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  1. 058A deal is worth 2.0x the equity after four years, an IRR of about 18.9%. Holding one more year would add 10% to the exit equity, taking it to 2.2x. Does the IRR rise or fall, and what growth in the extra year would keep the IRR flat?Returns mathsHardLarge-cap buyout fundMid-market buyout fund

    Try it first

    Hold a fifth year for 10% more equity. What happens to the IRR?

    Show the worked solution

    The IRR falls, from 18.9% to about 17.1%, even though the money multiple rises from 2.0x to 2.2x. IRR is an average yearly growth rate, and a year that adds 10% is below the 18.9% the deal has been earning. To keep the IRR flat, the fifth year must grow equity by 18.9% itself, to about 2.38x. The hurdle for holding on is the IRR already achieved.

    Why can a bigger multiple mean a lower IRR?

    Think of a batsman averaging 19 runs a match over four matches. If he scores 10 in the fifth, his total rises but his average falls. IRR is the average yearly growth of the equity, so any year that grows it by less than the current IRR lowers the average, even while the total keeps rising. The money multiple is the total; the IRR is the average. Here the deal has averaged 18.9% a year and the fifth year offers 10%.

    An extra year only helps IRR if it grows equity faster than the IRR already earned10%15%20%25%2.0x held longerYear 3Year 4Year 5Year 6Year 72.0x at year 4: 18.9%2.2x at year 5: 17.1%2.38x keeps 18.9%Year 5 decisionGrow equity 10%:MOIC 2.0x to 2.2x, upIRR 18.9% to 17.1%, downTo keep IRR flat, theextra year must add 18.9%2.0 x 1.189 = 2.38xThe hurdle is the IRR itself
    At 2.0x after four years the IRR is 18.9%; a fifth year that adds 10% lifts the multiple to 2.2x but drops the IRR to 17.1%, and only 2.38x at year 5 would hold the IRR flat.
    The relationship
    2.01/4=1.1892.21/5=1.1712.0×1.189=2.3782.0^{1/4} = 1.189 \qquad 2.2^{1/5} = 1.171 \qquad 2.0 \times 1.189 = 2.378
    2.0^(1/4)one plus the IRR of 2.0x over four years
    2.2^(1/5)one plus the IRR of 2.2x over five years
    2.378the multiple at year 5 that keeps the IRR at 18.9%
    What it says in wordsTake the root of the multiple by the number of years to get one plus the IRR; to hold it, the extra year must grow by the same factor.

    How would a fund actually weigh the choice?

    Both numbers matter to an investor, and they point opposite ways. The extra year adds 0.2x of money but costs about 1.8 points of IRR, so the right call depends on what the cash would earn if it were returned now. If the investors could put it to work at more than 10% elsewhere, selling at year 4 is better; if not, the extra 0.2x is real money. Say this trade-off out loud, then say the limit: the 10% is a forecast, while the 2.0x offer may be on the table today.

    Where candidates lose it

    Candidates hear that equity grows and say the IRR rises. They are describing the money multiple. IRR is a rate per year, and a below-average year pulls a rate down.

    The second miss is on the flat-IRR part: answering 10%, or the old IRR divided over five years. The extra year has to match the rate already earned, about 18.9%, which takes the multiple to roughly 2.38x.

    What the interviewer asks next

    • What if the extra year adds 25%? What IRR then?
    • Why do investors track both IRR and the money multiple rather than one of them?
    • How does a dividend recap at year 4 change this decision?
  2. 091Deal A returns 3x in 7 years. Deal B returns 2x in 3 years. Which has the higher IRR? Then show that if B's proceeds can only be reinvested to earn 1.5x over the remaining 4 years, both end at 3x after 7 years.Returns mathsHardLarge-cap buyout fundSecondaries and fund of funds

    Try it first

    Which deal has the higher IRR?

    Show the worked solution

    B has the higher IRR, about 26.0% against 17.0% for A. But if B's 2x can only earn 1.5x over the next four years, about 10.7% a year, it ends at 3x after seven years, exactly where A ends. A higher IRR is worth more only if the cash it returns early can be redeployed at a comparable rate.

    How do you get the two IRRs in your head?

    Use the rule of 72 and a couple of anchors. B doubles in three years, and 72 over 3 is 24, so B is in the mid twenties; exactly, 2 to the one-third is 1.26, so 26.0%. A triples in seven years. Tripling takes about 1.6 times as long as doubling, so a seven-year triple is like doubling in about 4.4 years, which the rule of 72 puts in the high teens. Exactly, 3 to the one-seventh is 1.170, so 17.0%.

    B's 26% IRR ends at the same 3x as A's 17% if its cash earns only 1.5x after1x2x3x01234567yearsB: 2x at year 3then reinvested at 10.7%A: steady 17.0%both 3xIRRA: 17.0%B: 26.0%Wealth at yr 7A: 3.0xB: 3.0x
    Deal A compounds steadily at 17.0% to 3x in year 7, while deal B reaches 2x in year 3 at 26.0% but, reinvested at only 10.7% a year, also ends at 3x in year 7, so its higher IRR adds no wealth.

