Chapter 9—Cost of Capital and Project Risk
MULTIPLE CHOICE
1. Operating and financial leverage may exist for firms. Which of the following statements is accurate
concerning leverage?
a.
The presence of common equity creates financial leverage.
b.
The presence of high levels of variable costs creates operating leverage.
c.
The presence of higher sales prices creates financial leverage.
d.
The presence of debt creates financial leverage.
e.
None of the above is accurate concerning leverage.
2. Nob-Orrow Inc. is considering an investment in a project that is similar in risk to its existing projects.
The firm makes no use of debt and is entirely financed by common stock with a beta of b. The
expected return on the market portfolio is rm percent and the risk-free rate is rf percent. The required
rate of return on this project is:
a.
ans1%
b.
ans2%
c.
ans3%
d.
rm%
e.
none of the above
3. If a firm is considering purchasing an asset whose beta is greater than the current beta of the firm’s
other assets, the financial manager:
a.
Should automatically reject this asset since its beta is larger
b.
Should give this asset more weight when calculating the firm’s asset portfolio beta since
this asset has a greater beta
c.
Should consider using a discount rate greater than the firm’s current cost of capital to
evaluate the possible investment and adjust for the greater risk
d.
Should use only the cost of equity rather than the cost of capital as a discount rate since
the beta only impacts the equity cost
e.
Should use the current cost of capital for the firm as the discount rate since a single asset
has no impact on the cost of capital
4. A firm with greater operating leverage:
a.
Shows a lower percentage change in earnings for a given percentage change in sales.
b.
Shows a higher percentage change in earnings for a given percentage change in sales.
c.
Tends to make greater use of variable costs in its cost structure.
d.
Will have greater sales than otherwise identical firms.
e.
None of the above
5. WACKO Ltd. has $d million in debt, equity of $e million, an after-tax cost of debt of rd percent, a cost
of equity of re percent, and a tax rate of t percent. The firm’s weighted average cost of capital (WACC)
is
a.
ans1%
b.
ans2%
c.
ans3%
d.
ans4%
e.
none of the above
6. Calculate the required return on a stock that just paid a $div dividend, has a current price of $price, and
a permanent growth rate of g percent:
a.
ans1%
b.
ans2%
c.
ans3%
d.
g.00%
e.
none of the above
7. Your firm has annual fixed costs of $fc, a selling price of $s per widget, variable costs of $vc per
widget, and it annually allocates $adm to administrative overhead for reporting purposes. Calculate the
break-even point.
a.
ans widget
b.
ans1 widgets
c.
adm widgets
d.
$ans1
e.
$adm
8. Sensitivity analysis:
a.
Examines how NPV changes as one variable is modified from a base-case.
b.
Examines how NPV changes as all variables are modified together.
c.
Examines how NPV changes as input variables are drawn from a range of potential values.
d.
All of the above.
e.
None of the above.
9. All of the following are examples of real options facing corporations EXCEPT:
a.
Expansion options
b.
Abandonment options
c.
Follow-on investment options
d.
Executive stock options
e.
Flexibility options
10. Your firm has issued nb bonds with a market price of $pb per bond. The firm also has Ns common
shares outstanding at a price of $Ps per share. If the common shares will pay a dividend of $div at the
end of the year and thereafter dividends will grow at a rate of g percent. If the after-tax yield on the
firm’s bonds is rd%, what is the firm’s weighted average cost of capital?
a.
ans1%
b.
re%
c.
ans3%
d.
ans4%
e.
none of the above
11. Requiring that all projects with risk comparable to that of the firm as a whole earn at least the
__________ means that firms will only invest in projects that have positive NPVs.
a.
Operational efficiency
b.
Cost of debt
c.
Cost of equity
d.
WACC
e.
All of the above
12. When managers use the capital asset pricing model (CAPM) to determine the discount rate for an
investment project, they must know __________.
a.
the project or asset beta
b.
the risk-free rate
c.
the expected risk premium on the market portfolio
d.
a and c only
e.
all of the above
13. The capital asset pricing model (CAPM) states that the required return on any asset is directly linked to
the asset’s __________.
a.
leverage
b.
