CHAPTER 15
CAPITAL STRUCTURE: BASIC CONCEPTS
Solutions to Questions and Problems
NOTE: All endofchapter problems were solved using a spreadsheet. Many problems require multiple steps. Due to space and readability constraints, when these intermediate steps are included in this solutions manual, rounding may appear to have occurred. However, the final answer for each problem is found without rounding during any step in the problem.
1. a. A table outlining the income statement for the three possible states of the economy is shown below. The EPS is the net income divided by the 2,500 shares outstanding. The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy.



Recession

Normal

Expansion



EBIT

$5,600

$14,000

$18,200



Interest

0

0

0



NI

$5,600

$14,000

$18,200



EPS

$ 2.24

$ 5.60

$ 7.28



%EPS

–60

–––

+30

b. If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Equity / Shares outstanding
Share price = $150,000/2,500
Share price = $60
Shares repurchased = Debt issued / Share price
Shares repurchased =$60,000/$60
Shares repurchased = 1,000
The interest payment each year under all three scenarios will be:
Interest payment = $60,000(.05) = $3,000
The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization.



Recession

Normal

Expansion



EBIT

$5,600

$14,000

$18,200



Interest

3,000

3,000

3,000



NI

$2,600

$11,000

$15,200



EPS

$1.73

$ 7.33

$10.13



%EPS

–76.36

–––

+38.18

3. a. Since the company has a markettobook ratio of 1.0, the total equity of the firm is equal to the market value of equity. Using the equation for ROE:
ROE = NI/$150,000
The ROE for each state of the economy under the current capital structure and no taxes is:



Recession

Normal

Expansion



ROE

.0373

.0933

.1213



%ROE

–60

–––

+30

The second row shows the percentage change in ROE from the normal economy.
b. If the company undertakes the proposed recapitalization, the new equity value will be:
Equity = $150,000 – 60,000
Equity = $90,000
So, the ROE for each state of the economy is:
ROE = NI/$90,000



Recession

Normal

Expansion



ROE

.0222

.1156

.1622



%ROE

–76.36

–––

+38.18

c. If there are corporate taxes and the company maintains its current capital structure, the ROE is:


ROE

.0243

.0607

.0789



%ROE

–60

–––

+30

If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is:


ROE

.0144

.0751

.1054



%ROE

–76.36

–––

+38.18

Notice that the percentage change in ROE is the same as the percentage change in EPS. The percentage change in ROE is also the same with or without taxes.
6. a. The income statement for each capitalization plan is:


 I 
II

Allequity



EBIT

$10,000

$10,000

$10,000



Interest

1,650

2,750

0



NI

$8,350

$7,250

$10,000



EPS

$7.59

$ 8.06

$ 7.14

Plan II has the highest EPS; the allequity plan has the lowest EPS.
b. The breakeven level of EBIT occurs when the capitalization plans result in the same EPS. The EPS is calculated as:
EPS = (EBIT – R_{D}D)/Shares outstanding
This equation calculates the interest payment (R_{D}D) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the allequity capital structure, the interest paid is zero. To find the breakeven EBIT for two different capital structures, we simply set the equations equal to each other and solve for EBIT. The breakeven EBIT between the allequity capital structure and Plan I is:
EBIT/1,400 = [EBIT – .10($16,500)]/1,100
EBIT = $7,700
And the breakeven EBIT between the allequity capital structure and Plan II is:
EBIT/1,400 = [EBIT – .10($27,500)]/900
EBIT = $7,700
The breakeven levels of EBIT are the same because of M&M Proposition I.
c. Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT, we get:
[EBIT – .10($16,500)]/1,100 = [EBIT – .10($27,500)]/900
EBIT = $7,700
This breakeven level of EBIT is the same as in part b again because of M&M Proposition I.
d. The income statement for each capitalization plan with corporate income taxes is:


