Venture Capital puzzles, solved step by step

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  1. 048A Rs 500 crore fund charges 2% a year on commitments for its first five years and 1.5% for the next five. How much is left to invest, and what gross multiple on invested capital does the portfolio need just to hand LPs their money back?Fund economics riddlesCoreFund of funds and LPsSeed and early-stage VC

    Try it first

    What gross multiple on invested capital returns exactly Rs 500 crore to LPs?

    Show the worked solution

    Rs 412.5 crore is left to invest, and the portfolio needs about 1.21x gross just to return the Rs 500 crore. Fees are 2% for five years, Rs 50 crore, plus 1.5% for five years, Rs 37.5 crore, a total of Rs 87.5 crore. LPs committed Rs 500 crore, so the Rs 412.5 crore that is invested must grow to Rs 500 crore: 500 over 412.5 is 1.21x before the fund earns a rupee of carry.

    Why does a fund need more than 1x just to break even?

    If a friend takes Rs 17.5 from every Rs 100 you give him to invest, the Rs 82.5 he does invest has to grow by a fifth just to give you your Rs 100 back. Management fees come out of commitments, so the portfolio is smaller than the money LPs put in, and it must earn the fees back before LPs see any profit. On a Rs 500 crore fund, ten years of fees at these rates take Rs 87.5 crore, 17.5% of the fund.

    A Rs 500 crore fund: what is left to invest, and what it must earn backCommitments, Rs croreInvested 412.5500 committedFees: 50 in years 1 to 5 + 37.5 in years 6 to 10 = 87.5Proceeds needed to return capital412.5500 = 1.21x the invested capitalProceeds needed for 2x net after 20% carry412.51,125 = 2.73xFees take 17.5% of commitments, so every rupee invested must earn back 1/0.825 = 1.21 rupees to break even
    Rs 87.5 crore of fees leaves Rs 412.5 crore to invest, so the portfolio must make 1.21x just to return the Rs 500 crore committed, and about 2.73x to hand LPs 2x after carry.
    The relationship
    fees=500×(0.02×5+0.015×5)=87.5gross to return capital=500500−87.5=500412.5≈1.21x\text{fees} = 500 \times (0.02 \times 5 + 0.015 \times 5) = 87.5 \qquad \text{gross to return capital} = \frac{500}{500 - 87.5} = \frac{500}{412.5} \approx 1.21x
    500commitments, in Rs crore
    0.02, 0.015the yearly fee rates in the two periods
    412.5the capital actually invested after fees
    What it says in wordsTotal the fees over the fund's life, subtract them from commitments, and divide what LPs put in by what was invested.

    What multiple does the fund need to deliver a good result to LPs?

    Run the same logic to a target. Say LPs want 2x net, Rs 1,000 crore, and the manager takes 20% carry on profit above the Rs 500 crore committed. The LPs' Rs 500 crore of profit is 80% of the total profit, so total profit must be Rs 625 crore and proceeds Rs 1,125 crore. That is 2.73x on the Rs 412.5 crore invested, so a 2x net fund is close to a 2.7x gross portfolio. The gap between gross and net is why LPs ask for both numbers and never compare one manager's gross with another's net.

    Where does the clean answer go wrong in practice?

    Funds often recycle: they reinvest early exit proceeds up to the amount of fees paid, so invested capital can approach the full Rs 500 crore and the break-even multiple falls towards 1x. The fee terms, the recycling allowance and the carry structure are set in each fund's limited partnership agreement, so confirm them there before using these figures for a real fund. Some funds also charge the later-period fee on invested capital rather than commitments, which lowers total fees.

    Where candidates lose it

    The common loss is saying 1x, or adding the fee percentage to 1 and answering about 1.18x. The fees shrink the base the return is earned on, so the break-even multiple is commitments divided by invested capital, 1.21x.

    The second loss is computing fees as 2% for all ten years, Rs 100 crore, and missing the step-down. Read the fee schedule as the question gives it; the second five years are cheaper.

