Question

A firm is considering a project that requires an initial investment of $180,000. The life of this project is five years. Cash flows for each year are estimated as follows:

Year 1	Year 2	Year 3	Year 4	Year 5
$105,000	$190,000	$50,000	-$60,000	-$110,000

The cost of capital of this project is 8%. Calculate the internal rate of return of the project and make a decision.

Accept since the IRR is 5.04%, which is less than the required rate. Accept since the IRR is 12.68%, which is greater than the required rate. Reject since the IRR is 5.04%, which is less than the required rate. Reject since the IRR is 12.68%, which is greater than the required rate. Cannot be determined.

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 12.00% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 12.00%	Present Value of Cash Flow ($)
1	1,05,000	0.892857	93,750
2	1,90,000	0.797194	1,51,467
3	50,000	0.711780	35,589
4	-60,000	0.635518	-38,131
5	-1,10,000	0.567427	-62,417
TOTAL			1,80,258

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

= $1,80,258 - $180,000

= $258

Step – 2, NPV at 12.00% is positive, Calculate the NPV again at a higher discount rate, Say 13.00% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 13.00%	Present Value of Cash Flow ($)
1	1,05,000	0.884956	92,920
2	1,90,000	0.783147	1,48,798
3	50,000	0.693050	34,653
4	-60,000	0.613319	-36,799
5	-1,10,000	0.542760	-59,704
TOTAL			1,79,868

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

= $1,79,868 - $180,000

= -$132 (Negative NPV)

The calculation of Internal Rate of Return using Interpolation method is as follows

IRR = R1 + NPV1(R2-R1)

                    NPV1-NPV2

= 0.12 + [$258 x (0.13 – 0.12)]

              $258 – (-$132)

= 0.12 + [$2.58 / $390]

= 0.12 + 0.0068

= 0.1268 or

= 12.68%

“Therefore, the Internal Rate of Return (IRR) for the Project will be 12.68%”

DECISION

Accept since the IRR is 12.68%, which is greater than the required rate.

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.