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 negative $ 48−$48 $ 27$27 $ 21$21 $ 21$21 $ 13$13 B negative $ 98−$98 $ 22$22 $ 39$39 $ 48$48 $ 60$60 a. What are the IRRs of the two​ projects? b. If your discount rate is 4.6 %4.6%​, what are the NPVs of the two​ projects? c. Why do IRR and NPV rank the two projects​ differently?

Answer 1

PROJECT A

0 = -$48 + $27/(1+ IRR)¹ + $ 21/ (1+IRR)² + $21/(A+IRR)³ + $13/(1+IRR)⁴

IRR = 29%

IRR = Where NPV is equal to Zero

Using trial and error approach we get

Year	Cash flow	PVF(29%)	PVCF(29%)	PVF(30%)	PVCF(30%)
0	-48	1	-48	1	-48
1	27	0.775194	20.93	0.769231	20.77
2	21	0.600925	12.62	0.591716	12.43
3	21	0.465834	9.78	0.455166	9.56
4	13	0.361111	4.69	0.350128	4.55
NPV			0.03		-0.69

IRR = 29% + (0.03-0)/(0.03 - (-.69))

= 29.04%

PROJECT B =

0 = -$98 + $22/(1+ IRR)¹ + $ 39/ (1+IRR)² + $48/(A+IRR)³ + $60/(1+IRR)⁴

IRR = 21.89%

IRR = Where NPV is equal to Zero

Using trial and error approach we get

Year	Cash flow	PVF(21%)	PVCF(21%)	PVF(22%)	PVCF(22%)
0	-98	1	-98	1	-98
1	22	0.826446	18.18	0.819672	18.03
2	39	0.683013	26.64	0.671862	26.20
3	48	0.564474	27.09	0.550707	26.43
4	60	0.466507	27.99	0.451399	27.08
NPV			1.90		-0.25

IRR = 21% + (1.9-0)/ (1.9 - (-.25))

= 21.89 %

b)

NPV

Project A

Year	Cash flow	PVF(4.6%)	PVCF(4.6%)
0	-48	1	-48
1	27	0.956023	25.81
2	21	0.91398	19.19
3	21	0.873786	18.35
4	13	0.835359	10.86
NPV			26.22

Project B

Year	Cash flow	PVF(4.6%)	PVCF(4.6%)
0	-98	1	-98
1	22	0.956023	21.03
2	39	0.91398	35.65
3	48	0.873786	41.94
4	60	0.835359	50.12
NPV			50.74

c)

NPV and IRR rank the two projects differently because they are measuring different things. NPV is measuring value creation, while IRR is measuring return on investment. Because returns do not scale with different levels of investment, the two measures may have different rankings when the initial investments are different.