Venture Capital puzzles, solved step by step

Puzzles: 100
Traced to a firm: 7
Topics: 12
Hard: 30

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001A Rs 300 crore fund put Rs 10 crore into each of 30 companies and returned 3.0x, Rs 900 crore. Fifteen companies were written off, and the best one returned Rs 540 crore. Had the fund passed on that best company and backed one more company earning the average of the other 29, what would the fund have returned?Power law and portfolio mathsCoreSeed and early-stage VCSeries A to C VC
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Before you work it: what does the fund return without its best company?
Show the worked solution
About 1.24x, down from 3.0x. The other 29 companies returned Rs 360 crore, an average of Rs 12.4 crore each. Replace the Rs 540 crore winner with one more average company and the fund returns Rs 372 crore on Rs 300 crore. Missing that one company costs Rs 528 crore, more than three times what all 15 write-offs cost together.
Why does one company out of thirty move the whole fund?
Picture a cricket team that scores 900 runs in a series, 540 of them from one batter. Drop that batter for an average player and the team's total collapses, however steady the rest were. A venture fund works the same way: returns are so uneven that the best company is often worth more than all the others put together. Here the winner returned 54x its cheque. The other 29 returned Rs 360 crore between them, an average of Rs 12.4 crore on Rs 10 crore each, about 1.24x.
The relationship
$M = \frac{900 - 540 + 360/29}{300} = \frac{372.4}{300} \approx 1.24\times$
900 what the fund actually returned
540 what the best company returned
360/29 one more company earning the average of the other 29
300 the fund's committed capital
What it says in wordsTake the winner out, put an average company in its place, and divide by the money the fund invested.
The fund returned Rs 900 crore, 3.0x. Removing the Rs 540 crore winner and adding one average company worth Rs 12.4 crore leaves Rs 372 crore, 1.24x, and that single miss costs Rs 528 crore against Rs 150 crore lost on all fifteen write-offs.
How does that compare with the cost of the failures?
Fifteen companies went to zero. At Rs 10 crore each, that is Rs 150 crore of lost capital, the most a write-off can ever cost. A write-off loses at most the cheque; a missed winner loses everything the winner would have returned, which has no ceiling. In this fund the one miss costs Rs 528 crore, about 3.5 times every write-off combined. This asymmetry is why venture investors say the error that matters is the company they passed on, not the one that failed.
What do you add after the number?
Say what it implies for how a fund behaves. A partner who rejects a deal because it might fail is guarding against the smaller of the two errors. The right question at the investment committee is whether a company could return the fund if it works. The limit is worth one sentence too: this is one fund's numbers, and a portfolio with a flatter spread of outcomes would care less about any single company.
Where candidates lose it
The instinctive answer is that one company in thirty moves the fund by about a thirtieth, so 2.9x. That treats venture outcomes as if they were spread evenly, which is exactly the assumption the interviewer wants you to drop.
The second loss is doing the arithmetic but not the comparison. The point of the question is that one missed winner costs more than every failure together; say that sentence, with the Rs 150 crore beside the Rs 528 crore.
What the interviewer asks next
How many companies earning 1.24x would you need to make up for missing the winner?
If write-offs cost at most the cheque, why do funds still care about their loss ratio?
What does this imply for how a seed fund should size its follow-on reserves?
013A seed fund makes 25 equal bets. Each bet independently has a 4% chance of returning 50x and otherwise returns 0.5x. What is the chance the fund finds no 50x winner at all, and what is its expected multiple?Power law and portfolio mathsCoreSeed and early-stage VCMulti-stage VC
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What is the chance the fund ends with no 50x winner?
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About 36% of such funds find no winner, even though the expected multiple is 2.48x. Each bet misses with probability 0.96, so all 25 miss with probability 0.96 to the power 25, which is 0.360. Each bet is worth 0.04 x 50 plus 0.96 x 0.5 on average, 2.48x. The average hides a wide spread: a fund with no winner returns 0.5x.
Why is one winner not guaranteed when 25 times 4% is 100%?
A batsman who hits a six once every 25 balls on average can still face 25 balls and hit none. Twenty five times 4% gives the expected number of winners, one, not the chance of getting at least one. To find that chance, count the way the fund fails: every bet must miss, and since the bets are independent the misses multiply, 0.96 x 0.96 and so on, 25 times. That is 0.360, so about 36% of identical funds never see a 50x company.
The relationship
$P(\text{no winner}) = 0.96^{25} \approx 0.360 \qquad E[M] = 0.04 \times 50 + 0.96 \times 0.5 = 2.48$
0.96 the chance any one bet is not a 50x winner
25 the number of independent bets
E[M] the expected multiple of each bet, and so of the fund
What it says in wordsMultiply the miss chances for the no-winner case, and average the two outcomes for the expected multiple.
Across 25 independent bets at 4%, 36.0% of funds find no winner and return 0.5x, 37.5% find exactly one and return 2.48x, and 18.8% find two and return 4.46x, even though every fund has the same expected multiple of 2.48x.
What does the spread tell you about running a seed fund?
