IRR (internal rate of return)

The formula

The rate r that solves Σ CFₜ ÷ (1 + r)^t = 0, with each cashflow dated and the closing NAV treated as a final inflow

There is no closed-form solution; it is found by iteration. The formula itself is never what two sources disagree about — the cashflow set and the as-of date are.

A worked example

An LP pays in €1,000,000 on 1 January 2023, receives €400,000 on 1 January 2025, and the remaining position is marked at €900,000 on 1 January 2026. Solving for the rate that discounts +400,000 and +900,000 back to 1,000,000 over those dates gives roughly 12 per cent. Move the final mark by ten per cent and the IRR moves by about three points — on a position where no cash changed hands.

The comparisons people search for

Net IRR vs gross IRR

Net IRR is calculated after management fees, expenses and carried interest; gross IRR before. The gap between them is routinely three to five points. They are not comparable, and a figure quoted without saying which one it is should be treated as unusable.

IRR vs TVPI

IRR is the only headline metric that accounts for timing, and TVPI is the only one that does not. Money returned early flatters IRR enormously and leaves TVPI untouched, which is why a fund can post an excellent IRR and a mediocre multiple, or the reverse.

Why do three systems give three IRRs?

Almost always one of four things: a different as-of date, a different treatment of the closing NAV, cashflows dated on the notice rather than the settlement, or recallable distributions handled differently. The arithmetic is not in dispute; the inputs are.

IRR vs annualised return

For a single lump sum held to a single exit they coincide. For a series of irregular calls and distributions — that is, for every real LP position — they do not, because IRR weights each cashflow by how long it was outstanding.

Worth knowing

• Early distributions raise IRR far more than late ones of the same size.
• A fund's IRR in its first two years is dominated by fee drag and is close to meaningless.
• Sign changes in the cashflow series can admit more than one mathematically valid IRR.
• Always paired with a multiple in credible reporting, because neither is sufficient alone.