978-1259709685 Chapter 16 Solution Manual Part 3

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CHAPTER 16 –

23. a. Before the announcement of the stock repurchase plan, the market value of the outstanding debt

is $3,100,000. Using the debt–equity ratio, we can find that the value of the outstanding equity

must be:

The value of a levered firm is equal to the sum of the market value of the firm’s debt and the

market value of the firm’s equity, so:

According to MM Proposition I without taxes, changes in a firm’s capital structure have no

b. The expected return on a firm’s equity is the ratio of annual earnings to the market value of the

firm’s equity, or return on equity. Before the restructuring, the company was expected to pay

interest in the amount of:

The return on equity, which is equal to RS, will be:

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

This problem can also be solved in the following way:

R0 = Earnings before interest / VU

According to Modigliani-Miller Proposition I, in a world with no taxes, the value of a levered

firm equals the value of an otherwise-identical unlevered firm. Since the value of the company

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d. In part c, we calculated the cost of an all-equity firm. We can use Modigliani-Miller Proposition

II with no taxes again to find the cost of equity for the firm with the new leverage ratio. The

cost of equity under the stock repurchase plan will be:

24. a. The expected return on a firm’s equity is the ratio of annual aftertax earnings to the market

value of the firm’s equity. The amount the firm must pay each year in taxes will be:

So, the return on the unlevered equity will be:

b. The company’s market value balance sheet before the announcement of the debt issue is:

Debt 0

The price per share is the total market value of the stock divided by the shares outstanding, or:

c. Modigliani-Miller Proposition I states that in a world with corporate taxes:

VL = VU + tCB

When Green announces the debt issue, the value of the firm will increase by the present value

of the tax shield on the debt. The present value of the tax shield is:

Therefore, the value of Green Manufacturing will increase by $720,000 as a result of the debt

issue. The value of Green Manufacturing after the repurchase announcement is:

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Since the firm has not yet issued any debt, Green’s equity is also worth $6,620,000.

Green’s market value balance sheet after the announcement of the debt issue is:

d. The share price immediately after the announcement of the debt issue will be:

e. The number of shares repurchased will be the amount of the debt issue divided by the new

share price, or:

The number of shares outstanding will be the current number of shares minus the number of

shares repurchased, or:

f. The share price will remain the same after restructuring takes place. The total market value of

the outstanding equity in the company will be:

The market-value balance sheet after the restructuring is:

g. According to Modigliani-Miller Proposition II with corporate taxes

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

RWACC = [B / (B + S)](1 – tC)RB + [S / (B + S)]RS

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

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

is:

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

equity. Doing so, we find:

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

The cost of levered equity will be:

And the weighted average cost of capital will be:

If debt–equity =1.30

The cost of levered equity will be:

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And the weighted average cost of capital will be:

Challenge

26. M&M Proposition II states:

And the equation for WACC is:

Substituting the M&M Proposition II equation into the equation for WACC, we get:

Rearranging and reducing the equation, we get:

27. The return on equity is net income divided by equity. Net income can be expressed as:

Now we can rearrange and substitute as follows to arrive at M&M Proposition II with taxes:

RS = [EBIT(1 – tC)/S] – [RB(B/S)(1 – tC)]

RS= R0VU/S – [RB(B/S)(1 – tC)]

28. M&M Proposition II, with no taxes is:

Note that we use the risk-free rate as the return on debt. This is an important assumption of M&M

Proposition II. The CAPM to calculate the cost of equity is expressed as:

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We can rewrite the CAPM to express the return on an unlevered company as:

We can now substitute the CAPM for an unlevered company into M&M Proposition II. Doing so and

rearranging the terms, we get:

Now we set this equation equal to the CAPM equation to calculate the cost of equity and reduce:

29. Using the equation we derived in Problem 28:

S = A(1 + B/S)

The equity beta for the respective asset betas is:

Debt–equity ratio Equity beta

0 1(1 + 0) = 1

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

30. We first need to set the cost of capital equation equal to the cost of capital for an all-equity firm, so:

B+S

RB +

B+S

RS = R0

Multiplying both sides by (B + S)/S yields:

RB + RS =

B+S

We can rewrite the right-hand side as:

RB + RS =

R0 + R0

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Moving (B/S)RB to the right-hand side and rearranging gives us: