MBA/MFM 220/253
STUDY GUIDE FOR EXAMINATIONS
FALL 2011
The study guide contains questions for review from each chapter and practice test questions divided by test based
upon the anticipated order of material from the syllabus. If the class is ahead or behind the schedule, the sample
questions may need to be adjusted to represent the material on the actual test. Any adjustments will be discussed at
the review session.
As always stop by the office, e-mail, or call anytime, I am in my office the majority of each day especially between
2:00 pm and 6:00 pm Tom.Root@Drake.edu (515) 271-4163
CHAPTERS 1 AND 2: INTRODUCTION AND OBJECTIVES IN DECISION MAKING
What is the main objective of the financial manager? Explain the difference between stock price maximization and
firm value maximization? (How are the two objectives similar? How are they different? Are they ever the same?)
What are the advantages of using stock price maximization? Be able to explain the principal agent problem and how it
impacts the goal of maximizing the value of the firm. When might the principal agent problem result in a stock price
increase that does not increase firm value – be able to give an example of such a case. How can principal agent
problems be reduced? Be able to explain how bondholders interests may conflict with shareholders and when an
increase in the share price might be viewed by bondholders as a decline in firm value. What is a bond covenant and
how can bond covenants decrease potential conflicts between bondholders and shareholders. What other ways can
potential conflicts between bondholders and shareholders? Explain how the Information problem and Market problem
can interfere with the use of stock price maximization as an objective. What are the Market and Information
problems? How are the Market and Information problems similar and how are they different? How does increasing
transparency impact the market and information problem? Discuss how an increase in the share price could decrease
society’s value of the firm. Can it be argued that firm value maximization benefits society as a whole? What
objective other than firm value could be used as the goal of financial management. Be able to explain the general idea
of the relationship between risk and return. What are the net present value rule and the rate of return rule? What is the
opportunity cost of capital? How does the opportunity cost of capital relate to the relationship between risk and
return?
APPENDIX 3 TIME VALUE OF MONEY
Calculations: Given the relevant data, you should be able to calculate: The PV of a future cash flow; The FV of a
current cash flow; The NPV given a single cash flow in the future and the current cost; The FVIF, and PVIF; The PV
and FV of an annuity (or annuity due); The FVIFA, and PVIFA; The PV of a perpetuity; The PV and FV of uneven
cash flows; the interest rate or discount rate given an annuity or cash flow; and the effective annual interest rate
(EAR). The PV of a growing annuity. You should also be able to combine the above situations.
Concepts and Ideas: Be able to represent cash flows using a time line. Explain what is meant by compounding
interest. Explain in words what the Present Value of a future cash flow means. (I know you can calculate it, but why
do we want to find that number?) What is meant by “discounting” a cash flow? What happens to the PV of a
payment to be received in the future if the interest rate increases (or decreases)? What happens to the PV of a
payment to be received in the future if the length of time before you receive it increases (or decreases)? What is an
annuity? Why is the appropriate discount rate referred to as an opportunity cost? How do opportunity costs relate to
the level of risk? How are an annuity and annuity due different? How would you adjust the calculation of the PV or
FV of an annuity to find the PV or FV of an annuity due. Given two cash flows, we generally prefer the one with the
highest PV, why? Explain in detail (be able to explain in words why we look at present value and what present value
means.). What happens to the PV of an annuity if there is an increase (or decrease) in the interest rate? What should
you do to compare two cash flows that compound at different intervals (for example quarterly vs. semi annually)?
How do you account for fractional time periods when calculating PV and FV of cash flows? What is the difference
between the nominal (or quoted) rate, the periodic rate and the effective annual rate?
CHAPTERS 3 AND 4, AND APPENDIX 1 THE BASICS OF RISK, RISK MEASUREMENT AND HURDLE RATES IN
PRACTICE (COST OF CAPITAL), AND STATISTICS REVIEW
Calculations: Given the relevant information be able to calculate or find: The expected return and standard deviation
of return’s for a security (or portfolio); The coefficient of variation; The required return using the Capital Asset
Pricing model (CAPM); Given all components of the CAPM except one, be able to find what is left; The security
market line; Be able to interpret regression analysis, in particular, be able to explain the following components of
regression output given the regression results: the coefficient on a dependent variable; the coefficients t-statistic; the
coefficients standard error; the intercept; and R-squared. How can the beta of a stock be found using regression
output? Be able to calculate and interpret Jensen's alpha. The before and after tax cost of debt; The cost of preferred
Stock; The cost of common equity with and without flotation costs; The growth rate (using the retention rate and
ROE); The weighted average cost of capital
Concepts and Ideas: Explain the difference between stand alone risk and portfolio risk. What type(s) of risk can be
eliminated via diversification? What type(s) of risk cannot be eliminated via diversification. Provide examples.
Given a level of standard deviation, what does it tell us about the return on the asset (or portfolio)? (What does it
mean if we know that an asset has an expected return of 30% with a standard deviation of 20%?) Relate this to the
idea of a probability distribution. Is the standard deviation a good measure of risk to use when comparing different
assets? When is it all right to use the standard deviation? When can it be misleading? Why is the coefficient of
variation a better measure of risk in many circumstances? Use the concepts of standard deviation and expected return
to explain what is meant by a risk averse investor. How do you calculate the expected return of a portfolio of assets?
Is the standard deviation of a portfolio the weighted average of the standard deviations of the assets in the portfolio?
Explain how the correlation coefficient between two stocks relates to the ability to eliminate risk by forming a
portfolio of those stocks. What type of risk is generally considered to be diversifiable? Explain the basic result of the
CAPM. What is meant by the market risk premium? How does beta relate to market risk? How is beta calculated for
a portfolio of assets? What happens to the beta of a portfolio as more stocks are added? Why can we say that the
slope of the security market line reflects the risk aversion of investors in the market? What happens to the security
market line if investors become more risk adverse? When investors become more risk averse, what variable in the
original equation is changing? and what happens to the required rate of return? Be able to interpret different
covariances and correlation coefficients for pairs of assets (what does it mean if the covariance is large and positive...).
