Venture Capital puzzles, solved step by step

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

Showing 31–40 of 47 · filtered from 100Clear filters

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?
067A founder signs three post-money SAFEs before her first priced round: Rs 2 crore at a Rs 20 crore valuation cap, Rs 3 crore at a Rs 30 crore cap, and Rs 4 crore at a Rs 40 crore cap. Assume the priced round comes in above all three caps. What do the SAFE holders own just before that round, and why does the order of signing not matter?Dilution and ownership riddlesCoreSeed and early-stage VCIndia VC
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Together, the three SAFE holders own:
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30% together, 10% each, and the founder keeps 70%. A post-money SAFE converts into its amount divided by its cap, as a share of the company measured after all the SAFEs: Rs 2 crore over Rs 20 crore, Rs 3 crore over Rs 30 crore and Rs 4 crore over Rs 40 crore are each 10%. Because each percentage is fixed against that full capitalisation, a later SAFE cannot dilute an earlier one; only the founder is diluted, so the order does not matter.
What does 'post-money' fix that older SAFEs did not?
Three friends each promised a tenth of a home-cooked biryani know exactly what they get, however many friends were promised a share before them; the cook's portion is what shrinks. A post-money SAFEA simple agreement for future equity whose conversion stake is fixed as the amount invested divided by the post-money valuation cap, measured after all SAFEs convert. promises its holder a fixed percentage, amount over cap, of a company that already counts every SAFE, so SAFE holders never dilute one another and the founder carries all of it. 2/20, 3/30 and 4/40 are each 10%, and the founder goes from 100% to {founder67*100:.0f}%. Under the older pre-money SAFE, each holder's stake was measured before the other SAFEs converted, so they diluted each other and no one could read their percentage until the round.
Signed in either order, the three post-money SAFEs each take a fixed 10%, so together they own 30% before the priced round and the founder alone falls to 70%.
The relationship
$s_i = \frac{\text{amount}_i}{\text{cap}_i}: \quad \frac{2}{20} + \frac{3}{30} + \frac{4}{40} = 0.10 + 0.10 + 0.10 = 0.30$
s_i SAFE holder i's stake just before the priced round
amount_i what holder i invested
cap_i holder i's post-money valuation cap
What it says in wordsEach SAFE's stake is its own amount over its own cap, so the stakes simply add up and the founder keeps the remainder.
What happens at the priced round, and when does the 10% change?
The priced round then dilutes everyone, SAFE holders included. If the Series A sells 20% of the company, each SAFE holder goes from 10% to 8% and the founder from 70% to 56%. The cap is a ceiling on the price a SAFE converts at, so if the round is priced below a holder's cap, that holder converts at the round price and gets more than 10%, at the founder's expense again. That is why the question fixes the round above all three caps.
Two limits worth saying. The figures leave out an option pool, which is usually added before the round and also comes out of the founder's side. And the SAFE is a US instrument; Indian startups raise early money through structures such as compulsorily convertible preference shares or notes whose conversion terms vary, so read the actual conversion clause rather than assuming post-money SAFE mechanics.
Where candidates lose it
The common error is diluting each SAFE by the ones signed after it and arriving near 27%. That is how pre-money SAFEs behave; the question says post-money precisely to test whether you know the difference.
The second trap is forgetting who pays. The SAFE holders' 30% comes entirely out of the founder's stake, and founders who sign several SAFEs often discover this only when the round's cap table arrives.
What the interviewer asks next
If the Series A is priced at a Rs 25 crore post-money valuation, what does the Rs 30 crore cap holder get?
How would the answer change if these were pre-money SAFEs?
Where would a 10% option pool created before the round come from?
06810% of the startups you meet are genuinely good. Your screen flags 80% of the good ones as worth pursuing, but also flags 20% of the bad ones. A company passes your screen. What is the chance it is actually good?Probability and expected valueCoreSeed and early-stage VCMulti-stage VC
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A company passes. The chance it is good is about:
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About 31%, not 80%. Picture 1,000 companies. 100 are good and your screen passes 80 of them. 900 are bad and it passes 20% of those, 180 companies. So 260 pass, and only 80 of them are good: 80 divided by 260 is 30.8%. The screen raises the odds from 10% to about 31%, which is useful, but most companies that pass are still bad because bad ones are so common.
