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	-$48	$27	$ 21	$ 19	$ 12
B	−$98	$20	$ 41	$ 51	$ 59

a. What are the IRRs of the two​ projects? (Round to one decimal​ place.)

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

Given: Cash flows for the project

Year	Project A ($)	Project B ($)
0	-48	-98
1	27	20
2	21	41
3	19	51
4	12	59

Step 1: Calculation of IRR

IRR is rate of return at which the NPV = 0, We will have to calculate the IRR of the Project by trail & error method

Let IRR be 20%

Calculation of NPV of Project A & B at discount rate = 20%

Year	Project A	Project B	PVF @ 20%	Present Value A	Present Value B
0	$(48.00)	$(98.00)	1	$(48.00)	$(98.00)
1	$27.00	$20.00	0.833333333	$22.50	$16.67
2	$21.00	$41.00	0.694444444	$14.58	$28.47
3	$19.00	$51.00	0.578703704	$11.00	$29.51
4	$12.00	$59.00	0.482253086	$5.79	$28.45
			NPV =	$5.87	$5.11

Since NPV at IRR - 20% is positive, we need to discount at a higher rate to get NPV = 0

Let IRR be 30%

Calculation of NPV of Project A & B at discount rate = 30%

Year	Project A	Project B	PVF @ 30%	Present Value A	Present Value B
0	$(48.00)	$(98.00)	1	$(48.00)	$(98.00)
1	$27.00	$20.00	0.769230769	$20.77	$15.38
2	$21.00	$41.00	0.591715976	$12.43	$24.26
3	$19.00	$51.00	0.455166136	$8.65	$23.21
4	$12.00	$59.00	0.350127797	$4.20	$20.66
			NPV =	$(1.96)	$(14.48)

Since , NPV at IRR = 30% is negative we can interpret that the IRR lies between 20% to 30%.

Using Interpolation

a1) IRR Project A = 20% + 10%*(5.87/(5.87-(-1.96)) = 20% + 10% * 0.75 = 20% + 7.5% = 27.5% ( approx)

IRR Project A = 27.5% ( approx)

a2) IRR Project B = 20% + 10%*(5.11/(5.11-(-14.48)) = 20% + 10% * 0.26 = 20% + 2.6% = 22.6% ( approx)

IRR Project B = 22.6% ( approx)

Step 2 : Calculation of NPV at discount rate = 4.7%

Year	Project A	Project B	PVF @ 30%	Present Value A	Present Value B
0	$(48.00)	$(98.00)	1	$(48.00)	$(98.00)
1	$27.00	$20.00	0.955109838	$25.79	$19.10
2	$21.00	$41.00	0.912234802	$19.16	$37.40
3	$19.00	$51.00	0.871284434	$16.55	$44.44
4	$12.00	$59.00	0.832172334	$9.99	$49.10
			NPV =	$23.49	$52.04

b1) NPV Project A =  $23.49

b2) NPV Project B = $52.04

Step 3: Ranking of Projects a per IRR & NPV

	Project A	Project B
IRR	Rank 1	Rank 2
NPV	Rank 2	Rank 1

As per IRR, Since the IRR of Project A is higher than IRR of Project B. therefore we should select Project A .

As per NPV, Since NPV of Project B is greater than NPV of Project A, therefore we should select Project B.

The difference in ranking between decision based on IRR & NPV arises due to two reasons
a) Different size of the project as size of project B is more than size of Project A
b) Cash flow distribution of the projects like in our case the cash flows of Project A are higher in the initial years whereas in case of project B they are higher in case of later years

Since NPV is a numerical measure, it ranks the project higher which adds more dollar value and is indifferent to the initial investment required. Whereas, IRR is a relative measure, and it ranks projects offer return higher regardless of the total value added.

Whenever an NPV and IRR conflict arises, always accept the project with higher NPV. This because IRR has an underlying assumption that the cash flows are reinvested at IRR which cannot always be the case.