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Answers and Solutions: 9 - 1
Chapter 9
The Cost of Capital
ANSWERS TO END-OF-CHAPTER QUESTIONS
9-1 a. The weighted average cost of capital, WACC, is the weighted average of the after-tax
component costs of capital—-debt, preferred stock, and common equity. Each
weighting factor is the proportion of that type of capital in the optimal, or target,
capital structure. The after-tax cost of debt, rd(1 - T), is the relevant cost to the firm
of new debt financing. Since interest is deductible from taxable income, the after-tax
cost of debt to the firm is less than the before-tax cost. Thus, rd(1 - T) is the
appropriate component cost of debt (in the weighted average cost of capital). If a
company has short-term debt with a cost of rstd, then its after-tax cost is rstd(1 - T) is
the appropriate component cost of debt (in the weighted average cost of capital).
c. The target capital structure is the relative amount of debt, preferred stock, and
common equity that the firm desires. The WACC should be based on these target
weights.
d. There are considerable costs when a company issues a new security, including fees to
an investment banker and legal fees. These costs are called flotation costs. The cost
of new common equity is higher than that of common equity raised internally by
reinvesting earnings. Projects financed with external equity must earn a higher rate of
return, since the project must cover the flotation costs.
9-3 Probable Effect on
rd(1 - T) rs WACC
a. The corporate tax rate is lowered. + 0 +
b. The Federal Reserve tightens credit. + + +
9-4 Stand-alone risk views a project’s risk in isolation, hence without regard to portfolio
effects; within-firm risk, also called corporate risk, views project risk within the context
of the firm’s portfolio of assets; and market risk (beta) recognizes that the firm’s
stockholders hold diversified portfolios of stocks. In theory, market risk should be most
relevant because of its direct effect on stock prices.
9-5 If a company’s composite WACC estimate were 10%, its managers might use 10% to
evaluate average-risk projects, 12% for high-risk projects, and 8% for low-risk projects.
Answers and Solutions: 9 - 3
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
9-1 a. rd(1 - T) = 13%(1 - 0) = 13.00%.
9-2 rd(1 - T) = 0.08(0.65) = 5.2%.
9-3 Vps = $50; Dps = $4.50; F = 0%; rps = ?
rps =
)F1(V
D
ps
ps
−
=
)0.01(50$
50.4$
−
= 9%.
9-4 rps =
)05.01(00.70$
)06.0(60$
−
=
50.66$
60.3$
= 5.41%.
9-6 rs = rRF + bi(RPM) = 0.06 + 0.8(0.055) = 10.4%.
9-7 30% Debt; 5% Preferred Stock; 65% Equity; rd = 6%; T = 40%; rps = 5.8%; rs = 12%.
WACC = (wd)(rd)(1 - T) + (wps)(rps) + (ws)(rs)
WACC = 0.30(0.06)(1-0.40) + 0.05(0.058) + 0.65(0.12) = 9.17%.
Answers and Solutions: 9 - 4
9-9 Enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I = 6% =
periodic rate. The nominal rate is 6%(2) = 12%, and the after-tax component cost of debt
is 12%(0.6) = 7.2%.
9-10 a. rs =
0
1
P
D
+ g =
23$
14.2$
+ 7% = 9.3% + 7% = 16.3%.
9-11 a. $6.50 = $4.42(1+g)5
(1+g)5 = $6.50/$4.42 = 1.471
(1+g) = 1.471(1/5) = 1.080
g = 8%.
Answers and Solutions: 9 - 5
9-12 a. rs =
0
1
P
D
+ g
0.09 =
00.60$
60.3$
+ g
0.09 = 0.06 + g
g = 3%.
9-13 P0 = $30; D1 = $3.00; g = 5%; F = 10%; rs = ?
rs = [D1/(1 - F) P0] + g = [$3/(1 - 0.10)($30)] + 0.05 = 16.1%.
9-14 Enter these values: N = 20, PV =1,000(1 - 0.02) = 980, PMT = -90(1 - 0.4) = -54, and
FV = -1000, to get I/YR = 5.57%, which is the after-tax component cost of debt.
9-16 The book and market value of the notes payable are $10,000,000.
The bonds have a value of
V = $60([1/0.10]-[1/(0.1*(1+0.10)20)]) + $1,000((1+0.10)-20)
= $60(8.5136) + $1,000(0.1486)
= $510.82 + $148.60 = $659.42.
