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 $ 51 $ 23 $ 22 $ 20 $ 16 B negative $ 100 $ 20 $ 39 $ 48 $ 60 a. What are the IRRs of the two​ projects? b. If your discount rate is 5.2 %​, what are the NPVs of the two​ projects? c. Why do IRR and NPV rank the two projects​ differently? a. What are the IRRs of the two​ projects? ​(Round to one decimal​ place.)

Answer 1

The cash flows for project A:
Year 0:-$51
Year 1:$23
Year 2:$22
Year 3:$20
Year 4:$16

The cash flows for project B:
Year 0:-$100
Year 1:$20
Year 2:$39
Year 3:$48
Year 4:$60

Given that the discount rate is 5.2%​.

In the NPV formula, we have used the discount rate=5.2%

Part a and b:

We will calculate the IRR and NPV using excel.
For project A, value of IRR=22.98% and NPV=$20.98
For project B, value of IRR=20.21% and NPV=$44.47

Part c:

Ranking as per IRR:
Rank 1: Project A with IRR=22.98%
Rank 2: Project B with IRR=20.21%

Ranking as per NPV:
Rank 1: Project B with NPV=$44.47
Rank 2: Project B with NPV=$20.98

The ranking are different because of the decision rule.
In case of IRR, a project with IRR greater than cost of capital should be accepted and in case of NPV, a project with positive NPV should be accepted because it increases the shareholder's value. In both the cases, higher values are given higher preference.