Question

A company is analyzing two mutually exclusive projects, S and L, with the following cash flows:

0 1    2 3 4

Project S -$1,000 $875.68 $260 $15 $5

Project L -$1,000 $10 $240 $400 $785.54

The company's WACC is 9.5%. What is the IRR of the better project? (Hint: The better project may or may not be the one with the higher IRR.) Round your answer to two decimal places.

Answer 1

To find better project we need to find NPV of the both project

Statement Showing NPV of Project S

Year	Cash flow	PVIF @ 9.5%	PV
0	-1000.00	1.0000	-1000.00
1	875.68	0.9132	799.71
2	260.00	0.8340	216.84
3	15.00	0.7617	11.42
4	5.00	0.6956	3.48
NPV = Sum of PV	31.45

Thus NPV of project S = $31.45

Statement Showing NPV of Project L

Year	Cash flow	PVIF @ 9.5%	PV
0	-1000.00	1.0000	-1000.00
1	10.00	0.9132	9.13
2	240.00	0.8340	200.16
3	400.00	0.7617	304.66
4	785.54	0.6956	546.40
NPV = Sum of PV	60.36

Thus NPV of project L = $60.36

Hence better project is project L

Now IRR of project L

IRR is rate at which NPV is 0

Assume rate to be 11% then NPV =

Year	Cash flow	PVIF @11%	PV
0	-1000.00	1.0000	-1000.00
1	10.00	0.9009	9.01
2	240.00	0.8116	194.79
3	400.00	0.7312	292.48
4	785.54	0.6587	517.46
NPV = Sum of PV	13.73

Now assume r = 12%, then NPV =

Year	Cash flow	PVIF @12%	PV
0	-1000.00	1.0000	-1000.00
1	10.00	0.8929	8.93
2	240.00	0.7972	191.33
3	400.00	0.7118	284.71
4	785.54	0.6355	499.22
NPV = Sum of PV	-15.81

Now using interpolation we can find IRR

R	NPV
11%	13.73
12%	-15.81
1%	30
?	13.73

= 13.73 / 30

= 0.46

Thus IRR of project L = 11%+0.46% = 11.46%