Venture Capital puzzles, solved step by step

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

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022A Rs 500 crore fund wants to return 3x net to its LPs after 20% carry on profits above returned capital. Ignore fees. What must the portfolio distribute in total, and how many exits each returning Rs 350 crore to the fund does that take?Power law and portfolio mathsHardSeed and early-stage VCFund of funds and LPs
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What must the portfolio distribute before carry?
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The portfolio must distribute Rs 1,750 crore, 3.5x the fund, which is exactly five Rs 350 crore exits. LPs want Rs 1,500 crore: Rs 500 crore of capital plus Rs 1,000 crore of profit. Their profit is 80% of the total, so total profit is Rs 1,250 crore and gross is Rs 1,750 crore. At Rs 350 crore an exit that needs five exits, where ignoring carry suggests just over four.
How do you work back from net to gross?
Picture a sales agent who keeps a fifth of whatever the house sells for above the owner's purchase price. If the owner wants to walk away with Rs 1 crore of profit, the house has to make Rs 1.25 crore of profit, because the agent takes a fifth of it. Carry only touches profit, so gross up the LPs' profit by 0.8 and leave their capital alone. LPs need Rs 1,000 crore of profit on top of their Rs 500 crore, so total profit is 1,000 divided by 0.8, Rs 1,250 crore, and gross distributions are Rs 1,750 crore.
The relationship
$D = 500 + \frac{1{,}500 - 500}{1 - 0.20} = 500 + 1{,}250 = 1{,}750 \qquad \frac{1{,}750}{350} = 5$
D gross distributions the portfolio must return, Rs crore
1,500 what LPs must receive for 3x net
500 committed capital, returned before carry
350 what each exit returns to the fund
What it says in wordsTake the LPs' target profit, divide by their 80% share to get total profit, add back the capital, then count exits.
Rs 1,750 crore of gross distributions returns Rs 500 crore of capital, pays Rs 250 crore of carry on Rs 1,250 crore of profit and leaves LPs Rs 1,500 crore, 3.0x; that takes five Rs 350 crore exits, while ignoring carry would suggest 4.3.
Why does the exit count matter more than the multiple?
Because exits come in whole companies. Forgetting carry gives Rs 1,500 crore, which looks like 4.3 exits and invites a partner to think four big outcomes plus some smaller ones will do; with carry it is exactly five, with nothing to spare. Each exit returning Rs 350 crore to the fund is itself rare: if the fund owns 10% at exit, each one is a Rs 3,500 crore company. Seen this way, a 3x net target is a statement about how many very large companies the fund must back and keep a meaningful stake in.
Say the simplifications. The rest of the portfolio is assumed to return nothing, which overstates the exits needed, while fees, which the question told you to ignore, would reduce the capital invested and raise the bar again. A real model would net the two.
Where candidates lose it
The common error is stopping at Rs 1,500 crore, 3x gross, and forgetting that the GP's carry sits between the portfolio and the LPs. The interviewer is checking whether you know which side of carry the 3x is measured on.
The second is dividing the whole Rs 1,500 crore by 0.8 to get Rs 1,875 crore, which charges carry on the LPs' own capital. Gross up the profit only.
What the interviewer asks next
If the rest of the portfolio returns 1x of its cost, how many Rs 350 crore exits are needed?
What ownership at exit turns a Rs 350 crore return into a specific company valuation, say for a 12% stake?
How would an 8% hurdle with full catch-up change the gross requirement?
033A fund has Rs 10 crore left. It can follow on at Series B at Rs 400 crore post-money in a company with a 30% chance of a Rs 2,000 crore exit, or write a new seed cheque at Rs 40 crore post-money that will be diluted by half before exit, with a 5% chance of the same exit. Everything else returns zero. Which has the higher expected multiple?Power law and portfolio mathsHardSeed and early-stage VCMulti-stage VC
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Which use of the Rs 10 crore has the higher expected multiple?
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The Series B follow-on, at 1.50x against 1.25x. Rs 10 crore at Rs 400 crore post buys 2.5%, worth Rs 50 crore in a Rs 2,000 crore exit; at a 30% chance that is Rs 15 crore expected. The seed buys 25%, halved to 12.5% by exit, worth Rs 250 crore; at 5% that is Rs 12.5 crore. The seed would need a 6% chance of the exit to draw level.
Why is the cheaper entry not automatically the better bet?
A lottery ticket costs very little and a fixed deposit costs a lot per rupee of payout, yet nobody thinks the ticket is the better deal just because it is cheap. What matters is the price multiplied by the chance of being paid. The expected multiple of a venture cheque is the chance of the exit times the stake you hold at exit times the exit value, divided by the cheque. The seed price is 10 times lower, so the stake starts 10 times bigger, but halving by dilution leaves it only 5 times bigger, and the odds are 6 times worse.
The relationship
$E[\text{multiple}] = \frac{p \times s_{\text{exit}} \times V}{\text{cheque}} \qquad \text{B: } \frac{0.30 \times 2.5\% \times 2{,}000}{10} = 1.5 \qquad \text{Seed: } \frac{0.05 \times 12.5\% \times 2{,}000}{10} = 1.25$
p the chance of the Rs 2,000 crore exit
