion to every contracting endomorphism of a noetherian local ring, and to give a characteristic-free interpretation of the definition of Hilbert-Kunz multiplicity. We also show that every finite endomorphism of a complete noetherian local ring of equal characteristic can be lifted to a finite endomorphism of a complete regular local ring. The local ring of an algebraic or analytic variety at a point fixed by a finite self-morphism inherits a local endomorphism whose entropy is well-defined. This situation arises at the vertex of the affine cone over a projective variety with a polarized self-morphism, where we compare entropy with degree.
"Entropy and Flatness in Local Algebraic Dynamic." Publ. Mat. 57 (2) 509 - 544, 2013.
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CC-MAIN-2024-18
| 948 | 2 |
https://www.physicsforums.com/threads/dynamics-incline-slope-derivation-simplification.860119/
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math
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1. The problem statement, all variables and given/known data No official problem, just a study guide fill-in-the-blanks with an extended simplification blank. Basically, no values were given, and it is a standard block on a standard slope with a north-east applied force pushing down on the block (not parallel to horizontal or vertical axis). 2. Relevant equations Fnet = ma Fnormal = Fay + Fgy Fnormal = (Fapplied)(sinØ) + (Fgravity)(cosØ) Fnet = Fax - Fgx - Ffk Fnet = (Fapplied)(cosØ) - (Fgravity)(sinØ) - (Uk)(Fnormal) 3. The attempt at a solution He asked us to substitute the second equation above into the third equation above. I am terrible at simplifying and so this is as far as I've gotten: ma = (Fapplied)(cosØ) - (Fgravity)(sinØ) -Uk(Fapplied)(sinØ) + (Fgravity)(cosØ) This is extremely messy and confusing, I am aware, so I am in deep gratitude to anyone taking time to help a scrub physics student like me. :D Thank you so much for any simplifying advice! I am solving for acceleration.
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CC-MAIN-2018-09
| 1,010 | 1 |
http://blogs.scienceforums.net/ajb/2020/01/28/construction-of-a-metric-on-the-antitangent-bundle/
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math
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|In a short preprint
The super-Sasaki metric on the antitangent bundle, I explicitly show how to lift a Riemannian metric and an almost symplectic two-form on a manifold \(M\) to a Riemannian metric on the antitangent bundle \(\Pi T M\), which is, of course, a supermanifold.
This example was first given in
Modular Classes of Q-Manifolds, Part II: Riemannian Structures & Odd Killing Vectors Fields, but in The super-Sasaki metric on the antitangent bundle I give more details and deduce some direct results.
In particular, I compare the construction with that of the Sasaki metric on the tangent bundle of a Riemannian manifold. Indeed the construction that I give is really the natural analog of Sasaki’s construction to the setting of antitangent (aka shifted tangent or odd) bundles. Due to the anticommuting nature of the fibre coordinates on \(\Pi T M\), it is clear that directly lifting the metric will not work. One requires an antisymmetric component to the construction and this is provided for by an almost symplectic structure, i.e., a non-degenerate two form that is not necessarily closed.
It is well-known that differential forms on a manifold \(M\) are functions on the antitangent bundle \(\Pi T M\). Furthermore, the de Rham differential, the interior product and the Lie derivative can all be realised as vector fields on the antitangent bundle. In the short preprint, I examine the super-Sasaki metric on these vector fields. We get some interesting formula in this way that related the ‘super-picture’ with the more classical framework of the underlying Riemannian metric and differential forms.
It is worth noting that the classical Sasaki metric plays a role in geometric mechanics. One can equip the configuration space of a Lagrangian system with the Jacobi metric and then, in turn, the tangent bundle of the configuration space naturally comes equipped with the associated Sasaki metric. Trajectories can then be understood as geodesics on the configuration space itself or as geodesic on the tangent bundle of the configuration space. This makes me wonder if the construction of the super-Sasaki metric can play some role in supermechanics.
Sasaki, S., On the differential geometry of tangent bundles of Riemannian manifolds Tohoku Math. J. (2) 10 (1958),338-354.
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http://nrich.maths.org/public/leg.php?code=32&cl=2&cldcmpid=5578
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math
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Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
56 406 is the product of two consecutive numbers. What are these
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Can you work out what a ziffle is on the planet Zargon?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
What is the largest number you can make using the three digits 2, 3
and 4 in any way you like, using any operations you like? You can
only use each digit once.
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
What is the sum of all the three digit whole numbers?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
There are four equal weights on one side of the scale and an apple
on the other side. What can you say that is true about the apple
and the weights from the picture?
