Chapter 15
Capital Structure Decisions
ANSWERS TO END-OF-CHAPTER QUESTIONS
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
percentage of each type of capital used by the firm—debt, preferred stock, and common
equity. Business risk is the risk inherent in the operations of the firm, prior to the
financing decision. Thus, business risk is the uncertainty inherent in a total risk sense,
future operating income, or earnings before interest and taxes (EBIT). 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 financing. Debt financing
increases the variability of earnings before taxes (but after interest); thus, along with
business risk, it contributes to the uncertainty of net income and earnings per share.
Business risk plus financial risk equals total corporate risk.
c. Reserve borrowing capacity exists when a firm uses less debt under “normal”
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.
15-2 Business risk refers to the uncertainty inherent in projections of future ROIC = ROEU.
15-4 Operating leverage affects EBIT and, through EBIT, EPS. Financial leverage has no effect
on EBIT—it only affects EPS, given EBIT.
15-6 Public utilities place greater emphasis on long-term debt because they have more stable
sales and profits as well as more fixed assets. Also, utilities have fixed assets which can
be pledged as collateral. Further, trade firms use retained earnings to a greater extent,
probably because these firms are generally smaller and, hence, have less access to capital
markets. Public utilities have lower retained earnings because they have high dividend
payout ratios and a set of stockholders who want dividends.
15-8 The tax benefits from debt increase linearly, which causes a continuous increase in the
firm’s value and stock price. However, financial distress costs get higher and higher as
more and more debt is employed, and these costs eventually offset and begin to outweigh
the benefits of debt.
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
SOLUTIONS TO END-OF-CHAPTER PROBLEMS
15-1 QBE = F/(P – V) = $500,000/($75 – $50) = 20,000.
15-3 If the company had no debt, its required return would be:
rs,U = rRF + bU x RPM = 5.5% + 1.0(6%) = 11.5%.
With debt, the required return is:
rs,L = rRF + bL RPM = 5.5% + 1.6(6%) = 15.1%.
Therefore, the extra premium required for financial risk is 15.1% – 11.5% = 3.6%.
15-5 VL = VU + TD= $400 + 0.25($100) = $425 billion.
15-6 VL = VU +
cs
d
(1 T )(1 T )
1(1 T )
−−
−
−
D
= $500 +
(1 0.28)(1 0.17)
1(1 0.29)
−−
−
−
100
15-7 SPost = (1 – wd)(VopNew) = (1 – 0.4)($500) = $300 million.
15-8 SPost = (1 – wd)(VopNew) = (1 – 1/3)($900) = $600 million.
PPost = (VopNew – Dold)/nprior = ($900 – 0)/30 = $30
15-10 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.
(3) Determine the incremental profit:
Profit = $1,350,000 – $500,000 = $850,000.
Since the return exceeds the 16 percent cost of equity, this analysis suggests that the
firm should go ahead with the change.
b. The change would increase the breakeven point:
c. It is impossible to state unequivocally whether the new situation would have more or
less business risk than the old one. We would need information on both the sales
probability distribution and the uncertainty about variable input cost in order to make
this determination. However, since a higher breakeven point, other things held
constant, is more risky. Also the percentage of fixed costs increases:
Old:
)Q(VFC
FC
+
=
000,500,2$000,000,2$
000,000,2$
+
= 44.44%.
15-11 a. Original value of the firm (D = $0):
Original free cash flow:
FCF = NOPAT = EBIT(1-T) since no growth = $600,000(1-0.25) = $450,000
Original cost of capital:
WACC = wd rd(1-T) + wcers
= 0 + (1.0)(10%) = 10%.
