Question

Assume you have just been hired as business manager of PizzaPalace, a pizza restaurant located adjacent to campus. The company's EBIT was $500,000 last year, and since the university's enrollment is capped, EBIT is expected to remain constant over time. Since no expansion capital will be required, PizzaPalace plans to pay out all earnings as dividends. The management group owns about 50% of the stock, and the stock is traded in the OTC market. The firm is currently financed with all equity; it has 100,000 shares outstanding; and P0 = $25 per share. When you took your MBA Financial Analysis course, your instructor stated that most firms' 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: % Debt Ratio rd 0% --- 20 8.0% 30 8.5 40 9.0 50 9.5 If the company were to recapitalize, debt would be issued, and the funds received would be used to repurchase stock. PizzaPalace is in the 40% state-plus-federal corporate tax bracket, its beta is 1.0 when debt ratio is 0%, the risk-free rate is 6%, and the market risk premium is 6%.

a. For each capital structure under consideration, calculate the WACC.

b. Now calculate the corporate value, the value of the debt that will be issued, and the resulting market value of equity.

Answer 1

If T=40%, then every dollar of debt adds 40 cents of extravalue to firm.

h.

(1) Leveragedbeta = Unleveraged beta*(1+Debt/equity weight*(1-taxrate))

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

=1+0.15

=1.15

FromCAPM,

Costof equity = Risk-free rate + Risk premiun*leveragedbeta

=6%+ 1.15*6%

=6% + 6.9%

=12.9%

CalculationofWACC:
We can repeat this for the capital structures underconside wd D/S bL rs
0% 0.00 1.000 12.00%
20% 0.25 1.150 12.90%
30% 0.43 1.257 13.54
40% 0.67 1.400 14.40%
50% 1.00 1.600 15.60%

WACC = Wight of debt*cost of debt aftertaxes + Weight of equity*cost of equity

= 0.2 (1 â 0.4) (8%) + 0.8 (12.9%)

=11.28%

wd rd rs WACC
0% 0.0% 12.00% 12.00%

20% 8.0% 12.90% 11.28%
30% 8.5% 13.54% 11.01%
40% 10.0% 14.40% 11.04%
50% 12.0% 15.60% 11.40%

(2)

For example the corporate value for wd = 20%is:
V = FCF /(WACC-g)
G=0, so investment in capital is zero; so FCF = NOPAT = EBIT(1-T). In this example, NOPAT = ($500,000)(1-0.40) =$300,000.Using these values, V = $300,000 / 0.1128= $2,659,574. Repeating this for all capital structures gives the followingtable:
wd WACC Corp. Value
0% 12.00% $2,500,000
20% 11.28% $2,659,574
30% 11.01% $2,724,796
40% 11.04% $2,717,391
50% 11.40% $2,631,579
As this shows, value is maximized at a capital structure with 30%debt.