Find out what a Deca Tree is and then work out how many leaves
there will be after the woodcutter has cut off a trunk, a branch, a
twig and a leaf.
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.
Take the number 6 469 693 230 and divide it by the first ten prime
numbers and you'll find the most beautiful, most magic of all
numbers. What is it?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
This problem is designed to help children to learn, and to use, the two and three times tables.
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
Resources to support understanding of multiplication and division through playing with number.
After training hard, these two children have improved their
results. Can you work out the length or height of their first
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Use this information to work out whether the front or back wheel of
this bicycle gets more wear and tear.
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
What is happening at each box in these machines?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?
Use the information to work out how many gifts there are in each
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Can you complete this jigsaw of the multiplication square?
Chandrika was practising a long distance run. Can you work out how
long the race was from the information?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
These sixteen children are standing in four lines of four, one
behind the other. They are each holding a card with a number on it.
Can you work out the missing numbers?
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?
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https://theknowledgenest.org/shop/subject/math/geometry
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math
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In the realm of mathematics, geometry plays a crucial role in understanding the properties and relationships of basic geometric figures. At The Knowledge Nest, we aim to provide a comprehensive guide to help you navigate through the fascinating world of geometry.
Shapes and Their Characteristics
Geometry introduces us to a variety of shapes, each with its own unique properties and characteristics. Let's explore some of the most common ones:
A circle is a closed shape with all points equidistant from the center. Its key properties include the radius, diameter, circumference, and area. Understanding the concept of pi (π) is fundamental in calculating values related to circles.
Triangles are polygons with three sides and three angles. They can be classified based on their side lengths and angle measurements. Equilateral, isosceles, and scalene triangles each possess distinct properties and formulas for calculating their area and perimeter.
Quadrilaterals are polygons with four sides. They include rectangles, squares, parallelograms, trapezoids, and rhombi. Learning about the properties of each of these quadrilaterals allows us to identify and differentiate them from one another.
A polygon is a two-dimensional shape with straight sides. Polygons can have any number of sides, and some examples include pentagons, hexagons, and octagons. Exploring the characteristics of polygons helps us understand their angles, sides, and diagonals.
Angles and Measurements
In geometry, angles are formed by two intersecting lines or line segments. Understanding angle measurements is crucial for solving geometric problems. Let's dive into some key concepts:
Types of Angles
Angles can be classified based on their measurements and relationships with other angles. Some common angle types include acute, right, obtuse, straight, and reflex angles. Complementary and supplementary angles also play a significant role in geometry.
Angles are measured in degrees using a protractor. By learning how to measure and compare angles accurately, we can apply this knowledge to various real-life situations and geometric problems.
Dimensions and Spatial Relationships
Geometry extends beyond two-dimensional figures, allowing us to explore three-dimensional objects and their spatial relationships. Let's delve into this fascinating realm:
Two-Dimensional versus Three-Dimensional
While two-dimensional figures exist on a flat plane, three-dimensional objects have length, width, and depth. Identifying and understanding the properties of 3D shapes such as cubes, spheres, cylinders, cones, and pyramids enables us to visualize and manipulate them in space.
Volume and Surface Area
Calculating the volume and surface area of three-dimensional figures is a crucial skill in geometry. By applying specific formulas, we can determine the amount of space a solid figure occupies and the sum of its exposed surfaces.
Putting it Into Practice
Geometry is not only a theoretical concept but also finds practical applications in various fields such as architecture, engineering, art, and design. Understanding geometric principles allows us to analyze patterns, create accurate drawings, and solve real-world problems.
Using Geometry in Everyday Life
From determining the right measurements for a home renovation project to analyzing the symmetry and proportion in visual arts, geometry surrounds us. Its concepts form the building blocks of numerous disciplines and provide a deeper understanding of our world.
Exploring Advanced Geometry
Once you've grasped the fundamentals of basic geometric figures, you can explore more advanced topics such as trigonometry, coordinate geometry, and analytic geometry. Each of these branches further expands our knowledge and aids in solving complex problems.
At The Knowledge Nest, we invite you to delve into the captivating realm of basic geometric figures. Understanding shapes, angles, and dimensions in geometry empowers us to make sense of the world around us, solve problems, and appreciate the beauty of mathematical concepts. Embark on this journey with us, and unlock a world of knowledge and endless possibilities.
