$$Integrative: Conflicting Rankings$$The$$ High$-$Flying Growth Company$($HFGC$)$ has been expanding very rapidly in recent$$ years, making its shareholders rich in the process. The average annual rate of return on the stock in the past few years has been $25\%,$ and HFGC managers believe that $25\%$ is a reasonable figure for the$$ firm's cost of capital. To sustain a high growth$$ rate, HFGC$\text{'}$s CEO argues that the company must continue to invest in projects that offer the highest rate of return possible. Two projects are currently under review. The first is an expansion of the$$ firm's production$$ capacity, and the second project involves introducing one of the$$ firm's products into a new market. Cash flows from each project appear in the following$$ table:

$0-4,000,000-500,000$

$12,750,000300,000$

$22,250,000400,000$

$32,250,000250,000$

$42,500,000300,000$

a$.$Calculate the NPV for both projects. Rank the projects based on their NPVs$.$

b$.$Calculate the IRR for both projects. Rank the projects based on their IRRs.

c$.$Calculate the PI for both projects. Rank the projects based on their PIs.

d$.$The firm can undertake only one investment. What do you think the firm should$$ do$?$