What is the difference between a bottom up beta and a top down beta? Given the relevant information be able to
interpret output from calculating beta using a regression (this includes regression output - R squared, and Jensen's
Alpha). Be able to explain what a regression attempts to do (explain providing a line of best fit – estimating the linear
relationship between two variables). What is the difference between the independent variable and a dependent
variable in a regression? Relate the concept of an independent variable and dependent variable to the relationship
between risk and return that the CAPM is trying to measure (what variable is the dependent variable in our regression,
what is the independent variable – why does this make sense given the risk return relationship we are attempting to
measure? What is the difference between an unlevered beta and a levered beta? Intuitively why does leverage impact
the level of risk that the CAPM is trying to measure (and why would that impact beta)? Is a top down (Historical or
regression) beta a levered or unlevered beta? Is a bottom up beta levered or unlevered? Explain. Be able to calculate
a bottom up beta given the relevant information. What different measures can be used to develop the weights of each
division when calculating a bottom up beta? What is the efficient frontier? What is the difference between the
Arbitrage pricing theory and the CAPM? How are they similar? What are the constraints to applying the APT? Why
can the cost of capital be thought of as an opportunity cost? Whose opportunity cost does it represent? What does it
mean to call the cost of capital a hurdle rate? When computing the cost new debt how is the required rate of return
found? How is the bond rating used to determine the cost of debt? How is a firm’s bond rating linked to the financial
performance of the firm? Have a general idea of the ratios discussed in class and their associated bond rating. Is the
cost of debt equal to the coupon rate on existing company debt? Explain. Why do we need to adjust for taxes when
calculating the cost of new debt? What are floatation costs? How do flotation costs change the calculation of the cost
of new debt? If the tax rate increases will the after tax cost of debt increase or decrease? If the firm does not currently
have any outstanding debt, or its debt is not traded frequently how would you find the cost of new debt? How do
flotation costs change the calculation of the cost of preferred stock? What two forms of common equity are there?
Why is there a cost associated with retained earnings? How are the discounted cash flow, CAPM, and bond plus risk
premium approaches used to estimate the cost of common equity? When applying the CAPM what issues exist in the
choice of the value to use the market risk premium? When estimating the market risk premium from historical data
what is the difference between an arithmetic mean and geometric mean? How do you use the retention rate and ROE
to estimate the growth rate of dividends? When do you need to account for flotation costs when calculating the cost of
common equity? What is capital structure? How does the capital structure relate to the weighted average cost of
capital?
SCENARIO AND SENSITIVITY ANALYSIS
Calculations: Be able to conduct a basic scenario or sensitivity analysis similar to the problems in the notes.
Concepts and Ideas: What are the three main types of project risk? Be able to explain each in detail. Which type of
risk is the largest concern when making a capital budgeting decision? Should stand alone risk be the only risk
assessed? Explain the concepts of sensitivity analysis. What are the problems associated with a sensitivity analysis?
Explain how to conduct a scenario analysis. How is a scenario analysis different from a sensitivity analysis? Does a
scenario analysis account for all of the problems associated with a sensitivity analysis? What are the problems
associated with using a scenario analysis? What is a Monte Carlo simulation? How is a Monte Carlo simulation
similar to a scenario analysis? What are the difficulties associated with conducting a Monte Carlo simulation?
CHAPTERS 7, 8, AND 9 CAPITAL STRUCTURE
The class notes are a combination of the two chapters, plus an example that extends the material in the book. Refer to
the notes to see which portions of the book are covered.
Calculations: Have an idea of the procedures and issues surrounding the calculation of the “optimal capital structure.”
Be able to calculate the estimated WACC at a given level of debt (be able to do the calculations in the homework)
Concepts and Ideas. What is the difference between business and financial risk? What was the main conclusion of
Modigliani and Millers original work on capital Structure? What assumptions was their original work based on?
Explain what is meant by bankruptcy costs. Does a firm have to declare bankruptcy to incur these costs? What is
trade off theory? How does it relate to the work of M&M? Explain the results of signaling theory. How does
signaling theory explain why a firm might not use its debt financing at the “optimal” level? How can debt be used to
“constrain” financial managers? Why is the “optimal” capital structure the one that maximizes the stock price explain.
Could you also claim that the “optimal” capital structure is the one that minimizes the cost of capital? How does
capital structure affect the price of a firm’s stock? How does it affect the cost of capital? What has to happen for the
“optimal” capital structure to be located at the point where the WACC is minimized (This relates to the cash flows -are they related to capital structure?) What are some other real world issues to that need to be addressed when
discussing capital structure? Explain how the estimate of the levered and unlevered beta can be used to find the cost
of equity at different debt levels. What is the interest coverage ratio? How is the interest coverage ratio important in
determining the firms estimated cost of debt at various debt levels. Explain how the interest coverage ratio relates to
the firms bond rating (and cost of debt). When will a firm be more likely to increase its use of debt gradually? When
will a firm be more likely to increase its use of debt quickly? Be able to explain methods of increasing debt either
gradually or quickly. Be able to explain the intuition underlying the adjusted present value approach.
CHAPTERS 10 AND 11: DIVIDEND POLICY
Concepts and Ideas: What are the two main ways that firms return cash to investors? What is meant by saying that
there is a tradeoff between dividends and growth? Explain. What were Modigliani and Miller’s conclusions
concerning the dividends? What is meant by shareholders establishing their own dividend policy? Explain the Bird in
a Hand Theory. How does it relate to the uncertainty associated with capital gains? Be able to explain tax advantages
that might cause an investor to prefer dividends or reinvestment. How does the signaling hypothesis figure into the
firms dividend decision? Why might corporations be afraid to decrease the level of dividends they are paying?
Explain how portfolio and Agency considerations are important in determining dividend policy. What are clientele
effects? How are they important in the dividend decision? Be able to briefly explain the Residual Dividend Model.
Does the model claim that determining the payout rate or level of dividends is the better approach? Explain. Be able
to identify other factors that influence dividend policy. (Constraint, Investment opportunities, Alternative Sources of
Capital...). Why do different firms and industries have different dividend policies (what determines dividend policies
-- there are 6 factors in the notes)? How is Free Cash Flow to Equity related to the firm’s dividend decision? What
are the consequences of low payout rates and high payout rates respectively. Do these consequences change based on
the quality of the projects available to the firm? What are the advantageous of using share repurchases in place of
dividends? What was mean by the “dilution illusion” relating to share repurchases that was discussed in class?
CHAPTER 5 MEASURING RETURN ON INVESTMENT AND APPENDIX 2
Calculations: Given the relevant information be able to calculate: Be able to find NOPAT and free cash flow The
payback period; the discounted payback period; the net present value; internal rate of return; modified internal rate
of return, profitability index, and modified profitability index. Be able to use the equivalent annual annuity approach
to compare projects with unequal lives.