 I 
II

Allequity



EBIT

$10,000

$10,000

$10,000



Interest

1,650

2,750

0



Taxes

3,340

2,900

4,000



NI

$5,010

$4,350

$6,000



EPS

$4.55

$ 4.83

$ 4.29

Plan II still has the highest EPS; the allequity plan still has the lowest EPS.
We can calculate the EPS as:
EPS = [(EBIT – R_{D}D)(1 – t_{C})]/Shares outstanding
This is similar to the equation we used before, except that now we need to account for taxes. Again, the interest expense term is zero in the allequity capital structure. So, the breakeven EBIT between the allequity plan and Plan I is:
EBIT(1 – .40)/1,400 = [EBIT – .10($16,500)](1 – .40)/1,100
EBIT = $7,700
The breakeven EBIT between the allequity plan and Plan II is:
EBIT(1 – .40)/1,400 = [EBIT – .10($27,500)](1 – .40)/900
EBIT = $7,700
And the breakeven between Plan I and Plan II is:
[EBIT – .10($16,500)](1 – .40)/1,100 = [EBIT – .10($27,500)](1 – .40)/900
EBIT = $7,700
The breakeven levels of EBIT do not change because the addition of taxes reduces the income of all three plans by the same percentage; therefore, they do not change relative to one another.
9. a. The rate of return earned will be the dividend yield. The company has debt, so it must make an interest payment. The net income for the company is:
NI = $73,000 – .10($300,000)
NI = $43,000
The investor will receive dividends in proportion to the percentage of the company’s share they own. The total dividends received by the shareholder will be:
Dividends received = $43,000($30,000/$300,000)
Dividends received = $4,300
So the return the shareholder expects is:
R = $4,300/$30,000
R = .1433 or 14.33%
b. To generate exactly the same cash flows in the other company, the shareholder needs to match the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net $30,000. The shareholder should then borrow $30,000. This will create an interest cash flow of:
Interest cash flow = .10(–$30,000)
Interest cash flow = –$3,000
The investor should then use the proceeds of the stock sale and the loan to buy shares in ABC. The investor will receive dividends in proportion to the percentage of the company’s share they own. The total dividends received by the shareholder will be:
Dividends received = $73,000($60,000/$600,000)
Dividends received = $7,300
The total cash flow for the shareholder will be:
Total cash flow = $7,300 – 3,000
Total cash flow = $4,300
The shareholders return in this case will be:
R = $4,300/$30,000
R = .1433 or 14.33%
c. ABC is an all equity company, so:
R_{E}_{ }= R_{A} = $73,000/$600,000_{ }
R_{E}_{ }= .1217 or 12.17%
To find the cost of equity for XYZ, we need to use M&M Proposition II, so:
R_{E} = R_{A} + (R_{A} – R_{D})(D/E)(1 – t_{C})
R_{E} = .1217 + (.1217 – .10)(1)(1)
R_{E} = .1433 or 14.33%
d. To find the WACC for each company, we need to use the WACC equation:
WACC = (E/V)R_{E} + (D/V)R_{D}(1 – t_{C})
So, for ABC, the WACC is:
WACC = (1)(.1217) + (0)(.10)
WACC = .1217 or 12.17%
And for XYZ, the WACC is:
WACC = (1/2)(.1433) + (1/2)(.10)
WACC = .1217 or 12.17%
When there are no corporate taxes, the cost of capital for the firm is unaffected by the capital structure; this is M&M Proposition II without taxes.
11. If there are corporate taxes, the value of an unlevered firm is:
V_{U} = EBIT(1 – t_{C})/R_{U}
Using this relationship, we can find EBIT as:
$35,000,000 = EBIT(1 – .35)/.13
EBIT = $7,000,000
The WACC remains at 13 percent. Due to taxes, EBIT for an allequity firm would have to be higher for the firm to still be worth $35 million.
12. a. With the information provided, we can use the equation for calculating WACC to find the cost of equity. The equation for WACC is:
WACC = (E/V)R_{E} + (D/V)R_{D}(1 – t_{C})
The company has a debtequity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, so
WACC = .12 = (1/2.5)R_{E} + (1.5/2.5)(.12)(1 – .35)
R_{E} = .1830 or 18.30%
b. To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so:
R_{E} = R_{0} + (R_{0} – R_{D})(D/E)(1 – t_{C})
.1830 = R_{0} + (R_{0} – .12)(1.5)(1 – .35)
R_{O} = .1519 or 15.19%
c. To find the cost of equity under different capital structures, we can again use M&M Proposition II with taxes. With a debtequity ratio of 2, the cost of equity is:
R_{E} = R_{0} + (R_{0} – R_{D})(D/E)(1 – t_{C})
R_{E} = .1519 + (.1519 – .12)(2)(1 – .35)
R_{E} = .1934 or 19.34%
With a debtequity ratio of 1.0, the cost of equity is:
R_{E} = .1519 + (.1519 – .12)(1)(1 – .35)
R_{E} = .1726 or 17.26%
And with a debtequity ratio of 0, the cost of equity is:
R_{E} = .1519 + (.1519 – .12)(0)(1 – .35)
R_{E} = R_{0} = .1519 or 15.19% 