Question

Assume you have just been hired as a business manager of Bernie’s Pizza Plaza a regional pizza restaurant chain. The company’s EBIT was $125 million last year and is not expected to grow. The firm is currently financed with all equity and it has 10 million shares outstanding. When you took your corporate finance course, your instructor stated that most firm’s owners would be financially better off if the firms used some debt. When you suggested this to your new boss, he encouraged you to pursue the idea. As a first step, assume that you obtained from the firm’s investment banker the following estimated costs of debt for the firm at different capital structures:

                                                   % Financed With Debt            r_d           

                                                               0%                              ---      

                                                              20                                 8.25%     

                                                              40                                 8.85      

                                                              60                                 11.4      

                                                              80                                 14.2      

If the company were to recapitalize, debt would be issued, and the funds received would be used to repurchase stock. Bernie’s is in the 25 percent state-plus-federal corporate tax bracket, its unlevered beta is 1.25, the risk-free rate is 4 percent, and the market risk premium is 6 percent.

a.   For each capital structure under consideration, calculate the levered beta, the cost of equity, and the WACC.

b.   Now calculate the corporate value for each capital structure.

c. Compute the value of the firms’ stock.

Show all work for answers!****

Answer 1

a) Levered Beta = Unlevered beta * ( 1 + (1-tax rate)* (Debt/Equity))

Levered beta in different cases

Debt = 0%, Levered Beta = Unlevered Beta = 1.25

Debt = 20%, Levered Beta = 1.25 * (1 + (1-0.25)*(20%/80%)) = 1.484

Debt = 40%, Levered Beta = 1.25* (1+ (1-0.25)*40%/60%)) = 1.875

Debt = 60%,Levered Beta = 1.25* (1+ (1-0.25)*60%/40%)) = 2.65

Debt = 80%, Levered Beta = 1.25* (1+ (1-0.25)*80%/20%)) = 5.00

Cost of equity =

a) Debt = 0%, Levered Beta = Unlevered Beta = 1.25,

Cost of equity = Rf + Levered Beta (Rm - Rf) = 4% + 1.25*(6-4) = 6.50%

b) Debt = 20%, Levered Beta = 1.25 * (1 + (1-0.25)*(20%/80%)) = 1.484

Cost of equity = Rf + Levered Beta (Rm - Rf) = 4% + 1.484*(6-4) = 6.97%

c) Debt = 40%, Levered Beta = 1.25* (1+ (1-0.25)*40%/60%)) = 1.875

Cost of equity = Rf + Levered Beta (Rm - Rf) = 4% + 1.875*(6-4) = 7.75%

d) Debt = 60%,Levered Beta = 1.25* (1+ (1-0.25)*60%/40%)) = 2.65

Cost of equity = Rf + Levered Beta (Rm - Rf) = 4% + 2.65*(6-4) = 9.30%

e) Debt = 80%, Levered Beta = 1.25* (1+ (1-0.25)*80%/20%)) = 5.00

Cost of equity = Rf + Levered Beta * (Rm-Rf) = 4% + 5*(6-4) = 14%

WACC - Debt = 0% = D/(D+E) * Rd (1-tc) + E/(D+E) * Re = 6.50%

WACC - Debt = 20% = D/(D+E) * Rd (1-tc) + E/(D+E) * Re = 0.2* 8.25%*(1-0.25) + 0.8 * 6.97% = 6.813%

WACC - Debt = 40% = D/(D+E) * Rd (1-tc) + E/(D+E) * Re = 0.4* 8.85%*(1-0.25) + 0.6 * 7.75% = 7.305%

WACC - Debt = 60% = D/(D+E) * Rd (1-tc) + E/(D+E) * Re = 0.6* 11.40%*(1-0.25) + 0.4 * 9.30% = 8.85%

WACC - Debt = 80% = 0.8*14.20%*(1-0.25) + 0.2*14% = 11.32%

b) Corporate value of firm when growth is zero = EBIT/ WACC

Case - I = $125 mio/0.065 = $ 1923.08 mio

Case - II = $125 mio/0.06813 = $1834.59 mio

Case - III = $125 mio/0.07305 = $1711.16 mio

Case - IV = $125 mio/0.0885 = $1412.43 mio

Case - V = $125 mio/0.1132 = $1104.24 mio