Concepts and ideas: What is meant by the term incremental cash flows? Be able to explain the goals of financial
planning (purpose, Scope, Objectives, strategy and Plans). What is meant by the word free in free cash flows (why
do we call it that???). What are some of the uses for Free Cash Flows? How does the capital budget relate to the
flexibility of a firm to finance future projects? What are the weaknesses of using the payback period as a tool for
capital budgeting decisions? Does the discounted payback period account for all of the problems associated with the
use of the payback period? What are its weaknesses? Explain in words what the net present value of a firm
represents. According to the net present value criteria when will a project be undertaken? How does the accept
decision relate to the value of a firm discussed in chapter 12? How are the internal rate of return and net present value
of a project related? Is it possible for a project to have multiple internal rates of return? Be able to analyze whether a
project might have multiple IRRs. Why is the internal rate of return thought of as a hurdle rate? How does it relate to
the cost of capital? Will NPV, IRR and PI always result in the same accept / reject decision for a project? What is the
difference between mutually exclusive projects and independent projects? Be ale to draw a graph depicting which of
two mutually exclusive projects will be chosen (there is an example of this in the notes). Which decision tool is used
most often by financial managers? Which tool is the best from a theoretical approach? Explain.
CHAPTER 6 PROJECT INTERACTIONS AND APPENDIX 4
Calculations: Given a cash flow stream be able to calculate equivalent annual annuities. Be able to conduct a
sensitivity and scenario analysis. Be able to calculate the expected NPV of a project given the data using a decision
tree. Be able to calculate the value of a real option given the inputs (using the tree as done in the class notes). Be able
to use a decision tree to value a real option (like the example in the notes).
Most new projects have a positive correlation with existing projects in the firm, does this imply that a new project will
not reduce the corporate risk of the firm? Explain. If a new project has a positive correlation with the market, can it
help diversify the firm’s projects and reduce its market risk? What are three reasons that corporate as well as market
risk should be evaluated? Be able to analyze a decision tree and the outcomes it shows. Given a decision tree and its
outcomes; be able to calculate the expected NPV of a project using a decision tree. What is meant by sequential
decision making? What are Real Options. Explain how each of the following can be used to manage risk: Variable
vs. Fixed Costs, Pricing Strategy, Financial Leverage, and Sequential Investment. What are Real Options? How are
they similar to financial options? Be able to explain each of the following types of real options and provide an
example of each: Flexibility Option, Capacity Option, New Product Option and Timing options.
CHAPTER 12 FIRM VALUATION
Be able to explain, the free cash flow to equity model and free cash flow to the firm model. What are the key inputs in
each model and how are they calculated (cash flow, interest rates, growth) Be able to explain how the models are
different and how they are similar. Do the dividend discount model and FCFE model provide the same value of
equity (do the get the same answer)? How do you use the FCFF model to calculate the value of equity? Would the
value of equity found from the FCFF. Is value of equity form FCFF the same as you would get from the FCFE
model? How would you use each of the TWO models to estimate the value of a share of stock? Be able to compare
the traits of a high growth firm to a stable growth firm. What is the difference between a two stage and three stage
growth model. Think about how corporate responsibility relates to the firm valuation model (can you show that
corporate social responsibility increase firm value?).
PRACTICE PROBLEMS FOR MIDTERM (MOST OF THESE WERE TAKEN FROM PREVIOUS TESTS)
Test tip: Work the problems prior to looking at the answer. We will discuss any or all of the questions in class the
week prior to the test.
1. FOR EACH OF THE FOLLOWING STATEMENTS STATE WHETHER IT IS TRUE OR FALSE AND EXPLAIN YOUR CHOICE. (IF
IT IS TRUE SHOW HOW YOU KNOW IT IS TRUE , IF IT IS FALSE EXPLAIN WHAT WOULD MAKE IT TRUE OR WHY IT IS
FALSE).
a) A Firm can use stock price maximization as its objective since it is identical to assuming that shareholder wealth
is maximized.
False: They are only identical in certain circumstances- what are they???
b) To calculate the bottom up beta for the firm, first run a regression to get a levered beta, then use the debt ratio of
the firm to calculate the unlevered (bottom up) beta.
False: You do not need to run a regression to get a bottom up beta. The bottom up beta is a weighted average of
the unlevered beta's for industries that the firm does business in
c) “The lower the firm’s tax rate, the lower will be the firm’s WACC other things held constant.”
False: A lower tax rate will increase the (1-t) term in the WACC this causes a higher WACC.
d) “An increase in the interest rate used to discount a future cash flow will cause the present value of the cash flow to
increase.” False
e) “Using book values instead of market values to calculate the weight of each type of financing will likely
overestimate the impact of debt on the firm” True
f)
“When comparing two stocks a risk averse investor will prefer the stock with a higher coefficient of variation”
False
g) When used in making capital budgeting decisions, the NPV, IRR and PI will always rank two mutually exclusive
investments in the same order. FALSE
2) Explain the difference between firm value maximization and stock price maximization. When will both goals be
the same? Explain in detail. Your answer should include: An explanation of any differences between the two and
examples other than the agency relationship
3) a) If $100 is placed in an account that earns a nominal (yearly) 4% compounded quarterly what will it be worth in
5 years?
100(1.01)20 = 122.019
b) What is the effective annual rate in the question in part a)?
(1+(.04/4)4-1 = .0406 or 4.06%
c) What is the current price of an annuity which pays a you $5000 every six months for a period of 10 years,
assume that the current nominal annual interest rate is 8%.
Since the annul interest rate is 8% it implies that we earn 4% every 6 months
PMT = 5,000 N=20, I = 4, FV = 0 PV = ? 67,951.63
You could also solve this finding the PVIFA4%,20
4) A) Your employer has agreed to make 20 yearly payments of $2000 each into a trust account to fund your early
retirement. The first payment will be made today, the last payment will be made 20 years from now at the
beginning of the year. Starting at the beginning of the 21st year you will receive an annuity payment for each of
the next ten years. During all periods the funds will be invested at a nominal rate of 8%, compounded
semiannually. What is the size of your annuity payment?
Since the first payment is made today it implies an annuity due. Since interest compounds semi annually we need
to find the effective annual rate which is 1.042 = 8.16%
PMT = ? = $13,984.29
B) Daffy Trump, Donald’s younger brother, just won the lottery. Daffy can earn a 10% return on any current
deposits. He has a choice between receiving $1.5 Million each year for the next 20 years with the first payment
being made today and $13.5 Million in one lump sum today. Daffy has ask for your advice concerning which
option he should choose. Explain in detail why and how you make your recommendation.
Find the PV of the annuity due payments and compare to the cash value today.
