Example $8$:

Kido Corp. currently has $35$ million common stocks each trading at $$24.$ Moreover, it has $1$ million, $2\mathrm{.}947\%$ coupon, $10-$year bonds $($$$1000$ par$)$ each trading at $84.$ Interest is paid annually. The management wants to change the firm$$s current capital structure $($debt$-$to$-$equity $($D:E$)$ ratio by market values$)$ by either changing the current D:E ratio to

$($i$)0\mathrm{.}43$:$1$ by selling more stocks and paying off debt or

$($ii$)2\mathrm{.}33$:$1$ by issuing more debt to raise cash which is used for stock repurchase

The current equity beta is $1\mathrm{.}5.$ The risk$-$free rate is $2\mathrm{.}5\%$ and market risk premium is $7\%.$ Corporate tax rate is $25\%.$ The current cost of debt $($before tax$)$ is $6\%.$ If the debt$-$to$-$equity ratio changes to $0\mathrm{.}43,$ the cost of debt $($before tax$)$ will be $3\%.$ If the debt$-$to$-$equity ratio is $2\mathrm{.}33,$ the cost of debt $($before tax$)$ will be $8\%.$

Required

a$)$ What is the firm$$s current WACC and debt$-$to$-$equity ratio?

b$)$ You are further told that for the year just ended, the firm$$s free cash flow $($FCF$)$ was $$64$M$.$ Financial analysts use the constant growth $($dividend discount$)$ model to value Kido Corp. Using this information and the WACC computed in part $($a$)$ above, compute the constant growth rate, g$,$ of the firm?

c$)$ What is the firm$$s WACC using debt$-$to$-$equity ratio of $0\mathrm{.}43?$

d$)$ What is the firm$$s WACC using debt$-$to$-$equity ratio of $2\mathrm{.}33?$

e$)$ From your computations in $($a$),($c$)$ and $($d$),$ what is the firm$$s optimal capital structure?

f$)$ What is the value of the firm using WACC associated with different capital structures and the growth rate derived in $($b$)$ above?