Assume you have just been hired as a business manager of PizzaPalace, a regional pizza restaurant chain. The company$$s EBIT was $$120$ million last year and is not expected to grow. PizzaPalace is in the $25\%$ state$-$plus$-$federal tax bracket, the risk$-$free rate is $6$ percent, and the market risk premium is $6$ percent. 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 firms$$ owners would be financially better off if the firms used some debt. When you suggested this to your new boss, he encouraged you to pursue the idea. If the company were to recapitalize, then debt would be issued, and the funds received would be used to repurchase stock. As a first step, assume that you obtained from the firm$$s investment banker the following estimated costs of debt for the firm at different capital structures:

Percent Financed with Debt,

$0\%$

$$

$20$

$8\mathrm{.}0\%$

$30$

$8\mathrm{.}5$

$40$

$10\mathrm{.}0$

$50$

$12.$With the preceding points in mind, now consider the optimal capital structure for PizzaPalace.

$(1)$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.

Describe the recapitalization process and apply it to PizzaPalace. Calculate the resulting value of the debt that will be issued, the resulting market value of equity, the price per share, the number of shares repurchased, and the remaining shares. Considering only the capital structures under analysis, what is PizzaPalace$$s optimal capital structure?