Question

Your company has a project available with the following cash flows: Year Cash Flow 0 −$81,100 1 21,500 2 25,000 3 30,800 4 26,000 5 19,800 If the required return is 14 percent, should the project be accepted based on the IRR?

Answer 1

Internal Rate of Return (IRR) for the Project

Step – 1, Firstly calculate NPV at a guessed discount Rate, Say 15% (R1)

Year	Annual Cash Flow ($)	Present Value factor at 15%	Present Value of Cash Flow ($)
1	21,500	0.869565	18,695.65
2	25,000	0.756144	18,903.59
3	30,800	0.657516	20,251.50
4	26,000	0.571753	14,865.58
5	19,800	0.497177	9,844.10
TOTAL			82,560.43

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

= $82,560.43 - $81,100

= $1,640.43

Step – 2, NPV at 15% is positive, Calculate the NPV again at a higher discount rate, Say 16% (R2)

Year	Annual Cash Flow ($)	Present Value factor at 16%	Present Value of Cash Flow ($)
1	21,500	0.862069	18,534.48
2	25,000	0.743163	18,579.07
3	30,800	0.640658	19,732.26
4	26,000	0.552291	14,359.57
5	19,800	0.476113	9,427.04
TOTAL			80,632.42

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

= $80,632.42 - $81,100

= -$467.58 (Negative NPV)

Therefore IRR = R1 + NPV1(R2-R1)

                                   NPV1-NPV2

= 0.15 + [$1,460.43 x (0.16 – 0.15)]

              $1,460.43 – (-$467.58)

= 0.15 + [$14.60 / $1,928.01]

= 0.15 + 0.0076

= 0.1576 or

= 15.76%

“Internal Rate of Return (IRR) for the Project = 15.76%”

DECISION

“YES”. The Project should be accepted, since the Internal Rate of Return for the Project (15.76%) is greater than the Required Rate of Return (14%) of the Project

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.