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?

Question

Quizplus · Accepted Answer

Step 1: Calculate EPS before recapitalization
- Earnings before taxes (EBT) = EBIT(1 - Tax rate) = $2,000,000(1 - 0.40) = $1,200,000
- Net income = EBT - Interest expense = $1,200,000 - 0 = $1,200,000 (because the company has no debt)
- EPS = Net income / Number of shares outstanding = $1,200,000 / 200,000 = $6.00

Step 2: Calculate the new beta after recapitalization
- Unlevered beta = current beta / (1 + (1 - Tax rate)(Debt/Equity)) = 0.90 / (1 + (1 - 0.40)(5,000,000/0)) = 0.465
- Levered beta = Unlevered beta x (1 + (1 - Tax rate)(Debt/Equity)) = 0.465 x (1 + (1 - 0.40)(5,000,000/2,000,000)) = 1.155

Step 3: Calculate the cost of equity before and after recapitalization
- Cost of equity before recapitalization = Risk-free rate + Beta x Market risk premium = 6.5% + 0.90(5.0%) = 11.0%
- Cost of equity after recapitalization = Risk-free rate + Beta x Market risk premium = 6.5% + 1.10(5.0%) = 12.0%

Step 4: Calculate the new stock price after recapitalization
- The value of the firm before recapitalization is: VU = EBIT/ Cost of unlevered equity = $2,000,000 / 0.11 = $18,181,818
- The value of the firm after recapitalization is: VL = VU + Interest tax shield = $18,181,818 + 0.40(10.0%)($5,000,000) = $20,181,818
- The new number of shares outstanding is: NL = (Value of the firm after recapitalization - Debt) / Price per share = ($20,181,818 - $5,000,000) / Price per share
- EPS after recapitalization = EPS before recapitalization, so
- EPS after recapitalization = Net income / NL = $1,200,000 / (($20,181,818-$5,000,000)/Price per share)= $6.00
- Solving for Price per share, we get
- Price per share = ($1,200,000 / (($20,181,818-$5,000,000)/$6.00)) = $69.23

Therefore, the new stock price after the recapitalization would be $69.23 (Option B).

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