$-$P$9-13-$Derek's Donuts is considering two mutually exclusive investments. The projects' expected net cash flows$=$ are as follows:

$\backslash$table$[[,$Expected$],[$Year$,$Project $A,$Cash Flows$],[0,$$$(300),$Project B$],[1,(387),134],[2,(193),134],[3,(100),134],[4,500,134],[5,500,134],[6,850,134],[7,100,0]]$

a$.$ Calculate NPV for Projects A and B$.$

b$.$ What is each project's IRR?

c$.$ If you were told that each project's required rate of return was $12$ percent, which project should be selected? If the required rate of return was $15$ percent, what would be the proper choice?