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14. a. The value of the unlevered firm is:
V = EBIT(1 – TC)/R0
15. We can find the cost of equity using M&M Proposition II with taxes. First, we need to find the market
value of equity, which is:
V = B + S
$879,283.33 = $185,000 + S
S = $694,283.33
Now we can find the cost of equity, which is:
16. Since Unlevered is an all-equity firm, its value is equal to the market value of its outstanding shares.
Unlevered has 3.8 million shares of common stock outstanding, worth $71 per share. Therefore, the
value of Unlevered:
VU = 3,800,000($71)
VU = $269,800,000
17. To find the value of the levered firm, we first need to find the value of an unlevered firm. So, the value
of the unlevered firm is:
VU = EBIT(1 – TC)/R0
18. a. With no debt, we are finding the value of an unlevered firm, so:
V = EBIT(1 – TC)/R0
b. The general expression for the value of a leveraged firm is:
c. According to M&M Proposition I with taxes:
VL = VU + TCB
With debt being 50 percent of the value of the levered firm, D must equal (.50)VL, so:
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
$3,100,000
20. a. Since Alpha Corporation is an all-equity firm, its value is equal to the market value of its
outstanding shares. Alpha has 18,000 shares of common stock outstanding, worth $35 per share,
so the value of Alpha Corporation is:
b. Modigliani-Miller Proposition I states that in the absence of taxes, the value of a levered firm
equals the value of an otherwise identical unlevered firm. Since Beta Corporation is identical to
c. The value of a levered firm equals the market value of its debt plus the market value of its equity.
So, the value of Beta’s equity is:
d. The investor would need to invest 20 percent of the total market value of Alpha’s equity, which
is:
Amount to invest in Alpha = .20($630,000)
e. Alpha has no interest payments, so the dollar return to an investor who owns 20 percent of the
company’s equity would be:
Dollar return on Alpha investment = .20($93,000)
Dollar return on Alpha investment = $18,600
f. From part d, we know the initial cost of purchasing 20 percent of Alpha Corporation’s equity is
$126,000, but the cost to an investor of purchasing 20 percent of Beta Corporation’s equity is
only $109,000. In order to purchase $126,000 worth of Alpha’s equity using only $109,000 of
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
b. We first need to calculate the cost of equity. To do this, we can use the CAPM, which gives us:
RS = RF + [E(RM) – RF]
RS = .04 + 1.15(.11 – .04)
c. According to Modigliani-Miller Proposition II with no taxes:
RS = R0 + (B/S)(R0 – RB)
.1205 = R0 + (.39)(R0 – .04)
22. a. To purchase 5 percent of Knight’s equity, the investor would need:
Knight investment = .05($3,550,000)
Knight investment = $177,500
And to purchase 5 percent of Veblen without borrowing would require:
Veblen investment = .05($4,400,000)
Cash flow from Knight to shareholder = $25,700
Veblen will distribute all of its earnings to shareholders, so the shareholder will receive:
Cash flow from Veblen to shareholder = .05($610,000)
Cash flow from Veblen to shareholder = $30,500
b. Both of the two strategies have the same initial cost. Since the dollar return to the investment in
Veblen is higher, all investors will choose to invest in Veblen over Knight. The process of
investors purchasing Veblen’s equity rather than Knight’s will cause the market value of
23. a. Before the announcement of the stock repurchase plan, the market value of the outstanding debt
is $2,700,000. Using the debt-equity ratio, we can find that the value of the outstanding equity
must be:
Debt-equity ratio = B/S
.35 = $2,700,000/S
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:
c. According to Modigliani-Miller Proposition II with no taxes:
RS = R0 + (B/S)(R0 – RB)
.0995 = R0 + (.35)(R0 – .064)
R0 = .0903, or 9.03%
d. In part c, we calculated the cost of an all-equity firm. We can use Modigliani-Miller Proposition
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:
Taxes = .21($1,450,000)
Taxes = $304,500
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
Assets
$6,100,000
Equity
$6,100,000
c. Modigliani-Miller Proposition I states that in a world with corporate taxes:
When the company 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:
PV(Tax Shield) = TCB
PV(Tax Shield) = .21($1,600,000)
PV(Tax Shield) = $336,000
Therefore, the value of the company will increase by $336,000 as a result of the debt issue. The
value after the repurchase announcement 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:
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
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-
b. We can use Modigliani-Miller Proposition II with corporate taxes to find the unlevered cost of
equity. Doing so, we find:
RS = R0 + (B/S)(R0 – RB)(1 – TC)
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:
If debt-equity = 1.30
B/(B + S) = 1.30/(1.30 + 1) = .5652
S/(B + S) = 1/(1.30 + 1) = .4348
The cost of levered equity will be:
RS = R0 + (B/S)(R0 – RB)(1 – TC)
26. M&M Proposition II states:
RS = R0 + (R0 – RB)(B/S)(1 – TC)
And the equation for WACC is:
27. The return on equity is net income divided by equity. Net income can be expressed as:
NI = (EBIT – RBB)(1 – TC)
So, ROE is:
28. M&M Proposition II, with no taxes is:
RS = RA + (RA – Rf)(B/S)
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:
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
30. We first need to set the cost of capital equation equal to the cost of capital for an all-equity firm, so:
SB
B
+
RB +
SB
S
+
RS = R0
Multiplying both sides by (B + S)/S yields:
