The formula
the rate r for which Σ flow ÷ (1 + r)^period = 0
Where it comes from
The internal rate of return is the discount rate at which a project exactly breaks even. There is no formula that solves for it directly, so it is found by trial and adjustment until the net present value lands on zero.
How to work it out by hand
- Write the flows in order, investment first and negative
- Pick a rate and work out the NPV
- If it is positive, try a higher rate; if negative, a lower one
- Repeat until the NPV is zero: that rate is the IRR
What is worth knowing
IRR is popular because it produces a percentage that sounds comparable to anything else, and that is also its weakness. It says nothing about size — a 40% return on 100 beats a 12% return on a million by this measure and not by any other. It assumes intermediate cash flows get reinvested at the IRR itself, which is optimistic for high figures. And when the flows change sign more than once, there can be several valid answers or none at all, which is what this calculator reports rather than inventing one. When IRR and NPV disagree about which project to pick, NPV is right.