Nicholson Roofing Materials Inc. is considering two mutually exclusive projects that both cost $$150,000.$ The company$$s board of directors has set a maximum four$-$year payback requirement, the cost of capital is $9\%.$ The project cash flows appear below.

Cash inflows $($CFt$)$

Year Project A Project B

$1$ $$45,000$ $$75,000$

$245,00060,000$

$345,00030,000$

$445,00030,000$

$545,00030,000$

$645,00030,000$

a$.$ Calculate the payback period for each project.

b$.$ Calculate the NPV of each project at $0\%.$

c$.$ Calculate the NPV of each project at $9\%.$

d$.$ Derive the IRR of each project.

e$.$ Rank the projects by each of the techniques used. Make and justify a recommendation.

f$.$ Go back one more time and calculate the NPV of each project using a cost of capital of $12\%.$ Does the ranking of the two projects change compared to your answer in part e$?$ Why?

Please show your work and any excel formulas. Thank you.