Question

3.   Assume you have just been hired as a business manager of Pamela’s Pizza, a regional      pizza restaurant chain. The firm is currently financed with all equity and it has 15 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%                                         ---      

                                                              10                                 8.0%     

                                                              25                                 9.0

                                                              35                               10.5      

                                                              45                                12.0      

      If the company were to recapitalize, debt would be issued, and the funds received would be used to repurchase stock. Pamela’s Pizza is in the 25 percent state-plus-federal corporate tax     bracket, its beta is 0.75, the risk-free rate is 4 percent, and the market risk premium is 7       percent.

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

Answer 1

i) Levered beta calculations :

Unlevered beta = 0.75,

Tax rate = 25% or 0.25

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

Weight of debt	Weight of equity (1 - weight of debt)	Debt/Equity	Levered beta (using formula)
10% or 0.10	0.90	=0.10/0.90 = 0.11	= 0.75 * (1+(1-0.25) * 0.11)) = 0.81
25% or 0.25	0.75	=0.25/0.75 = 0.33	=0.75 * (1+(1-0.25) * 0.33)) = 0.94
35% or 0.35	0.65	=0.35/0.65 = 0.54	=0.75 * (1+(1-0.25) * 0.54)) = 1.05
45% or 0.45	0.55	=0.45/0.55 = 0.82	=0.75 , (1+(1-0.25) * 0.82)) = 1.21

ii) Cost of equity = Rf + Beta * (Rm - Rf)

Here,

Rf (Risk free rate) = 4% or 0.04,

Rm - Rf (Market risk premium) = 7% or 0.07

Debt structure	Levered beta	Cost of equity (Ke)
10%	0.81	=0.04 + (0.81 * 0.07) = 0.0967 or 9.67%
25%	0.94	=0.04 + (0.94 * 0.07) = 0.1058 or 10.58%
35%	1.05	=0.04 + (1.05 * 0.07) = 0.1135 or 11.35%
45%	1.21	=0.04 + (1.21 * 0.07) = 0.1247 or 12.47%

iii) WACC calculations at each capital structure :

Cost of equity (Ke) = 0.0925,

Tax rate = 25% or 0.25

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

Weight of debt	Weight of equity	After tax cost of debt (cost of debt * (1 - tax @ 0.25))	Cost of equity	WACC (using formula)
0.10	0.90	=8% * (1-0.25) = 6% or 0.06	0.0967	=(0.10 * 0.06) + (0.90 * 0.0967) = 0.0930 or 9.30%
0.25	0.75	=9% * (1-0.25) = 6.75% or 0.0675	0.1058	=(0.25 * 0.0675) + (0.75 * 0.1058) = 0.0962 or 9.62%
0.35	0.65	=10.50% * (1-0.25) = 7.875% or 0.0785	0.1135	=(0.35 * 0.0785) + (0.65 * 0.1135) = 0.1013 or 10.13%
0.45	0.55	=12% * (1-0.25) = 9% or 0.09	0.1247	=(0.45 * 0.09) + (0.55 * 0.1247) = 0.1091 or 10.91%