PMT = 1.5M, I = 10, N = 20, FV = 0, PV = ? = $14,047,380.14 (Beg mode)
PV = 1.5M (PVIFA20,10%)
Since the PV of the annuity payments is larger you will want to take the annuity payments. In other words, if you
take the cash and earn 10%, you could not receive 1.5 Million each year (you would receive 1,441,549.94 each
year)
5) You are contributing money to an investment account so that you can purchase a house in five years. You plan to
contribute six payments of $3,000 a year -- the first payment will be made today (t = 0), and the final payment will be
made five years from now (t = 5). If you earn 11% each year in your investment account, how much money will you
have in the account five years from now? $23,738
FV = 23,738
6) An investment pays $100 every six months (semiannually) over the next 2.5 years. interest, however, is
compounded quarterly at a nominal yearly rate of 8%. What is the future value of the investment after 2.5 years?
What is the PV of the payments over the 2.5 years?
FV = 542.07 PV = 444.68
7) Read the following portion of an article taken from the October 3, 2006 Wall Street Journal and answer the
questions that follows. (The questions are continued on the next page to give you plenty of room). (This was on the
fall 2006 test)
S&P Cuts Harrah's Rating to Junk By MARINE COLE
October 3, 2006; Page C6
“Standard & Poor's Ratings Services cut the rating of Harrah's Entertainment Inc. to junk status after the
company confirmed it is in leveraged-buyout talks with private-equity firms. The ratings firm lowered the Las
Vegas casino operator's rating to BB+, the highest rung on the speculative-grade ladder, from BBB- and warned
that another downgrade could be forthcoming. The decision reflects "Harrah's announcement that it had
received a proposal from Apollo Management and Texas Pacific Group to acquire all of Harrah's outstanding
common stock for $81 per share in cash, or about $15 billion," S&P said in a press release. If a transaction were
agreed upon, leverage at the company would increase, which would likely result in further rating cuts, the creditratings firm said. Harrah's already has about $10.8 billion of reported debt outstanding as of June 30, according
to S&P. But the firm added that even if a deal doesn't go through, "the company will be faced with increasing
shareholder pressures for some form of leveraging transaction over the near term, given the company's stockprice appreciation since the public confirmation by Harrah's of the acquisition proposal." Harrah's stock ended
the day up 14%, or $9.25, to $75.68 in 4 p.m. New York Stock Exchange composite trading.”
Answers discussed in class.
7a) The goal of financial management is to increase the value of the firm, often stock price maximization is used as
the vehicle to accomplish this goal. However, in some cases an increase in the stock price may not represent an
increase in the value of the firm to all stakeholders. Explain whether you believe that the above situation represents a
case where a stock price increase did not represent an increase in the value of the firm in the eyes of the bondholders.
Explain your choice in detail, including an explanation of the impact of the ratings change and stock price increase on
an individual who held bonds at the time of the ratings decline.
7b) Later in the article it was reported that the company has 6.5% coupon bonds due in 2016 which fell dramatically
in price following the ratings decline. Given the approximate price quoted in the article the bonds would have a yield
to maturity of approximately 8.45%. Assuming that the current long term Treasury yield is between 4.75 and 5% does
this seem like the correct yield on the bonds based on the opportunity cost of capital represented by the new rating for
the bond? Make sure to explain the concept of the opportunity cost of capital in your answer. (In other words, what is
the cost of debt for the firm following the rating change based on the yield spreads given in class? Does your answer
agree with the information in the article? Relate your answer to the concept of the opportunity cost of capital).
7c) Explain what is meant by the principal agent problem. Given the information that you have, would you
characterize the above situation as an example of the principal agent problem? Explain in detail why you would or
would not characterize it as an example of the principal agent problem (or what information you need to be certain
that this represented a principal agent problem.)
8) The large electric utility firm TXU has recently agreed to be acquired by a private equity firm for $32 billion. The
deal includes the assumption of over $13 billion in debt by the new firms. On Feb 27 the Wall Street Journal
published the follow account of the impact of the buyout on the firms debt. Read the following portion of an article
from the Wall Street Journal and answer the questions that follow. Three are 3 questions relating to the article on the
next two pages (You do not need to use all of the space – I just wanted to make sure you had enough room)
Answers discussed in class
TXU Buyout Proposal's Mixed Effect
Bondholders Weigh Units Differently; Fitch Downgrade
By CYNTHIA KOONS
February 27, 2007; Page C8
The proposed buyout of TXU Corp. meant different things to different bondholders as it became clear the borrowing
needed to finance the proposed deal would disproportionately hit some business units more than others.
Investors saw parent TXU Corp. and its subsidiary TXU Energy as bearing the brunt of the added leverage, with the
TXU Electric Delivery unit insulated from the burden of new debt.
In its statement, the company said "the funding of the transaction will not result in new debt incurred at the regulated
utility business," referring to TXU Electric Delivery.
The bonds traded accordingly.
TXU Corp.'s bonds took the hardest beating, with risk premiums on its 5.55% notes due 2014 rising 0.69 percentage
point to 2.26 percentage points over Treasurys. Those notes had traded as high as 2.50 percentage points.
TXU Energy's 7% notes due 2013, meanwhile, rose 0.41 percentage point to trade at a risk premium of 1.56
percentage points, according to MarketAxess, an online bond- trading platform.
Moody's Investors Service said TXU and TXU Energy could be at the greatest risk for a multinotch downgrade as a
result of the buyout. TXU Electric Delivery, however, is the entity likely to experience the least amount of negative
ratings repercussions, because of expectation the unit would be divested or sold, the rater said.
TXU Electric Delivery's risk premiums rose just 0.16 percentage point to 0.88 percentage point over Treasurys.
"That's the most stable part of the business. Regulated operations from the business-risk standpoint are regarded as
very positive in general," said Dmitry Baron, director of research at Aladdin Capital. While possibly helping TXU pay
down debt, a divesture of this unit would also mean the loss of a stable source of cash flow.
Standard & Poor's warned that TXU Corp's corporate credit rating of triple-B-minus, the lowest rung in the
investment-grade ladder, could be downgraded into junk territory. Fitch Ratings went a step further and downgraded
its issuer default rating on TXU to double-B-plus, or junk, from triple-B-minus.
