$4.($Part $1)$ Suppose you have an investment opportunity that requires a $$40,000$ initial investment, but will repay you $$20,000$ at the end of each of the next three years $($first payment in one year$).$

$($a$)$ Calculate the payback period

$($b$)$ Calculate the IRR

$($c$)$ Assuming an interest rate of $6\%,$ calculate the NPV

$($Part $2)$ Suppose you are given a different investment opportunity, one that requires the same initial investment of $$40,000,$ but is estimated to pay out $$10,000$ the first year and $$26,000$ in each of the following two years. Compare this investment to the investment in Part $1.$ Which is more attractive? If it depends on interest rates, explain how.