Each extra winner adds 49.5x on one twenty-fifth of the fund, about 1.98 turns of the whole fund. So the fund's result is set almost entirely by how many winners it happens to land: none gives 0.5x, one gives 2.48x and two give 4.46x. The most likely single outcome is exactly one winner, at 37.5%, but no winner at all is nearly as likely. This is why seed managers want more shots on goal: with 57 bets the chance of finding no winner falls below 10%.
Say the limitation too. Real outcomes are not two-point, and they are not independent: a funding drought hurts every company in a vintage at once, which fattens the no-winner tail rather than thinning it.
Where candidates lose it
The fast wrong answer is that a winner is certain because 25 times 4% is 100%. The interviewer wants to hear you separate an expected count from a probability.
The second loss is giving 2.48x and stopping. The point of the question is the gap between the average and the typical fund; say that more than a third of funds lose half their money while the average fund makes 2.48x.
What the interviewer asks next
How many bets would the fund need to cut the no-winner chance below 10%?
If the outcomes are correlated, does the no-winner chance go up or down?
What is the chance the fund returns at least 2x?
062In a venture fund, 60% of the invested capital goes into companies that return nothing, and management fees take 17.5% of commitments off the top before anything is invested. What multiple must the surviving 40% of invested capital earn for the fund to return 3x its commitments?Power law and portfolio mathsCoreSeed and early-stage VCFund of funds and LPs
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What multiple do the survivors need?
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About 9.1x, not 7.5x. Take a Rs 100 crore fund. Fees take Rs 17.5 crore, leaving Rs 82.5 crore to invest. 60% of that, Rs 49.5 crore, goes to companies that return nothing, so only Rs 33 crore survives. To return Rs 300 crore, those survivors must earn 300 divided by 33, about 9.1x. Forgetting fees gives 300 over 40, or 7.5x, which understates the bar by a fifth.
Why does the base shrink twice before you divide?
A farmer who must sell 3 tonnes of grain for every tonne of seed bought, after setting aside some seed for the birds and losing most fields to flood, needs the surviving fields to yield far more than 3 tonnes each. A fund's target is set on every rupee committed, but only the rupees that are invested and survive can earn it, so the required survivor multiple is the target divided by the surviving share of commitments. Fees remove 17.5%; failures remove 60% of what is left. The surviving share is 0.825 x 0.4, which is 33% of commitments.
Of Rs 100 crore committed, Rs 17.5 crore goes to fees and Rs 49.5 crore to companies that return nothing, so the whole Rs 300 crore target must come from Rs 33 crore of survivors, a multiple of 9.1x rather than 7.5x.
The relationship
$M = \frac{3}{(1-f)(1-z)} = \frac{3}{0.825 \times 0.40} = 9.09$
M multiple the surviving investments must earn
f fees as a share of commitments, 17.5%
z share of invested capital that returns nothing, 60%
What it says in wordsDivide the fund's target by the share of commitments that is both invested and alive.
Is 3x on commitments the number LPs actually receive?
No, and saying so earns credit. The 3x here is before the manager's carried interest. If LPs want 3x after a 20% carry on profits, the fund must return about Rs 350 crore gross, and the survivors must earn about 10.6x. Recycling, where a fund reinvests early proceeds to put more than 82.5% of commitments to work, pushes the bar back down. Either way, the shape of the answer is the point: venture survivors need near ten-times outcomes as a group, which is why a fund cannot be built from companies that can only triple.
One honest limit: the 60% that returns nothing is a round assumption. Real portfolios have a middle band of companies returning 0.5x to 2x, which lowers the bar for the top performers, and the fee load varies by fund size and terms, so confirm both before using the figure.
Where candidates lose it
The common answer is 7.5x, from dividing 3 by 0.4. It forgets that fees are paid out of commitments before any company receives a rupee, and the interviewer included the fee precisely to see whether you would.
The second trap is applying the fee to the target instead of the base, multiplying 3 by 1.175. That gives about 8.8x for the wrong reason. Shrink the base first, then divide.
What the interviewer asks next
What multiple do survivors need for LPs to get 3x after a 20% carry?
How does recycling early proceeds change the answer?
If one company returns the whole fund, what must the rest of the survivors return?
074Venture returns follow an 80/20 rule that repeats inside itself: 20% of companies make 80% of returns, and within that top 20% the same split holds again, and again within that. What share of returns comes from the top 4% of companies, and from the top 0.8%?Power law and portfolio mathsCoreMulti-stage VCFund of funds and LPs
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What share of returns comes from the top 0.8% of companies?
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64% from the top 4%, and 51.2% from the top 0.8%. Each application of the rule keeps a fifth of the companies and four-fifths of the returns. The top 20% earn 80%. A fifth of those, the top 4%, earn 80% of 80%, or 64%. A fifth of those, the top 0.8%, earn 80% of 64%, or 51.2%. So fewer than one company in a hundred produces more than half of all returns.
Why do the shares multiply at each step?
If a fifth of a city's shops make four-fifths of its sales, and among those top shops a fifth again make four-fifths of their group's sales, then the very top shops make four-fifths of four-fifths. A rule that repeats inside itself compounds: k steps leave 0.2 to the power k of the companies with 0.8 to the power k of the returns. Three steps give 0.8% of companies and 51.2% of returns. The pattern is the signature of a power lawA distribution where a small number of very large outcomes account for most of the total, and the same shape repeats at every scale., and it is why venture is described as a business of outliers.
