Question

Projects A and B have the following cash flows:

year	A	B
0	-5000	-5000
1	2000	5000
2	0	1500
3	3000	1500
4	5000	1500

What is the IRR of the project A?

Please write an answer in decimals. For example, 12.34% would be 0.1234.

Also, round your answer to the fourth decimal.

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 25%

Year	Annual Cash Flow ($)	Present Value factor at 25%	Present Value of Cash Flow ($)
1	2,000	0.80000	1,600.00
2	0	0.64000	0
3	3,000	0.51200	1,536.00
4	5,000	0.40960	2,048.00
TOTAL			5,184.00

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $5,184.00 - $5,000

= $184

Step – 2, NPV at 25% is positive, Calculate the NPV again at a higher discount rate, Say 27%

Year	Annual Cash Flow ($)	Present Value factor at 27%	Present Value of Cash Flow ($)
1	2,000	0.78740	1,574.80
2	0	0.62000	0
3	3,000	0.48819	1,464.57
4	5,000	0.38440	1,922.01
TOTAL			4,961.38

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= $4,961.38 -- $5,000

= -$38.62 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.25 + [$184 x (0.27 – 0.25)]

              $184 – (-$38.62)

= 0.25 + 0.0165

= 0.2665

= 26.65%

“Therefore, the Internal Rate of Return (IRR) for the Project = 0.2665 (in decimals)”

NOTE

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.