978-1259709685 Chapter 16 Solution Manual Part 3

subject Type Homework Help
subject Pages 7
subject Words 1528
subject Authors Jeffrey Jaffe, Randolph Westerfield, Stephen Ross

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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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CHAPTER 16 -
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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CHAPTER 16 -
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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CHAPTER 16 -
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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CHAPTER 16 -
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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CHAPTER 16 -
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
B+S
RB +
S
B+S
RS = R0
Multiplying both sides by (B + S)/S yields:
B
S
RB + RS =
B+S
S
R0
We can rewrite the right-hand side as:
B
S
RB + RS =
B
S
R0 + R0
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CHAPTER 16 -
Moving (B/S)RB to the right-hand side and rearranging gives us:
B
S
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