A firm is considering two projects, each with an initial investment of $$500,000.$ The company's board of directors has set a maximum $3-$year payback requirement. The cash inflows associated with the two projects are shown in the following table. The cost of capital is $12\%.$

Cash Inflows

Years

Project A

$120,000$

$120,000$

$150,000$

$120,000$

$120\mathrm{.}000$

$120\mathrm{.}000$

Project B

$90,000$

$110,000$

$130,000$

$150\mathrm{.}000$

$170,000$

$190,000$

a$.$ Calculate the payback period for each project. Which project will you choose using this capital budgeting technique, if they are mutually exclusive? Which project will you choose if they are independent? Why?

b$.$ Calculate the NPV of each project. Which project will you choose using this capital budgeting technique, if they are mutually exclusive? Which project will you choose if they are independent? Why?

c$.$ Derive the IRR of each project. Which project will you choose using this capital budgeting technique, if they are mutually exclusive? Which project will you choose if they are independent? Why?

d$.$ Calculate the Profitability Index of each project. Which project will you choose using this capital budgeting technique, if they are mutually exclusive? Which project will you choose if they are independent? Why?

e$.$ Which project will you choose overall if they are mutually exclusive?