Solutions to Questions and Problems




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CHAPTER 15

CAPITAL STRUCTURE: BASIC CONCEPTS

Solutions to Questions and Problems



NOTE: All end-of-chapter 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 market-to-book 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

All-equity







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 all-equity 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 – RDD)/Shares outstanding
This equation calculates the interest payment (RDD) and subtracts it from the EBIT, which results in the net income. Dividing by the shares outstanding gives us the EPS. For the all-equity 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 all-equity capital structure and Plan I is:
EBIT/1,400 = [EBIT – .10($16,500)]/1,100

EBIT = $7,700


And the breakeven EBIT between the all-equity capital structure and Plan II is:
EBIT/1,400 = [EBIT – .10($27,500)]/900

EBIT = $7,700


The break-even 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 break-even 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

All-equity







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 all-equity plan still has the lowest EPS.


We can calculate the EPS as:
EPS = [(EBIT – RDD)(1 – tC)]/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 all-equity capital structure. So, the breakeven EBIT between the all-equity 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 all-equity 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 break-even 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:
RE = RA = $73,000/$600,000

RE = .1217 or 12.17%


To find the cost of equity for XYZ, we need to use M&M Proposition II, so:
RE = RA + (RA – RD)(D/E)(1 – tC)

RE = .1217 + (.1217 – .10)(1)(1)

RE = .1433 or 14.33%
d. To find the WACC for each company, we need to use the WACC equation:
WACC = (E/V)RE + (D/V)RD(1 – tC)
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:
VU = EBIT(1 – tC)/RU
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 all-equity 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)RE + (D/V)RD(1 – tC)
The company has a debt-equity 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)RE + (1.5/2.5)(.12)(1 – .35)

RE = .1830 or 18.30%


b. To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so:
RE = R0 + (R0 – RD)(D/E)(1 – tC)

.1830 = R0 + (R0 – .12)(1.5)(1 – .35)

RO = .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 debt-equity ratio of 2, the cost of equity is:
RE = R0 + (R0 – RD)(D/E)(1 – tC)

RE = .1519 + (.1519 – .12)(2)(1 – .35)

RE = .1934 or 19.34%

With a debt-equity ratio of 1.0, the cost of equity is:


RE = .1519 + (.1519 – .12)(1)(1 – .35)

RE = .1726 or 17.26%


And with a debt-equity ratio of 0, the cost of equity is:

RE = .1519 + (.1519 – .12)(0)(1 – .35)



RE = R0 = .1519 or 15.19%


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