s exit the stake held at exit, after any dilution
V the exit value, Rs 2,000 crore in both cases
cheque the Rs 10 crore invested
What it says in wordsMultiply the chance, the stake you will still own and the exit value, then divide by what you put in.
The follow-on turns Rs 10 crore into Rs 50 crore 30% of the time, an expected 1.50x, while the seed turns it into Rs 250 crore 5% of the time, an expected 1.25x, so a ten times higher entry price wins when the odds are six times better.
How do you compare them quickly in the room?
Compare the three ratios rather than the full sums. The seed stake at exit is 5 times the Series B stake, but its odds are 6 times lower, so its expected value is five sixths of the follow-on's. Five sixths of 1.5x is 1.25x. The same logic gives the break-even: the seed draws level only if its chance of the exit rises from 5% to 6%, or the Series B chance falls from 30% to 25%.
What does the expected multiple leave out?
Say the limits before the interviewer does. The seed's 1.25x comes with a 95% chance of losing everything, against 70% for the follow-on, so the two bets carry very different risk even before you compare averages. Time matters too: a Series B company is closer to exit, so the same multiple earns a higher annual rate. Against that, a seed fund's strategy depends on owning large stakes in a few outliers, and a partner may accept a lower expected multiple for the bigger stake. The arithmetic decides the comparison only once those preferences are stated.
Where candidates lose it
Candidates jump to the seed because the entry price is ten times lower, and some compute 25% of Rs 2,000 crore without the dilution, giving 2.5x. The question built in the halving precisely to see whether you track the stake to exit.
The second loss is answering correctly and stopping at the averages. The interviewer wants to hear that the follow-on is also the lower-variance bet, and that the break-even seed probability is 6%, which tells the partner how confident they would need to be.
What the interviewer asks next
What exit value for the seed company would make the two options equal at a 5% chance?
If the Series B company exits in three years and the seed company in eight, which has the higher IRR at these multiples?
How would a reserves policy decided at the start of the fund change this decision?
088Of 100 seed companies, 40% raise a Series A, half of those raise a Series B, half of those raise a Series C, and 40% of the Series C companies reach a Rs 8,000 crore exit. What is the chance that one seed bet gets there, and how many independent seed bets give a 90% chance of at least one such exit?Power law and portfolio mathsHardSeed and early-stage VCIndia VC
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How many seed bets give a 90% chance of at least one large exit?
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One seed bet has a 4% chance, and it takes 57 independent bets to have a 90% chance of at least one such exit. Multiply the stage rates: 0.4 x 0.5 x 0.5 x 0.4 = 0.04. For a portfolio, find the chance that every bet misses: 0.96 to the power n. It first falls below 10% at n = 57, where the chance of at least one exit is 90.2%. Correlated bets would need more.
How do the stage rates turn into one chance?
A cricket team must win the quarter final, the semi final and the final; its chance of the trophy is the product of the three, not the average. Each financing stage is a gate the company must pass, so the chance of reaching the end is the product of the conversion rates. 40% to Series A, then half, then half, then 40% to the large exit: 0.4 x 0.5 x 0.5 x 0.4 is 0.04. Out of 100 seed companies, 4 get there.
Of 100 seed companies, 40 raise a Series A, 20 a Series B, 10 a Series C and 4 reach a Rs 8,000 crore exit, so one bet has a 4% chance; the chance of at least one such exit rises to 64% with 25 bets and passes 90% only at 57 bets.
Why can you not just add the chances across bets?
Adding 4% twenty five times gives 100%, which would mean 25 bets make a hit certain. For at least one success, work with the opposite: the chance that every bet misses, which multiplies. Each bet misses with probability 0.96, so n independent bets all miss with probability 0.96 to the power n. Twenty five bets all miss 36% of the time, so the chance of at least one hit is only 64%. To push the miss chance under 10%, take logs: n is at least ln 0.1 over ln 0.96, which is 56.4, so 57 bets. At 56 bets the chance is still 89.8%.
The relationship
$1 - (1-p)^n \ge 0.9 \;\Rightarrow\; n \ge \frac{\ln 0.1}{\ln 0.96} = \frac{-2.303}{-0.0408} \approx 56.4$
p chance one seed bet reaches the large exit, 4%
n number of independent seed bets
(1-p)^n chance that every bet misses
What it says in wordsKeep adding bets until the chance that all of them miss falls below one in ten.
What does this tell you about how seed funds are built?
It explains why seed portfolios hold dozens of companies rather than a handful. With a 4% hit rate, a portfolio of 25 companies misses entirely about a third of the time, however good the picks look one by one. Then say the limit: the bets are not independent. Companies from the same year share a funding climate and an exit window, so a weak market lowers every stage rate at once. Correlation makes the true number of bets needed higher than 57, and the 4% itself is an assumption to test against a fund's own record.
Where candidates lose it
