$UB$ 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:

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 perpe$-$

tuity$)$