Question

A project has an initial cost of $54,200 and is expected to produce cash inflows of $19,200, $27,300, and $44,600 over the next 3 years, respectively. What is the project’s internal rate of return?

Answer 1

Project IRR calculation using Trial and Error method.

The NPV of the projet is 0 at IRR

We will select an arbitrary discount rate and compute NPV say 20%

NPV = PV of cash flows discounted at 20% - Initial Investment

= 19200(1.20) + 27300/(1.20)^2 + 44600/(1.20)^3 - 54200

= $60769 - $54200

= $6569

Since NPV is positive at 20% we will select higher rate to get negative NPV negative say 30%

NPV = 19200/(1.30) + 27300/(1.30)^2 + 44600/(1.30)^3 - 54200

= $51223 - $54200

= -$2977

Since NPV at 30% is negative it means IRR lies between 20% and 30%..In order to get correct IRR we need to interpolate using Interpolation formula

= LR +(HR-LR){(NPV at LR - 0 )/(NPV at LR - NPV at HR)

Where LR = Lower rate, HR = Higher rate

= 20 + (30-20){6569-0)/ (6569-(-2977))

= 20 + 10*6569/9546

= 20 + 6.88

= 26.88%

IRR = 26.88%