TXU agreed to be acquired by a private-equity consortium led by Kohlberg Kravis Roberts & Co. and Texas Pacific
Group for nearly $32 billion and assumption of nearly $13 billion in debt.
a) Given the approximate yield spread quoted in the article the bonds for TXU Corp (just that division by itself)
would have a yield to maturity of approximately 7 to 7.25% (assuming that the current long term Treasury yield
is between 4.75 and 5%) Does this seem like the correct yield on the bonds based on the opportunity cost of
capital represented by the new rating for the bonds? Make sure to explain the concept of the opportunity cost of
capital in your answer. (In other words, what is the cost of debt for TXU Corp the rating change based on the
yield spreads given in class? Does your answer agree with the information in the article? Relate your answer to
the concept of the opportunity cost of capital).
b) In the buyout negotiations, the private equity consortium agreed to scale down TXU’s plan to build 11 new coal
powered electric generating plants and only build 3 new plants. Your boss, a portfolio manager who has invested
in TXU stock, is afraid that the increase in the cost of capital associated with the increased debt load could cause a
substantial decrease in the value of the new power plants (their NPV) and also in the value of the firm. Use the
bond plus risk premium approach to calculating the cost of equity to explain the general impact of the buyout on
the firm’s cost of equity and also on its cost of capital (you must also explain the bond plus risk premium
approach and the intuition behind it to get full credit)
c) You then point out to your boss that using the risk premium for TXU Corp debt in your calculation of the cost of
capital might overstate the impact of the increased debt load on the value of the new electric generating plants
because the plants should be valued based on the project cost of capital. Use the information in the article to
explain why it is important to look at the project cost of capital instead of the weighted average cost of capital for
the entire firm.
9) Assume that you have the choice of purchasing one of the following securities (you do not have the option of
purchasing both). The table below lists the return for each of the securities for the last five years.
Year
1
2
3
4
5
Expect Ret
Standard Deviation
Asset A
9.9%
15.4
22
11
16.5
14.96%
4.832
Asset B
18.15%
12.1
16.94
24.2
10.89
16.46%
5.316
a) Assuming that the distribution of returns is normally distributed, and using one standard deviation within
what range will asset A’s returns fall? Explain this result (what does it mean?)
14.96 + 4.832 = 19.79 to 14.96 - 4.832 = 10.128
b) Calculate the coefficient of variation for each stock, and use your answer to explain which stock you would rather
own.
CofV = 4.832/14.96 = .323
5.316/16.46 = .323 The coefficient of variation is the same. This implies that you are
getting the same amount of return for each unit of risk you accept. Therefore you would be indifferent using the risk
as a guide. Since they are the same with respect to risk, look at expected return. Take stock B since it would have the
higher payout.
10) Below is the regression output of the monthly returns on two different firms Use the information relating to the
SUMMARY OUTPUT
Cisco
Regression Statistics
R Square
Observations
0.24397973
59
Intercept
S&P500
Coefficients Standard Error
t Stat
0.03358372
0.01311694 2.56033182
1.28470379 0.299540417 4.28891635
firm and the market as a whole to answer the questions that follow.
a) Calculate Jensen’s Alpha
(1-B)kRF = 1-1.28(.5%) = -.28(.5%) = -.14% Since we subtract this from the intercept we know that Jensen’s alpha
will be positive.
b) What is the beta and how confident are you concerning the estimate of beta?
Beta = 1.28 With a high t-statistic implying that we are very confident that Beta does not equal zero. THe standar4d
error is relatively low (The coefficient will be greater than one 68% of the time)
c) How much of the returns of Springt are determined by market risk?
24% of the output is explained by market risk (from the R- Squared).
See if you can answer the same questions for the output below
SUMMARY
Sprint
OUTPUT
Regression
Statistics
RSquare
0.13434788
d
5
Squared
Coefficient Standard Error
t Stat
Intercept
0.01607810
0.0086801 1.85227
Square
s
5
8
8
S&P500
0.58956632
0.1982218
2.97427
7
5
5
(1-B)kRF = 1-.5898(.5%) = -.28(.5%) = -.205% 1.6% - .205 % = 1.395%
Beta = .58 With a high t-statistic implying that we are very confident that Beta does not equal zero. The standard
error is relatively low
24% of the output is explained by market risk (from the R- Squared
10) Use the following information to answer the questions that follow:
You have been assigned the task of estimating the WACC for ABC Corporation. It currently has the following capital
structure:70% Debt, 30% Common Equity
It currently has a debt rating of A justifying a 1% yield spread compared to the risk free rate (Assume that the current
risk free rate is 5% and the long term market risk premium in the CAPM is 4.82% and the firm faces a marginal tax
rate of 35%.
You have ran a regression on the firms stock returns against the S&P 500 and estimated its Beta to be 1.4
a) Calculate the firms weighted average cost of capital assuming that all common equity comes from retained
earnings. (use the CAPM find the cost of new common equity)
b) Two alternatives to using the discounted cash flow approach to calculate the cost of common equity are the bond
plus risk premium approach and a discounted cash flow approach. Explain the intuition behind each of the
approaches. For the bond plus risk premium approach, your answer should include an explanation of what value
is used for the cost of debt in the applying the approach and why.
11) a) Briefly describe the process of sensitivity analysis, include in your explanation a detailed description of
1) How to conduct a sensitivity analysis, 2) What type of risk it measures, and 3) The problems associated with the
analysis (This question could also be asked for scenario analysis or Monte Carlo analysis)
12) Use the information that follows to answer the questions concerning risk analysis in capital budgeting.
The following table summarizes a sensitivity analysis that was conducted for a firms cash flow estimation.
Change in
NPV following a change in
variable
Sales
Operating Cost
Cost of Capital
-20%
- 200,000
2,050,000
1,650,000
-10%
325,000
1,450,000
1,250,000
0
850,000
850,000
850,000
10%
1,375,000
250,000
450,000
20%
1,900,000
-350,000
50,000
a) Which variable should the company be most concerned with forecasting? Explain your choice. The firm should
be most concerned with the operating costs since the NPV varies by more when costs change than it does when the
other inputs change. Operating Cost
b) Briefly explain the problems associated with the use of sensitivity analysis and whether Scenario analysis
accounts for the problems
13) The scenario analysis for a project under consideration by your firm is shown below. Assume that the firm has an
average coefficient of variation for its projects between 0.3 and 0.5, calculate the coefficient of variation for the
project given and discuss whether it would be necessary to adjust the firms WACC when considering this project.
Prob NPV
Worst Case
0.25
9,000
Most likely case
0.5
10,500
Best Case
0.25
12,000
Expected NPV
10,500
Standard Deviation
1060.666
Coefficient of variation = 1060.666/10500 = .11 it is less risky than the average project for the firm therefore you
can decrease the hurdle rate for the project.
14) Look at the decision tree example done in the notes, be able to use a decision tree in a similar fashion to value a
real option.
