Question

Jim is evaluating project that will pay him $5,000 per year for 5 years, and then cost him $4,000 per year for 12 years. Jim’s opportunity cost of capital for this project is 18 percent. What is the IRR of this investment? Based on this calculation, should Jim accept this project or not?

Answer 1

4.25%

Step-by-step explanation:

We need to calculate the net present value of the cash flows to determine the IRR.

NPV = PV of Cash inflows - PV of Cash outflows

As the cash inflow and outflow are fixed for specific period of time so, we will use the annuity formula to calculate the NPV.

NPV = [ $5,000 x ( 1 - ( 1 + 18% )^-5) /18% ] - [ ( $4,000 x ( 1 - ( 1 + 18% )^-12) /18%) x ( 1 + 18%)^-6 ]

NPV = $15,636 - $7,102 = $8,534

We need NPV on a higher rate of 10%

NPV = [ $5,000 x ( 1 - ( 1 + 10% )^-5) /10% ] - [ ( $4,000 x ( 1 - ( 1 + 10% )^-12) /10%) x ( 1 + 10%)^-6 ]

NPV = $18,954 - $15,385 = $3,569

IRR = Lower rate + [ Lower rate NPV / (Lower rate NPV - Higher rate NPV) ] (higher rate - lower rate)

IRR = 10% + [ 3,569 / ($3,569 - $8,534) ] (18% - 10%)

IRR = 4.25%