WACC
c.
contribution margin
d.
beta
e.
risk-adjusted discount rate
14. Which of the following is a competitive advantage for a firm?
a.
superior engineering
b.
superior R & D
c.
low-cost manufacturing process
d.
unique marketing programs
e.
all of the above
15. Identifying a(n) __________ is tantamount to identifying future points at which it may be possible for
managers to create and sustain competitive advantage.
a.
asset beta
b.
real option
c.
debt beta
d.
pure play
e.
project beta
16. Ideally, weights in the WACC formula should be determined using
a.
market value of equity and market value of debt
b.
book value of equity and market value of debt
c.
market value of equity and book value of debt
d.
book value of equity and book value of debt
17. If the firm applies its WACC to all projects, it will tend to accept some negative–NPV projects that are
a.
of shorter lifetime than the firm’s existing operations
b.
of longer lifetime than the firm’s existing operations
c.
riskier than the firm’s existing operations
d.
Safer than the firm’s existing operations
e.
none of the above
18. Two firms have the same asset beta but different equity betas. The direct cause is likely:
a.
The importance of variable costs varies across these firms
b.
The firms have different proportions of debt relative to equity
c.
One firm’s sales are more cyclical than the other
d.
All of the above
e.
None of the above
19. Looking at all three different approaches for estimating the expected market risk premium, the
consensus is that
a.
the expected premium is in line with its past performance
b.
the expected market risk premium is higher than the historical premium
c.
the expected market risk premium is lower than the historical premium
d.
the expected premium is the same as the historical premium
20. XYZ Corp. has equity beta be and market value of equity $e million. The required return on XYZ’s
debt is rd%. The market value of that debt is $d million and the face value is $df million. The risk-free
rate is rf% and the expected return on the market is rm%. What is XYZ’s WACC?
a.
ans1%
b.
ans2%
c.
ans3%
d.
ans4%
e.
None of the above.
21. Ergophonics Inc. initially has equity with market value $e billion. It has no debt. The equity has beta
be. The firm is planning to issue $D billion of debt, which will have beta of bd. The proceeds from the
debt issue will be used to retire equity, such that firm size does not change. What will the new equity
beta be?
a.
ans1
b.
ans2
c.
ans3
d.
ans4
e.
None of the above.
22. Which of the following is true for a large diversified conglomerate?
a.
The most appropriate discount rate is the WACC
b.
The most appropriate discount rate is the firm’s cost of equity
c.
Using the WACC may result in increasing the risk of the firm by erroneously accepting
higher risk projects and rejecting lower risk projects
d.
Using the firm’s cost of equity will reflect risk to the equity holders and keep the firm
from unintentionally increasing the risk of the firm
23. A real estate developer considers buying land that currently has substantial pine trees (pine trees are a
desired timber). The development will not occur for several years and is somewhat flexible, but when
it does, the pine trees will be harvested. The developer determines that the price uncertainty of the
timber will increase over the next few years (future prices are expected to be very volatile). Does this
increase or decrease the value of the land to the developer?
a.
It decreases the value of the land as the timber price is more uncertain
b.
It decreases the value of the land because increased volatility increases the discount rate
c.
It decreases the value of the land because the value of the timber option decreases
d.
It increases the value of the land because the value of the timber option increases
24. You and your friends reminisce about your spring break days on Panama City Beach and decide the
best way to recapture those times is combine your resources, buy a condominium on Panama City
Beach, get together there for two weeks a year and rent it out the remainder of the year. After
gathering the appropriate information you are very pleased to find the condominium has a positive
NPV. How do you interpret these results?
a.
Invest, positive NPVs are expected
b.
Positive NPVs are unexpected, assume your information is incomplete or in error
c.
Invest, but only after calculating and confirming using the IRR
d.
Invest, but only after calculating and confirming using the payback period
25. Generally, you would expect the beta of debt for a firm to be
a.
Negative
b.
The same as the equity beta
c.
A percentage of the equity beta based on the firm’s capital structure
d.
Near zero
26. Which of the following would explain a positive NPV calculation?
a.
Perfect competition
b.
Perfect capital markets
c.
Capital market frictions
d.
Barriers to entry
27. The capital budgeting process best able to evaluate a sequence of decisions is
a.
Decision trees
b.
Monte Carlo simulation analysis
c.
Scenario analysis
d.
Break even analysis
MATCHING
Match the following terms to the best description:
a.
asset beta
b.
unlevered beta
c.
break-even calculations
d.
sensitivity analysis
e.
scenario analysis
1. used by management to derive specific targets
2. often used to calculate a project’s NPV when a whole set of assumptions change in a particular way
3. a measure of the systematic risk of a real asset
4. removes the effects of leverage on an equity beta
5. allows managers to explore the importance of each assumption for a project
Match the definitions with the real option names:
a.
