Internal Rate of Return (IRR) — Definition and How It Differs from TWR

Internal rate of return is the discount rate that sets the net present value of a stream of cash flows to zero. Definition, formula, and comparison with TWR.

Definition

The internal rate of return (IRR) is the constant discount rate r that satisfies the equation in which the present value of all cash inflows equals the present value of all cash outflows. Because larger cash flows in any given period have a proportionally larger effect on the discounted sum, IRR is described as money-weighted. In private-equity, real-asset, and personal-portfolio reporting it is the conventional summary measure of investor outcomes over an irregular contribution and distribution schedule.

Formula

0 = sum_{t=0}^{N} CF_t / (1 + r)^t

where:
  CF_t = signed cash flow at time t (negative for contributions, positive for distributions and terminal NAV)
  r    = the IRR (solved iteratively, e.g. Newton-Raphson)

Worked example

An investor contributes 100,000 at t = 0, contributes a further 50,000 at t = 1 year, and the position is worth 180,000 at t = 2 years (the terminal NAV is treated as a distribution). The IRR solves 0 = −100,000 + (−50,000) / (1 + r) + 180,000 / (1 + r)^2. Numerical solution gives r ≈ 12.4% per year. A TWR over the same period would weight each year equally regardless of the capital base and would, in general, produce a different number.

IRR versus TWR

• TWR neutralises cash flows; IRR is driven by them.
• TWR is the methodology required by GIPS for composite manager returns; IRR is standard for private-market and household reporting.
• If no external flows occur during the period, TWR and IRR converge to the same number.
• IRR can return multiple roots when cash flow signs change more than once. Practitioners then fall back to modified IRR (MIRR) or report cash-on-cash multiples alongside.

Related terms

• Time-weighted return (TWR)
• Net present value (NPV)
• Modified internal rate of return (MIRR)
• Cash flow