Your division is considering two investment projects, each of which requires an up$-$front expenditure of $$10$ million. You estimate that the cost of capital is $10\%$ and that the investments will produce the following after$-$tax cash flows:

Year: Project N Project M

$1$ $$1$ million $$4$ million

$2$ $$2$ million $$3$ million

$3$ $$3$ million $$2$ million

$4$ $$4$ million $$2$ million

$5$ $$5$ million $$2$ million

a$.$ What is the regular payback period for each of the projects?

b$.$ What is the discounted payback period for each of the projects?

c$.$ Calculate the NPV and IRR of the two projects. If the two projects are independent and the cost of capital is $8\%,$ which project or projects should the firm undertake?

d$.$ If the two projects are mutually exclusive and the cost of capital is $8\%,$ which project should the firm undertake?

e$.$ What is the crossover rate?

f$.$ If the cost of capital is $8\%,$ what is the modified $($MIRR$)$ of each project?