Assume you have just been hired as a business manager of PizzaPalace, a regional pizza

restaurant chain. The company's EBIT was $$150$ million last year and is not expected to grow.

PizzaPalace is in the $25\%$ state$-$plus$-$federal tax bracket, the risk$-$free rate is $7$ percent, and the

market risk premium is $7$ percent. The firm is currently financed with all equity, and it has $12$

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:

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?$|$

Leverage only adds value if ROIC is greater than the after$-$tax

cost of debt

Following Example For: $w_d=20\%$

Calculating Levered Beta:

$b=b_U[1+(1-T)(\frac{w_d}{w_s})]$

$=1\mathrm{.}2[1+(1-0\mathrm{.}25)(\frac{0\mathrm{.}20}{0\mathrm{.}80})]$

$=1\mathrm{.}425$

$b_U=1\mathrm{.}2,T=25\%,r_{RF}=7\%,R{P}_M=7\%,r_d=9\%$

Calculating Cost of Equity:

$r_S=r_{RF}+b_L(R{P}_M)$

$=7\%+1\mathrm{.}425(7\%)$

$=0\mathrm{.}1697516\mathrm{.}975\%$

Calculating WACC:

WACC$=w_d(1-T)r_d+w_s{r}_s$

$=0\mathrm{.}20(1-0\mathrm{.}25)(9\%)+0\mathrm{.}80(16\mathrm{.}975\%)$

$=0\mathrm{.}149314\mathrm{.}93\%$