Exhibit 16.4
The Anson Jackson Court Company (AJC) currently has $200,000 market value (and book value) of perpetual debt outstanding carrying a coupon rate of 6%. Its earnings before interest and taxes (EBIT) are $100,000, and it is a zero growth company. AJC's current cost of equity is 8.8%, and its tax rate is 40%. The firm has 10,000 shares of common stock outstanding selling at a price per share of $60.00.
-Refer to Exhibit 16.4.Now assume that AJC is considering changing from its original capital structure to a new capital structure that results in a stock price of $64 per share.The resulting capital structure would have a $336,000 total market value of equity and a $504,000 market value of debt.How many shares would AJC repurchase in the recapitalization?

Question

Quizplus · Accepted Answer

First, we need to calculate the cost of equity under the new capital structure:
$336,000 = 10,000 shares x $64 per share
Cost of equity = dividend yield + growth rate
We know AJC is a zero growth company, so growth rate is 0.
$4 dividend per share / $64 stock price = 0.0625 dividend yield
Cost of equity = 0.0625 + 0 = 6.25%

Next, we can calculate the WACC for the new capital structure:
WACC = (E/V) x r(e) + (D/V) x r(d) x (1 - Tc)
V = E + D = $336,000 + $504,000 = $840,000
E/V = $336,000 / $840,000 = 0.4
D/V = $504,000 / $840,000 = 0.6
r(e) = 6.25%
r(d) = 6%
Tc = 40%
WACC = (0.4 x 6.25%) + (0.6 x 6% x (1 - 40%)) = 4.05%

Now, we can calculate the new earnings per share (EPS):
EPS = (EBIT - Interest) x (1 - Tc) / Shares
Interest = $504,000 x 6% = $30,240
EPS = ($100,000 - $30,240) x (1 - 40%) / 10,000 = $3.456

Finally, we can calculate the new stock price if AJC buys back some shares:
New EPS = $100,000 x (1 - 40%) / (10,000 - x)
$3.456 = $100,000 x 60% / (10,000 - x)
x = 4,750

Therefore, AJC would repurchase 4,750 shares in the recapitalization.

Exhibit 16.4 The Anson Jackson Court Company (AJC) Currently Has $200,000 Market