Question

• An all-equity firm with 200,000 shares outstanding, 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) equals dividends per share (DPS). Its tax rate is 40%. The company is considering issuing $5,000,000 of 10% 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 that the 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?

Answer 1

First we will calculate the share price before recapitalization

No of shares outstanding before recapitalization = 200000, Constant EBIT = 2000000

Since the firm is all equity firm, hence debt = 0, also interest expense = 0

Net income before recapitalization = (EBIT - interest)(1-tax rate) = (2000000 - 0)(1-40%) = 1200000

Earning per share before recapitalization = Net income before recapitalization / No of shares outstanding before recapitalization = 1200000 / 200000 = $6

Since company pays all its earnings as dividends, therefore dividend per share before recapitalization = earnings per share before recapitalization = $6

According to capital asset pricing model

Cost of equity before recapitalization = Risk free rate x Beta before recapitalization x market risk premium = 6.5% + 0.90 x 5% = 6.5% + 4.5% = 11.00%

As EBIT is expected to remain constant and company pays all its earnings are dividends hence, Dividend per share will also remain constant and form a perpetuity

Price of a stock is equal to present value of future dividends and dividends in this question for a perpetuity

Present value of perpetuity = cash flow / discount rate

So, Price of share before recapitalization = dividend per share before recapitalization / Cost of equity before recapitalization = $6 / 11% = $54.5454 = $54.55 (rounded to two decimal places)

No of shares repurchased = Total value of bonds issued / Price of share before recapitalization = 5000000 / 54.55 = 91659.02 = 91659 (rounded to nearest whole number as shares cannot be in decimal)

Total shares outstanding after recapitalization = Shares before recapitalization - shares purchased = 2000000 - 91659 = 108341

Interest expense after recapitalization = Bonds issued x interest rate = 5000000 x 10% = 500000

Net income after recapitalization = (2000000 - 500000)(1-40%) =1500000 x 60% = 900000

Dividend per share after recapitalization = Earnings per share after recapitalization = Net income after recapitalization / Total shares outstanding after recapitalization = 900000 / 108341 = 8.3071

Cost of equity after recapitalization = Risk free rate x Beta after recapitalization x market risk premium = 6.5% + 1.10 x 5 = 6.50% + 5.50% = 12%

Price per share after recapitalization = Dividend per share after recapitalization / Cost of equity after recapitalization = 8.3071 / 12% = 69.2258 = $69.23 (rounded to two decimal places)

Hence price per share after recapitalization = $69.23