Jim Campbell is founder and CEO of$$ OpenStart, an innovative software company. The company is$$ all$-$equity financed, with $100$ million shares outstanding. The shares are trading at a price of $ $1.$ Campbell currently owns $20$ million shares. There are two possible states in one year. Either the new version of their software is a$$ hit, and the company will be worth $ $175$million$,$ or it will be a$$ disappointment, in which case the value of the company will drop to $ $75$ million. The current$$ risk$-$free rate is $3\mathrm{.}2\%.$ Campbell is considering taking the company private by repurchasing the rest of the outstanding equity by issuing debt due in one year. Assume the debt is$$ zero$-$coupon and will pay its face value in one year.

a$.$ What is the market value of the new debt that must be$$ issued?

b$.$ Suppose OpenStart had$$ risk$-$free debt with a face value of $ $75$ million. What would be the value of its debt and levered equity$$ today?

c$.$ What fraction of the levered equity in $($b$)$ would you need to combine with the$$ risk$-$free debt in $($b$)$ to raise the amount in left parenthesis Bold a right parenthesis$?$

d$.$ What are the payoffs of the portfolio in $($c$)?$ What face value of risky debt would have the same$$ payoffs?