Michaely Inc. is an all-equity firm with 200,000 shares outstanding. It 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?

Question

Quizplus · Accepted Answer

The price following the recapitalization can be calculated using the formula for the price of a stock in a leveraged firm. First, calculate the current EPS: EBIT*(1-tax rate)/shares = $2,000,000*(1-0.40)/200,000 = $6. Then, calculate the current cost of equity using the CAPM: 6.5% + 0.90*5% = 11%. The current stock price is EPS/cost of equity = $6/0.11 = $54.55. After recapitalization, the new cost of equity is 6.5% + 1.10*5% = 12%. The new EPS is ($2,000,000 - $500,000)*(1-0.40)/150,000 = $6.67. The new stock price is $6.67/0.12 = $55.58. However, the price should be adjusted for the debt tax shield: $55.58 + ($5,000,000*0.10*0.40)/150,000 = $69.23.