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,
b. The cost of preferred stock, rps, is the cost to the firm of issuing new preferred stock.
For perpetual preferred, it is the preferred dividend, Dps, divided by the net issuing
price, Pn. Note that no tax adjustments are made when calculating the component
cost of preferred stock because, unlike interest payments on debt, dividend payments
c. The target capital structure is the relative amount of debt, preferred stock, and
d. There are considerable costs when a company issues a new security, including fees to
9-2 The WACC is an average cost because it is a weighted average of the firm’s component
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
9-5 If a company’s composite WACC estimate were 10%, its managers might use 10% to
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
9-1 a. rd(1 – T) = 13%(1 – 0) = 13.00%.
rps =
)F1(V
D
ps
ps
=
)0.01(50$
50.4$
= 9%.
WACC = (wd)(rd)(1 – T) + (wps)(rps) + (ws)(rs)
9-8 40% Debt; 60% Equity; rd = 9%; T = 40%; WACC = 9.96%; rs = ?
WACC = (wd)(rd)(1 – T) + (ws)(rs)
9-9 Enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I = 6% =
d. The bond-yield-plus-judgmental-risk-premium approach and the CAPM method both
9-11 a. $6.50 = $4.42(1+g)5
9-12 a. rs =
0
1
P
D
+ g
0.09 =
00.60$
60.3$
+ g
0.09 = 0.06 + g
g = 3%.
b. Current EPS $5.400
Less: Dividends per share 3.600
0
1
P
D
9-15 a. Common equity needed:
b. Cost using rs:
After-Tax
Percent Cost = Product
c. rs and the WACC will increase due to the flotation costs of new equity.
9-16 The book and market value of the notes payable are $10,000,000.
The bonds have a value of
Alternatively, using a financial calculator, input N = 20, I/YR = 10, PMT = 60, and FV =
Short-term debt $10,000,000 11.14%
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
Debt:
The long-term debt has a market value found as follows:
Common Stock:
The market value of the common stock is
Therefore, here is the firm’s market value capital structure, which we assume to be
optimal:
Long-term debt $ 20,970,000 20.05%
Step 2.
Establish cost rates for the various capital structure components.
Debt cost:
Preferred stock cost:
Common equity cost:
There are three basic ways of estimating rs: CAPM, the dividend growth approach, and
judgmental risk premium over own bonds. None of the methods is very exact.
CAPM:
We would use rRF = T-bond rate = 10%. For RPM, we would use 4.5% to 5.5%. For beta,
Highest: rs = 10% + (5.5)(1.7) = 19.35%.
Dividend growth approach:
The company seems to be in a rapid, non-constant growth situation, but we do not have
We could use as a growth estimator this method:
It would not be appropriate to base g on the 30% ROE, because investors do not expect
that rate.
Highest: rs = 5.6% + 15% = 20.6%.
Generalized risk premium:
Highest: rs = 12% + 6% = 18%.
Based on the three midpoint estimates, we have rs in this range:
Step 3.
Calculate the WACC:
It would be appropriate to calculate a range of WACCs based on the ranges of component
SPREADSHEET PROBLEM
9-18 The detailed solution for the problem is available in the file Ch09 P18 Build a Model
Solution.xlsx at the textbook’s web site.