CP

Estimating the Optimal Capital Structure 499

Here D 0 is the amount of debt the company had before the recap, which for Strasburg

was zero.

For example, at the optimal capital structure, Strasburg will issue $88,889 in debt

and use the proceeds to repurchase stock .Thus, the total wealth of the sharehold-

ers after the repurchase will be the cash they receive in the repurchase ($88,889) plus

the value of their remaining equity ($133,333), for a total wealth of $222,222 .No-

tice that their total wealth increases from its original level of $200,000 to the new

level of $222,222, a gain of $22,222 .This is exactly equal to the increase in total

value experienced by Strasburg, so the shareholders reap the full rewards of the re-

capitalization.

Prior to the announced recap, Strasburg had a $200,000 market value of equity

and 10,000 shares of stock outstanding (n 0 ). Therefore, its stock price prior to the re-

cap was $20 per share ($200,000/10,000 $20).

To find the price per share after the recap, consider the sequence of events. (1) The

company announces the recap and issues new debt. (2) The company uses the

proceeds from the debt issue to repurchase shares of stock. These events don’t occur

exactly simultaneously, so let’s examine each event separately.

Strasburg Issues New Debt Strasburg announces its plans to recapitalize, and

borrows $88,889. It has not yet repurchased the stock, and so the $88,889 of debt pro-

ceeds are temporarily used to purchase short-term investments such as T-bills or

other marketable securities. Using the corporate valuation model from Chapter 12,

the total corporate value is now equal to the value of operations, calculated by dis-

counting the expected free cash flows by the new WACC, plus the value of any non-

operating assets such as short-term investments. Therefore, Strasburg’s total value

after issuing debt but before repurchasing stock is

$222,222 
$88,889 $311,111.

Total corporate valueValue of operations
Value of short-term investments

TABLE 13-4 Strasburg’s Stock Price and Earnings per Share

Percent Market Market Number of
Financed Value of Value Value Shares after Earnings
with Debt, Firm, of Debt, of Equity, Stock Price, Repurchase, Net Income, per Share,
wd V (D) S P n NI EPS
(1) (2)a (3)b (4)c (5)d (6)e (7)f (8)g
0% $200,000 $0 $200,000 $20.00 $10,000 $24,000 $2.40
10 206,186 20,619 185,567 20.62 9,000 23,010 2.56
20 212,540 42,508 170,032 21.25 8,000 21,934 2.74
30 217,984 65,395 152,589 21.80 7,000 20,665 2.95
40 222,222 88,889 133,333 22.22 6,000 19,200 3.20
50 216,216 108,108 108,108 21.62 5,000 16,865 3.37
60 200,000 120,000 80,000 20.00 4,000 13,920 3.48

Notes:
aThe value of the firm is taken from Table 13-3.
bThe value of debt is found by multiplying the percent of the firm financed with debt in Column 1 by the value of the firm in Column 2.
cThe value of equity is found by subtracting the value of debt in Column 3 from the total value of the firm in Column 2.
dThe number of outstanding shares prior to the recap is n 0 10,000. The stock price is P [S
(D D 0 )]/n 0 [S
D]/10,000.
eThe number of shares after the recapitalizations is n S/P.
fNet income is NI (EBIT rdD) (I T), where EBIT $40,000 (taken from Table 13-1), rdcomes from Table 13-2, and T 40%.
gEPS NI/n.

Capital Structure Decisions 495