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# c12.exercises

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Capital Structure: Basic Concepts

1. EBIT and Leverage Money, Inc., has no debt outstanding and a total market value of

\$150,000. Earnings before interest and taxes, EBIT, are projected to be \$14,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 30 percent higher. If there is a recession, then EBIT will be 60 percent lower. Money is considering a \$60,000 debt issue with a 5 percent interest rate. The proceeds will be used to repurchase shares of stock. There are currently 2,500 shares outstanding. Ignore taxes for this problem.

a. Calculate earnings per share, EPS, under each of the three economic scenarios before any debt is issued. Also, calculate the percentage changes in EPS when the economy expands or enters a recession.

b. Repeat part (a) assuming that Money goes through with recapitalization. What do you observe? 4. Break-Even EBIT Rolston Corporation is comparing two different capital structures, an allequity plan (Plan I) and a levered plan (Plan II). Under Plan I, Rolston would have 150,000 shares of stock outstanding. Under Plan II, there would be 60,000 shares of stock outstanding and \$1.5 million in debt outstanding. The interest rate on the debt is 10 percent and there are no taxes. a. If EBIT is \$200,000, which plan will result in the higher EPS?

b. If EBIT is \$700,000, which plan will result in the higher EPS?

c. What is the break-even EBIT?

5. MM and Stock Value In Problem 4, use MM Proposition I to ?nd the price per share of

equity under each of the two proposed plans. What is the value of the ?rm?

13. Calculating WACC Shadow Corp. has no debt but can borrow at 8 percent. The ?rm’s

WACC is currently 12 percent, and the tax rate is 35 percent.

a. What is Shadow’s cost of equity?

b. If the ?rm converts to 25 percent debt, what will its cost of equity be?

c. If the ?rm converts to 50 percent debt, what will its cost of equity be?

d. What is Shadow’s WACC in part (b)? In part (c)?

18. Firm Value Old School Corporation expects an EBIT of \$9,000 every year forever. Old School currently has no debt, and its cost of equity is 17 percent. The ?rm can borrow at 10 percent. If the corporate tax rate is 35 percent, what is the value of the ?rm? What will the value be if Old School converts to 50 percent debt? To 100 percent debt?

19. MM Proposition I with Taxes The Maxwell Company is ?nanced entirely with equity. The

company is considering a loan of \$1 million. The loan will be repaid in equal installments over the next two years, and it has an 8 percent interest rate. The company’s tax rate is 35 percent.

According to MM Proposition I with taxes, what would be the increase in the value of thecompany after the loan?

21. Cost of Capital Acetate, Inc., has equity with a market value of \$20 million and debt with a market value of \$10 million. The cost of the debt is 14 percent per year. Treasury bills that mature in one year yield 8 percent per year, and the expected return on the market portfolio over the next year is 18 percent. The beta of Acetate’s equity is .90. The ?rm pays no taxes.

a. What is Acetate’s debt-equity ratio?

b. What is the ?rm’s weighted average cost of capital?

c. What is the cost of capital for an otherwise identical all-equity ?rm?

25. MM with Taxes Williamson, Inc., has a debt-to-equity ratio of 2.5. The ?rm’s weighted

average cost of capital is 15 percent, and its pretax cost of debt is 10 percent. Williamson is subject to a corporate tax rate of 35 percent.

a. What is Williamson’s cost of equity capital?

b. What is Williamson’s unlevered cost of equity capital?

c. What would Williamson’s weighted average cost of capital be if the ?rm’s debt-to-equity ratio

were .75? What if it were 1.5?

29. Stockholder Risk Suppose a ?rm’s business operations are such that they mirror movements in the economy as a whole very closely, that is, the ?rm’s asset beta is 1.0. Use the result of previous problem to ?nd the equity beta for this ?rm for debt-equity ratios of 0, 1, 5, and

20. What does this tell you about the relationship between capital structure and shareholder risk? How is the shareholders’ required return on equity affected? Explain.