15)
Testing Inc. is considering two mutually exclusive projects given below. Use the information to answer the
questions that follow.
Project A
Project B
Initial Cost
$500
$800
Year 1
$200
$300
Year 2
$200
$300
Year 3
$200
$300
IRR
9.70
6.13
a) What is the payback period for each project? Proj A 2.5 years Project B 2.667 years
b) Assuming that the discount rate is 8% find the discounted payback period of each project Proj A 2.9029 years
Proj B no payback
c) Assuming that the discount rate is 8% find the NPV of each project. Proj A 15.419 Proj B -26.87
d) Assuming that the discount rate is 8% what is the approximate modified internal rate of return for project A?
9.09%
e) Based upon you answers in a through d which project would you choose at the given level of interest rates?
f) Since the two projects are mutually exclusive we can only choose one of them. If the current level of interest
rates changes it is possible that you may not still prefer the project you chose in part d). Draw a graph (rate
vs. NPV) that shows which project will be chosen at different levels of interest rates and explain in words
when each project will be chosen.
g) When deciding whether or not to undertake an independent project with conventional cash flows, IRR, NPV
and PI provide the accept reject decision, explain in detail why this occurs.
h) Briefly explain how you could perform sensitivity analysis on the results above and why you might be
interested in doing one
i) Briefly explain how a scenario analysis might differ
16)
You have been ask to evaluate a new project for Bulldog Enterprises, a screen printer that produces collegiate
memorabilia (t-shirts, sweat shirts etc..) The firm is currently considering upgrading its equipment with a system that
includes new computerized graphics. The owners have produced the following estimate of the cash flows generated
by the project over the next five years. At the end of five years it expects to sell off the machinery for $50,000.
Initial Cost
250,000
Year 1
58,000
Year 2
55,000
Year 3
56,000
Year 4
60,000
Year 5
64,000
a) The firm believes that the cost of capital will be 10%, what is the NPV of the project?
The NPV at 10% is $2021.2852
b) The firm is not confident about its ability to forecast the cash flows, salvage value, and the WACC. Conduct a
sensitivity analysis for the firm assuming that each of the three variables might be 10% above each years
estimate or 10% below each years estimate in the case listed above. Interpret your results in detail explaining
what the sensitivity analysis tells the firm.
NPV when there is a change in
Cash Flow
Salvage Value
-10% -20,076.2367 -1083.3214
0
2,021.2852
2,021.2852
+10% 24,118.8071
5,125.8918
Cost of Capital
9,343.3744
2,021.2852
-4,984.4867
Looking at the results it is easy to see that changes in the cash flow have the largest impact on the NPV of the
project. This implies that the firm will be most concerned with its ability to forecast future cash flows.
c) Conduct a scenario analysis using the following assumptions. The best case has a 25% probability. In the best
case all three variables change by 10% in a manner that increases the NPV. Likewise the worst case scenario has
a 25% probability and would consist of all three variables changing by 10% in a manner that decreases the NPV.
The most likely case was found in part a) and has a 50% probability. Interpret your results. Find the expected
NPV and standard deviation of the NPV and interpret your results.
Worst Case
Base Case
Best Case
Expected return =
Standard Deviation =
-29,486.038
2,021.285
35,227.712
2,446.061
22,883.71
The project has an expected return of 2,446.061 and a standard deviation of 22,883.71. The large standard
deviation implies that the project is risky. A one standard deviation confidence interval would produce a range of
-20,437.649 to 25,329.771 given these results it is possible that the NPV of the project will be negative. Given the
small NPV and the range of possible negative outcomes this project is much riskier than the original analysis
would have indicated.
NON COMPREHENSIVE PRACTICE PROBLEMS
1. STATE WHETHER EACH OF THE FOLLOWING STATEMENTS IS TRUE OR FALSE AND EXPLAIN YOUR CHOICE. (IF IT IS
TRUE SHOW HOW YOU KNOW IT IS TRUE, IF IT IS FALSE EXPLAIN WHAT WOULD MAKE IT TRUE OR WHY IT IS FALSE).
a) The optimal capital structure will occur at the point where the firm maximizes its earnings per share. False,
The optimal capital structure is the point where the firm minimizes the weighted average cost of capital, this
should maximize the value of the firm. However it does not always coincide with the point where EPS is
maximized.
b) According to the original Modigilani and Miller model the optimal capital structure occurs when the WACC
is minimized, False, The original model claims that the capital structure decision is irrelevant.
c) A firm with a higher interest coverage ratio will also have a higher before tax cost of debt. False, A higher
interest coverage ratio signals the firm is capable of paying its interest expense so it would have a lower cost
of debt.
d) Real options occur when managers have the opportunity to change the cash flows of a project by responding
to changing conditions after the project has been implemented. True
e) A firm with a higher interest coverage ratio will also have a higher before tax cost of debt. False
2) Briefly explain the concepts discussed in class relating to a “trade off theory” of capital structure. A complete
answer will include: (10 points)
a) A description of how it relates to the original Modigilani and Miller Model
b) A description of the theory itself (what is the “tradeoff” how does it relate to capital structure...)
d) The conclusions of the theory concerning capital structure.
See notes for description of each
3) Use the following analysis of the capital structure for Reebok to answer the questions that follow.
Current
Optimal Change
Debt Ratio
4.42%
60.00%
55.58%
Beta for the stock
1.95
3.69
1.74
Cost of equity
18.61%
28.16%
9.56%
Bond Rating
AB+
After Tax Cost of Debt 5.92%
6.87%
0.95%
WACC
18.04%
15.38%
-2.66%
Firm Value (no growth) 3,343 million 3,921 million 578 Million
Stock Price
39.50
46.64
7.14
Average Industry debt ratios
Textiles 27% Clothing Manufactures 29.18% Consumer Products 44.7%
a) Given the information above what concerns would you have about Reebok moving to its optimal debt ratio?
(Assuming the numbers are correct, why might it not move toward its “optimal debt ratio”?)
a) Under what conditions would think that Reebok should move quickly toward its optimal capital structure?
(you probably do not have all the information you need to decide that they should or should not move quickly,
what issues would you look at to make that decision?)
The firm would be more likely to move quickly if it was the target for a takeover, one indication of this would be a
large cash surplus. Just the fact that they have a low debt ratio now makes them attractive since an acquiring
firm would not be saddled with a large amount of debt.
4) Answer the following questions concerning dividend policy
a) Briefly explain the Modigilani and Miller model concerning the irrelevance of dividend policy. Include an
explanation of the assumptions necessary for Modigilani and Miller to reach their conclusions and explain the role
played by those assumptions.
