Venture Capital puzzles, solved step by step

Above Rs 120 crore. A non-participating investor chooses the better of two payouts: the Rs 30 crore preference, or 25% of the exit as common. 25% of the exit equals Rs 30 crore at an exit of Rs 120 crore, so below that the investor takes the preference and above it converts. At Rs 100 crore the preference pays Rs 30 crore against Rs 25 crore as common; at Rs 160 crore converting pays Rs 40 crore.

What exactly is the investor choosing between?

A shopper with a Rs 300 voucher or a 25% discount uses the voucher on small bills and the discount once the bill passes Rs 1,200. A 1x non-participating preference is the same either-or: the investor takes its money back or its percentage of the exit, never both, so it switches at the exit where the two are equal. Rs 30 crore equals 25% of Rs 120 crore. The non-participatingThe holder takes either its preference or its as-converted share of the proceeds, whichever is larger, but not both. label is what makes it a choice; a participating preference would take the Rs 30 crore and then a share of the rest as well.

Why is the answer the same as the price the investor paid?

Rs 30 crore for 25% means the investor valued the company at Rs 120 crore post-money. For a 1x non-participating preference, the conversion point is always the post-money valuation of the round, so the preference only bites in exits below the price the investor came in at. That gives a quick reading of any term sheet: below the round's post-money the investor is protected, above it the investor is just another shareholder. In between Rs 30 and Rs 120 crore, the common holders share whatever is left after the Rs 30 crore comes off the top.

The limit: this holds with one preferred class. With several classes, each with its own price, the junior classes convert later than their own simple line because senior preferences taken first shrink the pool. And a 2x preference doubles the conversion point to Rs 240 crore, which is why the multiple on a preference matters more to founders than it first appears.

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.

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.

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.

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.

Both reach Rs 337.5 crore, but only A keeps growing when new sales stop. Each year A's ARR becomes 130% from existing customers plus 20% from new ones, and B's becomes 90% plus 60%: both 1.5x. Three years of 1.5x takes Rs 100 crore to Rs 337.5 crore. Stop new sales and A still grows 30% a year, to about Rs 741 crore in three more years, while B shrinks 10% a year, to about Rs 246 crore.

How can a company losing revenue from its existing customers grow as fast as one expanding them?

Two water tanks can both rise by 50 litres an hour: one has a strong tap and a small leak, the other a small tap and no leak at all, plus a booster on the old water. ARR growth is net retention plus new-customer ARR, so the same headline growth can come from customers who spend more each year or from a sales team refilling a leaking base. A gets 30 points from existing customers and 20 from new ones; B loses 10 points from existing customers and replaces them with 60 points of new sales. Both add 50%.

Why would an investor pay more for A at the same ARR?

Because A's growth does not depend on the sales team hitting target every quarter. High net retention is growth the company has already earned; new-logo growth must be bought again every year, usually at a high sales and marketing cost. B has to replace 10% of its base before it grows at all, and as B gets bigger that hole gets bigger in rupees: Rs 10 crore in year one, Rs 22.5 crore in year three. If its market saturates or a recession slows buying, B shrinks; A keeps compounding from the customers it already has.

State the assumptions. The model applies the same retention to new customers from their first year, which flatters B if new customers churn faster than old ones, as they often do. It also treats retention as constant; very high NRR tends to fall as customers reach full deployment. A real diligence would read retention by customer cohort, not a single blended number.

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.

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.

DPI 0.75x, RVPI 1.75x, TVPI 2.5x. All three divide by the Rs 200 crore paid in. Distributions of Rs 150 crore give a DPI of 0.75x; the Rs 350 crore still held gives an RVPI of 1.75x; the total value of Rs 500 crore gives a TVPI of 2.5x. An LP trusts DPI most, because it is cash already returned. The fund looks like a 2.5x but has not yet given back the money it called.

What does each ratio measure?

A friend who borrowed Rs 2,000, has repaid Rs 1,500 and promises the rest plus Rs 3,500 more from a deal still underway has given you back 0.75 times your money in cash and promised 1.75 times more. DPIDistributions to paid-in capital: cash returned to LPs divided by capital called. counts cash returned, RVPIResidual value to paid-in capital: the portfolio's current marked value divided by capital called. counts value still on paper, and TVPI is the two added together, all divided by the capital called. The fund called Rs 200 crore, so DPI is 150 / 200 = {dpi72:.2f}x, RVPI is 350 / 200 = {rvpi72:.2f}x and TVPI is {tvpi72:.1f}x.

Why does an LP care more about the 0.75x than the 2.5x?

Because the marks can move and the cash cannot. RVPI rests on the fund's own valuation of private companies, often at the last round's price, so 70% of this fund's reported value is an estimate that has not been tested by a sale. If those marks fell 40%, RVPI would drop to 1.05x and TVPI to 1.8x, while DPI would stay at 0.75x. That is why many LPs judge older funds on DPI, and why the phrase 'DPI is the only metric that counts' gets repeated in fundraising conversations.

The fair limit is timing. A young fund naturally has low DPI because its companies have not been sold yet; judging a three-year-old venture fund on DPI alone would punish every fund for being young. Read DPI against the fund's age, and ask how the marks were set, last round, a comparable, or a recent offer, before trusting the RVPI.

About 13.3%. Every fund's estimate is right on average, but the deal goes to the fund with the highest estimate, and the highest of five errors is not average. For errors spread evenly from minus 20% to plus 20%, the highest of n sits on average (n - 1)/(n + 1) of the way to the top: with five bidders that is 4/6 of 20%, or 13.3%. Winning is itself evidence that you guessed high.

Why does winning tell you that you overestimated?

Ask five friends to guess the weight of a goat at a fair and give the goat to whoever guesses highest; the winner will nearly always have guessed too much. When the prize goes to the highest estimate, the winner is selected for being too optimistic, so even unbiased bidders overpay on average. This is the winner's curseThe tendency for the winner of an auction with uncertain value to have overestimated that value, because winning selects the most optimistic estimate.. No one bid foolishly here; each estimate was fair. The overpayment comes entirely from the selection.

What should a disciplined bidder do about it?

Bid below your estimate, and more so when there are more bidders or more uncertainty. The curse grows with the number of bidders and with the width of the errors: two bidders overpay by 6.7% on average, five by 13.3%, ten by 16.4%. So a fund in a crowded growth round should shade its bid by roughly the expected overestimate, about 12% of its estimate here, and a fund that keeps winning contested deals should ask whether it is better informed or just more optimistic. A simulation of 200,000 auctions in the source file gives 13.3%, matching the formula.

The limit: the model assumes every fund's estimate is equally noisy and that all bid their raw estimate. Better-informed funds face a smaller curse, and in practice everyone shades, so real overpayment is smaller than the raw figure. The direction of the effect is what to carry into the room.

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.

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.

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.

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.

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.

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.

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.