CHAPTER 14
CAPITAL STRUCTURE: BASIC
CONCEPTS
Answers to Concept 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
is reasonable when applying MM’s theory to the real world. If a firm were able to borrow at a rate
lower than individuals, the firm’s value would increase through corporate leverage. As MM
2. False. A reduction in leverage will decrease both the risk of the stock and its expected return.
out and leave the price of the stock and the overall value of the firm unchanged.
3. False. Modigliani-Miller Proposition II (No Taxes) states that the required return on a firm’s equity is
4. Interest payments are tax deductible, where payments to shareholders (dividends) are not tax
deductible.
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
the firm’s chosen capital structure. As financial leverage, or the use of debt financing, increases, so
6. No, it doesn’t follow. While it is true that the equity and debt costs are rising, the key thing to remember
is that the cost of debt is still less than the cost of equity. Since we are using more and more debt, the
7. Because many relevant factors such as bankruptcy costs, tax asymmetries, and agency costs cannot
easily be identified or quantified, it’s practically impossible to determine the precise debt/equity ratio
that maximizes the value of the firm. However, if the firm’s cost of new debt suddenly becomes much
8. It’s called leverage (or “gearing” in the UK) because it magnifies gains or losses.
9. Homemade leverage refers to the use of borrowing on the personal level as opposed to the corporate
level.
10. The basic goal is to minimize the value of non-marketed claims, which will maximize shareholder
wealth.
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.
Basic
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
the percentage change in EPS the company will experience in a recession or an expansion
economy.
Recession
Normal
Expansion
EBIT
$19,500
$26,000
$31,200
Interest
0
0
0
NI
$19,500
$26,000
$31,200
EPS
$ 3.90
$ 5.20
$ 6.24
%EPS
–25
–
+20
b. If the company undergoes the proposed recapitalization, it will repurchase:
Share price = Equity/Shares outstanding
Share price = $305,000/5,000
Share price = $61.00
Shares repurchased = Debt issued/Share price
The interest payment each year under all three scenarios will be:
Interest payment = $95,000(.06)
Recession
Normal
Expansion
EBIT
$19,500
$26,000
$31,200
Interest
5,700
5,700
5,700
NI
$13,800
$20,300
$25,500
EPS
$ 4.01
$ 5.90
$ 7.41
%EPS
–32.02
––
+25.62
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 still $61, and there are still 5,000 shares outstanding. The last
row shows the percentage change in EPS the company will experience in a recession or an
expansion economy.
Recession
Normal
Expansion
EBIT
$19,500
$26,000
$31,200
Interest
0
0
0
Taxes
6,825
9,100
10,920
NI
$12,675
$16,900
$20,280
EPS
$2.54
$3.38
$4.06
%EPS
–25
––
+20
b. A table outlining the income statement with taxes for the three possible states of the economy
and assuming the company undertakes the proposed capitalization is shown below. The interest
payment and shares repurchased are the same as in part b of Problem 1.
Recession
Normal
Expansion
EBIT
$19,500
$26,000
$31,200
Interest
5,700
5,700
5,700
Taxes
4,830
7,105
8,925
NI
$8,970
$13,195
$16,575
EPS
$2.61
$3.83
$4.81
%EPS
–32.02
––
+25.62
Notice that the percentage change in EPS is the same both with and without taxes.
market value of equity. Using the equation for ROE:
ROE = NI/$305,000
Recession
Normal
Expansion
ROE
6.39%
8.52%
10.23%
%ROE
–25
–––
+20
The second row shows the percentage change in ROE from the normal economy.
Equity = $305,000 – 95,000
Equity = $210,000
So, the ROE for each state of the economy is:
ROE = NI/$210,000
c. To find the breakeven EBIT for two different capital structures, we set the equations for EPS
equal to each other and solve for EBIT. The breakeven EBIT is:
EBIT/145,000 = [EBIT – .08($3,047,000)]/90,000
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 = $3,047,000/(145,000 – 90,000)
Share price = $55.40 per share
The value of the company under the all-equity plan is:
6. a. The income statement for each capitalization plan is:
I
II
All-equity
EBIT
$7,600
$7,600
$7,600
Interest
959
2,110
0
NI
$6,641
$5,490
$7,600
EPS
$ 1.79
$ 1.77
$ 1.81
b. The breakeven level of EBIT occurs when the capitalization plans results in the same EPS. The
EPS is calculated as:
EPS = (EBIT – RDD)/Shares outstanding
This equation calculates the interest payment (RDD) 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
structure, the interest term is zero. To find the breakeven EBIT for two different capital structures,
c. Setting the equations for EPS from Plan I and Plan II equal to each other and solving for EBIT,
we get:
[EBIT – .07($13,700)]/3,700 = [EBIT – .07($30,140)]/3,100
d. The income statement for each capitalization plan with corporate income taxes is:
I
II
All-equity
EBIT
$7,600
$7,600
$7,600
Interest
959
2,110
0
Taxes
2,656
2,196
3,400
NI
$3,985
$3,249
$4,560
EPS
$ 1.08
$ 1.06
$ 1.09
We can calculate the EPS as:
EPS = [(EBIT – RDD)(1 – tC)]/Shares outstanding
This is similar to the equation we used before, except that now we need to account for taxes.
Again, the interest expense term is zero in the all-equity capital structure. So, the breakeven EBIT
between the all-equity plan and Plan I is:
And the breakeven between Plan I and Plan II is:
[EBIT – .07($13,700)](1 – .40)/3,700 = [EBIT – .07($30,140)](1 – .40)/3,100
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:
So, under Plan I, the value per share is:
This shows that when there are no corporate taxes, the stockholder does not care about the capital
structure decision of the firm. This is M&M Proposition I without taxes.
8. a. The earnings per share are:
EPS = $36,000/7,600 shares
EPS = $4.74
So, the cash flow for the shareholder is:
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 = $55(7,600)
V = $418,000
Under the proposed capital structure, the firm will raise new debt in the amount of:
This means the EPS under the new capital structure will be:
Shareholder cash flow = $491.82
c. To replicate the proposed capital structure, the shareholder should sell 35 percent of their shares,
or 35 shares, and lend the proceeds at 8 percent. The shareholder will have an interest cash flow
of:
The total cash flow for the shareholder under these assumptions will be:
Total cash flow = $473.68
d. The capital structure is irrelevant because shareholders can create their own leverage or unlever