UB is examining its capital structure with the intent of arriving at an optimal debt ratio. It currently has no debt and has a beta of $1\mathrm{.}5.$ The riskless interest rate is $9\%.$ Your research indicates that the debt rating will be as follows at different debt levels:

D$/($D$+$E$)(\%)$ Rating Interest Rate $(\%)$

$0$ AAA $10$

$10$ AA $10\mathrm{.}5$

$20$ A $11$

$30$ BBB $12$

$40$ BB $13$

$50$ B $14$

$60$ CCC $16$

$70$ CC $18$

$80$ C $20$

$90$ D $22$

The firm currently has $1$ million shares outstanding at $$20$ per share $($tax rate $=40\%).$

a$.$ What is the firm$$s optimal debt ratio? b$.$ Assuming that the firm restructures by repurchasing stock with debt, what will the value of the stock be after the restructuring? $($with $5\%$ growth in perpetuity$)$