Gladstone Corporation is about to launch a new product. Depending on the success of the new product, Gladstone may have one of four values next year: $$150$ million, $$135$ million, $$95$ million, and $$80$ million. These outcomes are all equally likely, and this risk is diversifiable. Suppose the risk$-$free interest rate is $5\%$ and that, in the event of default, $25\%$ of the value of Gladstone's assets will be lost to bankruptcy costs. $($Ignore all other market imperfections, such as taxes.$)$

a$.$ What is the initial value of Gladstone's equity without leverage?

Now suppose Gladstone has zero$-$coupon debt with a $$100$ million face value due next year.

b$.$ What is the initial value of Gladstone's debt?

c$.$ What is the yield$-$to$-$maturity of the debt? What is its expected return?

d$.$ What is the initial value of Gladstone's equity? What is Gladstone's total value with leverage?

Suppose Gladstone has $10$ million shares outstanding and no debt at the start of the year.

e$.$ If Gladstone does not issue debt, what is its share price?

f$.$ If Gladstone issues debt of $$100$ million due next year and uses the proceeds to repurchase shares, what will its share price be$?$ Why does your answer differ from that in part $($e$)?$

a$.$ What is the initial value of Gladstone's equity without leverage?

The initial value of Gladstone's equity without leverage is $ million. $($Round to two decimal places.$)$