Q#$3.(20$ pts$.)$ Alliance Corporation is considering investing in a project that will incur an initial investment of $$500,000.$ The project has a useful life of $5$ years. The project's projected free after tax cash flow is $$150,000$ per year throughout the life of the project. The firm requires a rate of return for similar risk project at $16\%.$ Based on the above information compute the following and determine under each criteria if the firm should accept the project $($solve and show answers$).$

a$)$ The NPV

b$)$ The IRR

c$)$ Payback period, the firm's minimum acceptable payback period is $3\mathrm{.}5$ years.

d$)$ Discounted Payback Period. Minimum acceptable discounted payback period is $4\mathrm{.}0$ years.

e$)$ Compute the Profitability Index for this investment. What purpose does Profitability Index serve in capital budgeting processes?