The common slip is to add: 90% divided by 4% gives about 23 bets, or 25 bets for one expected winner, which candidates then read as a near certainty. One expected winner still leaves a 36% chance of none, because winners arrive unevenly.
The second loss is treating the bets as independent without saying so. The interviewer will usually push on it, and the right answer is that correlation within a vintage raises the number, not lowers it.
What the interviewer asks next
How many bets give a 50% chance of at least one large exit?
If the Series A rate drops from 40% to 30%, how many bets are needed for 90%?
Why does correlation between companies in the same vintage raise the number of bets needed?
098Strategy A makes 20 equal bets and strategy B makes 5 equal bets with the same total money. Every bet, independently, has a 10% chance of returning 20x and otherwise returns nothing, so both strategies expect to return 2x. What is the chance that each strategy returns less than the money invested?Power law and portfolio mathsHardSeed and early-stage VCFund of funds and LPs
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What is the chance the 5-bet strategy loses money?
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About 12% for 20 bets and 59% for 5 bets. In both strategies a single hit returns at least the whole fund: 20x on 5% is 1x, and 20x on 20% is 4x. So a strategy loses money only when every bet misses. Twenty bets all miss with chance 0.9 to the twentieth, 12.2%; five bets all miss with chance 0.9 to the fifth, 59.0%. Expected value is 2x either way.
When does each strategy lose money?
Buying one lottery ticket in each of twenty draws and buying four tickets in each of five draws can cost the same and win the same on average, yet the second leaves you empty-handed far more often. Find the outcome that loses money first: here one hit already pays back the whole fund in both strategies, so losing means getting no hits at all. With 20 bets each worth 5% of the fund, a hit returns 20 x 5% = 1x the fund, exactly the money back. With 5 bets of 20%, a hit returns 4x. Either way, zero hits is the only losing outcome.
Both strategies expect 2x, but 20 bets spread the outcomes across 0x to about 6x with only a 12.2% chance of 0x, while 5 bets put the outcomes at 0x, 4x, 8x and 12x with a 59.0% chance of returning nothing.
The relationship
$P(\text{loss}) = (1-p)^n \qquad 0.9^{20} = 12.2\% \qquad 0.9^{5} = 59.0\%$
p chance each bet returns 20x, 10%
n number of equal bets, 20 or 5
What it says in wordsA strategy loses only when every bet misses, and the chance of that falls fast as bets are added.
If the expected value is the same, why does it matter?
Because a fund's investors live through one draw, not the average of many. Concentration leaves the expected multiple at 2x but stretches the outcomes: B loses money 59% of the time, yet also returns 4x or more 41% of the time, against 13% for A. A returns at least 3x 32% of the time and rarely does spectacularly. Neither is better in the abstract; the choice depends on how much the fund's investors can bear a blank.
What does the model leave out?
It assumes the bets are independent and identical. In practice a concentrated fund argues that it can pick better and support each company more, raising p; a diversified one argues that nobody can pick reliably at seed. Correlation also matters: if all twenty companies depend on the same funding climate, the 12% understates how often A has a blank decade. Say the result, then say which assumption you would test first.
Where candidates lose it
The trap is stopping at expected value: both strategies return 2x on average, so candidates call them equivalent. The question asks about the chance of loss, which depends on the spread, not the mean.
The second slip is computing the loss chance for A as something like one minus 20 times 10%, which goes negative. Use the chance that every bet misses, which multiplies.
What the interviewer asks next
How many bets does strategy A need for the chance of losing money to fall below 5%?
If the 5-bet strategy can raise p to 15% through better selection, what is its chance of losing money?
Why might an investor in many funds prefer each fund to be concentrated?

D	gross distributions the portfolio must return, Rs crore
1,500	what LPs must receive for 3x net
500	committed capital, returned before carry
350	what each exit returns to the fund

p	the chance of the Rs 2,000 crore exit
s exit	the stake held at exit, after any dilution
V	the exit value, Rs 2,000 crore in both cases
cheque	the Rs 10 crore invested

p	chance one seed bet reaches the large exit, 4%
n	number of independent seed bets
(1-p)^n	chance that every bet misses

p	chance each bet returns 20x, 10%
n	number of equal bets, 20 or 5

Try it first

How do you work back from net to gross?

Why does the exit count matter more than the multiple?

Where candidates lose it

What the interviewer asks next

Try it first

Why is the cheaper entry not automatically the better bet?

How do you compare them quickly in the room?

What does the expected multiple leave out?

Where candidates lose it

What the interviewer asks next

Try it first

How do the stage rates turn into one chance?

Why can you not just add the chances across bets?

What does this tell you about how seed funds are built?

Where candidates lose it

What the interviewer asks next

Try it first

When does each strategy lose money?

If the expected value is the same, why does it matter?

What does the model leave out?

Where candidates lose it

What the interviewer asks next