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	−$52	$24	$20	$22	$14
B	−$101	$22	$39	$49	$60

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

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

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

Answer 1

a)

Project A:

IRR is the rate of return that makes NPV equal to 0

NPV = -52 + 24 / (1 + R)¹ + 20 / (1 + R)² + 22 / (1 + R)³ + 14 / (1 + R)⁴

Using trial and error method, i.e., after trying values for R, lets try R as 21.49

NPV = -52 + 24 / (1 + 0.2149)¹ + 20 / (1 + 0.2149)² + 22 / (1 + 0.2149)³ + 14 / (1 + 0.2149)⁴

NPV = -52 + 19.7547 + 13.5503 + 12.26877 + 6.42637

NPV = 0

Therefore, IRR of project A is 21.49%

Project B:

IRR is the rate of return that makes NPV equal to 0

NPV = -101 + 22 / (1 + R)¹ + 39 / (1 + R)² + 49 / (1 + R)³ + 60 / (1 + R)⁴

Using trial and error method, i.e., after trying values for R, lets try R as 20.76

NPV = -101 + 22 / (1 + 0.2076)¹ + 39 / (1 + 0.2076)² + 49 / (1 + 0.2076)³ + 60 / (1 + 0.2076)⁴

NPV = -101 + 18.2180 + 26.74351 + 27.82446 + 28.21362

NPV = 0

Therefore, IRR of project A is 20.76%

b)

Project A:

NPV = Present value of cash inflows - present value of c ash outflows

NPV = -52 + 24 / (1 + 0.047)¹ + 20 / (1 + 0.047)² + 22 / (1 + 0.047)³ + 14 / (1 + 0.047)⁴

NPV = $19.99

Project B:

NPV = Present value of cash inflows - present value of c ash outflows

NPV = -101 + 22 / (1 + 0.047)¹ + 39 / (1 + 0.047)² + 49 / (1 + 0.047)³ + 60 / (1 + 0.047)⁴

NPV = $48.21

c)

IRR measures the rate of return on investment. NPV shows how much value is created. Conflicts between NPV and IRR due arises to differing cash flow patterns. The conflicting results can also occur because of the size and investment of the projects