Why is the answer so far below 80%?
A smoke alarm that rings for every real fire and for one in five burnt toasts will mostly ring for toast, because toast is far more common than fire. When the thing you are looking for is rare, even a small false alarm rate applied to the large crowd of negatives produces more false passes than true ones. Here 20% of 900 bad companies is 180, against 80% of 100 good companies, 80. The screen's 80% describes how it treats good companies; the question asks what a pass tells you, which also depends on how many bad companies get in.
Of 1,000 companies, the screen passes 80 good ones and 180 bad ones, so the 260 passes are mostly false alarms and the chance a passing company is good is 80 out of 260, about 31%, not the 80% the screen's hit rate suggests.
The relationship
$P(G \mid \text{pass}) = \frac{0.8 \times 0.1}{0.8 \times 0.1 + 0.2 \times 0.9} = \frac{0.08}{0.26} = 0.308$
G the company is genuinely good
0.8 share of good companies the screen passes
0.2 share of bad companies the screen also passes
0.1 share of all companies that are good, the base rate
What it says in wordsOf everything that passes, the good share is the true passes divided by all passes, true and false.
What would actually improve the screen?
Run the alternatives. Halving the false pass rate to 10% lifts the answer to 80 out of 170, about 47%, while raising the hit rate from 80% to 95% only takes it to 95 out of 275, about 35%. When good companies are rare, cutting false passes matters more than catching every good one. A second, independent check helps the same way: if a passing company goes through another screen with the same rates, the base rate is now 31%, and a second pass takes it to about 64%.
The limit is that the two checks must be independent; a second partner who looks at the same deck with the same biases is not a second screen. And the 10% base rate is an assumption about your deal flow; a fund with better sourcing starts from a higher base and every pass means more.
Where candidates lose it
The trap is answering 80%, confusing the chance a good company passes with the chance a passing company is good. It is the most common probability error there is, and the interviewer expects you to spot it.
The second loss is reaching 31% through a formula and fumbling the explanation. Use natural frequencies, 1,000 companies, 80 true passes, 180 false ones; it is faster and harder to get wrong.
What the interviewer asks next
If a company passes two independent screens with the same rates, what is the chance it is good?
Which matters more here, raising the hit rate or cutting false passes?
How would better sourcing change these numbers?
070Two co-founders will answer one yes-or-no or which-one question between them. One always tells the truth and the other always lies, and you do not know which is which. Two data rooms are open, and only one holds the real files. What single question, asked of either founder, finds the real one?Logic and brainteasersCoreSeed and early-stage VCMulti-stage VC
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Which question works whoever you ask?
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Ask either founder, 'Which room would your co-founder say is real?', then take the other room. If you asked the truth-teller, she honestly reports the liar's false answer. If you asked the liar, he falsely reports the truth-teller's true answer. Either way the answer has passed through exactly one lie, so it always names the fake room. You do not need to know who answered.
Why does a direct question fail?
If you ask a stranger for directions and know only that they are either always honest or always lying, their answer alone is worth nothing: you cannot tell which kind of answer you got. A direct question returns the truth from one founder and its opposite from the other, so without knowing who answered, the reply carries no information. 'Are you the truth-teller?' is worse: both say yes. The question has to be built so the answer comes out the same whoever gives it.
Asked directly, the two founders give opposite answers, but asked which room the other founder would call real, both name the fake room, because the answer passes through exactly one lie either way, so taking the other room is right every time.
Why does routing the question through the other founder fix it?
Count the lies along each path. Truth then lie, or lie then truth, both contain exactly one lie, so the indirect question always returns a false answer, and a reliably false answer is as useful as a true one: you simply take the opposite. There is a second classic: 'If I asked you whether room 1 is real, would you say yes?' The truth-teller answers honestly; the liar would say no to the inner question and then lies about that, so he says yes. That version uses two lies or none, which gives the truth directly.
