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CHAPTER 16
CAPITAL STRUCTURE:
BASIC CONCEPTS
Answers to Concepts Review and Critical Thinking Questions
1. Assumptions of the Modigliani-Miller theory in a world without taxes: 1) Individuals can borrow at
the same interest rate at which the firm borrows. Since investors can purchase securities on margin, an
individual’s effective interest rate is probably no higher than that for a firm. Therefore, this assumption
2. False. A reduction in leverage will decrease both the risk of the stock and its expected return.
3. False. Modigliani-Miller Proposition II (No Taxes) states that the required return on a firm’s equity is
5. Business risk is the equity risk arising from the nature of the firm’s operating activity, and is directly
related to the systematic risk of the firm’s assets. Financial risk is the equity risk that is due entirely to
6. No, it doesn’t follow. While it is true that the equity and debt costs are rising, the key thing to remember
7. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot
8. It’s called leverage (or “gearing” in the UK) because it magnifies gains or losses.
10. The basic goal is to minimize the value of non-marketed claims.
Solutions to Questions and Problems
NOTE: All end-of-chapter problems were solved using a spreadsheet. Many problems require multiple
steps. Due to space and readability constraints, when these intermediate steps are included in this solutions
manual, rounding may appear to have occurred. However, the final answer for each problem is found
without rounding during any step in the problem.
1. a. A table outlining the income statement for the three possible states of the economy is shown
below. The EPS is the net income divided by the 5,000 shares outstanding. The last row shows
EPS
$ 2.28
$ 3.80
$ 4.75
%EPS
–40
–––
+25
b. If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Market value/Shares outstanding
EPS
$1.76
$ 3.76
$ 5.01
%EPS
–53.16
–––
+33.23%
2. a. A table outlining the income statement with taxes for the three possible states of the economy is
shown below. The share price is $49, and there are 5,000 shares outstanding. The last row shows
the percentage change in EPS the company will experience in a recession or an expansion
EPS
$1.80
$3.00
$3.75
%EPS
–40
–––
+25
b. A table outlining the income statement with taxes for the three possible states of the economy
EPS
$1.39
$2.97
$3.96
3. a. Since the company has a market-to-book ratio of 1.0, the total equity of the firm is equal to the
market value of equity. Using the equation for ROE:
ROE
4.65%
7.76%
9.69%
%ROE
–40
–––
+25
The second row shows the percentage change in ROE from the normal economy.
ROE
3.60%
7.68%
10.23%
ROE
3.68%
6.13%
7.66%
ROE
2.84%
6.07%
8.08%
4. a. Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax. The
EPS under this capitalization will be:
EPS = $1,250,000/365,000 shares
EPS = $3.42
Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest
And the EPS will be:
b. Under Plan I, the net income is $1,750,000 and the EPS is:
EPS = $1,750,000/365,000 shares
EPS = $4.79
Under Plan II, the net income is:
5. We can find the price per share by dividing the amount of debt used to repurchase shares by the number
of shares repurchased. Doing so, we find the share price is:
Share price = $4,560,000/(365,000 – 245,000)
6. a. The income statement for each capitalization plan is:
I
II
All-equity
EBIT
$14,800
$14,800
$14,800
b. The break-even level of EBIT occurs when the capitalization plans result in the same EPS. The
EPS is calculated as:
EPS = (EBIT – RBB)/Shares outstanding
This equation calculates the interest payment (RBB) and subtracts it from the EBIT, which results
in the net income. Dividing by the shares outstanding gives us the EPS. For the all-equity capital
c. Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT,
we get:
d. The income statement for each capitalization plan with corporate income taxes is:
I
II
All-equity
EBIT
$14,800
$14,800
$14,800
The all-equity plan has the highest EPS; Plan I has the lowest EPS.
We can calculate the EPS as:
EPS = [(EBIT – RBD)(1 – TC)]/Shares outstanding
7. To find the value per share of the stock under each capitalization plan, we can calculate the price as
the value of shares repurchased divided by the number of shares repurchased. The dollar value of the
shares repurchased is the increase in the value of the debt used to repurchase shares, or:
Dollar value of repurchase = $66,560 – 37,440
Dollar value of repurchase = $29,120
The number of shares repurchased is the decrease in shares outstanding, or:
8. a. The earnings per share are:
EPS = $43,600/5,000 shares
EPS = $8.72
b. To determine the cash flow to the shareholder, we need to determine the EPS of the firm under
the proposed capital structure. The market value of the firm is:
V = $49(5,000)
V = $245,000
Shares repurchased = 1,750
Under the new capital structure, the company will have to make an interest payment on the new
debt. The net income with the interest payment will be:
NI = $43,600 – .07($85,750)
NI = $37,598
c. To replicate the proposed capital structure, the shareholder should sell 35 percent of their shares,
or 35 shares, and lend the proceeds at 7 percent. The shareholder will have an interest cash flow
of:
Interest cash flow = 35($49)(.07)
Interest cash flow = $120.05
d. The capital structure is irrelevant because shareholders can create their own leverage or unlever
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 = $61,000 – .08($270,000)
NI = $39,400
The investor will receive dividends in proportion to the percentage of the company’s shares he
owns. 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 $30,000.
The shareholder should then borrow $30,000. This will create an interest cash flow of:
Interest cash flow = .08(–$30,000)
Interest cash flow = –$2,400
The investor should then use the proceeds of the stock sale and the loan to buy shares in ABC.
The investor will receive dividends in proportion to the percentage of the company’s share he
owns. The total dividends received by the shareholder will be:
c. ABC is an all equity company, so:
RS = RA = $61,000/$540,000
RS = .1130, or 11.30%
d. To find the WACC for each company, we need to use the WACC equation:
WACC = (S/V)RS + (B/V)RB(1 – TC)
So, for ABC, the WACC is:
10. With no taxes, the value of an unlevered firm is the EBIT divided by the unlevered cost of equity, so:
V = EBIT/WACC
11. If there are corporate taxes, the value of an unlevered firm is:
VU = EBIT(1 – TC)/RU
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 1.5, which implies the weight of debt is 1.5/2.5, and the
weight of equity is 1/2.5, so
b. To find the unlevered cost of equity, we need to use M&M Proposition II with taxes, so:
RS = R0 + (R0 – 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 = R0 + (R0 – RB)(B/S)(1 – TC)
RS = .1121 + (.1121 – .06)(2)(1 – .21)
RS = .1945, or 19.45%
13. a. For an all-equity financed company:
b. To find the cost of equity for the company with leverage, we need to use M&M Proposition II
with taxes, so:
c. Using M&M Proposition II with taxes again, we get:
d. The WACC with 25 percent debt is:
WACC = (S/V)RS + (B/V)RB(1 – TC)