Drawn to scale by share of companies, each nested square keeps a fifth of the companies and four-fifths of the returns, so the top 4% earn 64% and the tiny top 0.8% square earns 51.2%, more than half of everything.
The relationship
$\text{share of returns}(p) = p^{\ln 0.8 / \ln 0.2} = p^{0.139}: \quad 0.04^{0.139} = 0.64, \quad 0.008^{0.139} = 0.512$
p top fraction of companies
ln 0.8 / ln 0.2 the exponent that makes a fifth of any group earn four-fifths of its returns
What it says in wordsOne formula reproduces every level of the repeating 80/20 rule, and it can be read at any fraction, not just the three steps.
What does this mean for how a venture fund is built?
Half the returns come from the top 0.67% of companies, fewer than one in a hundred. A fund of 30 companies, picked at random from this population, has only about a 21% chance of owning even one company from that top 0.8%, so portfolio size and access to the best deals matter more than average picking skill. That is the logic behind funds holding more companies, reserving money to double down on the winners, and refusing to cap the upside of any single investment. A fund cannot diversify its way to the median here; the median company returns little.
State the limit. A clean, repeating 80/20 rule is a stylised model, not a measured fact about any dataset; real venture returns are lumpy and vary by vintage and stage. The value of the puzzle is the shape: concentration at the top is far more extreme than one application of 80/20 suggests.
Where candidates lose it
The common error is miscounting steps, giving 64% for the top 0.8%. Write the fractions out: 20%, then 4%, then 0.8% is three steps, so the share is 0.8 cubed.
The second trap is adding instead of multiplying, or answering 80% minus 16% and similar. Each step takes four-fifths of the previous share, not of the whole, so keep multiplying.
What the interviewer asks next
What share of companies earns 90% of returns under this rule?
With 30 companies in a fund, what is the chance of holding at least one top-0.8% company?
How should this shape change a fund's reserve policy?
076A Rs 400 crore seed fund buys 15% of a company. It does not take its pro rata in the next two rounds, and each of those rounds sells 20% of the company to new investors. How large must that one company's exit be for the fund's stake to return the whole Rs 400 crore fund?Power law and portfolio mathsCoreSeed and early-stage VCIndia VC
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Before you calculate the exit: what stake does the fund hold after the two rounds?
Show the worked solution
About Rs 4,167 crore, against Rs 2,667 crore if the fund had kept 15%. A round that sells 20% leaves existing holders 80% of what they had, so 15% becomes 12% and then 9.6%. Returning Rs 400 crore from 9.6% needs an exit of 400 divided by 0.096. Skipping pro rata raised the bar by about 56%, and later rounds would raise it further.
Why does a round that sells 20% not cut your stake by 20 points?
Think of a pizza shared by four friends. A fifth friend arrives and is given a fifth of the whole pizza; every original slice shrinks by a fifth of itself, not by a fixed number of slices. Dilution is multiplicative: a round that sells 20% of the company leaves every existing holder with 80% of their previous stake. So 15% becomes 15 x 0.8 = 12%, and the next round makes it 12 x 0.8 = 9.6%. The fund has lost 5.4 points, 36% of what it bought, without selling a single share.
The fund's stake falls from 15% to 12% to 9.6% as two rounds each sell 20% of the company, so the exit needed to return the Rs 400 crore fund rises from Rs 2,667 crore to Rs 4,167 crore, about 56% higher.
How do you turn a stake into a fund-returner exit?
A fund returnerA single investment whose proceeds alone equal the whole fund size, the bar many seed funds use when they decide whether a company could matter. is one company whose proceeds alone pay back the whole fund. The exit it needs is the fund size divided by the ownership held at exit. At 15%, Rs 400 crore needs 400 / 0.15 = Rs 2,667 crore. At 9.6%, it needs 400 / 0.096 = Rs 4,167 crore. Same company, same fund, and the bar moved up by Rs 1,500 crore because of two decisions not to write a cheque.
The relationship
$E = \frac{F}{s_0(1-d)^k} = \frac{400}{0.15 \times 0.8^2} \approx 4{,}167$
E exit value needed, Rs crore
F fund size, Rs 400 crore
s_0 ownership bought at seed, 15%
d share of the company each later round sells, 20%
k rounds skipped, 2
What it says in wordsShrink the stake by 80% for each skipped round, then divide the fund size by what is left.
What should you say about the assumptions?
Say three out loud: no further rounds before exit, no option pool top-up, and a clean sale in which preferences do not change the split. Each of those would push the number higher, never lower. Rs 4,167 crore is therefore a floor, not an estimate. Then add the reason the question exists: a seed fund keeps reserves precisely so it can defend its stake in the companies that are working, because the seed cheque buys the option and the pro rata cheque keeps it.
Where candidates lose it
The common slip is subtracting instead of multiplying: 15 minus 3 minus 3 gives 9%, and a nervous candidate sometimes even writes 15% minus 40%. The second round dilutes the already smaller 12%, so the stake is 9.6%, and the gap matters once you divide the fund size by it.
The second loss is stopping at the percentage. The interviewer asked for an exit value, so convert ownership into the fund-returner number and say it is a floor, because every later round only dilutes further.
What the interviewer asks next
What share of each round would the fund have to buy to hold exactly 15%?
If two more rounds each sell 15% before the exit, what is the fund-returner exit now?
Why might a fund rationally skip its pro rata in a company that is doing well?