The limit is the setup itself. The trick relies on people who lie with perfect consistency, which nobody does; real diligence on two founders who tell different stories relies on documents, not on clever questions. What the puzzle tests is whether you can design one check whose answer does not depend on who answers it, which is the logic behind cross-referencing a claim against two sources with opposite incentives.
Where candidates lose it
The common loss is asking 'Are you the truth-teller?' or a direct question and then trying to argue your way out. Both founders say yes to the first, and the second depends on who you asked, so neither works.
The other trap is finding the right question and then going to the room named. The indirect question always points at the fake room; say clearly that you take the other one.
What the interviewer asks next
Give a question whose answer is always true rather than always false.
What if a third founder answers at random?
Where in diligence do you deliberately ask the same question of two people with opposite incentives?
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?
075A startup sells bus-tracking to schools at Rs 400 per bus per month. Estimate the number of school buses in a city of 1.4 crore people, and the startup's annual revenue there if it wins 10% of them.Market sizing and estimationCoreSeed and early-stage VCIndia VC
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Roughly what annual revenue does 10% of the city's buses bring?
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About 7,000 buses, and about Rs 34 lakh a year at 10% share. Take 1.4 crore people; about 20% are of school age, 28 lakh children. Assume half attend schools that run buses, 14 lakh, and a quarter of those ride, 3.5 lakh. At about 50 riders a bus, that is 7,000 buses, in a range of roughly 4,667 to 10,500. Winning 700 of them at Rs 4,800 a year each is about Rs 33.6 lakh.
How do you build the count so each step can be challenged?
Planning a wedding, you do not guess the number of plates; you count families, then members per family, then how many will turn up. A sizing is only as good as its weakest stated assumption, so each step should be a single number with a reason the interviewer can push on. Here the chain is people, school-age children, children in schools that run buses, children who ride, and riders per bus. The 20% school-age share is the firmest; whether half of children attend schools that run buses is the least certain and depends on the city's mix of private and government schools.
Four stated assumptions take 1.4 crore people to about 7,000 school buses, within a range of roughly 4,667 to 10,500, and winning 10% of them at Rs 400 a month brings only about Rs 34 lakh a year.
The relationship
$\text{Buses} = \frac{1.4\text{ cr} \times 0.20 \times 0.50 \times 0.25}{50} = 7{,}000$
0.20 share of the population of school age
0.50 share of those children in schools that run buses
0.25 share of those who ride the school bus
50 riders served by one bus, counting two routes a day
What it says in wordsShrink the population to the children who actually ride, then divide by how many each bus carries.
What does the number tell an investor?
Give the range, then the judgement. Riders between 20% and 30% and buses carrying 40 to 60 riders give 4,667 to 10,500 buses, and revenue between about Rs 22 lakh and Rs 50 lakh a year. Even at the top of the range, one city at 10% share is a small business, so the case for investing rests on winning many cities, a higher share, or more revenue per bus, not on this city alone. A parent subscription for live tracking, or selling route planning and fuel tracking to the school, could change the revenue per bus more than any share assumption.
To check it outside the room, ask the transport department how many vehicles are registered as school buses in the city, since many states register them under a separate category, and call three or four large schools to ask how many buses they run per thousand students. Confirm the 20% school-age share against the latest census or survey for that city rather than taking it from memory.
Where candidates lose it
The first way to lose this is a zero slip at the end: buses times share times price times twelve has enough steps to drop a factor of ten, and Rs 3.4 crore instead of Rs 34 lakh changes the conclusion entirely.
The second is presenting the bus count and stopping. The interviewer wants to hear that the answer is small, and what would have to be true for the business to matter.
What the interviewer asks next