    Why does the higher IRR not make B the better deal?

    Think of two fixed deposits: one pays 26% but matures in three years, after which the best rate on offer is 10%; the other locks in 17% for seven. Over seven years you end up in the same place. IRR assumes the cash a deal returns can be reinvested at the same IRR, and when it cannot, the IRR overstates what the investor actually ends up with. B ties A when its proceeds earn 10.7% a year after year 3; any less and A wins over seven years, any more and B does.

    The relationship
    2×1.5=3.0×1.51/4−1=10.7%31/7−1=17.0%2 \times 1.5 = 3.0\times \qquad 1.5^{1/4} - 1 = 10.7\% \qquad 3^{1/7} - 1 = 17.0\%
    2B's money multiple at year 3
    1.5what the proceeds earn over the next four years
    3^(1/7)the seven-year rate both deals deliver
    What it says in wordsB's two stages multiply to the same 3x over seven years as A, so the seven-year rate is identical.

    This is why fund investors look at both numbers. A fund with high IRRs from quick flips may return less money over a decade than one with lower IRRs and bigger multiples, if the investors cannot put the early cash back to work at a similar rate.

    Where candidates lose it

    Candidates pick A because 3x sounds better than 2x, confusing size with speed. Or they pick B on IRR alone and never ask what happens to the cash after year 3.

    The point of the second half is reinvestment. Say the condition: B is better only if its proceeds can be redeployed above about 10.7% a year for the remaining four years.

    What the interviewer asks next

    • What reinvestment multiple makes B end at 3.5x after seven years?
    • Why do secondaries buyers often care more about the money multiple than the IRR?
    • How can a fund raise its reported IRR without raising its money multiple?
  3. 100A sponsor invests 100, sells half its stake for 150 in year 3 and the rest for 200 in year 5. The money multiple is 3.5x. Estimate the IRR by trial, and explain why it beats receiving the full 3.5x in year 5.Returns mathsHardLarge-cap buyout fundSecondaries and fund of funds

    Try it first

    Which is closest to the IRR?

    Show the worked solution

    About 36.9%, against 28.5% if the full 3.5x came back in year 5. Try 30%: the 150 and 200 are worth about 122 today, too much. Try 42%: about 87, too little. The rate that values them at exactly 100 is about 37%. The early 150 is discounted for three years, not five, which pulls the IRR up for the same money multiple.

    How do you find an IRR by trial?

    The IRR is the discount rate at which the money coming back is worth exactly what went in. Pick a rate, discount each inflow, and see whether the total is above or below 100. At 30%, 150 over 1.3 cubed is 68.3 and 200 over 1.3 to the fifth is 53.9, together 122.1, so 30% is too low; at 42% they come to 87.0, too high. Interpolating between the two lands near 37%, and the exact answer is 36.9%.

    Half the money back early lifts the IRR from 28.5% to 36.9%Yr 0Yr 1Yr 2Yr 3Yr 4Yr 5-100+150+200half the stake sold in year 3the rest in year 5: 3.5x30%: +22.142%: -13.0IRR 36.9%bullet 28.5%20%30%40%50%discount rate0NPV
    The sponsor puts in 100 and gets 150 back in year 3 and 200 in year 5; the value of those flows falls as the discount rate rises, from +22.1 at 30% to -13.0 at 42%, crossing zero at an IRR of 36.9%, well above the 28.5% of a single year-5 exit.
    The relationship
    −100+150(1+r)3+200(1+r)5=0⇒r≈36.9%-100 + \frac{150}{(1+r)^3} + \frac{200}{(1+r)^5} = 0 \quad\Rightarrow\quad r \approx 36.9\%
    rthe IRR
    150proceeds from selling half the stake in year 3
    200proceeds from the rest in year 5
    What it says in wordsThe IRR is the rate that makes the discounted inflows exactly equal to the 100 invested.

    Why does the partial exit beat 3.5x in year 5?

    Rs 150 received in year 3 is worth more than Rs 150 received in year 5, just as a bonus paid this year is worth more than the same bonus promised later. IRR measures speed, so pulling part of the money forward lifts it even though the total returned, 3.5x, is the same. A single year-5 exit of 350 is 3.5 to the one-fifth, 28.5%. That gap is why sponsors like early dividends and partial sales, and why investors check the money multiple alongside the IRR.

    Where candidates lose it

    The common slip is treating 3.5x as if it all arrived in year 5 and answering 28.5%. The timing of the 150 is the whole question.

    The other is guessing without a bracket. Name a rate that is too low and one that is too high, then interpolate out loud; an answer within a couple of points, reached that way, is what the interviewer is looking for.

    What the interviewer asks next

    • If the 150 had come in year 2 instead of year 3, roughly what is the IRR?
    • Why might an investor prefer the single 3.5x exit despite the lower IRR?
    • How does a dividend recap in year 1 change the IRR and the money multiple?