9-17 Several steps are involved in the solution of this problem. Our solution follows:
Step 1.
Establish a set of market value capital structure weights. In this case, A/P and accruals
should be disregarded because they are not sources of financing from investors. Instead
of being incorporated into the WACC, they are accounted for when calculating cash
Debt:
The long-term debt has a market value found as follows:
Preferred Stock:
The preferred has a value of
Pps =
4/11.0
2$
= $72.73.
Common Stock:
The market value of the common stock is
4,000,000($20) = $80,000,000.
We would round these weights to 20% debt, 4% preferred, and 76% common equity.
Step 2.
Establish cost rates for the various capital structure components.
Debt cost:
rd(1 - T) = 12%(0.6) = 7.2%.
Preferred stock cost:
CAPM:
We would use rRF = T-bond rate = 10%. For RPM, we would use 4.5% to 5.5%. For beta,
we would use a beta in the 1.3 to 1.7 range. Combining these values, we obtain this
range of values for rs:
DCF:
The company seems to be in a rapid, non-constant growth situation, but we do not have
the inputs necessary to develop a non-constant rs. Therefore, we will use the constant
growth model but temper our growth rate; that is, think of it as a long-term average g that
may well be higher in the immediate future than in the more distant future.
One could look at a range of yields, based on P in the range of $17 to $23, but
because we believe in efficient markets, we would use P0 = $20. Thus, the DCF model
suggests a rs in the range of 15.6% to 20.6%:
Highest: rs = 5.6% + 15% = 20.6%.
Lowest: rs = 5.6% + 10% = 15.6%.
Midpoint: rs = 5.6% + 12.5% = 18.1%.
Generalized risk premium:
CAPM 17.5%
DCF 18.1%
Risk Premium 17.0%
Step 3.
Calculate the WACC:
WACC = (D/V)(rdAT) + (P/V)(rps) + (S/V)(rs or re)
Answers and Solutions: 9 - 11
SPREADSHEET PROBLEM
9-18 The detailed solution for the problem is available in the file Ch09 P18 Build a Model
Solution.xls at the textbook’s web site.
Mini Case: 9 - 12
MINI CASE
During the last few years, Harry Davis Industries has been too constrained by the high cost
of capital to make many capital investments. Recently, though, capital costs have been
declining, and the company has decided to look seriously at a major expansion program
that has been proposed by the marketing department. Assume that you are an assistant to
Leigh Jones, the financial vice-president. Your first task is to estimate Harry Davis’s cost
of capital. Jones has provided you with the following data, which she believes may be
relevant to your task:
1. The firm's tax rate is 40%.
2. The current price of Harry Davis’s 12% coupon, semiannual payment, noncallable
bonds with 15 years remaining to maturity is $1,153.72. Harry Davis does not use
short-term interest-bearing debt on a permanent basis. New bonds would be privately
placed with no flotation cost.
To help you structure the task, Leigh Jones has asked you to answer the following
questions.
Mini Case: 9 - 13
a. 1. What sources of capital should be included when you estimate Harry Davis’s
weighted average cost of capital (WACC)?
Answer: The WACC is used primarily for making long-term capital investment decisions, i.e.,
for capital budgeting. Thus, the WACC should include the types of capital used to
a. 2. Should the component costs be figured on a before-tax or an after-tax basis?
Answer: Stockholders are concerned primarily with those corporate cash flows that are
a. 3. Should the costs be historical (embedded) costs or new (marginal) costs?
Answer: In financial management, the cost of capital is used primarily to make decisions
Mini Case: 9 - 14
b. What is the market interest rate on Harry Davis’s debt, and what is the
component cost of this debt for WACC purposes?
Answer: Harry Davis’s 12% bond with 15 years to maturity is currently selling for $1,153.72.
Thus, its yield to maturity is 10%:
Optional Question
Should flotation costs be included in the estimate?
Answer: The actual component cost of new debt will be somewhat higher than 6% because the
Mini Case: 9 - 15
Optional Question
Should you use the nominal cost of debt or the effective annual cost?
Answer: Our 10% pre-tax estimate is the nominal cost of debt. Since the firm's debt has
semiannual coupons, its effective annual rate is 10.25%:
c. 1. What is the firm's cost of preferred stock?