How many cities would the startup need to reach Rs 50 crore of revenue at this price?
What would a parent subscription at Rs 50 a month add per city?
How would you size the same market from the supply side, starting with schools?
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?
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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?
078A customer pays Rs 10,000 a month at an 80% gross margin, churns at 2% a month, and costs Rs 1.2 lakh to acquire. What are lifetime value and LTV to CAC, first undiscounted and then discounting at 2% a month?SaaS and unit economics riddlesCoreSaaS-focused VCSeries A to C VC
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Before working it: what does discounting at 2% a month do to the LTV here?
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Undiscounted, LTV is Rs 4 lakh and LTV to CAC is 3.3; discounted at 2% a month, LTV is Rs 2 lakh and the ratio is 1.7. Gross profit is Rs 8,000 a month and 2% churn means an average life of 50 months, so 8,000 x 50 is Rs 4 lakh. Discounting adds the 2% rate to the 2% churn, so LTV becomes 8,000 over 0.04, which is Rs 2 lakh.
Why is the average customer life one over the churn rate?
A gym that loses 2 of every 100 members each month, month after month, keeps the average member for 50 months: some leave in the first month, some stay ten years, and the steady 2% leak averages out to one over 0.02. With a constant monthly churn c, the expected customer life is 1 / c months, and lifetime value is the monthly gross profit times that life. Use gross profit, not revenue: Rs 10,000 at 80% margin is Rs 8,000 a month, and 8,000 x 50 is Rs 4 lakh, against a Rs 1.2 lakh acquisition cost, a ratio of 3.3.
Monthly gross profit per customer starts at Rs 8,000 and decays by 2% a month, an area of Rs 4.0 lakh; discounting each month at 2% as well makes the stream decay twice as fast, halving the area to Rs 2.0 lakh and taking LTV to CAC from 3.3 to 1.7.
What does discounting do to a stream that already decays?
A rupee of gross profit in month 40 is worth about 0.45 today at 2% a month. When churn and the discount rate are both monthly rates, discounted LTV is monthly gross profit divided by churn plus the discount rate, because each month the stream shrinks by survival and by time together. Here that is 8,000 / (0.02 + 0.02), exactly Rs 2 lakh if each month's profit arrives at the month end.
The relationship
$\text{LTV} = \frac{m}{c + r} = \frac{8{,}000}{0.02 + 0.02} = 2{,}00{,}000$
m monthly gross profit per customer, Rs 8,000
c monthly churn, 2%
r monthly discount rate, 2%
What it says in wordsDivide monthly gross profit by the total rate at which it leaks away, through customers leaving and through time.
Is 2% a month a fair rate? It compounds to about 27% a year, a venture-style hurdle rather than a bank rate, so the halving here is at the harsh end. The point survives a gentler rate: a ratio that looks comfortable at 3.3 can sit much closer to 1 once time is priced, and the 15-month payback on gross profit is often the more honest single number to quote alongside it.
Where candidates lose it
The first loss is using revenue: Rs 10,000 x 50 gives Rs 5 lakh and a ratio of 4.2, which flatters the business by a quarter. A customer's value to the company is the gross profit they leave behind, not the invoice.
The second is saying churn already handles time. Churn counts customers who leave; discounting prices the wait for the ones who stay. Leave either out and the ratio looks healthier than the cash.
What the interviewer asks next
What monthly churn gives an undiscounted LTV to CAC of exactly 3?
Price rises 10% a year for customers who stay. How does that change the formula?
Why might a seed investor care more about payback months than LTV to CAC?
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
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With full recycling, what gross multiple does the invested capital need?
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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.
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
$M = \frac{2.5\,C + R}{C - F + R} = \frac{250 + 15}{100 - 17.5 + 15} \approx 2.72\times$
C commitments, Rs 100 crore
F lifetime fees, Rs 17.5 crore
R proceeds recycled, Rs 15 crore
M gross 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?
084Without a calculator, what is the IRR of an investment that returns 2.5x the money in 4 years? Use anchors you already know, such as 2x in 3 years and 3x in 5 years.Mental maths and speed testsCoreGrowth equityFund of funds and LPs
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Pick the closest before you work it.
Show the worked solution
