Answers and Solutions: 9 – 1
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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
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
on preferred stock are not tax deductible. The cost of new common equity, re, is the
increasing the supply of stock, and (3) any drop in price due to informational
asymmetries.
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
return, since the project must cover the flotation costs.
Answers and Solutions: 9 – 2
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
c. The firm uses more debt; that is, it
increases its debt/assets ratio. + + 0
f. Investors become more risk averse. + + +
9-4 Stand-alone risk views a project’s risk in isolation, hence without regard to portfolio
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
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
9-1 a. rd(1 – T) = 13%(1 – 0) = 13.00%.
9-3 Vps = $50; Dps = $4.50; F = 0%; rps = ?
D
ps
9-8 40% Debt; 60% Equity; rd = 9%; T = 40%; WACC = 9.96%; rs = ?
7.8% = 0.6rs
9-9 Enter these values: N = 60, PV = -515.16, PMT = 30, and FV = 1000, to get I = 6% =
1
D
14.2$
c. rs = Bond rate + Risk premium = 12% + 4% = 16%.
d. The bond-yield-plus-judgmental-risk-premium approach and the CAPM method both
9-11 a. $6.50 = $4.42(1+g)5
(1+g)5 = $6.50/$4.42 = 1.471
b. D1 = D0(1 + g) = $2.60(1.08) = $2.81.
c. rs = D1/P0 + g = $2.81/$36.00 + 8% = 15.81%.
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9-12 a. rs =
0
1
P
D
+ g
0.09 =
00.60$
60.3$
+ g
0.09 = 0.06 + g
g = 3%.
b. Current EPS $5.400
Less: Dividends per share 3.600
Next year’s EPS $5.562
Alternatively, EPS1 = EPS0(1 + g) = $5.40(1.03) = $5.562.
9-13 P0 = $30; D1 = $3.00; g = 5%; F = 10%; rs = ?
9-14 Enter these values: N = 20, PV =1,000(1 – 0.02) = 980, PMT = -90(1 – 0.4) = -54, and
9-15 a. Common equity needed:
0.5($30,000,000) = $15,000,000.
Debt 0.50 4.8%* 2.4%
Common equity 0.50 12.0 6.0
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9-16 The book and market value of the notes payable are $10,000,000.
The bonds have a value of
1000 to arrive at a PV = $659.46.
The total market value of the long-term debt is 30,000($659.46) = $19,783,800.
Long-term debt 19,783,800 22.03
Common equity 60,000,000 66.83
9-17 Several steps are involved in the solution of this problem. Our solution follows:
Step 1.
Establish a set of market value capital structure weights. In this case, A/P and accruals
should be disregarded because they are not sources of financing from investors. Instead
Answers and Solutions: 9 – 7
Debt:
The long-term debt has a market value found as follows:
V0 =
40
1t 40t)06.1(
000,1$
)06.1(
40$
= $699,
or 0.699($30,000,000) = $20,970,000 in total. Notice that short-term debt is not included
the company does not use short-term debt as a permanent source of financing. Indeed, as
The preferred has a value of
Pps =
4/11.0
2$
= $72.73.
There are $5,000,000/$100 = 50,000 shares of preferred outstanding, so the total market
value of the preferred is
50,000($72.73) = $3,636,500.
Answers and Solutions: 9 – 8
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Common Stock:
The market value of the common stock is
4,000,000($20) = $80,000,000.
Therefore, here is the firm’s market value capital structure, which we assume to be
optimal:
Long-term debt $ 20,970,000 20.05%
Preferred stock 3,636,500 3.48
Common equity 80,000,000 76.47
$104,606,500 100.00%
Preferred stock cost:
Annual dividend on new preferred = 11%($100) = $11. Therefore,
rps = $11/$100(1 – 0.05) = $11/$95 = 11.6%.
Common equity cost:
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CAPM:
We would use rRF = T-bond rate = 10%. For RPM, we would use 4.5% to 5.5%. For beta,
Dividend growth approach:
The company seems to be in a rapid, non-constant growth situation, but we do not have
the inputs necessary to develop a non-constant rs. Therefore, we will use the constant
growth model but temper our growth rate; that is, think of it as a long-term average g that
Finally, we could use the analysts’ forecasted g range, 10% to 15%. The dividend
yield is D1/P0. Assuming g = 12%,
0
1
P
D
=
20$
)12.1(1$
= 5.6%.
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 dividend
growth approach suggests a rs in the range of 15.6% to 20.6%:
Highest: rs = 12% + 6% = 18%.
Lowest: rs = 12% + 4% = 16%.
Midpoint: rs = 12% + 5% = 17%.
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CAPM 17.5%
Dividend growth 18.1%
Risk Premium 17.0%
these cost rates, here is the WACC calculation: