CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
a
MODERATE
14-3 Determining the Optimal Capital Structure
77. As a consultant to First Responder Inc., you have obtained the following data (dollars in millions). The company plans
to pay out all of its earnings as dividends, hence g = 0. Also, no net new investment in operating capital is needed because
growth is zero. The CFO believes that a move from zero debt to 20.0% debt would cause the cost of equity to increase
from 10.0% to 12.0%, and the interest rate on the new debt would be 8.0%. What would the firm’s total market value be if
it makes this change? Hints: Find the FCF, which is equal to NOPAT = EBIT(1 − T) because no new operating capital is
needed, and then divide by (WACC − g).
$800
Tax rate
40.0%
12.00%
New wd
20.0%
8.00%
a.
$2,982
b.
$3,314
c.
$3,682
d.
$4,091
e.
$4,545
e
MODERATE
Comprehensive
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
78. You plan to invest in one of two home delivery pizza companies, High and Low, that were recently founded and are
about to commence operations. They are identical except for their use of debt (wd) and the interest rates on their
debt⎯High uses more debt and thus must pay a higher interest rate. Based on the data given below, how much higher or
lower will High’s expected EPS be versus that of Low, i.e., what is EPSHigh − EPSLow?
Applicable to Both Firms
Firm High’s Data
Firm Low’s Data
Capital
$3,000,000
wd
70%
wd
20%
EBIT
$500,000
Shares
90,000
Shares
240,000
Tax rate
35%
Int. rate
12%
Int. rate
10%
a.
$0.49
b.
$0.54
c.
$0.60
d.
$0.66
e.
$0.73
c
MODERATE/CHALLENGING
14-3 Determining the Optimal Capital Structure
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
79. Firms HD and LD are identical except for their use of debt and the interest rates they pay⎯HD has more debt and thus
must pay a higher interest rate. Based on the data given below, how much higher or lower will HD’s ROE be versus that of
LD, i.e., what is ROEHD − ROELD?
Applicable to Both Firms
Firm HD’s Data
Firm LD’s Data
Capital
$3,000,000
wd
70%
wd
20%
EBIT
$500,000
Int. rate
12%
Int. rate
10%
Tax rate
35%
a.
5.41%
b.
5.69%
c.
5.99%
d.
6.29%
e.
6.61%
c
MODERATE/CHALLENGING
14-3 Determining the Optimal Capital Structure
FOFM.BRIG.16.14.03 – Determining the Optimal Capital Structure
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.10 – Capital structure
Bloom’s: Evaluation
Multiple Choice: Problem
80. Firm A is very aggressive in its use of debt to leverage up its earnings for common stockholders, whereas Firm NA is
not aggressive and uses no debt. The two firms’ operations are identical⎯they have the same total investor-supplied
capital, sales, operating costs, and EBIT. Thus, they differ only in their use of financial leverage (wd). Based on the
following data, how much higher or lower is A’s ROE than that of NA, i.e., what is ROEA − ROENA?
Applicable to Both Firms
Firm A’s Data
Firm NA’s Data
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
Capital
$150,000
wd
50%
wd
0%
EBIT
$40,000
Int. rate
12%
Int. rate
10%
Tax rate
35%
a.
8.60%
b.
9.06%
c.
9.53%
d.
10.01%
e.
10.51%
c
MODERATE/CHALLENGING
14-3 Determining the Optimal Capital Structure
FOFM.BRIG.16.14.03 – Determining the Optimal Capital Structure
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.10 – Capital structure
ROE and capital structure
Bloom’s: Evaluation
Multiple Choice: Problem
81. Your firm’s debt ratio is only 5.00%, but the new CFO thinks that more debt should be employed. She wants to sell
bonds and use the proceeds to buy back and retire common shares so the percentage of common equity in the capital
structure (wc) = 1 − wd. Other things held constant, and based on the data below, if the firm increases the percentage of
debt in its capital structure (wd) to 60.0%, by how much would the ROE change, i.e., what is ROENew − ROEOld?
Operating Data
Other Data
Capital
$150,000
Old wd
5%
ROIC = EBIT(1 − T)/Capital
13.00%
Old interest rate
10%
Tax rate
35%
New wd
60%
New interest rate
12%
a.
6.73%
b.
7.09%
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
c.
7.46%
d.
7.83%
e.
8.22%
c
14-3 Determining the Optimal Capital Structure
82. You have been hired by a new firm that is just being started. The CFO wants to finance with 60% debt, but the
president thinks it would be better to hold the percentage of debt in the capital structure (wd) to only 10%. Other things
held constant, and based on the data below, if the firm uses more debt, by how much would the ROE change, i.e., what is
ROENew − ROEOld?
Operating Data
Other Data
Capital
$4,000
Higher wd
60%
ROIC = EBIT(1 − T)/Capital
13.00%
Higher interest rate
13%
Tax rate
35%
Lower wd
10%
Lower interest rate
9%
a.
5.44%
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
b.
5.73%
c.
6.03%
d.
6.33%
e.
