Consider a project with free cash flows in one year of $ $147$ comma $930$ in a weak market or $ $177$ comma $995$ in a strong$$ market, with each outcome being equally likely. The initial investment required for the project is $ $95$ comma $000,$ and the$$ project's unlevered cost of capital is $17\%.$ The$$ risk$-$free interest rate is $9\%.($Assume no taxes or distress$$ costs.$)$

a$.$ What is the NPV of this$$ project?

b$.$ Suppose that to raise the funds for the initial$$ investment, the project is sold to investors as an$$ all$-$equity firm. The equity holders will receive the cash flows of the project in one year. How much money can be raised in this waylong dashthat $$is$,$ what is the initial market value of the unlevered$$ equity?$$

c$.$ Suppose the initial $ $95$ comma $000$ is instead raised by borrowing at the$$ risk$-$free interest rate. What are the cash flows of the levered equity in a weak market and a strong market at the end of year$1,$ and what is its initial market value of the levered equity according to$$ MM$?$