Question

* The Rivoli Company has no debt outstanding, and its financial position is given by the following data;

                Asset (book = market)                  $3,000,000

                  EBIT                                             $ 500,000

                  Cost of equity, rs                                      10%

                  Stock price, P₀                                          $15

                  Shares outstanding, n₀                       200,000

                  Tax rate, T (federal +state)                       40%

The firm is considering bonds and simultaneously repurchasing some of its stock. If it moves to capital structure with 30% debt based on market values, its cost of equity, rs, will increase to 11 % to reflect the increased risk. Bonds can be sold at a cost (rd) of 7%. Rivoli is a no growth firm. Hence, all its earnings are paid out as dividends, and earnings are expected constant over time.                                                    

1. What effect would this use of leverage have on the value of the firm? Calculate the value of the firm with new capital structure. (hint: first calculate WACC, then…get the value of firm).   

2. What would be the price of Rivoli’s stock after new capital structure with 30% debt?

3. What is the firm’s earnings per share before and after the recapitalization?

V = FCF / (WACC – g),     b_L= b_U[1 + (1 - T)(D/S)],    P = [S + (D-D₀)]/n₀

* New co. is considering a change in its capital structure. New co. currently has $20 million in debt carrying a rate of 8%, and its stock price is $40 per share with 2 million shares outstanding. Assume no growth and pays all of its earnings as dividends. EBIT is $14.933 million, and tax rate is 40%. The market risk premium is 4%, and the risk free rate is 6%. New co. is considering increasing its debt level to a capital structure with 40% debt, and repurchasing shares with the extra money that it borrows. New co. will have to retire the old debt in order to issue new debt, and the rate on the new debt will be 9 %. New co. has beta of 1.0.                                                                           

4. What is New co’s unlevered beta? Use market value D/S when levering.

5. What are New co’s new beta and cost of equity if it has 40 percent debt?

6. What are New co’s WACC and total value of the firm with 40% debt?

Answer 1

answering first four questions including sub-section as per policy.

Answer a ) The leverage will increase the value of firm in market

Value of firm before new capital structure = Share price * number of outstanding shares = 15*200,000= $ 30,00,000.

Answer b)after leverage , WACC = K_e * W_e + Interest on debt *(1-tax)* W_d

W_d = 30% , W_e = 1-30% = 70%

WACC= 11%*0.70 + 7%(1-0.40)*0.30 = 8.96%

Free cash flow (FCF) = 500000 * (1-0.40) = 300000

New Value of firm (V) = FCF / (WACC – g) , where g= 0

V = 300000 / 8.96% = $ 33,48,214.29.

Answer c)New price of share after leverage , b_L= b_U[1 + (1 - T)(D/S)] = 15*(1+(1-0.4)*(0.3/0.7)) = $ 18.857.

Answer d) Before leverage EPS = FCF/ no of outstanding share = 300000/200000 = $ 1.5 per share

After leverage Number shares : Value of equity / price of equity = (33,48,214.29* 70%)/ 18.857 =124290

Earning after interest and tax = (EBIT - Interest)* (1-tax) = (500000-33,48,214.29* 30%*7%)*(1-0.40)= 295788.899

EPS after leverage = 295788.899 /124290= 2.3798 = $ 2.38 per share