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	−$49	$24	$20	$18	$13
B	−$100	$22	$38	$48	$62

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

b. If your discount rate is

4.6%​,

what are the

NPVs

of the two​ projects?

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

Answer 1

(a): IRR is the rate which makes the NPV as nil. I have computed the IRRs using the trial and error approach.

Project A:

Year	Cash flow	1+r	PVIF	PV = PVIF * cash flow
0	-          49.00	1.21866	1.00	-        49.00
1	24.00		0.820573	19.69
2	20.00		0.67334	13.47
3	18.00		0.552524	9.95
4	13.00		0.453386	5.89
			NPV	0.000000

Thus IRR of A = 21.866%

Project B:

Year	Cash flow	1+r	PVIF	PV = PVIF * cash flow
0	-        100.00	1.210701	1.00	-      100.00
1	22.00		0.83	18.17
2	38.00		0.68	25.92
3	48.00		0.56	27.05
4	62.00		0.47	28.86
			NPV	0.000000

Thus B's IRR = 21.07%

	A	B
IRR	21.866%	21.070%

(b): Using a discount rate of 4.6% we get the following NPVs:

A's NPV

Year	Cash flow	1+r	PVIF	PV = PVIF * cash flow
0	-          49.00	1.04600	1.00	-          49.00
1	24.00		0.956023	22.94
2	20.00		0.91398	18.28
3	18.00		0.873786	15.73
4	13.00		0.835359	10.86
			NPV	18.811961

B's NPV:

Year	Cash flow	1+r	PVIF	PV = PVIF * cash flow
0	-        100.00	1.046000	1.00	-        100.00
1	22.00		0.96	21.03
2	38.00		0.91	34.73
3	48.00		0.87	41.94
4	62.00		0.84	51.79
			NPV	49.497725

	A	B
NPV ($ million)	18.81	49.50

(c): IRR ranks project A as a better project while NPV ranks project B as a better project. This is because in case of A the cash inflows is decreasing every year from the 1st year onwards. However in case of project B the cash inflows are increasing every year from 1st year onwards. This caused the NPV and the IRR method to give contradictory results.