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	$25	$19	$22	$14
B	$99	$21	$42	$51	$61

a. What are the IRRs of the two​ projects? b. If your discount rate is 5.1%​, what are the NPVs of the two​ projects? c. Why do IRR and NPV rank the two projects​ differently?

Answer 1

Project	A
Year	Cashflow	PV @ 10%	Amount	PV @ 20%	Amount
0	-49	1	-49	1	-49
1	25	0.91	22.73	0.83	20.83
2	19	0.83	15.70	0.69	13.19
3	22	0.75	16.53	0.58	12.73
4	14	0.68	9.56	0.48	6.75
			15.52		4.51
	By interpolation formula
	IRR         =	10+(15.52/(15.52-4.51)*(20-10))
		24.09628
		24.10%
Project	B
Year	Cashflow	PV @ 10%	Amount	PV @ 20%	Amount
0	-99	1	-99	1	-99
1	21	0.91	19.09	0.83	17.50
2	42	0.83	34.71	0.69	29.17
3	51	0.75	38.32	0.58	29.51
4	61	0.68	41.66	0.48	29.42
			34.78		6.60
	By interpolation formula
	IRR         =	10+(34.78/(34.78-6.60)*(20-10))
		22.34209
		22.34%
Assuming $99 as outflow of cash, therefore showing in negative. As such is required
for the correct answer.
Project	A				Project	B
Year	Cashflow	PV @ 5.1%	Amount		Year	Cashflow	PV @ 5.1%	Amount
0	-49	1	-49		0	-99	1	-99
1	25	0.95	23.79		1	21	0.95	19.98
2	19	0.91	17.20		2	42	0.91	38.02
3	22	0.86	18.95		3	51	0.86	43.93
4	14	0.82	11.47		4	61	0.82	49.99
		NPV	22.41				NPV	52.93
As per IRR project A is acceptable but as per NPV project B
IRR and NPV rank the project differently because IRR will rank the project showing higher investment
return regardless of total value added whereas NPV rank the project adding more value higher
regardless of the initial investment required.