Solutions

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 ? 7.284

60 ––– +30 %;EPS

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

76.36 ––– +38.18 %;EPS

4. a. Under Plan I, the unlevered company, net income is the same as EBIT with no

corporate tax. The EPS under this capitalization will be:

EPS = ?220,000/150,000 shares

EPS = ?1.47

Under Plan II, the levered company, EBIT will be reduced by the interest payment.

The interest payment is the amount of debt times the interest rate, so:

NI = ?220,000 – .10(?1,500,000)

NI = ?70,000

And the EPS will be:

EPS = ?70,000/60,000 shares

EPS = ?1.17

Plan I has the higher EPS when EBIT is ?220,000.

b. Under Plan I, the net income is ?650,000 and the EPS is:

EPS = ?650,000/150,000 shares

EPS = ?4.33

Under Plan II, the net income is:

NI = ?650,000 – .10(?1,500,000)

NI = ?500,000

And the EPS is:

EPS = ?500,000/60,000 shares

EPS = ?8.33

Plan II has the higher EPS when EBIT is ?650,000.

c. To find the breakeven EBIT for two different capital structures, we simply set the

equations for EPS equal to each other and solve for EBIT. The breakeven EBIT is:

EBIT/150,000 = [EBIT .10(?1,500,000)]/60,000

EBIT = ?250,000

5. We can find the price per share by dividing the amount of debt used to repurchase shares by

the number of shares repurchased. Doing so, we find the share price is:

Share price = ?1,500,000/(150,000 – 60,000)

Share price = ?16.67 per share

The value of the company under the all-equity plan is:

V= ?16.67(150,000 shares) = ?2,500,000

And the value of the company under the levered plan is:

V = ?16.67(60,000 shares) + ?1,500,000 debt = ?2,500,000

13. a. For an all-equity financed company:

WACC = R = R = .12 or 12% UE

b. To find the cost of equity for the company with leverage, we need to use M&M

Proposition II with taxes, so:

R = R + (R R)(D/E)(1 t) E00DC

R = .12 + (.12 .08)(.1/.9)(1 .35) E

R = .1243 or 12.43% E

c. Using M&M Proposition II with taxes again, we get:

R = R + (R R)(D/E)(1 t) E00DC

R = .12 + (.12 .08)(.50/.50)(1 .35) E

R = .1460 or 14.60% E

d. The WACC with 10 percent debt is:

WACC = (E/V)R + (D/V)R(1 t) EDC

WACC = .90(.1243) + .10(.08)(1 .35)

WACC = .1171 or 11.71%

And the WACC with 50 percent debt is:

WACC = (E/V)R + (D/V)R(1 t) EDC

WACC = .50(.1460) + .50(.08)(1 .35)

WACC = .0990 or 9.90%

should continue to increase its debt/equity ratio to maximize the value of the firm.

18. With no debt, we are finding the value of an unlevered firm, so:

V = EBIT(1 t)/R C0

V = \$9,000(1 .35)/.18

V = \$32,500

With debt, we simply need to use the equation for the value of a levered firm. With 50

percent debt, one-half of the firm value is debt, so the value of the levered firm is:

V= V + tD U C

V = \$32,500 + .35(\$32,500/2)

V = \$38,187.50

And with 100 percent debt, the value of the firm is:

V= V + tD U C

V = \$32,500 + .35(\$32,500)

V = \$43,875

19. According to M&M Proposition I with taxes, the increase in the value of the company will

be the present value of the interest tax shield. Since the loan will be repaid in equal

installments, we need to find the loan interest and the interest tax shield each year. The loan

schedule will be:

Year Loan Balance Interest Tax Shield

0 1,000,000

1 500,000 80,000 .35(80,000) = 28,000

2 0 40,000 .35(40,000) = 14,000

So, the increase in the value of the company is:

2 Value increase = 28,000/1.08 + 14,000/(1.08)

Value increase = 37,928.67

21. a. A firm’s debt-equity ratio is the market value of the firm’s debt divided by the market

value of a firm’s equity. So, the debt-equity ratio of the company is:

