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 $95 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%                              ---      

                                                              35                                 8.0%     

                                                              45                                 8.5      

                                                              55                                10.5      

                                                              65                               12.5      

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 30 percent state-plus-federal corporate tax bracket, its unlevered beta is .95, the risk-free rate is 3 percent, and the market risk premium is 8 percent.

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

2, Now calculate the corporate value for each capital structure.

PLEASE SHOW ALL WORK IN EXCEL**!!!

Answer 1

The levered beta B(l) would be calculated from the unlevered beta B(u) by using the following formula:

B(l) = B(u) x [1+ (1-tax rate) x (D/E)] where D is the market value of debt and E is the market value of equity in the firm's capital structure.

The cost of equity (levered) would be calculated using the CAPM as per the given equation:

Levered Cost of Equity = Risk-Free Rate + Levered Beta x Market Risk Premium

The firm's WACC would be calculated as per the given relationship:

WACC = (1-tax rate) x r(d) x (D/V) + r(e) x (E/V) where V = D + E

Debt Proportion	DE Ratio	Levered Beta	Cost of Equity	WACC
0%	0	0.95	10.6	10.6
35%	(0.35/0.65)	1.378	14.024	11.0756
45%	(0.45/0.55)	1.4941	14.9528	10.90154
55%	(0.55/0.45)	1.763	17.104	11.7393
65%	(0.65/0.35)	2.185	20.48	12.8555

The corporate value or firm value at each capita structure is calculated using the following formula:

Free Cash Flow = EBIT x (1-Taxes) + Depreciation - Changes in NWC - CapEx

FCF = EBIT x (1-taxes)

Corporate Value = FCF / WACC

Perpetual EBIT = $ 95 million

Perpetual FCF = 95 x (1-0.3) = $ 66.5 million

WACC	Perpetual FCF	Corporate Value
10.6	66.5	$ 627.358
11.0756	66.5	$ 600.4189
10.90154	66.5	$ 610.0055
11.7393	66.5	$ 566.4733
12.8555	66.5	$ 517.3084