Venture Capital puzzles, solved step by step

About Rs 120 crore, the second-highest value. As the price rises, Fund A drops out at Rs 100 crore and Fund B at Rs 120 crore. Fund C, which would pay up to Rs 150 crore, wins the moment it bids one step above Rs 120 crore and has no reason to go further. The founder cannot capture C's top value because no one else is willing to push the price there, and C never says what its number is.

Why does the price stop at the runner-up's value?

At a house auction, the buyer who would pay Rs 2 crore often gets the house for Rs 1.6 crore, because the last rival stopped there. In an open ascending auction the winner pays roughly what the second-highest bidder was willing to pay, because the bidding ends the moment the second bidder quits. Fund C's private valuation decides who wins; Fund B's valuation decides the price. The Rs 30 crore between them is the winner's surplus, and it stays with Fund C.

Could the founder run the process differently and get closer to Rs 150 crore?

A sealed bid, where each fund names one price and the highest wins at its own bid, looks as if it would extract more. It usually does not, because funds shade their sealed bids below their true value; under textbook assumptions the expected price ends up about the same as in the open auction. What actually moves the price is more serious bidders: a fourth fund valuing the deal at Rs 140 crore would push the clearing price to Rs 140 crore. That is why bankers and founders work so hard to keep several funds in the process to the end.

Say the limits. Venture rounds are not pure price auctions: founders often take a lower valuation from a fund they want on the board, and term sheets differ on preferences, board seats and option pools, so the headline number is only part of the price. The bid step matters too; the price is Rs 120 crore plus one increment, which in practice is a negotiation rather than a fixed step.

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.

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.

Roughly 35,000 to 50,000 trucks a day, call it 40,000. From the goods: about 3 crore people, each accounting for some 10 kg of goods leaving the region daily, gives 3 lakh tonnes; at 12 tonnes a truck that is 25,000 loaded trucks, or about 35,714 once empty departures are added. From the trucks: about 4 lakh trucks serving NCR, each leaving once every 8 days, gives 50,000. Two routes within 1.4x of each other make the range defensible.

Why build the number twice?

A carpenter measures twice before cutting, not because the first measurement was careless but because a second, separate measurement catches the slip the first one hid. An estimate built from one chain of assumptions can be precise and still out by ten times; a second route built from different assumptions is the only check you can run in the room. Here the first route starts from what has to move, goods, and the second from what moves it, trucks. They share no inputs, so their agreement means something.

Walk route A slowly. Assume about 3 crore people in NCR. Outbound freight is the manufactured goods from the industrial belts plus wholesale trade re-sent to the rest of north India; assume 10 kg per resident a day, so 3 lakh tonnes. A loaded truck averages perhaps 12 tonnes across small and large vehicles, giving 25,000 loaded departures. Trucks that came in loaded often leave empty; if 30% of departures are empty, total departures are 25,000 divided by 0.7, about 35,714. Route B: assume 4 lakh intercity trucks, from NCR and outside, serve the region, and an average round trip takes 8 days, so 50,000 leave each day.

How would you check it outside the room?

The best check is a third, measured source: GST e-way bills, which are generated for goods moved above a value threshold and are published at state level, and toll plaza counts of goods vehicles on the main exits from NCR. Each has its own bias; e-way bills miss low-value loads and toll counts mix through traffic with NCR departures, so use them to test the range rather than replace it. A morning spent with brokers at a transport hub would test the 30% empty share and the 8-day trip, the two inputs most likely to be wrong.

Then say what the number is for. Trucks leaving a day is not the market; the marketplace earns on loads it matches. At 40,000 departures a day, if a third are booked through brokers and the platform takes a fee per load, the next step is the fee times the brokered loads. The truck count is the base everything else multiplies, which is why it deserves two routes.

About 12.6x, against 32x at a steady 100%. Multiply the yearly factors one at a time: 2 x 1.8 is 3.6, x 1.64 is 5.9, x 1.512 is 8.9, x 1.41 is about 12.6. Steady doubling gives 2 to the fifth, or 32. A growth rate that fades by a fifth each year leaves you with less than 40% of the steady outcome, which is why the fade assumption moves a valuation more than the opening growth rate.

How do you compute this quickly without losing the thread?

Turn each year's growth into a factor and keep a running product, like a cricket scorer adding each over to the total rather than recomputing the innings. Revenue after five years is the product of the five yearly factors, so a fading rate must be multiplied year by year; there is no single rate you can raise to the fifth power. The running total goes 2, 3.6, 5.9, 8.9 and 12.6. Rounding each step to one decimal keeps it mental and still lands within a few per cent.

Which matters more, the starting growth rate or how fast it fades?

Run a few cases. A company that starts at 150% but keeps only 60% of its growth each year ends at about 11.6x, below the 100% company that keeps 80%, and well below a 100% company that keeps 90%, which reaches about 19.7x. The opening rate is the number in the pitch deck; the fade is the number that decides the outcome. Diligence time is better spent on why growth should persist, such as retention and new markets, than on last year's growth figure.

The limit: a constant fade is a convenient shape, not a law. Real growth can stall, then re-accelerate on a new product, and a smooth curve will miss both. Use it to show the sensitivity, then test the specific reasons this company's growth would or would not hold.

Yes, guess every remaining question; the expected score rises from 25.5 to 29.5. Your 30 careful answers at 85% are worth 25.5 points. A blind guess on a five-option question is right one time in five, and a wrong answer costs nothing, so 20 guesses add 20 x 0.2, or 4 expected points. A blank is a sure zero. The only real decision is leaving yourself the last 30 seconds to fill them in.

Why is a blind guess worth anything at all?

A free raffle ticket is worth taking even if the odds are poor, because it costs nothing. When wrong answers carry no penalty, every guess has a positive expected value, one point times the chance of being right, and a blank has an expected value of exactly zero. With five options that chance is 1 in 5, so each guess is worth 0.2 points and twenty are worth 4. On a 50-question test, 4 points is often the gap between two scoring bands.

What changes if wrong answers are penalised, and how do you manage the clock?

Suppose a wrong answer cost a quarter of a point. A blind guess would then be worth 0.2 minus 0.8 x 0.25, which is exactly zero. The rule is to guess whenever the chance of being right times the reward beats the chance of being wrong times the penalty, and eliminating even one option tips a penalised guess back into positive value. On the clock: 12 minutes for 50 questions is 14.4 seconds each. Skip any question that will take more than about 30 seconds, come back if time allows, and stop answering carefully with half a minute left to fill every blank.

Two honest notes. The 4 points are an average: 20 guesses have a standard deviation of about 1.8 points, and there is roughly a 1% chance none of them land. And the no-penalty rule is the premise of this question; tests differ, so check the instructions of the one you are sitting before deciding.

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.