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http://wikis.controltheorypro.com/PSD
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math
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- 1 Introduction to PSDs in Controls
- 2 PSD Definition (para-phrased from Wikipedia)
- 3 Using PSDs in Controls
- 4 References
1 Introduction to PSDs in Controls
In reality many disturbances and noise sources are not well represented by Gaussian distributions. Instead the system will have random and periodic disturbances and noise. This type of behavior cannot be described with a probability distribution (such as Gaussian) but rather are better described by a Power Spectral Density (PSD).
For example, satellites often employ momentum wheels for attitude control. These momentum wheels spin at a constant speed for long periods of time and then they are sped up or slowed down to steer the spacecraft. This raises 2 issues. First, the disturbance is not truly random. Second, a measured PSD of the disturbance due to these wheels will show a spike at one wheel speed and then at another. Typically, the PSD is enveloped in these circumstances (this will be discussed below). There is, however, a random component to the disturbance created by the moementum wheels. Remember that they have their own controllers and sensors and random noise on the sensor will pass to the controller. The random noise will go through the controller (and plant) causing random fluctuations in the wheel speed. While these fluctuations are small they are not always inconsequential.
Note: While I have not taken a course on Stochastic Controls I believe that this falls into that category of control theory.
2 PSD Definition (para-phrased from Wikipedia)
The PSD is a positive real function of a frequency variable associated with a stationary stochastic process, or a deterministic function of time, which has dimensions of power per Hz. For example, many rate sensors will provide an output in Volts which can be converted to rad/sec. A PSD of the ambient noise from this rate sensor will have units of (rad/sec)^2 / Hz.
2.1 Mathematical Definition of the PSD (heavily lifted from Wikipedia and needs rewrite and references)
The PSD describes how the power of the signal or time series is distributed with frequency. Here power can be the actual physical power, or more often, for convenience with abstract signals, can be defined as the squared value of the signal (the actual power if the signal was a voltage applied to a 1-Ohm load). This instantaneous power (the mean or expected value of which is the average power) is then given by:
Since a signal with nonzero average power is not square integrable, the Fourier transforms do not exist in this case. Fortunately, the Wiener-Khinchin therorem provides a simple alternative. The PSD is the Fourier transform of the autocorrelation function of the signal if the signal can be treated as a wide-sense stationary random process. The result is
The power of the signal in a given frequency band can be calculated by integrating over positive and negative frequencies,
The power spectral density of a signal exists if and only if the signal is a wide-sense stationary process. If the signal is not stationary, then hte autocorrelation function must be a function of two variables, so no PSD exists.
3 Using PSDs in Controls
PSDs are used in many places in controls. For time-domain simulation and performance analysis a PSD derived from measured sensor noise data can be turned into a time series of noise values at specifics times. When done correctly the PSD of these time series are close or identical to the original measured sensor noise PSD. Disturbances can be dealt with in a similar manner.
In frequency domain analyses and moedling the key equation is
Various texts will make different claims about the input PSD. Some state the input PSD must be both stationary and ergodic while others claim that it only needs to be weakly stationary. In practice the PSD is often used whenever it is consistent from measurement to measurement. In other words, if the magnitude of the PSD and RMS remain approximately constant from hour to hour or day to day then the PSD is good enough.
An example of how this is used, with MATLAB code, can be found in the article on Frequency Domain Modeling.
3.1 How PSDs are used in Controls
PSDs are used in a variety of ways:
- Disturbance Modeling
- Noise Modeling
- Residual Error Characteristics
All of these applications are generically part of Frequency Domain Modeling. The basic purpose of frequency domain modeling is to determine the steady-state residual error due to disturbances and noise.
3.2 PSDs and RMS
Measured (and calculated) PSDs are basically a vector of magnitudes at specific frequencies. Obviously, dealing with this and discussing it are cumbersome. The RMS is a common metric. The RMS (or Root Mean Squared value) is essentially an integration under the PSD curve. This cumulative value allows a quicker, simpler discussion of total disturbance power and requirements. Like all metrics the RMS is not an all encompassing value in that a particular PSD may have a lot of RMS contribution from the lower frequencies where rejection is good. Therefore the disturbance RMS will be high and the residual (what's left over after rejection) is low but the system still may not meet performance specifications because the remaining RMS in the mid to high frequency ranges is unacceptable.
As an example consider a Hubble image. It may require that Hubble stares at the same object for minutes or even hours. Staring this long means that the camera is collecting photons for a long time but the final image will still likely be made up of several individual images taken over time. Low frequency drift can be subtracted out while mid to high frequency jitter will cause the image to blur. The control system's residual error RMS may be low due to very good low frequency rejection but the overall system performance (blurry images) is unacceptable.
