Orange County Industry $($OCI$)$ is an unlevered firm and has $$10$ million in internal capital that it can invest in one of four mutually exclusive capital investment projects, which have cash flows as shown in Table below $($all numbers are in thousands$).$

a$.$ Define NPV$,$ IRR, Payback, and Profitability Index. How does one make decisions using these measures if projects are i$)$ Independent and ii$)$ Mutually exclusive

b$.$ Draw an NPV profile of the four projects. Rank the company$$s four projects using the NPV criteria under two discount rates $10\%$ and $35\%$

c$.$ Rank the company$$s four projects according under the other capital budgeting criteria $($IRR$,$ Payback, and discounted payback$)$ under two discount rates $10\%$ and $35\%$

d$.$ Why do the rankings differ under the four criteria? What are the correct rankings, i$.$e$.,$ rank the projects based on the wealth they add to the shareholders?