6.65%
c
MODERATE/CHALLENGING
14-3 Determining the Optimal Capital Structure
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.10 – Capital structure
Bloom’s: Evaluation
Multiple Choice: Problem
83. Your girlfriend plans to start a new company to make a new type of cat litter. Her father will finance the operation, but
she will have to pay him back. You are helping her, and the issue now is how to finance the company, with equity only or
with a mix of debt and equity. The price per unit will be $10.00 regardless of how the firm is financed. The expected fixed
and variable operating costs, along with other information, are shown below. How much higher or lower will the firm’s
expected EPS be if it uses some debt rather than only equity, i.e., what is EPSL − EPSU?
0% Debt, U
60% Debt, L
Expected unit sales
225,000
225,000
Price per unit
$10.00
$10.00
Fixed costs
$1,000,000
$1,000,000
Variable cost/unit
$3.50
$3.50
Required investment
$2,500,000
$2,500,000
Shares issued at $10/share
250,000
100,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
a.
$0.54
b.
$0.60
c.
$0.67
d.
$0.75
e.
$0.83
e
CHALLENGING
14-2 Business and Financial Risk
FOFM.BRIG.16.14.02 – Business and Financial Risk
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.10 – Capital structure
Bloom’s: Evaluation
Multiple Choice: Problem
84. Southeast U’s campus book store sells course packs for $15.00 each, the variable cost per pack is $11.00, fixed costs
for this operation are $300,000, and annual sales are 100,000 packs. The unit variable cost consists of a $4.00 royalty
payment, VR, per pack to professors plus other variable costs of VO = $7.00. The royalty payment is negotiable. The book
store’s directors believe that the store should earn a profit margin of 10% on sales, and they want the store’s managers to
pay a royalty rate that will produce that profit margin. What royalty per pack would permit the store to earn a 10% profit
margin on course packs, other things held constant?
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
a.
$2.55
b.
$2.84
c.
$3.15
d.
$3.50
e.
$3.85
CHALLENGING
14-2 Business and Financial Risk
85. Dye Industries currently uses no debt, but its new CFO is considering changing the capital structure to 40.0% debt
(wd) by issuing bonds and using the proceeds to repurchase and retire common shares so the percentage of common equity
in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would this recapitalization change the
firm’s cost of equity, i.e., what is rL − rU?
Risk-free rate, rRF
6.00%
Tax rate, T
40%
Market risk premium, RPM
4.00%
Current wd
0%
Current beta, bU
1.15
Target wd
40%
a.
1.66%
b.
1.84%
c.
2.02%
d.
2.23%
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
e.
2.45%
CHALLENGING
14-3 Determining the Optimal Capital Structure
Levered beta and rs
86. Dyson Inc. currently finances with 20.0% debt (i.e., wd = 20%), but its new CFO is considering changing the capital
structure so wd = 60.0% by issuing additional bonds and using the proceeds to repurchase and retire common shares so the
percentage of common equity in the capital structure (wc) = 1 − wd. Given the data shown below, by how much would
this recapitalization change the firm’s cost of equity? (Hint: You must unlever the current beta and then use the unlevered
beta to solve the problem.)
Risk-free rate, rRF
5.00%
Tax rate, T
40%
Market risk premium, RPM
6.00%
Current wd
20%
Current beta, bL1
1.15
Target wd
60%
a.
4.05%
b.
4.50%
c.
4.95%
d.
5.45%
e.
5.99%
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
CHALLENGING
14-3 Determining the Optimal Capital Structure
a.
$28.27
b.
$29.76
c.
$31.25
d.
$32.81
e.
$34.45
CHALLENGING
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE
88. You were hired as the CFO of a new company that was founded by three professors at your university. The company
plans to manufacture and sell a new product, a cell phone that can be worn like a wrist watch. The issue now is how to
finance the company, with equity only or with a mix of debt and equity. The price per phone will be $250.00 regardless of
how the firm is financed. The expected fixed and variable operating costs, along with other data, are shown below. How
much higher or lower will the firm’s expected ROE be if it uses 60% debt rather than only equity, i.e., what is ROEL −
ROEU?
0% Debt, U
60% Debt, L
Expected unit sales (Q)
28,500
28,500
Price per phone (P)
$250.00
$250.00
Fixed costs (F)
$1,000,000
$1,000,000
Variable cost/unit (V)
$200.00
$200.00
Required investment
$2,500,000
$2,500,000
% Debt
0.00%
60.00%
Debt, $
$0
$1,500,000
Equity, $
$2,500,000
$1,000,000
Interest rate
NA
10.00%
Tax rate
35.00%
35.00%
a.
5.68%
b.
5.94%
c.
6.22%
d.
6.52%
e.
6.83%
e
14-3 Determining the Optimal Capital Structure
FOFM.BRIG.16.14.03 – Determining the Optimal Capital Structure
United States – BUSPROG.FOFM.BRIG.16.03 – Analytic skills
United States – OH – DISC.FOFM.BRIG.16.10 – Capital structure
Recapitalization
Bloom’s: Analysis
Multiple Choice: Problem
CHAPTER 14—CAPITAL STRUCTURE AND LEVERAGE