Question

What is the internal rate of return (IRR) of this project given the following cash flows?

Year                 CF
0                -$9,800
1                   $1,000
2                   $4,500
3                   $1,000
4                   $1,500
5                   $1,700
6                   $2,700

Convert your answer to percentage and round off to two decimal points. Do not enter % in the answer box.

Answer 1

Ans.

At IRR the NPV of a project is zero.

We can calculate it by hit and trial method

Let the IRR be 7%

PROJECT	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Net Cash Flow	$    (9,800.00)	$ 1,000.00	$ 4,500.00	$ 1,000.00	$     1,500.00	$ 1,700.00	$ 2,700.00
Discount Factor @ 7%	1	0.93457944	0.87343873	0.81629788	0.762895212	0.71298618	0.66634222
Present Value of Cash Flows	$    (9,800.00)	$      934.58	$ 3,930.47	$      816.30	$     1,144.34	$ 1,212.08	$ 1,799.12
NPV @ 7.0%	$             36.89

Let the IRR be 7.5%

PROJECT	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Net Cash Flow	$ (9,800.00)	$1,000.00	$4,500.00	$1,000.00	$1,500.00	$1,700.00	$2,700.00
Discount Factor @ 7.5%	1	0.930233	0.865333	0.804961	0.74880053	0.696559	0.647962
Present Value of Cash Flows	$ (9,800.00)	$930.23	$3,894.00	$804.96	$1,123.20	$1,184.15	$1,749.50
NPV @ 7.5%	$    (113.96)

So the rate will be in between of 7% and 7.5% but closer to 7% as with 7.5% we see that the NPV is negative.

Let the IRR be 7.12%

PROJECT	Year 0	Year 1	Year 2	Year 3	Year 4	Year 5	Year 6
Net Cash Flow	$ (9,800.00)	$1,000.00	$4,500.00	$1,000.00	$1,500.00	$1,700.00	$2,700.00
Discount Factor @ 7.12%	1	0.933532	0.871483	0.813558	0.75948245	0.709002	0.661876
Present Value of Cash Flows	$ (9,800.00)	$933.53	$3,921.67	$813.56	$1,139.22	$1,205.30	$1,787.07
NPV @ 7.12%	$               0

So the NPV will be 0 if the rate will be 7.12%

So the IRR of project is 7.12%