a$.$ Calculate the detailed modified payback period for a project with the following cash flows: Year $0$: $-$$$2,000$; Year $1$: $$1,000$; Year $2$: $-$$$1,000$; Year $3$: $$1,000$; Year $4$: $$3,000$; Year $5$: $$2,000.$

b$.$ A project has an initial investment requirement of $$100,000.$ In Year $1,$ it should earn $$25,000$; in Year $2,$ $$30,000$; and in Year $3,$ $$50,000.$ What is the project's internal rate of return?

c$.$ A project has a finance rate of $8\%$ and a reinvestment rate of $10\%.$ The project requires an initial investment of $$10,000.$ In Year $1,$ it will have cash flows of $$12,000$; in Year $2,-$$$5,000$; and in Year $3,$ $$8,000.$ What is the project's MIRR?

d$.$ A company is considering a project that has a discount rate of $5\%.$ In the first year, it will have $-$$$100,000$ in cash flows. In Year $2,$ it will have cash flows of $$100,000,$ and in Year $3,$ the project will generate $$200,000.$ What is the project's NPV$?$

e$.$ Each choice listed here represents a net present value of a potential project. If you were the CFO of a company, which project would you choose?