You are an owner of a firm that has cash flows of $$150($good state$)$ or $$50($bad state$)$ next year with equal probability. Your firm has senior debt with face value $$70$ and junior debt with face value $$10$ outstanding. Ignore taxes and time value of money.a$.$ What is the market value of equity?b$.$ The firm has a positive NPV investment opportunity that costs $$110$ and yields $$130$ in the good state and $$100$ in the bad one. The project must be financed through an equity issue at a fair price in the market $($and will be junior to the existing debt$).$ Will the project go ahead?c$.$ If the project does not go ahead, then what haircut should existing senior debt holders agree on$?$ Assume that existing junior debt holders will agree to write down $$4$ from their face value and that shareholders want an extra $$1$ from the new investment.