Original value of operations is:
b. Using its target capital structure of 30% debt:
With financial leverage (wd=30%):
WACC = wd rd(1-T) + wcers
= (0.3)(7%)(1-0.25) + (0.7)(12%) = 9.975%.
c. The stock price after the debt is issued but before shares are purchased, PPrior:
PPrior = (Vop + ST investments – Debt)/nPrior
= (Vop + New Debt – (Old debt + New Debt)/nPrior
= (Vop – Old debt)/nPrior
= ($4,511,278.195 – $0)/200,000 =$22.5564
With financial leverage:
EPS = [($600,000 – 0.07($1,353,383.459))(1-0.25)] / 140,000
= [($600,000 – $94,736.8421)(0.75)] / 140,000
= $378,947.3684 / 140,000 = $2.7068 ≈ $2.71.
15-12 a. Present situation (50% debt):
WACC = wd rd(1-T) + wcers
= (0.5)(10%)(1-0.15) + (0.5)(14%) = 11.25%.
70 percent debt:
WACC = wd rd(1-T) + wcers
= (0.7)(12%)(1-0.15) + (0.3)(16%) = 11.94%.
Vop =
1194.0
)15.01)(24.13($
WACC
)T1)(EBIT(
WACC
FCF −
=
−
=
= $94.255 million.
30 percent debt:
15-13 a. BEA’s unlevered beta is bU=b/(1+ (1-T)(D/S))=1.0/(1+(1-0.25)(20/80)) = 0.8421.
b. b = bU (1 + (1-T)(D/S)).
At 40 percent debt: bL = 0.8421 (1 + 0.75(40%/60%)) = 1.2632.
rS = 6 + 1.2632(4) = 11.0528%
15-14 Tax rate = 25% 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
ws
D/S
rd
rd(1 – T)
Levered
betaa
rsb
WACCc
0.00
1.00
0.00
6.0%
4.50%
0.800
9.800%
9.80%
0.1
0.9
0.111
6.4%
4.80%
0.867
10.200%
9.66%
0.2
0.8
0.250
7.0%
5.25%
0.950
10.700%
9.61%
0.3
0.7
0.429
8.2%
6.15%
1.057
11.343%
9.79%
0.4
0.6
0.667
7.50%
1.200
12.200%
Notes:
a These beta estimates were calculated using the Hamada equation,
b = bU[1 + (1 – T)(D/S)].
15-15 a. The inputs to the Black and Scholes option pricing model are P = 100, X = 50, rRF =
6%, = 50%, and t = 10 years. Given these inputs, the value of a call option is
calculated as:
t
t]2/r[)X/Pln(
d
2
RF
1
++
=
=
8191.1
25.0
2]2/5.006.0[)2/5ln( 2=
++
.
)][N(dXe)]P[N(dV 2
t-r
1RF
−=
=
3.29 [0.8669]2e5[0.9656] )2(06.0– =−
million
b. The debt must therefore be worth 5-3.29 = $1.71 million. Its yield is
%1.881.0171.1/0.2 ==−
.
SOLUTIONS TO SPREADSHEET PROBLEMS
15-16 The detailed solution for the problem is available in the file Ch15 P16 Build a Model
Solutions.xlsx on the textbook’s Web site.
MINI CASE
Assume you have just been hired as a business manager of PizzaPalace, a regional pizza
restaurant chain. The company’s EBIT was $120 million last year and is not expected to
grow. Pizza Palace is in the 25% state-plus-federal tax bracket, the risk-free rate is 6
percent, and the market risk premium is 6 percent. The firm is currently financed with all
equity and it has 10 million shares outstanding.
When you took your corporate finance course, your instructor stated that most
firms’ owners would be financially better off if the firms used some debt. When you
suggested this to your new boss, he encouraged you to pursue the idea. If the company were
to recapitalize, debt would be issued, and the funds received would be used to repurchase
stock. As a first step, assume that you obtained from the firm’s investment banker the
following estimated costs of debt for the firm at different capital structures:
Percent Financed with Debt
wd rd
0% —
20 8.0%
a. Using the free cash flow valuation model, show the only avenues by which capital
structure can affect value.