5) Be able to estimate the cost of capital at various debt levels similar to HW 3. In other words, be able to perform
the calculations that the excel spreadsheet performed this includes (example problem 6 below):
a. Levering and Unlevering beta
b. Calculating the cost of equity
c. Calculating the Value of the firm and the $ value of debt
d. Finding the interest coverage ratio based on an assumed rate, and confirming your assumption
e. Using the spread information to find a cost of debt
f. Calculating the cost of capital.
6) The firm you are working for is considering changing its capital structure. The CFO believe that your firm could
decrease its cost of capital by increasing its use of debt. The firm currently has 20% debt and 80% equity and has
been stable at that level for the last 10 years. The CFO has asked you analyze the impact of increasing the use of debt
to a point where the firm uses 25% debt and 85% equity. Use the information below to answer the following
questions for the CFO. (Bond ratings and spreads are given on your equation sheet assume the firm is financing based
on a 10 year project -- use the spread on the 10 yr bond)
Current Market value of the firm = market value of debt + market value of equity = $8 billion
EBIT = $950 Million Current Debt Rating = AA
Current Cost of Debt = 5.05%
Current Risk Free Rate = 3.75% Regression Beta = 1.51 Marginal Tax Rate for Firm = 35%
Current Market Risk Premium = 4.82% BL = BU(1+(1-t)(D/E))
a) Calculate the cost of equity at the new level of debt and equity
b) Calculate the cost of debt at the new level of debt and equity (what is the new rating?)
c) Calculate the new cost of capital for the firm.
7) Explain the difference between choosing to use FCFE and FCFF to value the firm. For each explain the
appropriate rate to use as the cost of capital when selecting the respective cash flow
8) Explain the difference between a two stage and three stage growth model for firm valuation
9) What are clientele effects and how do they impact the choice of dividend policy? What types of firms are most
likely to be impacted by clientele effects?
10) Use the information below to answer the questions that follow concerning capital structure decisions. Assume
that the firm represented uses only debt and common equity for financing. Its total capital budget is $20 Million.
VALUE OF
DEBT
(Millions)
0
2
4
6
8
10
12
Kd
(%)
8.0
8.3
9.0
10.0
12.0
15.0
Ks
(%)
12%
12.2
12.6
13.2
14.0
15.2
16.8
VALUE OF
STOCK
(Millions)
20.00
18.89
17.47
15.73
13.71
11.05
7.85
VALUE OF
THE FIRM
(Millions)
20.00
20.885
21.467
21.727
21.714
21.053
19.857
STOCK
PRICE
($)
20.00
20.89
21.47
21.73
21.71
21.05
19.86
WACC
(%)
12
11.5
11.2
11.0
11.1
11.4
12.1
EPS
($)
2.40
2.55
2.70
2.87
3.04
3.20
3.34
a) If the firm above currently has $4 million in debt is it operating at its “optimal” capital structure according to the
theories discussed in class? List and explain TWO reasons that the firm above may not be using the amount of debt
that could be termed its “optimal capital structure.” (We listed many reasons in class that the firm may not move
toward its optimal capital structure what are two of them)
b) Use the numbers above to explain the ideas of bankruptcy costs and how they relate to the concept of an optimal
capital structure
COMPREHENSIVE PORTION
The comprehensive portion will consist of approximately 75 points, the questions will be very similar to the questions
below. For the numeric problems a check solution has been provided. Since the problems will be very similar to the
question below, the complete solution is up to you, however you can verify that you have done it correctly by looking
at the check solution where provided.
a) Briefly explain what is meant by the agency problem (or the principal /agent problem) and how it relates to the
financial management of a firm.
b) Explain the difference between firm value maximization and stock price maximization. When will both goals
be the same? Explain in detail. Your answer should include: An explanation of any differences between the
two and examples other than the agency relationship.
Answer each of the following question concerning the time value of money
a) Your brother deposited $1,000 in a savings account that pays 8 % interest compounded quarterly, planning to
use it to finish his last year in college. Eighteen months later he decided to go to the Rocky Mountains to
become a ski instructor rather than continue in school, so he closed the account. How much money will he
receive?
b) You have the opportunity to buy a perpetuity which pays $1,000 annually. Your required rate of return on
this investment is 15%. Find the Present value of the perpetuity.
c) If a 5 year annuity has a present value of $1,000 and if the interest rate is 10%, what is the amount of each
annuity payment?
d) You are considering buying a new car. The sticker price is $15,000 and you have $2,000 to put toward a
down payment. If you can negotiate a nominal annual interest rate of 12% and you wish to pay for the car
monthly over a 5-year period, what are your monthly car payments?
2a) $1,126.16 2b) $6,666.66 2c) $263.797 2d) $289.177
Below is regression output for Intel Corporation. The data encompasses five years of monthly data ending in May of
2002. Use the output to answer the questions that follow:
SUMMARY OUTPUT
Regression Statistics
R Square
0.33966256
Observations
59
Intercept
S&P
Coefficients
Standard Error
0.006616273 0.015842115
1.70999419 0.315803056
t Stat
0.4176383
5.4147487
This implies a line of kIntel = .006616273 + 1.70999419kS&P500 + 
Assume: That the average annual risk free rate for the period is 6%; Intel’s current Debt to Equity Ratio is
approximately 4% and has been either lower or in the same range for the last five years. Assume that the marginal tax
rate for the firm is 40%
a) What is the estimate for beta according to the output and how confident are you in the estimate? Include in your
answer an explanation of beta and what it measures and evidence from the output to support your answer.
b) Is your estimate of beta in part a) a good approximation of an unlevered beta for Intel? Explain in detail what an
unlevereed beta is and why your answer is or is not an unlevered beta.
