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CHAPTER 14 B - 1
22. a. To purchase 5 percent of Knight’s equity, the investor would need:
Knight investment = .05($1,550,000)
Knight investment = $77,500
And to purchase 5 percent of Veblen without borrowing would require:
However, to have the same initial cost, the investor has borrowed $55,000 to invest in Veblen,
so interest must be paid on the borrowings. The net cash flow from the investment in Veblen will
be:
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
market values of the two firms are equal.
23. a. Before the announcement of the stock repurchase plan, the market value of the outstanding debt
is $4,960,000. Using the debt-equity ratio, we can find that the value of the outstanding equity
must be:
Debt-equity ratio = B/S
CHAPTER 14 B - 2
.20 = $4,960,000/S
S = $24,800,000
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:
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:
Interest payment = .07($4,960,000)
c. According to Modigliani-Miller Proposition II with no taxes:
RS = R0 + (B/S)(R0 – RB)
.1037 = R0 + (.20)(R0 – .07)
R0 = .0981, or 9.81%
This problem can also be solved in the following way:
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:
Taxes = .40($1,860,000)
Taxes = $744,000
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
$7,700,000
Equity
$7,700,000
Total assets
$7,700,000
Total D&E
$7,700,000
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 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:
Old assets
$7,700,000
Debt
0
PV(tax shield)
640,000
Equity
$8,340,000
Total assets
$8,340,000
Total D&E
$8,340,000
CHAPTER 14 B - 4
d. The share price immediately after the announcement of the debt issue will be:
New share price = $32.08
e. The number of shares repurchased will be the amount of the debt issue divided by the new share
price, or:
Shares repurchased = $1,600,000/$32.08
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:
Market value of equity = $32.08(210,119.90)
Market value of equity = $6,740,000
The market-value balance sheet after the restructuring is:
CHAPTER 14 B - 5
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 = .60
B/(B + S) = .60/(.60 + 1) = .3750
S/(B + S) = 1/(.60 + 1) = .6250
The cost of levered equity will be:
Challenge
26. M&M Proposition II states:
RS = R0 + (R0 – RB)(B/S)(1 – tC)
And the equation for WACC is:
WACC = (S/V)RS + (B/V)RB(1 – tC)
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:
RS = (EBIT – RBB)(1 – tC)/E
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:
CHAPTER 14 B - 7
RS = A(RM – Rf) + Rf + [A(RM – Rf) + Rf – Rf](B/S)
RS = A(RM – Rf) + Rf + [A(RM – Rf)](B/S)
E = A(1 + B/S)
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
high. These higher levels of risk will be reflected in the shareholder’s required rate of return RE, which
will increase with higher debt/equity ratios.
SB
B
+
RB +
SB
S
+
RS = R0
Multiplying both sides by (B + S)/S yields:
S
B
RB + RS =
S
SB +
R0
S
