Question
McKean Inc. is an all-equity firm with 200,000 shares outstanding. The company’s EBIT is $2,000,000, and EBIT is expected to remain constant over time. The company pays out all of its earnings each year, so its earnings per share (EPS) equals its dividends per shares (DPS). The company’s tax rate is 40%.
The company is considering issuing $2 million worth of bonds (at par) and using the proceeds for a stock repurchase. If issued, the bonds would have an estimated YTM of 10%. The risk-free rate is 6.5%, and the market risk premium is 5.0%. The company’s beta is currently 0.90, but investment bankers say the beta will rise to 1.10 if the recapitalization occurs.
Assume that the shares are repurchased at a price equal to the stock market price prior to the recapitalization. What would be the company’s stock price following the recapitalization?
Explanation / Answer
Calculating the cost of equity using CAPM: Re = Rf + Beta [E(Rm) - Rf] Where Re is cost of equity E(Rm) is the return on market Rf is the risk-free rate [E(Rm) - Rf] is the market risk premium. Substituting the values in the above equation, Re = 0.065 + 0.90 (0.05) = 0.065 + 0.045 = 0.11 or 11% Therefore, the unlevered cost of equity is 11% Calculating the cost of equity using CAPM: Re = Rf + Beta [E(Rm) - Rf] Where Re is cost of equity E(Rm) is the return on market Rf is the risk-free rate [E(Rm) - Rf] is the market risk premium. Substituting the values in the above equation, Re = 0.065 + 0.90 (0.05) = 0.065 + 0.045 = 0.11 or 11% Therefore, the unlevered cost of equity is 11% The company is currently an all equity-firm, so the values equals the present value of after-tax cash flows, discounted at the cost of the firm's unlevered cost of equity.So, the current value of the company is Value = EBIT (1 - Tc) / Ru = $2,000,000 (1 - 0.40) / 0.11 = $10,909,091 The price per share before recapitalization is Price per share = Value / Number of outstanding share = $10,909,091 / 200,000 = $54.5 per share Calculating the new cost of equity: Re = 0.065 + 1.10 (0.05) = 0.065 + 0.055 = 0.12 or 12% Value of new equity = EBIT (1 - Tc) / Ru = $2,000,000 (1 - 0.40) / 0.12 = $10,000,000 Value of the firm after recapitalization = Value of equity + value of debt = $10,000,000 + $2,000,000 * (1 - 0.40) = $11,200,000 = 0.065 + 0.055 = 0.12 or 12% Value of new equity = EBIT (1 - Tc) / Ru = $2,000,000 (1 - 0.40) / 0.12 = $10,000,000 Value of the firm after recapitalization = Value of equity + value of debt Value of new equity = EBIT (1 - Tc) / Ru = $2,000,000 (1 - 0.40) / 0.12 = $10,000,000 = $2,000,000 (1 - 0.40) / 0.12 = $10,000,000 Value of the firm after recapitalization = Value of equity + value of debt = $10,000,000 + $2,000,000 * (1 - 0.40) = $11,200,000 = $10,000,000 + $2,000,000 * (1 - 0.40) = $11,200,000 New share price after recapitalization: Share price = $11,200,000 / 200,000 = $56