$15.$ Consider the two mutually exclusive projects. Whichever project you choose, if any, you require a $13\%$ return on your investment.

a$.$ If you apply the payback criterion, which investment will you choose? Why?

b$.$ If you apply the NPV criterion, which investment will you choose? Why?

c$.$ If you apply the IRR criterion, which investment will you choose? Why?

d$.$ If you apply the profitability index criterion, which investment will you choose? Why?

e$.$ Based on your answers in $($a$)$ through $($d$),$ which project will you finally choose? Why?$\backslash$table$[[$Year$,$Cash Flow$($A$),$Cash Flow$($B$)],[0,-$$$415,000,-$$$3,500],[1,49,000,1,920],[2,57,000,1,390],[3,74,000,1,420],[4,530,000,1,050]]$