One number for the return of a project
When an investment pays back over several years, its return is not simply total profit divided by the cost. Money received in year 4 is worth less than money received in year 1. The internal rate of return (IRR) is the discount rate that makes the net present value of all the cash flows exactly zero:
0 = −I₀ + C₁ ÷ (1 + IRR) + C₂ ÷ (1 + IRR)² + … + Cₙ ÷ (1 + IRR)ⁿ
If the IRR is above your cost of capital, the project earns more than the money costs, and its NPV at that cost is positive.
How the calculator finds it
There is no general formula for this equation. The calculator uses Newton’s method: it starts at 10%, computes the NPV and its slope, jumps to a better estimate, and repeats 40 times. For ordinary projects, where an investment is followed by positive cash flows, this converges to the exact rate. If the NPV is not zero at the end, the calculator warns that no IRR was found.
Worked example
You invest $10,000 in equipment that returns $3,000, $3,500, $4,000 and $4,000 over four years. Your cost of capital is 8%.
- IRR: 15.81%.
- NPV at 8%: $1,894.
- MIRR with a 6% reinvestment rate: 12.02%.
- Undiscounted net gain: $4,500.
The IRR is almost twice the cost of capital, so the investment creates value.
The modified IRR
The IRR implicitly assumes that every cash flow is reinvested at the IRR itself, which is often unrealistic for high returns. The MIRR fixes this:
- Grow the positive cash flows to the final year at a reinvestment rate you choose.
- Discount the investment and any negative cash flows to today at your finance rate.
- MIRR = (future value of inflows ÷ present value of outflows)^(1/n) − 1.
Here, reinvesting at 6% gives an MIRR of 12.02%, lower than the IRR but still well above the cost of capital.
Traps to avoid
- Multiple sign changes: a project with a large cleanup cost at the end can have two IRRs or none. Use NPV instead.
- Scale: IRR says nothing about the size of the gain. Between two projects that exclude each other, prefer the higher NPV.
- Timing: the calculator assumes cash flows at the end of each year. For monthly flows or irregular dates, use a spreadsheet’s XIRR function.
- Comparing with an interest rate: IRR is an annual return, comparable to a loan rate or an expected market return over the same horizon.
This calculator gives estimates for education and planning. It is not investment, tax or legal advice; for decisions about your own situation, talk to a qualified financial professional.