Internal rate of return (IRR)

Internal rate of return is the discount rate at which the present value of an investment's expected future cash flows exactly equals its initial cost — equivalently, the rate that makes the investment's net present value zero. It expresses a return as a single annualized percentage, making very different investments easier to compare at a glance.

IRR is closely related to discounted cash flow analysis: where DCF starts with a chosen discount rate and solves for value, IRR starts with the actual cash flows and value and solves backward for the implied rate. It is usually found numerically, since there is no general closed-form solution once cash flows are irregular, and projections that feed it often draw on scenario modeling or Monte Carlo simulation to stress-test the assumptions. A project is typically considered attractive if its IRR exceeds the investor's required rate of return, or hurdle rate.

IRR is the standard performance metric in private equity and venture capital, where cash flows, including calls on working capital, are irregular and there is no continuously traded market price to measure return against. Its well-known pitfalls: IRR assumes interim cash flows are reinvested at the IRR itself, which can be unrealistic; cash flow streams with sign changes can produce multiple valid IRRs or none at all; and a high IRR on a small, short-lived investment can look better than a larger, longer one with a lower IRR but far more total value created.