Answer: Since the preferred issue is perpetual, its cost is estimated as follows:
c. 2. Harry Davis’s preferred stock is riskier to investors than its debt, yet the
preferred's yield to investors is lower than the yield to maturity on the debt.
Does this suggest that you have made a mistake? (Hint: Think about taxes.)
Answer: Corporate investors own most preferred stock, because 70% of preferred dividends
d. 1. What are the two primary ways companies raise common equity?
d. 2. Why is there a cost associated with reinvested earnings?
Mini Case: 9 - 16
Answer: Management may either pay out earnings in the form of dividends or else retain
d. 3. Harry Davis doesn’t plan to issue new shares of common stock. Using the
CAPM approach, what is Harry Davis’s estimated cost of equity?
Answer: rs = 0.056 + (0.06)1.2 = 12.8%.
e. 1. What is the estimated cost of equity using the discounted cash flow (DCF)
approach?
e. 2. Suppose the firm has historically earned 15% on equity (ROE) and retained
62% of earnings, and investors expect this situation to continue in the future.
How could you use this information to estimate the future dividend growth rate,
and what growth rate would you get? Is this consistent with the 5.8% growth
rate given earlier?
Answer: Another method for estimating the growth rate is to use the retention growth model:
e. 3. Could the DCF method be applied if the growth rate was not constant? How?
Answer: Yes, you could use the DCF using nonconstant growth. You would find the PV of the
Mini Case: 9 - 17
f. What is the cost of equity based on the bond-yield-plus-judgmental-risk-
premium method?
Answer: rs = Company’s own bond yield + judgmental risk premium.
g. What is your final estimate for the cost of equity, rs?
Answer: The final estimate for the cost of equity would simply be the average of the values
found using the above three methods.
h. What is Harry Davis’s weighted average cost of capital (WACC)?
Answer: WACC= wdrd(1 – T) + wpsrps + ws(rs)
i. What factors influence a company’s WACC?
Answer: There are factors that the firm cannot control and those that they can control that
influence WACC.
Mini Case: 9 - 18
j. Should the company use the overall, or composite, WACC as the hurdle rate for
each of its divisions?
Answer: No. The composite WACC reflects the risk of an average project undertaken by the
k. What procedures can be used to estimate the risk-adjusted cost of capital for a
particular division? What approaches are used to measure a division’s beta?
Answer: The following procedures can be used to determine a division’s risk-adjusted cost of
capital:
(1) Subjective adjustments to the firm’s composite WACC.
Mini Case: 9 - 19
l. Harry Davis is interested in establishing a new division that will focus primarily
on developing new Internet-based projects. In trying to determine the cost of
capital for this new division, you discover that specialized firms involved in
similar projects have on average the following characteristics:
• Their capital structure is 10% debt and 90% common equity.
• Their cost of debt is typically 12%.
• The beta is 1.7.
Given this information, what would your estimate be for the division’s cost of
capital?
Answer:
rs DIV. = rRF + (rM – rRF)bDIV.
= 5.6% + (6%)1.7 = 15.8%.
m. What are three types of project risk? How can each type of risk be considered
when thinking about the new division’s cost of capital?
Answer: The three types of project risk are:
Stand-Alone Risk
n. Explain in words why new common stock that is raised externally has a higher
percentage cost than equity that is raised internally as retained earnings.
Mini Case: 9 - 20
Answer: The company is raising money in order to make an investment. The money has a
cost, and this cost is based primarily on the investors’ required rate of return,
o. 1. Harry Davis estimates that if it issues new common stock, the flotation cost will
be 15%. Harry Davis incorporates the flotation costs into the DCF approach.
What is the estimated cost of newly issued common stock, taking into account
the flotation cost?
Answer:
g) + (1
D
o. 2. Suppose Harry Davis issues 30-year debt with a par value of $1,000 and a
coupon rate of 10%, paid annually. If flotation costs are 2%, what is the after-
tax cost of debt for the new bond?
Answer: Using a financial calculator, N = 30, PV = (1 – 0.02)(1,000) = 980, PMT = -(1 – 0.40)(100) = -60,
p. What four common mistakes in estimating the WACC should Harry Davis
avoid?
Answer: 1. Don’t use the coupon rate on a firm’s existing debt as the pre-tax cost of debt.
Use the current cost of debt.
Mini Case: 9 - 21
