Question

Determine the internal rate of return on the following​ project: An initial outlay of 9000 resulting in a cash inflow of 1800 at the end of year​ 1, 4800 at the end of year 2, and 7800 at the end of year 3

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 21% (R1)

Year

Annual Cash Flow ($)

Present Value factor at 21%

Present Value of Cash Flow ($)

1

1,800

0.82645

1,487.60

2

4,800

0.68301

3,278.46

3

7,800

0.56447

4,402.90

TOTAL

9,168.96

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

= $9,168.96 - $9,000

= $168.96

Step – 2, NPV at 21% is positive, Calculate the NPV again at a higher discount rate, Say 22% (R2)

Year

Annual Cash Flow ($)

Present Value factor at 22%

Present Value of Cash Flow ($)

1

1,800

0.81967

1,475.41

2

4,800

0.67186

3,224.94

3

7,800

0.55071

4,295.51

TOTAL

8,995.86

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

= $8,995.86 - $9,000

= -$4.14 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.21 + [$168.96 x (0.22 – 0.21)]

              $168.96 – (-$4.14)

= 0.21 + [$1.69 / $173.10]

= 0.21 + 0.0098

= 0.2198 or

= 21.98%

“Hence, the Internal Rate of Return (IRR) for the Project would be 21.98%”