Chapter 16: Capital Structure: Basic Concepts

16.1 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
$7,600
$19,000
$24,700

Interest 0 0 0

NI
$7,600
$19,000
$24,700

EPS
$ 1.52
$ 3.80
$ 4.94

%EPS
–60
–––
+30

b. If the company undergoes the proposed recapitalization, it will repurchase:

Share price = Equity / Shares outstanding Share price = $225,000/5,000 Share price = $45

Shares repurchased = Debt issued / Share price Shares repurchased =$90,000/$45 Shares repurchased = 2,000 The interest payment each year under all three scenarios will be:

Interest payment = $90,000(0.08) = $7,200

The last row shows the percentage change in EPS the company will experience in a recession or an expansion economy under the proposed recapitalization.

Recession
Normal
Expansion

EBIT
$7,600
$19,000
$24,700

Interest 7,200 7,200 7,200

NI
$ 400
$11,800
$17,500

EPS
$0.13
$ 3.93
$ 5.83

%EPS
–96.61
–––
+48.31

16.2 a. A table outlining the income statement with taxes for the three possible states of the economy is shown below. The share price is $45, 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 economy.

Recession
Normal
Expansion

EBIT
$7,600
$19,000
$24,700

Interest
0
0
0

Taxes 2,660 6,650 8,645

NI
$4,940
$12,350
$16,055

EPS
$0.99
$2.47
$3.21

%EPS
–60
–––
+30

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
$7,600
$19,000
$24,700

Interest
7,200
7,200
7,200

Taxes 140 4,130 6,125

NI
$ 260
$7,670
$11,375

EPS
$0.09
$2.56
$3.79

%EPS
–96.91
–––
+48.31

Notice that the percentage change in EPS is the same both with and without taxes.

16.3 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 = NI/$225,000

The ROE for each state of the economy under the current capital structure and no taxes is:

Recession
Normal
Expansion

ROE
3.38%
8.44%
10.98%

%ROE
–60
–––
+30

The second row shows the percentage change in ROE from the normal economy.

b. If the company undertakes the proposed recapitalization, the new equity value will be:

Equity = $225,000 – 90,000 Equity = $135,000

So, the ROE for each state of the economy is:

ROE = NI/$135,000

Recession
Normal
Expansion

ROE
0.30%
8.74%
12.96%

%ROE
–96.61
–––
+48.31

c. If there are corporate taxes and the company maintains its current capital structure, the ROE is:

ROE
2.20%
5.49%
7.14%

%ROE
–60
–––
+30

If the company undertakes the proposed recapitalization, and there are corporate taxes, the ROE for each state of the economy is:

ROE
0.19%
5.68%
8.43%

%ROE
–96.61
–––
+48.31

Notice that the percentage change in ROE is the same as the percentage change in EPS. The percentage change in ROE is also the same with or without taxes.

16.4 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 = $750,000/240,000 shares EPS = $3.13 Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:

NI = $750,000 – 0.10($3,100,000) NI = $440,000

And the EPS will be:

EPS = $440,000/160,000 shares EPS = $2.75