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9. a. The rate of return earned will be the dividend yield. The company has debt, so it must make an
interest payment. The net income for the company is:
NI = $70,000 – .08($325,000)
NI = $44,000
The investor will receive dividends in proportion to the percentage of the company’s share they
own. The total dividends received by the shareholder will be:
b. To generate exactly the same cash flows in the other company, the shareholder needs to match
the capital structure of ABC. The shareholder should sell all shares in XYZ. This will net
$20,000. The shareholder should then borrow $20,000. This will create an interest cash flow of:
Interest cash flow = .08($20,000)
Interest cash flow = $1,600
c. ABC is an all equity company, so:
RS = RA = $70,000/$650,000
RS = .1077, or 10.77%
RS = .1077 + (.1077 – .08)(1)(1)
d. To find the WACC for each company, we need to use the WACC equation:
WACC = (S/V)RS + (D/V)RD(1 – tC)
So, for ABC, the WACC is:
WACC = (1)(.1077) + (0)(.08)
10. With no taxes, the value of an unlevered firm is the interest rate divided by the unlevered cost of equity,
so:
V = EBIT/WACC
$51,300,000 = EBIT/.086
11. If there are corporate taxes, the value of an unlevered firm is:
VU = EBIT(1 – tC)/RU
Using this relationship, we can find EBIT as:
$51,300,000 = EBIT(1 – .35)/.086
12. a. With the information provided, we can use the equation for calculating WACC to find the cost
of equity. The equation for WACC is:
WACC = (S/V)RS + (B/V)RB(1 – tC)
The company has a debt-equity ratio of 1.4, which implies the weight of debt is 1.4/2.4, and the
weight of equity is 1/2.4, so
b. To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:
RS = RU + (RU – RB)(B/S)(1 – tC)
c. To find the cost of equity under different capital structures, we can again use M&M Proposition
II with taxes. With a debt-equity ratio of 2, the cost of equity is:
RS = RU + (RU – RB)(B/S)(1 – tC)
RS = .1043 + (.1043 – .057)(2)(1 – .35)
RS = .1658, or 16.58%
With a debt-equity ratio of 1, the cost of equity is:
13. a. For an all-equity financed company:
WACC = R0 = RS = .0920, or 9.20%
with taxes, so:
RS = R0 + (R0 – RB)(B/S)(1 – tC)
c. Using M&M Proposition II with taxes again, we get:
RS = R0 + (R0 – RB)(B/S)(1 – tC)
RS = .0920 + (.0920 – .0585)(.50/.50)(1 – .35)
d. The WACC with 25 percent debt is:
WACC = (S/V)RS + (B/V)RB(1 – tC)
V = EBIT(1 – tC)/R0
V = $81,400(1 – .35)/.14
V = VU + tCB
V = $377,928.57 + .35($145,000)
15. We can find the cost of equity using M&M Proposition II with taxes. Doing so, we find:
RE = R0 + (R0 – RB)(B/S)(1 – tC)
RS = .14 + (.14 – .07)[$145,000/($428,678.57 – 145,000)](1 – .35)
RS = .1633, or 16.33%
Using this cost of equity, the WACC for the firm after recapitalization is:
WACC = (S/V)RE + (B/V)RB(1 – tC)
Unlevered has 25,000 shares of common stock outstanding, worth $66 per share. Therefore, the value
of Unlevered:
VU = 25,000($66)
VU = $1,650,000
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 Levered is identical to Unlevered in every
way except its capital structure and neither firm pays taxes, the value of the two firms should be equal.
Therefore, the market value of Levered, Inc., should be $1,650,000 also. Since Levered has 19,000
VL = $1,292,000 + 310,000
VL = $1,602,000
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
VU = ($48,700)(1 – .35)/.11
VU = $287,772.73
Now we can find the value of the levered firm as:
VL = VU + tCB
VL = $287,772.73 + .35($90,000)
VU = EBIT(1 – tC)/R0
VU = $27,750(1 – .35)/.128
VU = $140,917.97
VL = VU + tCB
If debt is 50 percent of VU, then B = (.50)VU, and we have:
VL = VU + tC[(.50)VU]
VL = $140,917.97 + .35(.50)($140,917.97)
VL = $165,578.61
VL = VU + tC[(1.0)VU]
VL = $140,917.97 + .35(1.0)($140,917.97)
VL = $190,239.26
VL = VU + tCB
According to M&M Proposition I with taxes:
VL = VU + TCD
With debt being 50 percent of the value of the levered firm, D must equal (.50)VL, so:
VL = VU + TC[(.50)VL]
VL = $140,917.97 + .35(.50)(VL)
VL = $170,809.66
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
$640,000
1
320,000
$44,800
.35($44,800) = $15,680
2
0
22,400
.35($22,400) = $7,840
Value increase = $15,860/1.07 + $7,840/(1.07)2
Value increase = $21,501.97
so the value of Alpha Corporation is:
VAlpha = 19,000($23)
VAlpha = $437,000
Alpha Corporation in every way except its capital structure and neither firm pays taxes, the value
of the two firms should be equal. So, the value of Beta Corporation is $437,000 as well.
So, the value of Beta’s equity is:
VL = B + S
S = $352,000
Amount to invest in Alpha = .20($437,000)
Amount to invest in Alpha = $87,400
Beta has less equity outstanding, so to purchase 20 percent of Beta’s equity, the investor would
need:
Amount to invest in Beta = .20($352,000)
Amount to invest in Beta = $70,400
company’s equity would be:
Dollar return on Alpha investment = .20($71,000)
Dollar return on Alpha investment = $14,200
Beta Corporation has an interest payment due on its debt in the amount of:
Interest on Beta’s debt = .07($85,000)
Interest on Beta’s debt = $5,950
$70,400. In order to purchase $87,400 worth of Alpha’s equity using only $70,400 of his own
money, the investor must borrow $17,000 to cover the difference. The investor will receive the
same dollar return from the Alpha investment, but will pay interest on the amount borrowed, so
Net dollar return = $14,200 – .07($17,000)
Net dollar return = $13,010
firm’s earnings may be needed to repay its debt holders, and equity holders will receive nothing.
21. a. A firm’s debt-equity ratio is the market value of the firm’s debt divided by the market value of
Debt-equity ratio = MV of debt/MV of equity
Debt-equity ratio = $3,200,000/$7,100,000
Debt-equity ratio = .4507
RS = RF + [E(RM) – RF]
RS = .04 + 1.10(.11 – .04)
RS = .1170, or 11.70%
In the absence of taxes, a firm’s weighted average cost of capital is equal to:
RWACC = [B/(B + S)]RB + [S/(B + S)]RS
RWACC = ($3,200,000/$10,300,000)(.075) + ($7,100,000/$10,300,000)(.1170)
RWACC = .1040, or 10.40%
.1170 = R0 + (.4507)(R0 – .075)
R0 = .1040, or 10.40%
identical levered firm.