Answer: The basic definitions are:
(1) V = Value of Firm
(2) FCF = Free Cash Flow
b. (1) What is business risk? What factors influence a firm’s business risk?
b. (2) What is operating leverage, and how does it affect a firm’s business risk? Show
the operating break even point if a company has fixed costs of $200, a sales price
of $15, and variables costs of $10.
Answer: Operating leverage is the change in EBIT caused by a change in quantity sold. The
higher the proportion of fixed costs within a firm’s overall cost structure, the greater
the operating leverage. Higher operating leverage leads to more business risk,
because a small sales decline causes a larger EBIT decline.
c. Explain the difference between financial risk and business risk.
Answer: Business risk increases the uncertainty in future EBIT. It depends on business factors
d. To illustrate the effects of financial leverage for PizzaPalace’s management,
consider two hypothetical firms: Firm U (which uses no debt financing) and Firm
L (which uses $4,000 of 8% interest rate debt). Both firms have $20,000 in net
operating capital, a 25% tax rate, and an expected EBIT of $2,400.
d. 1. Construct partial income statements, which start with EBIT, for the two firms.
Answer: Partial Income Statements:
Firm U
Firm L
EBIT
$2,400
$2,400
Interest
EBT
$2,400
$2,080
Taxes
d. 2. Calculate NOPAT, ROIC, and ROE for both firms.
Answer:
Firm U
Firm L
EBIT =
$2,400
$2,400
NOPAT = EBIT(1 − T) =
$1,800
$1,800
$20,000
$20,000
ROIC = NOPAT/Op. Cap. =
$20,000
$16,000
$1,800
$1,560
d. 3. What does this example illustrate about the impact of financial leverage on ROE?
Answer:
1. ROIC wasn’t affected by financial leverage.
d. 4. Why did leverage increase ROE in this example?
Answer:
1. More total dollars paid to L’s investors:
a. U: NI = $1,800.
b. L: NI + Int = $1,560 + $320 = $1,880.
e. What happens to ROE for Firm U and Firm L if EBIT falls to $1,600? What
happens if EBIT falls to $1,200? What is the after-tax cost of debt? What does this
imply about the impact of leverage on risk and return?
Answer:
x
Firm U
Firm L
EBIT
$1,600
$1,600
Interest
$0
$320
EBT
$1,600
$1,280
Taxes
$400
$320
$1,200
$960
ROIC
6.0%
ROE
6.0%
EBIT
$1,200
Interest
EBT
Taxes
ROIC
ROE
f. What does capital structure theory attempt to do? What lessons can be learned
from capital structure theory? Be sure to address the MM models.
Answer: MM theory begins with the assumption of zero taxes. MM prove, under a very
restrictive set of assumptions, that a firm’s value is unaffected by its financing mix:
VL = VU.
Therefore, capital structure is irrelevant. Any increase in roe resulting from financial
leverage is exactly offset by the increase in risk (i.e., rs), so WACC is constant.
Miller later included personal taxes. Personal taxes lessen the advantage of corporate
debt. Corporate taxes favor debt financing since corporations can deduct interest
expenses, but personal taxes favor equity financing, since no gain is reported until
stock is sold, and long-term gains are taxed at a lower rate. Miller’s conclusions with
personal taxes are that the use of debt financing remains advantageous, but benefits
are less than under only corporate taxes. Firms should still use 100% debt. Note:
MM assumed that investors and managers have the same information. But managers
often have better information. Thus, they would sell stock if stock is overvalued, and
sell bonds if stock is undervalued. Investors understand this, so view new stock sales
as a negative signal. This is signaling theory.
A second agency problem is the potential for “underinvestment”. Debt increases risk
of financial distress. Therefore, managers may avoid risky projects even if they have
positive NPVs.
Firms with many investment opportunities should maintain reserve borrowing
capacity, especially if they have problems with asymmetric information (which would
cause equity issues to be costly).