Input Flexibility Option
b.
Expansion Option
c.
Output Flexibility Option
d.
Follow-on Investment Option
e.
Abandonment Option
f.
Capacity Flexibility Option
6. the opportunity to enlarge a successful project
7. the opportunity to withdraw resources from an unsuccessful project
8. the opportunity to maintain excess production capacity
9. the ability to switch between production raw materials
10. the ability to make future complex additional investments to go with successful projects
11. the ability to switch between finished goods produced
SHORT ANSWER
1. A firm is considering diversifying and investing in a line of business in an industry in which the firm
does not currently operate. In doing some research, you determine the new industry has an average
equity beta of b, an average debt-to–equity ratio of de% ,and an average tax rate of t%. Your firm has a
debt ratio of de1%, but the same average tax rate of t%. Assume that debt betas in the firm and new
industry are zero.
a.
b.
c.
b = A[1 + (1 – t%)(de0)]
2. Assume you calculated a base case NPV for two projects and arrived at $npv for each project. Then
you used sensitivity analysis to examine each project and developed a pessimistic case and an
optimistic case by individually altering the variables by + / – p%. This yielded the following
information for the two projects. Is there an implication for which project should be preferred?
PROJECT A
Variable Altered
Pessimistic (–p%)
Base
Optimistic (+p%)
Unit Sales
NPV = $s1down
NPV = $npv
NPV = $s1up
Price / Unit
NPV = $p1down
NPV = $npv
NPV = $p1up
PROJECT B
Variable Altered
Pessimistic (–p%)
Base
Optimistic (+p%)
Unit Sales
NPV = $s2down
NPV = $npv
NPV = $s2up
Price / Unit
NPV = $p2down
NPV = $npv
NPV = $p2up
3. What is a decision tree and for what is it used?
4. The NPV technique doesn’t always give the right answer when an investment has an embedded real
option. Describe real options, how the NPV may not give the right answer when real options exist, and
how a firm can incorporate these into their capital budgeting decisions.
5. Two firms, Marchand and Gruenler, from the same industry reported the following income statements.
Calculate the operating leverage for the two firms (using 2003 sales as the base) and then compare the
leverage of all types used by the two firms and discuss its impact on the firms’ cost of capital.
Marchand, Inc.
2003
2004
Sales
$s1
$s2
–COGS and Other Variable Operating Costs
– cogsm1
– cogsm2
–Fixed Operating Costs
– FCM
– FCM
EBIT
ebtm1
ebtm2
–Interest
– 0
– 0
EBT
ebtm1
ebtm2
–Taxes
– tm1
– tm2
Net Income
$ nim1
$ nim2
Gruenler, Inc.
2003
2004
Sales
$s1
$s2
–COGS and Other Variable Operating Costs
– cogsg1
– cogsg2
-Fixed Operating Costs
– fcg
– fcg
EBIT
ebitg1
ebitg2
–Interest
– intg
– intg
EBT
ebtg1
ebtg2
–Taxes
– tg1
– tg2
Net Income
$ nig1
$ nig2
6. You have been asked to calculate the weighted average cost of capital for Weird Books Inc. Weird
Books Inc. has book value of debt of $db million, and book value of equity of $eb million. Weird
Book’s bonds offer bondholders rd percent, and equity investors require a re percent rate of return on
their common stock. The market value of Weird Book’s debt and equity is $d million and $e million,
respectively. The firms marginal tax rate is t percent.
a.
b.
a.
7. Leatherneck Machine Company has fixed costs of $FC1 per year. The sales price for the product it
produces is $sp per unit and variable costs per unit are $c1. Winslow Machine Company has fixed
costs of only $FC2 per year but its variable costs per unit are $c2. Its sales price per unit is the same as
Leatherneck’s.
a.
b.
c.
d.
8. You are considering an investment in a project to introduce a new product to the market. The initial
investment required is $invest. If the new product is successful, next period’s demand will produce
after-tax cash flows of $CF1 per year indefinitely into the future. If the product is not successful,
future after-tax cash flows will only be $CF2 per year for the next fifteen years (and zero thereafter).
Assume a discount rate of r percent.
a.
b.
9. Intuitively describe how an increase in the volatility of a variable can increase real option value,
whereas more traditional analysis suggests that an increase in volatility leads to lower value.
10. You are considering an investment in a project that requires an initial outlay of $io and will produce
after-tax cash flows of $Cf per year for the next 15 years. Your firm uses p1 percent debt and p2
percent equity in its financing. The after-tax costs of debt and equity are rd% and re%, respectively.
a.
