Theo currently owns 700 shares of JKL, which is an all-equity firm with 320,000 shares of stock outstanding at a market price of $25 a share. The company's earnings before interest and taxes are $160,000. JKL has decided to issue $500,000 of debt at 7.5 percent interest and use the proceeds to repurchase shares of stock. How many shares of JKL stock must Theo sell to unlever his position if he can loan out funds at 7.5 percent interest? (Assume partial shares can be sold.)
A) 38.50
B) 42.50
C) 50.00
D) 43.75
E) 46.67

Question

Quizplus · Accepted Answer

First, we need to find out how much the repurchase of shares will be. $500,000 / $25 per share = 20,000 shares.
Next, we need to find out how many shares will be outstanding after the share repurchase: 320,000 - 20,000 = 300,000 shares.
Now, we need to find out how much the interest expense will be: $500,000 x 0.075 = $37,500.
The new earnings before interest and taxes will be: $160,000 - $37,500 = $122,500.
To unlever his position, Theo needs to borrow $500,000 at 7.5 percent interest and use the proceeds to buy more shares of JKL. The interest expense on the loan will offset the interest income Theo earns on the cash received from selling his shares. Therefore, we can set up the following equation:
$500,000 x 0.075 = (700 - X) / 300,000 x $122,500
Solving for X gives us X = 43.75 shares.

Theo Currently Owns 700 Shares of JKL, Which Is an All-Equity