Question

There are two projects with the following cash flows.

Years: 0 1 2 3 4 5

Project 1: -210 125 125 175 175 -400

Project 2:  300 -95 -75 -125 -400 600

a. What are the NPVs of these two projects if market interest rate is 3%?

b. With the interest rate of 6%, please modified these two projects to let them have only one IRR for each one of them. (That means the sign of cash flows of each project only changes for one time.) And then, calculate the Modified IRRs.

c. With the interest rate of 6%, compute the discounted payback periods of both projects.

d. Please calculate the IRR of incremental cash flows based on two projects.

Answer 1

a) NPV can be calculated by NPV function in excel

NPV of Project 1 = -$0.2248

NPV of Project 2 = $184.85

b) We modify the cash-flows

For project 1, the negative cash-flow is discounted back to year 0 using 6% rate so that the sign changes only once

For project 2, the positive cash-flow is discounted back to year 0 using 6% rate so that the sign changes only once

Here, MIRR for Project 1 = 6.30%

MIRR for Project 2 = 13.06%

c. The discounted payback period is the time period taken for the cumulative discounted cash-flows to become 0

In Project 1, cumulative discounted cash-flows to become 0 after year 1

In Project 2, cumulative discounted cash-flows is positive upfront. Hence the discounted payback period cannot be estimated.

d)

Since, the incremental cash-flows have sign change more than once, IRR cannot be calculated.