IRR

Internal rate of return (IRR) is a financial metric used to assess the profitability of investments and projects. It is defined as the discount rate that makes the net present value of all cash flows from the project equal to zero. In this framework, cash inflows are treated as positive and the initial investment as a negative cash flow.

In practice, IRR is found by solving the equation sum over t of CF_t divided by (1 plus IRR) raised to the t equals zero, where CF_t is the cash flow at time t and CF_0 is the initial investment. Because this equation is nonlinear, IRR is determined numerically using iterative methods, financial calculators, or software tools.

IRR is commonly used to evaluate projects and compare alternative investments. A project is often considered acceptable if its IRR exceeds a specified hurdle rate or the organization's cost of capital. It can also be used to rank multiple proposals. However, IRR has limitations: it assumes that interim cash flows are reinvested at the IRR, which may be unrealistic; it may produce multiple IRRs for non-conventional cash flows; and it does not measure the scale of the investment or the timing beyond the rate at which the net present value becomes zero. Additionally, IRR can disagree with net present value when projects differ in size or timing.

Related concepts include the modified internal rate of return (MIRR), which uses explicit reinvestment and financing rates, and NPV, which remains a straightforward measure of value in absolute terms.