What is the firm’s WACC?
b.
What is the project NPV? Should the project be accepted?
The expected net present value of the project is:
X ($CF1) [1.0 / r0] + (1 – X) ($CF2)[1 – (1 + r0) –15 ] [1 / r01] -$invest = $0
Solving for X = x. Therefore, the expected NPV will be positive and the project will increase firm
11. Explain how static NPV analysis is insufficient in that it does not consider how management decisions
can evolve with changes in the environment.
12. Divided Furniture Inc. has Nb bonds outstanding with a market price of $pb per bond. The firm also
has Np preferred shares outstanding and Nc common shares outstanding. Preferred stock and common
stock are both expected to pay a year-end dividend of $d per share. The current price per share of
common stock is $pc per share. Preferred stock is priced at $pp per share. Preferred dividends do not
grow and common stock dividends are expected to grow at a rate of g percent. The firm’s tax rate is t1
percent. If the yield on the firm’s bonds is rd%, what is the firm’s weighted average cost of capital?
13. What is the role of sensitivity and scenario analyses and how do they differ?
14. We run a delivery service, and we believe our firm has market risk equally between that of UPS and
FedEx. We know the following about these 2 firms:
Stock Price per share
# shares outstanding
Market Value of Debt
UPS
$p1
n11 billion
$ d1 billion
FedEx
$p2
n2 million
$ d2 billion
We also have the following data on the securities of these firms:
E
D
UPS
be1
0
FedEx
be2
bd2
Assume that our firm has risk-free debt with market value $d million and equity with market value $e
million. Assume that taxes are not relevant.
Estimate our firm’s equity beta.
15. A firm has an equity beta of b. The expected market risk premium is rm%. T-bills currently pay rf%.
The firm has two bond issues outstanding. The first currently sells for s1% of par and has a yield to
maturity of ytm1%. Par value of bond issues is $par. The second has a current market price of s2% of
par with a yield to maturity of ytm2%. There are n1 outstanding bonds in the first issue and n2 in the
second. The firm’s equity has a current market price of $ps and there are ns million shares outstanding.
What is the firm’s WACC if the relevant tax rate is t%?
16. Consider the following project:
A food processing company will lease a warehouse from a real estate firm in order to produce potato
chips. This is a typical cancelable lease with a purchase clause at the lease end. The initial facilities to
produce the potato chips will only take up part of the warehouse facilities. The food processing firm is
also considering expanding its operations in the future to produce gourmet quality chips that would
require different machinery.
Determine the real options in this project.
17. When is scenario analysis likely to be superior to sensitivity analysis?
18. Describe the process of Monte Carlo simulation.
19. How is the market risk premium determined?
20. A firm is considering two compensation schemes. The first pays a low base salary and large bonuses
tied to performance. The second offers a higher base salary with small bonuses. Which strategy would
lead to a higher equity beta (ceteris paribus), and why?
21. Comment on how the economic concepts of perfect competition and barriers of entry can serve as a
reality check in NPV calculations?
ESSAY
1. Why do managers want to know more about a project than just its NPV?
2. Identify the advantages of using a sensitivity analysis.
3. When would it be prudent for a firm not to use the firm’s cost of equity capital to discount a project’s
cash flows?
4. The Rich Corporation has $e million worth of common stock on which investors require a re% rate of
return. It has $d million in bonds that offer a rd% return.
a.
b.
c.
5. Data is given below for A Corporation’s and B Corporation’s beta and capital structure.
A
B
Stock beta
ba
bb
% Debt
da
db
% Equity
ea
eb
D/E ratio
dea%
deb%
Asset beta
= stock beta / (1 + D / E)
Calculate the asset beta for Corporations A and B above assuming a debt beta of 0.00.
and stockholders to increase their required rate of return due to the increase in financial
leverage.
6. Why should managers use breakeven analysis in the context of NPV rather than earnings?
7. Describe how managers conduct sensitivity analysis.
8. What should be your objective when performing scenario analysis?
9. What should a manager consider when determining the value of a project to the firm and its
shareholders?
10. How can management maximize an investment’s option value?
11. Carefully consider an investment in an oil field as a strategic option. Explain how a manager will
choose to use the option to extract the oil.
12. How should a firm analyze the risk and discount rate of a project with a different level of risk than the
firm’s other projects?
13. Why should managers be wary of distributions of NPVs produced by simulation programs?
14. What are the difficulties in using decision trees?