What IRR Actually Is
The internal rate of return is the discount rate at which an investment's net present value equals zero — the rate at which what you put in and what you get out exactly balance once timing is accounted for:
0 = CF0 + CF1/(1+IRR) + CF2/(1+IRR)2 + … + CFn/(1+IRR)n
There is no closed-form solution beyond simple cases, so it is found numerically. This calculator uses bisection, which converges reliably for the conventional pattern of one outflow followed by inflows.
Why Timing Changes Everything
Two projects returning the same total look identical to a simple return figure and very different to IRR:
| Year | Project A | Project B |
|---|---|---|
| 0 | −$50,000 | −$50,000 |
| 1 | $30,000 | $5,000 |
| 2 | $25,000 | $10,000 |
| 3 | $15,000 | $25,000 |
| 4 | $5,000 | $35,000 |
| Total | $75,000 | $75,000 |
| IRR | 24.6% | 13.8% |
Project A returns the same money sooner, so it can be reinvested sooner. Total return cannot see this; IRR can.
IRR Against NPV
IRR gives a percentage, which is easy to compare against a hurdle rate. NPV gives a dollar amount, which measures how much value is actually created. When the two disagree — typically between projects of very different sizes — NPV is the correct guide. A 40% IRR on $10,000 creates less wealth than a 15% IRR on $500,000.
Where IRR Misleads
- Multiple sign changes. If cash flows go negative again after turning positive, several rates can satisfy the equation. The mathematics permits as many IRRs as there are sign changes.
- The reinvestment assumption. IRR implicitly assumes interim cash is reinvested at the IRR itself, which is optimistic for high-IRR projects. The modified IRR fixes this by specifying a separate reinvestment rate.
- Scale blindness. A percentage says nothing about size.
- Short projects flatter. A quick project with a high IRR may not be repeatable, leaving capital idle afterwards.
Reading the Result
Accept the project when the IRR exceeds your cost of capital or required return; reject it when it does not. The gap between the two is the margin of safety — a project at 8.2% against an 8% hurdle is, in practice, a coin flip once the estimates are wrong by a few percent.
Frequently Asked Questions
What is a good IRR?
Entirely context-dependent. Private equity targets 20–30%; real estate projects often 12–20%; corporate capital projects clear a hurdle of 8–15%. The only universal test is whether it beats the cost of capital for that risk.
Can IRR be negative?
Yes, when total inflows are less than the outflow. It means the investment lost money.
What is the difference between IRR and ROI?
ROI is total gain over cost with no regard for when the money moved. IRR is annualized and timing-aware. For anything longer than a year with more than one cash flow, IRR is the more honest measure.