Question

You are choosing between two projects. The cash flows for the projects are given in the following table ($ million): Year 1 Year 2 Year 3 Year 4 Project A Year 0 - $50 - $100 $27 $19 $18 $38 $21 $49 $17 $58 В a. What are the IRRS of the two projects? b. If your discount rate is 4.8%, what are the NPVS of the two projects? c. Why do IRR and NPV rank the two projects differently?

Answer 1

a. The IRR is the rate at which the NPV of a project is zero.

( $50 ) + $27/(1 + IRR)^1 + $18/ (1 + IRR)^2 + $21/ (1 + IRR)^3 + $17/ (1 + IRR)^4

= 26.0113%

Similarly, the IRR for project B is :

= 19.3518%

b. The NPV of project A at 4.8% discount rate is,

NPV of A =

($50 ) + $27/ (1.048)^1 + $18/ (1.048)^ 2 + $21/ (1.048)^3 + $17/ (1.048)^4

= $24.4899

Similarly, for project B NPV is,

=$43.3814

According to the NPV rule, the highest NPV will be ranked first

So, Project B - 1

project A - 2

According to the IRR rule,

The highest IRR will be ranked first,

Project A - 1st
Project B - 2nd

The ranking difference between the NPV and the IRR is due to the different cash flow patters in the two projects and the reinvestment rate difference between the two projects.

The NPV believes that the cash flows will be reinvested at the cost of capital and the IRR assumes that the cash flows will be reinvest at the IRR.