Debt-equity ratio = MV of debt / MV of equity

Debt-equity ratio = ?10,000,000 / ?20,000,000

Debt-equity ratio = .50

b. We first need to calculate the cost of equity. To do this, we can use the CAPM, which

gives us:

R = R + [E(R) R] SFMF

R = .08 + .90(.18 .08) S

R = .1700 or 17.00% S

In the absence of taxes, a firm’s weighted average cost of capital is equal to:

R = [B / (B + S)]R + [S / (B + S)]RWACCBS

R = (?10,000,000/?30,000,000)(.14) + (?20,000,000/?30,000,000)(.17) WACC

R = .16000 or 16.00% WACC

c. According to Modigliani-Miller Proposition II with no taxes:

R = R + (B/S)(R R) S00B

.17 = R + (.50)(R .14) 00

R = .1600 or 16.00% 0

This is consistent with Modigliani-Miller’s proposition that, in the absence of taxes, the

cost of capital for an all-equity firm is equal to the weighted average cost of capital of

an otherwise identical levered firm.

25. a. In a world with corporate taxes, a firm’s weighted average cost of capital is equal to:

R = [B / (B+S)](1 t)R + [S / (B+S)]RWACCCBS

We do not have the company’s debt-to-value ratio or the equity-to-value ratio, but we

can calculate either from the debt-to-equity ratio. With the given debt-equity ratio, we

know the company has 2.5 dollars of debt for every dollar of equity. Since we only

need the ratio of debt-to-value and equity-to-value, we can say:

B / (B+S) = 2.5 / (2.5 + 1) = .7143

E / (B+S) = 1 / (2.5 + 1) = .2857

We can now use the weighted average cost of capital equation to find the cost of equity,

which is:

.15 = (.7143)(1 0.35)(.10) + (.2857)(R) S

R = .3625 or 36.25% S

b. We can use Modigliani-Miller Proposition II with corporate taxes to find the unlevered

cost of equity. Doing so, we find:

R = R + (B/S)(R R)(1 t) S00BC

.3625 = R + (2.5)(R .10)(1 .35) 00

R = .2000 or 20.00% 0

c. We first need to find the debt-to-value ratio and the equity-to-value ratio. We can then

use the cost of levered equity equation with taxes, and finally the weighted average cost

of capital equation. So:

If debt-equity = .75

B / (B+S) = .75 / (.75 + 1) = .4286

E / (B+S) = 1 / (.75 + 1) = .5714

The cost of levered equity will be:

R = R + (B/S)(R R)(1 t) S00BC

R = .20 + (.75)(.20 .10)(1 .35) S

R = .2488 or 24.88% S

And the weighted average cost of capital will be:

R = [B / (B+S)](1 t)R + [S / (B+S)]R WACCCBS

R = (.4286)(1 .35)(.10) + (.5714)(.2488) WACC

R = .17 WACC

If debt-equity =1.50

B / (B+S) = 1.50 / (1.50 + 1) = .6000

E / (B+S) = 1 / (1.50 + 1) = .4000

The cost of levered equity will be:

R = R + (B/S)(R R)(1 t) 00BCS

R = .20 + (1.50)(.20 .10)(1 .35) S

R = .2975 or 29.75% S

And the weighted average cost of capital will be:

R = [B / (B+S)](1 t)R + [S / (B+S)]R WACCCBS

R = (.6000)(1 .35)(.10) + (.4000)(.2975) WACC

R = .1580 or 15.80% WACC

29. Using the equation we derived in Problem 28:

= (1 + D/E) EA

The equity beta for the respective asset betas is:

Debt-equity ratio Equity beta

0 1(1 + 0) = 1

1 1(1 + 1) = 2

5 1(1 + 5) = 6

20 1(1 + 20) = 21

The equity risk to the shareholder is composed of both business and financial risk. Even if

the assets of the firm are not very risky, the risk to the shareholder can still be large if the

financial leverage is high. These higher levels of risk will be reflected in the shareholder’s

required rate of return R, which will increase with higher debt/equity ratios. E

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