About 26%; the exact figure is 25.7%. Two anchors bracket it: 2x in 3 years is 26.0% and 3x in 5 years is 24.6%. For a sharper figure, take ln 2.5, about 0.92, divide by 4 to get 0.23, and add half its square: about 25.6%. Check by squaring twice: 1.26 squared is 1.59, and 1.59 squared is about 2.5.
Which anchors should you carry into the room?
You judge a distance on a road by the milestones, not by pacing it out. Carry a few multiple and years pairs and interpolate between them rather than calculating from scratch. 2x in 3 years is 26.0%, 3x in 5 years is 24.6%, 2x in 4 years is 18.9% and 3x in 4 years is 31.6%. The target, 2.5x in 4 years, lies between the last two and is bracketed by the first two.
IRRs for 2x, 2.5x and 3x over 3, 4 and 5 years show that the anchors 2x in 3 years and 3x in 5 years both sit near 25%, and that 2.5x in 4 years is 25.7%, well below the 37.5% a simple average gives.
How do you land on 26% out loud?
Route one: interpolate on a log scale. 2.5 sits about 55% of the way from 2 to 3 in log terms, so the IRR sits about 55% of the way from 18.9% to 31.6%, near 26%. Route two uses the log directly. The continuous growth rate is the log of the multiple divided by the years, and adding half its square converts it to an annual rate: 0.23 plus 0.026 is about 25.6%.
The relationship
$\text{IRR} \approx \frac{\ln M}{n} + \frac{1}{2}\left(\frac{\ln M}{n}\right)^2 = 0.229 + 0.026 \approx 25.6\%$
M money multiple, 2.5
n years, 4
ln M natural log of the multiple, about 0.92
What it says in wordsSpread the log of the multiple evenly over the years, then nudge it up slightly for annual compounding.
Then check. Squaring twice is the fastest test of a four year rate: 1.26 squared is 1.59, and 1.59 squared is 2.52, close enough to 2.5. The check matters more than the method, because it catches a slip in either route in five seconds.
Where candidates lose it
The expensive slip is the simple average: a 150% gain over 4 years is 37.5% a year. It ignores compounding, and it overstates the IRR by more than ten points. Anyone who has done this before hears it immediately.
The second loss is getting to 25.7% in silence. The interviewer wants the anchors and the check said aloud, because that is how you would sanity check a fund's reported return on a call.
What the interviewer asks next
What IRR is 3x in 7 years?
A fund makes 2.5x in 4 years, but half its money was only invested for the last 2 years. Is its IRR above or below 26%?
Why do investors in a fund ask for both the multiple and the IRR?

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%

s_i	SAFE holder i's stake just before the priced round
amount_i	what holder i invested
cap_i	holder i's post-money valuation cap

G	the company is genuinely good
0.8	share of good companies the screen passes
0.2	share of bad companies the screen also passes
0.1	share of all companies that are good, the base rate

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

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Why does the base shrink twice before you divide?

Is 3x on commitments the number LPs actually receive?

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What the interviewer asks next

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What does 'post-money' fix that older SAFEs did not?

What happens at the priced round, and when does the 10% change?

Where candidates lose it

What the interviewer asks next

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Why is the answer so far below 80%?

What would actually improve the screen?

Where candidates lose it

What the interviewer asks next

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Why does a direct question fail?

Why does routing the question through the other founder fix it?

Where candidates lose it

What the interviewer asks next

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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

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How do you build the count so each step can be challenged?

What does the number tell an investor?

Where candidates lose it

What the interviewer asks next

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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

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Why is the average customer life one over the churn rate?

What does discounting do to a stream that already decays?

Where candidates lose it

What the interviewer asks next

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Why can a fund not invest all of its commitments?

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

Where candidates lose it

What the interviewer asks next

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Which anchors should you carry into the room?

How do you land on 26% out loud?

Where candidates lose it

What the interviewer asks next