An all-equity firm with 200,000 shares outstanding,Antwerther Inc. ,has $2,000,000 of EBIT,which is expected to remain constant in the future.The company pays out all of its earnings,so earnings per share (EPS)equal dividends per shares (DPS).Its tax rate is 40%.
The company is considering issuing $5,000,000 of 10.0% bonds and using the proceeds to repurchase stock.The risk-free rate is 6.5%,the market risk premium is 5.0%,and the beta is currently 0.90,but the CFO believes beta would rise to 1.10 if the recapitalization occurs.
Assuming that the shares can be repurchased at the price that existed prior to the recapitalization,what would the price be following the recapitalization?
A) $65.77
B) $69.23
C) $72.69
D) $76.33
E) $80.14

Question

Quizplus · Accepted Answer

Step 1: Calculate the cost of debt

Cost of debt = 10% 
Cost of debt after tax = 10% x (1 - 40%) = 6%

Step 2: Calculate the new beta

New beta = 0.9 + (0.1 x 1.5) = 1.05

Step 3: Calculate the required return on equity

Risk-free rate = 6.5%
Market risk premium = 5%
Required return on equity = 6.5% + (1.05 x 5%) = 12.25%

Step 4: Calculate the new WACC

Weight of equity = 1 
Weight of debt = 5,000,000 / (5,000,000 + 2,000,000) = 71.43%
WACC = (0.7143 x 6%) + (0.2857 x 12.25%) = 7.78%

Step 5: Calculate the new EPS

New EPS = (2,000,000 x (1 - 40%)) / 200,000 = $7.20

Step 6: Calculate the new stock price

New stock price = $7.20 / 7.78% = $92.31

Step 7: Calculate the price per share after repurchasing

Price per share after repurchasing = ($2,000,000 - $5,000,000 x 6%) / 200,000 = $67.00

Therefore, the new stock price is $67.00, and the price after the repurchase is $69.23, so the answer is B.

An All-Equity Firm with 200,000 Shares Outstanding,Antwerther Inc