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 −$48 $ 26 $ 18 $22 $ 13

B −$102 $ 20 $ 42 $50 $61

a. What are the IRRs of the two​ projects?

b. If your discount rate is 4.7 % 4.7%​, what are the NPVs of the two​ projects?

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

Answer 1

Project A :

CF0 = ($48)

CF1= $26

CF2= $18

CF3= $22

CF4= $13

($48) + $26/ (1 + IRR)^1 + $18/ (1 + IRR)^2 + $22/ (1 + IRR)^3 + $13/(1 + IRR)^4 = 0

The IRR is 26.17%

Similarly, the project B is :

IRR = 20.95%

B. ($48) + $26/ (1.047)^1 + $18/ (1.047)^2 + $22/ (1.047)^3 + $13/(1.047)^4

The NPV for Project A at 4.7% discount rate is = $23.24%

Simialrly, the NPV of project B  = $49.74

c. Due to the difference in the discount rates of the two projects, while the NPV discounts at the cost of capital. The IRR discounts projects at the IRR itself. The NPV is the more reliable indicator than the IRR. Due to the difference in the reinvestment assumption, there is difference in the rankings of the projects as per the NPV and the IRR.