Consider a firm with assets in place which generate a random cash flow of $50$ in state L$,100$ in state M$,$ and $150$ in state H$.$ Each state occurs with equal probability. The firm hasdebt outstanding with face value $125,$ the discount rate is $0\%,$ and the firm will liquidate next year when debt matures.

$($a$)$ Construct the balance sheet.

$($b$)$ The company has discovered a risk$-$free project that costs $20$ and generates a safepayoff of $30.$ There are no internal funds. Would a shareholder$-$oriented managerissue new equity to fund the project?

$($c$)$ Is taking up new junior debt an alternative to issuing new equity? Show your calcu$-$lations.

$($d$)$ Is there a bargaining solution? formulas: E $=$ max$[$V $$ Fs $$ Fj $,0].$

Ds $=$ min$[$V$,$ Fs$].$

Dj $=$ min$[$max$($V $$ Fs$,0),$ Fj $].$