In more detail
IRR is the rate r that solves Σ CFₜ / (1 + r)^t = 0, where the cash flows CFₜ include the initial outlay as a negative number. A project is attractive if its IRR beats your required return (the hurdle rate). There is no formula to solve it directly, so calculators find it by iteration. When cash flows change sign more than once, there can be several IRRs or none, and IRR implicitly assumes interim cash can be reinvested at the IRR itself, which flatters high-IRR projects.
Why it matters
IRR is the standard single figure for comparing projects, property deals and private investments of different sizes and timings. Used alone it can mislead: a small project with a high IRR may add less value than a large one with a lower IRR.
Example
An outlay of $1,000 followed by $450 a year for three years:
| Discount rate | NPV |
|---|---|
| 10% | $119.08 |
| 16.65% | $0.00 |
| 20% | −$52.08 |
The NPV crosses zero at 16.65%, so that is the IRR.
Common confusion
NPV gives a value in money at a chosen rate; IRR gives the rate at which that value is zero. When they rank projects differently, NPV is the more reliable guide.