Question

A project has an initial cost of $300,000, expected net cash inflows of $67,500 per year for 7 years, and a cost of capital of 11%. What is the project's NPV? What is the IRR and the PI? What is the payback period?

Answer 1

1) Statement showing NPV

Year	Cash flow	PVIF @ 11%	PV
0	-300000	1	-300000
1	67500	0.9009	60811
2	67500	0.8116	54785
3	67500	0.7312	49355
4	67500	0.6587	44464
5	67500	0.5935	40058
6	67500	0.5346	36088
7	67500	0.4817	32512
NPV			18073

2) IIR is the rate at which NPV is 0,

let us assume rate to be 13%

Statement showing NPV

Year	Cash flow	PVIF @ 11%	PV
0	-300000	1.0000	-300000
1	67500	0.8850	59735
2	67500	0.7831	52862
3	67500	0.6931	46781
4	67500	0.6133	41399
5	67500	0.5428	36636
6	67500	0.4803	32422
7	67500	0.4251	28692
NPV			-1474

Now assume assume rate to be 12%

statement showing NPV

Year	Cash flow	PVIF @ 11%	PV
0	-300000	1.0000	-300000
1	67500	0.8929	60268
2	67500	0.7972	53811
3	67500	0.7118	48045
4	67500	0.6355	42897
5	67500	0.5674	38301
6	67500	0.5066	34198
7	67500	0.4523	30534
NPV			8054

using interpolation method we can find IRR

R	NPV
12%	8,054
13%	-1,474
1% up	9,528
?	8,054

=8054/9528

=0.85%

Thus IRR = 12+0.85 = 12.85%

3) PI = PV of cash Inflow/PV of cash outflow

=318073/300000

=1.06

4) Payback period = Investment/Cash flow

=300000/67500

=4.44 years