Answers and Solutions: 15 – 1
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Chapter 15
Capital Structure Decisions
15-1 a. Capital structure is the manner in which a firm’s assets are financed; that is, the right–
hand side of the balance sheet. Capital structure is normally expressed as the
Business risk is caused by many factors. Two of the most important are sales
variability and operating leverage. Financial risk is the risk added by the use of debt
If a high percentage of a firm’s total costs are fixed costs, then the firm is said to have
a high degree of operating leverage. Operating leverage is a measure of one element
degree of financial leverage. The breakeven point is that level of unit sales at which
costs equal revenues. Breakeven analysis may be performed with or without the
conditions than called for by the tradeoff theory. This allows the firm some
flexibility to use debt in the future when additional capital is needed.
15-3 Firms with relatively high nonfinancial fixed costs are said to have a high degree of
Answers and Solutions: 15 – 2
15-4 Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no
15-5 If sales tend to fluctuate widely, then cash flows and the ability to service fixed charges
than those whose sales are subject to only moderate fluctuations.
15-6 Public utilities place greater emphasis on long-term debt because they have more stable
markets. Public utilities have lower retained earnings because they have high dividend
15-7 EBIT depends on sales and operating costs. Interest is deducted from EBIT. At high debt
15-8 The tax benefits from debt increase linearly, which causes a continuous increase in the
15-9 If equity is viewed as an option on the total value of the firm with a strike price equal to
the face value of debt then the equity value should be affected by risk in the same way
that an option is affected by risk. An option is worth more if the underlying asset is more
Answers and Solutions: 15 – 3
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SOLUTIONS TO END-OF-CHAPTER PROBLEMS
15-2 If wd = 0.2, then wce = 1 – 0.2 = 0.8. So D/S = wd/we = 0.2/0.8.
15-3 If the company had no debt, its required return would be:
Therefore, the extra premium required for financial risk is 15.1% – 11.5% = 3.6%.
15-5 SPost = (1 – wd)(VopNew) = (1 – 1/3)($900) = $600 million.
15-6 nPost = Original shares – shares repurchased
nPost = nPrior [(VOpNew – DNew)/(VOpNew – DOld)] can be used if you note that
15-7 a. Here are the steps involved:
(1) Determine the variable cost per unit at present, V:
Profit = P(Q) – FC – V(Q)
$500,000 = ($100,000)(50) – $2,000,000 – V(50)
50(V) = $2,500,000
V = $50,000.
(2) Determine the new profit level if the change is made:
New profit = P2(Q2) – FC2 – V2(Q2)
= $95,000(70) – $2,500,000 – ($50,000 – $10,000)(70)
Answers and Solutions: 15 – 4
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= $1,350,000.
(3) Determine the incremental profit:
Profit = $1,350,000 – $500,000 = $850,000.
(4) Estimate the approximate rate of return on new investment:
VP
000,50$000,100$
New: QBE =
000,40$000,95$
000,500,2$
= 45.45 units.
FC
000,000,2$
New:
)Q(VFC
FC
222
2
=
000,800,2$000,500,2$
000,500,2$
= 47.17%.
The change in breakeven points—and also the higher percentage of fixed costs—
suggests that the new situation is more risky.
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15-8 a. Original value of the firm (D = $0):
We are given that the book value of assets is equal to the market value of assets, so
the value is $3,000,000. Alternatively, we can calculate the value as the sum of the
debt (which is zero) and the stock (200,000 shares at a price of $15 per share):
V = D + S = 0 + ($15)(200,000) = $3,000,000.
Original cost of capital:
WACC = wd rd(1-T) + wcers
= 0 + (1.0)(10%) = 10%.
With financial leverage (wd=30%):
WACC = wd rd(1-T) + wcers
= (0.3)(7%)(1-0.40) + (0.7)(11%) = 8.96%.
Because growth is zero, FCF is equal to EBIT(1-T). The value of operations is:
Vop =
.286.214,348,3$
0896.0
)40.01)(000,500($
WACC
)T1)(EBIT(
WACC
FCF
Increasing the financial leverage by adding $900,000 of debt results in an increase in
Therefore, its value of equity is:
S = V – D = $2,343,750.
c. The number of shares repurchased, X, is:
X = (D – D0)/P = $1,004,464.286 / $16.741 = 60,000.256 60,000.
The number of remaining shares, n, is:
n = 200,000 – 60,000 = 140,000.
EPS = [($500,000 – 0.07($1,004,464.286))(1-0.40)] / 140,000
= [($500,000 – $70,312.5)(1-0.40)] / 140,000
= $257,812.5 / 140,000 = $1.842.
Thus, by adding debt, the firm increased its EPS by $0.342.
15-9 a. Present situation (50% debt):
WACC = wd rd(1-T) + wcers
= (0.5)(10%)(1-0.15) + (0.5)(14%) = 11.25%.
1125.0
WACC
WACC
)15.01)(24.13($
)T1)(EBIT(
FCF
V =
1194.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF
= $94.255 million.
30 percent debt:
WACC = wd rd(1-T) + wcers
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15-11 Tax rate = 40% rRF = 5.0%
bU = 0.8 rM – rRF = 6.0%
From data given in the problem and table we can develop the following table:
wd
wce
D/S
rd
rd(1 – T)
Levered
betaa
rsb
WACCc
0
100%
0.00
6.0%
3.60%
0.80
9.80%
9.80%
0.2
80%
0.25
7.0%
4.20%
0.92
10.52%
9.26%
0.4
60%
0.67
8.0%
4.80%
1.12
11.72%
8.95%
0.6
40%
1.50
9.0%
5.40%
1.52
14.12%
8.89%
0.8
20%
4.00
10.0%
6.00%
2.72
21.32%
9.06%
WACC = wd(rd)(1 – T) + (wce)(rs).
The firm’s optimal capital structure is that capital structure which minimizes the firm’s
WACC. The WACC is minimized at a capital structure consisting of 60% debt and 40%
15-12 a. The inputs to the Black and Scholes option pricing model are P = 5, X = 2, rRF = 6%,
= 50%, and t = 2 years. Given these inputs, the value of a call option is calculated
as:
t]2/r[)X/Pln(
RF
2]2/5.006.0[)2/5ln( 2
Answers and Solutions: 15 – 10
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SOLUTIONS TO SPREADSHEET PROBLEMS
15-13 The detailed solution for the problem is available in the file Ch15 P12 Build a Model
Solution.xlsx on the textbook’s Web site.