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  1. 086Two private deals each return 2.0 times the money invested, in a single payout at the end. One pays out after three years, the other after seven. What IRR does each earn?Private and real asset mathsCoreInvescoNew York · 2025

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    Roughly, what IRR does the seven-year deal earn?

    Show the worked solution

    About 26% a year for the three-year deal and 10.4% for the seven-year deal. The IRR of a single payout is the multiple to the power one over the years, less one: 2 to the one third and 2 to the one seventh. Same money back, very different speed. The multiple says how much, the IRR says how fast, and a deal needs both.

    Why does the same multiple give such different returns?

    Two friends each double their savings; one takes three years, the other seven. Nobody would call them equally good investors. A multiple of money ignores time entirely, while IRR is a rate per year, so the same 2.0x falls from 26% to 10.4% as the wait stretches from three years to seven. The curve is steep early: each extra year cuts the IRR most when the holding period is short.

    The same 2.0x, earned over different lengths of time1234567891010%20%30%40%3 years: 26.0% a year7 years: 10.4% a yearYears to get 2.0x backBoth deals2.0x moneyTo match 26%over 7 years5.0xis needed,not 2.0x
    A fixed 2.0 times multiple earns about 26% a year if it arrives in three years and only 10.4% if it takes seven; to match the three-year IRR, the seven-year deal would need about 5.0 times the money.
    The relationship
    IRR=M1/T−1:21/3−1=26.0%,21/7−1=10.4%\text{IRR} = M^{1/T} - 1: \quad 2^{1/3} - 1 = 26.0\%, \quad 2^{1/7} - 1 = 10.4\%
    Mmultiple of money, 2.0
    Tyears until the single payout
    What it says in wordsFor one cash flow in and one out, the IRR is the yearly growth rate that turns the investment into the multiple.

    So which number should an investor care about?

    Both, because each can be gamed alone. A short, quick flip can post a high IRR on a small absolute gain, while a long hold can post a big multiple at a return below the cost of capital. Limited partners look at IRR for speed and at the multiple, often called the equity multiple or MOIC, for how much wealth was actually created. To match 26% over seven years, the second deal would need about 5.0 times the money, not 2.0.

    One caution for the room: this clean formula holds only with one outflow and one inflow. With interim distributions, the IRR assumes those cash flows are reinvested at the IRR itself, which is rarely true, so a quoted IRR on a deal with early payouts flatters it.

    Where candidates lose it

    The common slip is linear: 100% gain over seven years is about 14% a year. That forgets compounding and overstates the return by more than three points.

    The second loss is treating a higher IRR as automatically better. Say that a 26% IRR on a small cheque held briefly can create less wealth than 10% on a large one held for years.

    What the interviewer asks next

    • What multiple does a 20% IRR produce over five years?
    • A deal returns 1.5x in one year. Is that better than 2.0x in three?
    • Why do sponsors sometimes use a credit line to delay capital calls, and what does it do to IRR?

    Asked at Invesco, Real Estate, New York, 2025 (Wall Street Oasis): Lots of basic questions asked about IRR, EM, Cap Rates etc