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  1. 042Which makes more money on the same cheque: a 25% IRR for 3 years, or a 20% IRR for 5 years?Returns mathsWarm upMid-market buyout fund

    Try it first

    Which ends with more money?

    Show the worked solution

    The 20% for 5 years makes more money: 2.49x against 1.95x. 1.25 cubed is about 1.95 and 1.2 to the fifth is about 2.49. On a cheque of 100 that is a profit of 149 against 95. The 25% deal is faster, but the money is back after three years, and it only catches up if it can be reinvested at about 13% for the remaining two.

    Why does the higher IRR make less money?

    A car doing 100 km an hour for three hours covers 300 km; one doing 80 km an hour for five hours covers 400. Speed and distance are different questions. IRR measures how fast money grows, the multiple measures how much money you end with, and a longer hold at a lower speed can end further ahead. Here 1.25 cubed is 1.95 and 1.2 to the fifth is 2.49.

    The faster deal stops sooner; the slower one makes more money1.0x1.5x2.0x2.5xYr 0Yr 1Yr 2Yr 3Yr 4Yr 5A: 25% for 3 years = 1.95xB: 20% for 5 years = 2.49xA reinvested at 12.9%only matches BOn 100A +95B +149profit
    Compounding at 25% for three years ends at 1.95x, while 20% for five years ends at 2.49x, so the higher IRR makes less money unless its proceeds can be reinvested at about 12.9% for the two years it is not running.

    So which would an LP prefer?

    It depends on what happens to the money after year three. If the LP can redeploy A's proceeds at more than about 12.9% a year, A ends ahead; below that, B wins. Reinvested at 20%, A reaches 2.81x by year five; parked at 8%, only 2.28x. That is why LPs read IRR and the money multiple together, and why GPs who sell early to protect a high IRR are sometimes accused of leaving money on the table.

    The relationship
    1.253=1.951.205=2.49(1+r)2=2.491.95⇒r≈12.9%1.25^3 = 1.95 \qquad 1.20^5 = 2.49 \qquad (1+r)^2 = \frac{2.49}{1.95} \Rightarrow r \approx 12.9\%
    1.25^3A's money multiple after three years
    1.20^5B's money multiple after five years
    rthe reinvestment rate at which A catches B by year five
    What it says in wordsCompare the two multiples, then ask what rate A's money must earn in the gap years to catch up.

    Say the limitation. Both deals here are a single cheque in and out. A fund's IRR also depends on when capital is called and returned, and a high IRR on a small, quick deal can flatter a fund that made little money overall.

    Where candidates lose it

    The common loss is picking the higher IRR on reflex. The interviewer is checking whether you know that IRR is a rate and says nothing on its own about how much money comes back.

    The second loss is giving the right answer without the reinvestment point. The full answer is that B makes more money, and A wins only if its proceeds can be redeployed at about 13% or better.

    What the interviewer asks next

    • What IRR over 3 years would match 2.49x?
    • Why might a GP sell a winner early even though holding would make more money?
    • How does the timing of capital calls affect a fund's IRR but not its multiple?