Consider a project with free cash flows in one year of $$144,700$ or $$176,000,$ with each outcome being equally likely. The initial investment required for the project is $$98,300,$ and the project's cost of capital is $15\%.$ The risk$-$free interest rate is $11\%.$

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 $$98,300$ 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$?$