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	$27	$19	$18	$17
B	−$101	$19	$40	$51	$58

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

b. If your discount rate is 5.4%​, what are the NPVs of the two​ projects?

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

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

​(Round to one decimal​ place.)

Answer 1

a) Calculation of IRR

IRR for the project is calculated as follows,

IRR=L+((NPV_L/(NPV_L-NPV_H)*(H-L))

Where,

L means Lower discount rate taken

H means Higher discount rate taken

NPV_Lmeans NPV at Lower discount rate taken

NPV_H means NPV at Higher discount rate taken

PROJECT A
Year	Cash Flow	Discounting Factor @ 10%	Present Value @10%	Discounting Factor @20%	Present Value @ 20%
0	-52	1.00	-52.00	1.00	-52.00
1	27	0.91	24.55	0.83	22.50
2	19	0.83	15.70	0.69	13.19
3	18	0.75	13.52	0.58	10.42
4	17	0.68	11.61	0.48	8.20
NPV	13.38	NPV	2.31

IRR=L+((NPV_L/(NPV_L-NPV_H)*(H-L))

IRR = 10 + ((13.38/(13.38-2.31)) x (20-10))

IRR =10 + ((13.38/11.07) x 10)

IRR =10+12.087

IRR of Project A = 22.08%

PROJECT B
Year	Cash Flow	Discounting Factor @ 10%	Present Value @10%	Discounting Factor @20%	Present Value @ 20%
0	-101	1.00	-101.00	1.00	-101.00
1	19	0.91	17.27	0.83	15.83
2	40	0.83	33.06	0.69	27.78
3	51	0.75	38.32	0.58	29.51
4	58	0.68	39.61	0.48	27.97
NPV	27.26	NPV	0.10

IRR=L+((NPV_L/(NPV_L-NPV_H)*(H-L))

IRR = 10 + ((27.26/(27.26-0.1)) x (20-10))

IRR =10 +10.0368

IRR =20.04%

IRR of Project B = 20.04%

b)

NPV of PROJECT A
Year	Cash Flow	Discounting Factor @ 5.4	Present Value
0	-52	1.00	-52.00
1	27	0.95	25.62
2	19	0.90	17.10
3	18	0.85	15.37
4	17	0.81	13.77
NPV	19.87

NPV of PROJECT B
Year	Cash Flow	Discounting Factor @ 5.4	Present Value
0	-101	1.00	-101.00
1	19	0.95	18.03
2	40	0.90	36.01
3	51	0.85	43.56
4	58	0.81	47.00
NPV	43.59

c) As per IRR rule of project selection a project with higher IRR rate of return over the required rate of return is selected over lower IRR projects so in this case Project A is selected

Were as on the other hand as per NPV rule a project with possitive NPV is slecected .for comparing between 2 projects , project with higher NPV is selcted over Lower NPV projects. so in this case Project B will be prefered.

So, its clear that  IRR and NPV rank the two projects​ differently in this case, this is becuase both NPV and IRR measures different things. IRR computes the return rate , were as NPV calculates the value added by choosing the project,returns donot increaases with diffrent initial investments , both NPV and IRR rate projects diffrents for diffrent initial investment projects.