Consider a project with free cash flows in one year of $$144,100$ or $$177,100,$ with each outcome being equally likely. The initial investment required for the project is $$90,100,$ and the$$ project's cost of capital is $20\%.$ The$$ risk$-$free interest rate is $7\%.$

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 way$$that is$,$ what is the initial market value of the unlevered$$ equity?$$

c$.$ Suppose the initial $$90,100$ is instead raised by borrowing at the$$ risk$-$free interest rate. What are the cash flows of the levered$$ equity, what is its initial value and what is the initial equity according to$$ MM$?$