East West Mining Company is considering investing in a new mining project. The firm's cost of capital is $10\%$ and the project is expected to have an initial cost of $$5,000,000.$ Furthermore, the project is expected to provide after$-$tax operating cash flows of $$2,500,000$ in year $1,$ $$2,300,000$ in year $2,$ $$2,200,000$ in year $3$ and $($$$1,300,000)$ in year $4.$

Should the firm make the investment?

$($a$)$ Calculate the project's NPV$.$

$($b$)$ Calculate the project's IRR.

$($c$)$ Should the firm make the investment?