3.2.1 Lessons Learned
Many times measured data of all types come with irregularities or oddities. Measured time series and PSD data is no different. Here are some lessons learned:
- Some analysis programs will take time series data and spit out a PSD. The minimum frequency of the PSD is often times automatically set to 0. Obviously, with measured data there is only a finite data length. With that finite data capture time frame comes a minimum measurable frequency (1 / time length of data capture). The result is that the low end frequencies of the PSD must be used with caution.
- Low frequency samples for PSD measurements take a long time to capture. As a result most PSDs have very few data points at lower frequencies. This leads to a coarseness in the measurements that can create errors in the RMS calculation. Specifically, when calculating the RMS (either forward or backward) the first point of the RMS is at the second frequency of the PSD. If the data is coarse at the low end then the method of calculation can lead to errors in the RMS calculation - especially when the lowest frequency point is at 0. However, interpolation can solve this problem.
3.2.2 PSD Interpolation in MATLAB
Often PSDs are provided with only a few points. This is done with convenience and as a measure of being conservative - i.e. the PSD contains all of the expected disturbances by enveloping the expected PSD.
Using the PSD with only a few points will almost always cause problems. As a result interpolation on a log scale is used to fill in PSD with lots of points.
If a PSD's frequency vector is defined by the vector x and the PSD's magnitude by y then interpolating a new vector of frequencies xi can be done using the interp1q command as follows
>> logX = log10(x); >> logY = log10(y); >> logXi = log10(xi); >> yi = 10.^interp1q(logX, logY, logXi);
- yi is the interpolated PSD magnitudes corresponding to the frequencies of xi.
Sun, Jian-Qiao (2006). Stochastic Dynamics and Control, Volume 4. Amsterdam: Elsevier Science. ISBN 0444522301.
- Sun, pp. ??-??
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http://chemistry.about.com/b/2014/01/21/significant-figures.htm
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math
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Science is less about certainty than it is about measuring the degree of uncertainty. For example, you never prove
a hypothesis using the scientific method
. Similarly, there is always a degree of uncertainty in the numbers used in calculations. The level of uncertainty is expressed in the number of significant figures used to report any measured value. For example, if you measure a volume with a graduated cylinder you may be certain the measurement is reported to the nearest milliliter. If you eyeball the amount of water in a drinking glass, you'll be lucky to get within a hundred milliliters of the actual value. So, how do you know how many significant figures to use? How does this relate to accuracy and precision? These are things you need to know.
Uncertainty, Accuracy, & Precision
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| 796 | 4 |
https://www.omnicalculator.com/physics/synodic-period
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math
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Synodic Period Calculator
The synodic period calculator is a tool designed to help you calculate the time between two successive identical configurations as seen from any planet. In other words, if you missed the last time Mars came to opposition, you can find out when the next opportunity to see the Red Planet will be. It can also be used in reverse as a sidereal period calculator!
If you don't know what the sidereal and synodic periods are or would simply like to learn more about them, read on! This article will explain the difference between these two, show you how to calculate them, and present the orbital periods of the planets in the Solar System.
What is a synodic period?
If you've ever peeked through a window while driving a vehicle or tried to look around from a merry-go-round, you must've noticed that the world outside your frame of reference had appeared to move slightly differently than it would've if you were watching it while still.
As we know, the planets in our system move in elliptical orbits about the Sun. The orbital period is the time needed to complete one revolution. You can read more about them in the article accompanying the orbital period calculator.
What is the synodic period, then? Well, although determining the time elapsed may seem fairly simple - after all, we just need to monitor the planets and wait for them to return to their initial positions - it is not that easy. We must bear in mind that the Earth is also moving, affecting our observations. This is the gist of the synodic period. You could think of it as a subjective period, as it varies depending on the planet you choose as your point of reference.
On the other hand, the sidereal period is the true, objective amount of time it takes the planet to complete one full orbit of the Sun relative to the stars. This value has to be found by calculation, either using the formula applied in our sidereal period calculator or Kepler's third law calculator.
How to calculate the synodic period and sidereal period?
Fortunately, we have much more data than our predecessors did. It means that we know either the sidereal or synodic period of many celestial bodies and can therefore calculate the other. It turns out that obtaining the sidereal period tends to be easier as it does not require any observations. They can take a really long time - for example, astronomers(supposedly a black hole!).
