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)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

The price after recapitalization can be calculated using the formula: Price = EPS / (Cost of Equity). The cost of equity before recapitalization is calculated using the CAPM formula: Cost of Equity = Risk-free rate + Beta * Market risk premium. Before recapitalization, Cost of Equity = 6.5% + 0.90 * 5% = 11%. EPS before recapitalization = EBIT / Shares = $2,000,000 / 200,000 = $10. After recapitalization, the new beta is 1.10, so the new Cost of Equity = 6.5% + 1.10 * 5% = 12%. The new EPS is calculated by subtracting the interest on the new debt from EBIT and dividing by the new number of shares. Interest = $5,000,000 * 10% = $500,000. New EPS = ($2,000,000 - $500,000) / (200,000 - $5,000,000/$65) = $1,500,000 / 123,077 = $12.19. The new price = $12.19 / 12% = $69.23.