4) For each of the following statements decide whether it is true or false and explain your choice:
a) The revenue and cost figures shown on a standard income statement are a good representation of the actual cash
inflows and outflows of a project. Therefore the revenue and cost figures should be used for financial decisions
such as capital budgeting. FALSE
b) The present value of a future sum decreases as either the discount rate or number of periods increases. TRUE
c) The portfolio return is a weighted average of realized security returns and likewise the portfolio standard deviation
is a weighted average of the standard deviations of the assets in the portfolio. FALSE
For all equations: FV = Future Value, PV = Present Value, PMT = Payment, r = interest rate (which rate depends
upon the equation), n = number of periods, PMT = payment, CF = cash flow, D = Dividend, P = Price
FV  PV(1  r) n  PV(FVIF r,n )
FVIFi,n  (1  r) n
FV
PV 
(1  r) n
 FV(PVIF r,n )
PVIF r,n 
1
(1  r) n
n
FVannuity  PMT  PMT(1  r)  PMT(1  r) 2      PMT(1  r) n -1  PMT
 (1  r)
n -t
 PMT(FVIFA
r,n )
t 1
n
FVannuitydue  (FVannuity )(1  r)  [PMT
 (1  r)
n -t
](1  r)  PMT(FVIFA
r, n )(1 
FVIFA r,n  [(1  r) n  1]/r  (FVIF r,n  1)/r
r)
t 1
n

PMT
PMT
PMT
PMT
1
PVannuity 


  
 PMT
 PMT(PVIFA
(1  r) (1  r) 2 (1  r) 3
(1  r) n
(1

r) n
t 1
n

1 
PVannuitydue  (PVannuity )(1  r)  PMT
 (1  r)  PMT(PVIFA
(1

r) n 
t 1


PVperpituity 
PMT
r
r, n )(1 
r)
r, n )
PVIFA r,n  [1 - [1/(1  r) n ]]/i  [1 - PVIF r.n ]/r
m
r


effective annual rate  1  nom   1
m 

Cap Gains Yield  % change in Price 
End of Period Price - Begining of Period Price
Begining of Period Price
Constant Growth Annuity : Cash Flow 0 (1  g constant )  Cash Flow 1
r - g constant
r - g constant
n
Amount Received - Amount Invested
rate of return 
Amount Invested
standard deviation   
n
 (k
i 1
i
variance   2   (k i - k̂) 2 Pi
i 1
coefficien t of variantio n 
- k̂) 2 Pi
security market line (SML) ri  rRF  (rM - rRF ) i
beta =

k̂

s tan dard deviation
return
Cov X ,Y
VarX
NOPAT = EBIT(1- tax rate)
Free Cash Flow to Firm = NOPAT + Depreciation and Amortization - Changes in NWC – New capital expenditure
Free Cash Flow to Common Equity (assuming no preferred stock) = Net Income + Depreciation and Ammortization
– Change in NWC – New Capital Expenditure – Principal repayments + new debt issued
WACC  Wd rd (1  T)  Wps rps  We re Wi is the weight in each type of financing ri is the cost of type i
rps  D/P w/o flotation costs
rps  D/[P(1 - F)] with flotation costs
rd = rRF+ yield spread form bond rating or YTM on existing debt
re  D1/P  g w/o flotation costs re  D1/[P(1 - f)]  g with flotation costs
re  rd  Risk Premium
re  rRF  (rM - rRF ) i
BL =Bu(1+(1-t)(D/E))
n
CFt
CFt
IRR : 0  
solve for IRR
t
(1

IRR) t
(1

r
)
t 0
t 0
MIRR : PV costs  PV terminal value or PV cash outflows  PV of (The future vlaue of cash outflows)
n
NPV  
n
n
MIRR :

t 0
Cash out Flow t
(1  r ) t
 Cash in Flow (1  r)
n t
t

t 1
(1  MIRR) n
PI  { CFt /[(1  r ) t ] I 0 1   NPVI 0 
MPI  1  NPV/(I 0  PV of future commitment s)
DATA AND ACCOUNTING RATIOS (FYI) ARE ON THE OTHER SIDE OF THE SHEET.
Historical Market Risk Premiums
Stock – TBill
Stock - TBond
Arith
Geo
Arith
Geo
1928-2003
7.92%
5.99%
6.54%
4.82%
1962-2003
6.09%
4.85%
4.70%
3.82%
1992-2003
8.43%
6.68%
4.87%
3.57%
Historical Average Yield Spreads Based on Bond Rating
7/14/2010
Rating
1 yr
2 yr
3 yr
5 yr
7 yr
10 yr
30 yr
Aaa/AAA
30
35
75
25
80
55
80
Aa1/AA+
40
40
85
30
85
60
85
Aa2/AA
45
45
90
40
90
65
90
Aa3/AA50
50
95
45
95
70
95
A1/A+
55
55
100
60
100
85
115
A2/A
75
65
105
70
105
90
125
A3/A105
95
110
85
115
100
135
Baa1/BBB+
125
125
150
145
195
170
190
Baa2/BBB
175
155
175
160
200
195
210
Baa3/BBB200
245
285
250
275
255
270
Ba1/BB+
450
400
475
440
425
400
375
Ba2/BB
510
450
525
525
450
450
450
Ba3/BB535
525
550
550
475
475
475
B1/B+
625
600
650
600
550
500
500
B2/B
650
650
700
750
625
575
525
B3/B675
825
725
775
700
625
550
Caa/CCC+
750
850
850
850
850
800
775
US Treasury Yield
0.27
0.62
1.02
1.82
2.49
3.07
4.03
BondsOnline (http://www.bondsonline.com); FT Interactive Data
Current Ratio =
Cash Ratio=
Current Assets
Current Liabilities
Quick Ratio =
(Acid test Ratio)
Cash
net working capital = Net Working Capital
Debt to = Total Debt
Current Liabilities to total assets
Total Assets Equity Total Equity
Interval Measure = Current Assets
Average Daily Operating Costs
Total Debt Ratio =
Long-term =
Long-Term Debt Times Interest =
EBIT
Debt Ratio Long-term Debt + Total Equity
Earned Interest
Days’ Sales in =
365 days
Inventory Inventory Turnover Turnover
Days' Sales
=
in Receivables
Current Assets - Inventory Equity = Total Assets
Current Liabilities
Multiplier Total Equity
Total Assets - Total Equity
Total Assets
Cash Coverage
= EBIT + Depreciation
Interest
Inventory = Sales
Receivables =
Sales
Inventory
Turnover Accounts Receivable
365 Days
Days’ Sales =
Receivables
NWC = Sales
Receivables Turnover
Outstanding Average Sales per Day
Turnover NWC
Fixed Assets = Sales
Turnover
Net Fixed Assets
Return on = Net Income
Assets
Total Assets
Total Asset = Sales
Turnover Total Assets
Return on = Net Income
Equity
Total Equity
Profit = Net Income Market = Market Value Per Share
Margin
Sales
To Book Book Value Per Share
Earnings Per = Net Income
Share
# Shares outstanding
PE Ratio = Price per share
EPS
DuPont Identity ROE = Profit Margin x Total Asset Turnover x Equity Multiplier
internal growth rate = (ROA)b/[1-(ROA)b] sustainable growth rate = (ROE)b/[1-(ROE)b] b=retention rate