United Producers (UP), an unleveraged firm, has a total market value of $15 million, consisting of 600,000 shares of common stock selling at $25 per share

1). Computation of the current cost of equity:-

Earnings per share = EBIT * (1 - Tax rate) / Number of shares outstanding.

=$2,500,000 * (1 - 40%) / 600,000

= $1,500,000 / 600,000

= $2.50 per share

Current cost of equity = (Earnings per share / Market price per share)

= $2.50 / $20

= 12.50%

2). Computation of the unlevered beta:-

Cost of equity = Risk free rate + (Unlevered beta*Market risk premium)

12.50% = 2% + (Unlevered beta * 8%)

Unlevered beta * 8% = 12.50% - 2%

Unlevered beta = 10.50% / 8%

= 1.28

3). Computation of the levered beta:-

Levered beta = Unlevered beta*(1+(1-Tax rate)*(Debt/Equity))

= 1.28*(1+(1-40%)*(20%/80%))

= 1.28*1.15

= 1.47

4). Computation of the new cost of equity:-

New cost of equity = Risk free rate + (Levered beta*Market risk premium)

= 2% + (1.47 * 8%)

= 2% + 11.73%

= 13.73%

5). Computation of the new weighted average cost of capital (WACC):-

New WACC = (Weight of debt * After tax cost of debt) + (Weight of equity * New cost of equity)

= (20% * 8% * (1 - 40%)) + (80% * 13.73%)

= 0.96% + 10.98%

= 11.94%

6). Computation of the new corporate value:-

New corporate value = EBIT*(1-Tax rate) / New WACC

= $2,500,000*(1-40%) / 11.94%

= $1,500,000 / 11.94%

= $12,558,606.83

7). Computation of the new stock price:-

New stock price = Value of the firm / Number of shares outstanding

= $12,558,606.83 / 600,000

= $20.93 per share

8). Computation of the number of shares remain outstanding after the recapitalization:-

Value of debt = $12,558,606.83 * 20%

= $2,511,721.37

Number of shares repurchased = Value of debt / Price per share

= $2,511,721.37 / $20.93

= 120,000 shares

Remaining shares = 600,000 - 120,000

= 480,000 shares