You are choosing between two projects. The cash flows for the projects are given

Question

You are choosing between two projects. The cash flows for the projects are given in the following table ($ million):

Project

Year 0

Year 1

Year 2

Year 3

Year 4

A

negative $ 52

$ 23

$ 20

$ 20

$ 15

B

negative $ 102

$ 22

$ 38

$ 48

$ 60

a. What are the IRRs of the two projects?

b. If your discount rate is 5.1 %, what are the NPVs of the two projects?

c. Why do IRR and NPV rank the two projects differently?

Project

Year 0

Year 1

Year 2

Year 3

Year 4

A

negative $ 52

$ 23

$ 20

$ 20

$ 15

B

negative $ 102

$ 22

$ 38

$ 48

$ 60

Explanation / Answer

a. IRR is the rate that makes the NPV of the project as nil. It is computed using a trial and error method.

Thus IRR of project A is 1.1985 - 1 = 0.1985 or 19.85%

IRR of project B is 1.1975-1 = 0.1975 or 19.75%

b. NPV at discount rate of 5.1%:

Thus NPV of A = $17.51 and of B = $43.85

c. IRR ranks A as a better project while NPV ranks B as a better project. This is because in case of project A the positive cash flow's amount are decreasing starting from year 2. It is decreasing every year until the 4th year. This causes its NPV to be lower as well. On the other hand in case of B its positive cash flows are increasing every year causing its NPV to be higher.

Project A: Year Cash flow 1+r PV 0 -52.00 1.1985 -52.00 1 23.00 19.19 2 20.00 13.92 3 20.00 11.62 4 15.00 7.27 NPV 0.00

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