    What the interviewer asks next

    • If the fund recycles Rs 50 crore of early proceeds, what gross multiple does it need to return capital?
    • What gross multiple delivers 3x net with 20% carry?
    • Why do larger funds usually charge lower fee rates, and what does that do to this calculation?
  2. 080A Rs 100 crore venture fund will pay Rs 17.5 crore of management fees over its life, and its terms let it recycle up to Rs 15 crore of early exit proceeds into new investments. How much does it invest with and without recycling, and what gross multiple on invested capital does each case need to hand investors 2.5x their commitments?Fund economics riddlesCoreFund of funds and LPsSeed and early-stage VC

    Try it first

    With full recycling, what gross multiple does the invested capital need?

    Show the worked solution

    Without recycling the fund invests Rs 82.5 crore and needs 3.03x; with full recycling it invests Rs 97.5 crore and needs about 2.72x. Investors want Rs 250 crore back. Without recycling, Rs 82.5 crore must produce all of it. With recycling, Rs 97.5 crore must produce Rs 265 crore, because Rs 15 crore of proceeds was put back to work rather than paid out. Carry is ignored throughout.

    Why can a fund not invest all of its commitments?

    A family sets aside Rs 1,00,000 for a wedding and the planner's fee is Rs 17,500 of it: only Rs 82,500 buys food and flowers. Management fees are paid out of the same commitments that fund the investments, so a fund that never recycles invests less than its headline size. Rs 17.5 crore could be 2% a year for five years and 1.5% for five more; schedules vary, but the arithmetic is the same. To turn Rs 100 crore into Rs 250 crore for investors, Rs 82.5 crore has to earn 250 / 82.5 = 3.03x.

    Recycling puts more capital to work, so each rupee needs a lower multipleNo recyclingFees 17.5Invested 82.5Needed on invested capital: 250 / 82.5 = 3.03xWith recyclingFees 17.5Invested 82.5+15Needed on invested capital: 265 / 97.5 = 2.72xRs 100 crore committedrecycled fromearly exitsTempting but wrong: 250 / 97.5 = 2.56x forgets that the recycled Rs 15 crore was also proceeds
    Without recycling, Rs 82.5 crore of invested capital must produce Rs 250 crore, 3.03x; recycling Rs 15 crore of early proceeds lifts invested capital to Rs 97.5 crore, which must produce Rs 265 crore, about 2.72x, not the 2.56x that dividing 250 by 97.5 suggests.

    How does recycling change the multiple, and why is it not 250 over 97.5?

    RecyclingReinvesting proceeds from early exits into new companies instead of distributing them, usually capped at about the amount of fees paid. lets the fund put Rs 15 crore of early exit money back into new companies, so invested capital reaches Rs 97.5 crore. But that Rs 15 crore was proceeds the portfolio had already earned and did not pay out, so the portfolio must produce Rs 250 crore for investors plus the Rs 15 crore it recycled. Gross proceeds of 265 on cost of 97.5 is 2.72x: still well below 3.03x, but not the 2.56x a quick division gives.

    The relationship
    M=2.5 C+RC−F+R=250+15100−17.5+15≈2.72×M = \frac{2.5\,C + R}{C - F + R} = \frac{250 + 15}{100 - 17.5 + 15} \approx 2.72\times
    Ccommitments, Rs 100 crore
    Flifetime fees, Rs 17.5 crore
    Rproceeds recycled, Rs 15 crore
    Mgross multiple needed on invested capital
    What it says in wordsThe portfolio must earn what investors receive plus what was reinvested, on everything that was invested.

    Say the limit too. Recycling delays money investors would have received early, so it can lift the multiple while lowering the IRR, and it works only if the fund finds good companies for the recycled rupees. It is a tool for getting fees back to work, not free return.

    Where candidates lose it

    The quick slip is 250 over 97.5, which gives 2.56x and looks like the natural answer. It counts the recycled Rs 15 crore as money invested but forgets it was also money the portfolio had to earn first, so it understates the bar.

    The other loss is forgetting fees entirely and saying 2.5x on Rs 100 crore. The interviewer set the fee number so you would take it out of the investable pool before anything else.

    What the interviewer asks next

    • If the fund recycles only Rs 7.5 crore, what multiple does the invested capital need?
    • Carry is 20% of profits above commitments. What gross proceeds give investors 2.5x net?
    • Why might an investor in the fund prefer no recycling even though it lowers the bar?