The money-weighted return (MWR) that causes the beginning value and intermediate cash flows to grow to the ending value. It the rate of discount on an investment that equates the present value of cash outflows with the present value of cash inflows associated with an investment. In the following equation, it is the value that solves for IRR:

MV_E = MV_B x (1+IRR) + CF₁ x (1+ IRR)¹ +…. + CF_N x (1+IRR)^N

Where: CF denotes the amount of the cash inflow or cash outflow and N is the percentage of the period that the cash flow was available for investment (the period weight).

The IRR reflects the rate of return implied by the growth in the market values of the invested funds, in addition to generated cash flows. It explains the growth in assets over the measurement period. However, this rate is based on the assumption that each dollar invested grows at the same rate, regardless of the timing of investment.

For an example, see: internal rate of return- calculation.