Question

Better Health, Inc. is evaluating two investment projects, each of which requires an up-front expenditure of $2.5 million. The projects are expected to produce the following net cash inflows:
Year	Project A	Project B
0	-$2,500,000	-$2,500,000
1	$500,000	$1,200,000
2	$1,100,000	$1,300,000
3	$1,400,000	$800,000
a. What is each project's IRR?
b. What is each project's NPV if the cost of capital is 10 percent? c. Which one would you buy?

Please include the input used in a financial calculator if it is needed.

Answer 1

a) IRR is the rate at which NPV = 0
IRR can be calculated using either a financial calculator or excel or through hit and trial:

Project A:

Calculator inputs are CF0 = -2500000, CF1 = 500000, CF2 = 1100000, CF3 = 1400000

Using Excel we get the IRR = 8.33% rounded to two decimal places:

Year	CF	Discount Factor	Discounted CF
0	$ -25,00,000.00	1/(1+0.0833245898465279)^0=	1	1*-2500000=	$ -25,00,000.00
1	$     5,00,000.00	1/(1+0.0833245898465279)^1=	0.923084373	0.92308437320865*500000=	$     4,61,542.19
2	$ 11,00,000.00	1/(1+0.0833245898465279)^2=	0.85208476	0.852084760062006*1100000=	$     9,37,293.24
3	$ 14,00,000.00	1/(1+0.0833245898465279)^3=	0.786546127	0.78654612666248*1400000=	$   11,01,164.58
				NPV = Sum of all Discounted CF	$                    0.00

Project B:

Calculator inputs are CF0 = -2500000, CF1 = 1200000, CF2 = 1300000, CF3 = 800000

Using Excel we get the IRR = 16.34% rounded to two decimal places:

Year	CF	Discount Factor	Discounted CF
0	$ -25,00,000.00	1/(1+0.1633943888366)^0=	1	1*-2500000=	-25,00,000.00
1	$ 12,00,000.00	1/(1+0.1633943888366)^1=	0.859553742	0.859553741702334*1200000=	10,31,464.49
2	$ 13,00,000.00	1/(1+0.1633943888366)^2=	0.738832635	0.738832634874483*1300000=	9,60,482.43
3	$     8,00,000.00	1/(1+0.1633943888366)^3=	0.635066356	0.635066355798156*800000=	5,08,053.08
				NPV = Sum of all Discounted CF	$                    0.00

b) NPV is calculated as follows:

Project A:

Calculator inputs are CF0 = -2500000, CF1 = 500000, CF2 = 1100000, CF3 = 1400000

Using Excel we get the I = 10% rounded to two decimal places:

Year	CF	Discount Factor	Discounted CF
0	$ -25,00,000.00	1/(1+0.1)^0=	1	1*-2500000=	$ -25,00,000.00
1	$     5,00,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*500000=	$     4,54,545.45
2	$ 11,00,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*1100000=	$     9,09,090.91
3	$ 14,00,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*1400000=	$   10,51,840.72
				NPV = Sum of all Discounted CF	$ -84,522.92

Project B:

Calculator inputs are CF0 = -2500000, CF1 = 1200000, CF2 = 1300000, CF3 = 800000

Using Excel we get the I = 10% rounded to two decimal places:

Year	CF	Discount Factor	Discounted CF
0	$ -25,00,000.00	1/(1+0.1)^0=	1	1*-2500000=	$ -25,00,000.00
1	$ 12,00,000.00	1/(1+0.1)^1=	0.909090909	0.909090909090909*1200000=	$   10,90,909.09
2	$ 13,00,000.00	1/(1+0.1)^2=	0.826446281	0.826446280991735*1300000=	$   10,74,380.17
3	$     8,00,000.00	1/(1+0.1)^3=	0.751314801	0.751314800901578*800000=	$     6,01,051.84
				NPV = Sum of all Discounted CF	$ 2,66,341.10

c) Project B should be selected as it has a higher NPV and even using the IRR rule, project B is correct as it has a higher IRR.