So, how to calculate the synodic period without spending years watching the celestial bodies, and how to calculate the sidereal period if you know the synodic period? Well, it depends on the planet's location, and it is typically represented as a relationship rather than a direct formula. In this synodic period calculator, we use three relationships:
- An inferior planet is closer to the object in the center (e.g., Sun) than the planet you observe it from (usually assumed to be Earth). The relationship is as follows:
- A superior planet is further from the center than the reference planet. The only change in the relationship is the sign:
- Another way to calculate the sidereal period (or the synodic one) is to use the absolute value without worrying about the planet's position:
- Planet's synodic period;
- Planet's sidereal period; and
- Reference planet's sidereal period. If the synodic period is (or is meant to be) observed from Earth, this value is equal to 1 year or 365.25 days.
Depending on what you wish to determine, it requires playing with fractions a little bit.
Sidereal and synodic periods of the planets
It may be tricky to understand the difference - or even the fact that there is any discrepancy - between the sidereal and synodic periods without seeing the numbers for yourself. This is why we prepared the orbital periods of planets of the Solar System - using Earth as the reference planet.
Sidereal period [yrs]
Synodic period [days]
As you might have noticed, the differences can be huge - the synodic period of Neptune is approximately a year, whereas, in reality, it takes nearly 165 years to complete one revolution around the Sun. Similarly, the sidereal period of Saturn is 29.5 years, but its synodic period is almost the same as Neptune's.
Are there other types of orbital periods of planets?
Yes, although they are rarely used. The other types of orbital periods of planets are:
- The anomalistic period is the time between successive periapsis passages. The periapsis (in Solar System called the perihelion) is the point of the closest approach between a planet and the attracting body. If you would like to learn about the elliptical orbits, check out our orbital velocity calculator.
- The nodal (draconic) period applies to the satellites, both natural (such as the Moon) and artificial (e.g., navigation satellites). It's the time that elapses between successive passages of an object through successive ascending (north) nodes - when the satellite moves north from the plane of reference. For instance, the Moon's nodal period is slightly different from its sidereal and synodic periods, with a value of 27.2 days.
- The tropical period, or solar year, applies only to Earth. It's the time between two successive vernal equinoxes (around the 21st of March) when the number of hours of daytime and darkness is the same. The tropical period is .
- You might have heard about a lunar month or a lunation. These phrases usually relate to the time between two identical phases. Therefore, this is not a different type but simply the synodic period of the Moon.
How long does the moon take to orbit the Earth? - an example
The time between two successive lunar phases (e.g., full moons) observed from Earth is approximately 29.5 days. But have you ever wondered how long does the moon take to orbit the Earth in reality?
Luckily, we already know how to calculate the sidereal period, so this shouldn't be too tricky. Since the synodic period calculator takes the Earth to be the default reference planet, all we need to do is convert this into days (365.25) and input 29.5 days as the synodic period. This way, we find that the moon needs approximately 27.3 days to orbit 360° around the Earth - which is less than we see. In other words, the sidereal period of the Moon is 27.3 days.
How to find the synodic period?
You can use the following formula to find the synodic period without worrying about the relative position of the planet:
1/planet's synodic period = |1/planet's sidereal period - 1/reference planet's sidereal period|
What is the difference between the sidereal and synodic period?
The sidereal period is the time the planet needs to complete one full orbit relative to the "fixed" stars. The synodic period is observed from a planet, so it varies depending on the point of reference.
Can the synodic period be measured as seen from other planet than Earth?
Yes, although Earth is the usual point of reference, you can choose to consider any other planet so long as you know its sidereal period (or other related variables).
Is the sidereal period of the Moon the same as its synodic period?
No. Although it's relatively close to Earth and we may think our observations are accurate, the sidereal period is shorter (27.3 days) than the synodic period of the Moon (29.5 days).
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https://eprints.soton.ac.uk/63323/
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math
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Woods, David C. and Lewis, Susan M.
Continuous optimal designs for generalised linear models under model uncertainty
Journal of Statistical Theory and Practice
We propose a general design selection criterion for experiments where a generalised linear model describes the response. The criterion allows for several competing aims, such as parameter estimation and model discrimination, and also for uncertainty in the functional form of the linear predictor, the link function and the unknown model parameters. A general equivalence theorem is developed for this criterion. In practice, an exact design is required by experimenters and can be obtained by numerical rounding of a continuous design. We derive bounds on the performance of an exact design under this criterion which allow the efficiency of a rounded continuous design to be assessed.
||exponential family, general equivalence theorem, logistic regression, nonlinear regression, optimal design.
|2 October 2008||Submitted|
||03 Oct 2008
||16 Apr 2017 17:26
|Further Information:||Google Scholar|
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