900	what the fund actually returned
540	what the best company returned
360/29	one more company earning the average of the other 29
300	the fund's committed capital

0.96	the chance any one bet is not a 50x winner
25	the number of independent bets
E[M]	the expected multiple of each bet, and so of the fund

M	multiple the surviving investments must earn
f	fees as a share of commitments, 17.5%
z	share of invested capital that returns nothing, 60%

p	top fraction of companies
ln 0.8 / ln 0.2	the exponent that makes a fifth of any group earn four-fifths of its returns

Try it first

Why does one company out of thirty move the whole fund?

How does that compare with the cost of the failures?

What do you add after the number?

Where candidates lose it

What the interviewer asks next

Try it first

Why is one winner not guaranteed when 25 times 4% is 100%?

What does the spread tell you about running a seed fund?

Where candidates lose it

What the interviewer asks next

Try it first

Why does the base shrink twice before you divide?

Is 3x on commitments the number LPs actually receive?

Where candidates lose it

What the interviewer asks next

Try it first

Why do the shares multiply at each step?

What does this mean for how a venture fund is built?

Where candidates lose it

What the interviewer asks next

Try it first

Why does a round that sells 20% not cut your stake by 20 points?

How do you turn a stake into a fund-returner exit?

What should you say about the assumptions?

Where candidates lose it

What the interviewer asks next