Question

You are choosing between two projects. The cash flows for the projects are given in the following table ($ million): Project Year 0 - $50 - $100 Year 1 $25 $18 Year 2 $20 $38 Year 3 $19 $48 Year 4 $16 $60 a. What are the IRRs of the two projects? b. If your discount rate is 5.4%, 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? The IRR for project Ais %. (Round to one decimal place.)

Answer 1

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

So, let us first calculate the IRR of Project A :

($50 ) + $25/ (1 + IRR)^1 + $20/(1 + IRR)^2 + $19/(1 + IRR)^3 + $16/(1+ IRR)^4 = 0

= 23.9%

Similarly, the IRR for project B is :

= 19.2%

b. If the discount rate is 5.4%, the NPV of project A is :

= ($50) + $25/ (1.054)^1 + $20/(1.054)^2 + $19/(1.054)^3 + $16/(1.054)^4

= $20.9136

Simialrly, the NPV of Project B is :

= $40.8948

c. The IRR and NPV rank projects differently because of the different reinvestment rate assumption. The NPV assumes that the cash flows are reinvested at the cost of capital, the IRR assumes that the cash flows are reinvested at the IRR. The NPV is a more reliable measure and gives accurate results in comparison to the IRR.