Venture Capital puzzles, solved step by step

Above about Rs 250 crore, and Series B sets that line. A non-participating holder converts when its share of the exit beats its preference, so each class's line is preference divided by stake: seed Rs 5 crore over 10% is Rs 50 crore, Series A Rs 20 crore over 20% is Rs 100 crore, Series B Rs 50 crore over 20% is Rs 250 crore. The class that paid the most per percentage point is the last to convert.

Why is the line for each class its preference divided by its stake?

Suppose a friend offers you a choice: your Rs 500 back, or a tenth of whatever the raffle raises. You take the tenth only once the pot is above Rs 5,000. A 1x non-participating preference is exactly that choice, so a class converts once its stake times the exit value beats its money back, and the crossover is preference divided by stake. Preference over stake is also the price the class paid for the whole company, which is why the class that bought at the highest valuation, here Series B at an implied Rs 250 crore, holds out longest.

Why does the question say 'roughly', and do the lower lines move?

The simple division assumes everyone else has converted. Below Rs 250 crore Series B keeps its Rs 50 crore, and that comes out of the pot before the others share it. When a senior class holds its preference, the pool left for everyone else shrinks, so the junior classes need a bigger exit before converting pays. Series A with B holding gets 20/80 of the exit less Rs 50 crore, which beats Rs 20 crore only above Rs 130 crore. Seed, with both A and B holding, needs Rs 100 crore. The top line does not move, because by the time Series B is deciding, everyone below it has already converted.

In the room, give Rs 250 crore and Series B first, then offer the refinement as a check. It shows you understand that preferences interact, which matters when you are the junior investor negotiating behind a large late round.

Rs 40 crore today, Rs 96 crore after the first round, Rs 64 crore after the second. Each round sells 20% of the company, so she keeps 80% of her stake: 40% becomes 32%, then 25.6%. Her rupees are that stake times the post-money value: 32% of Rs 300 crore is Rs 96 crore, and 25.6% of Rs 250 crore is Rs 64 crore. Dilution cut her percentage both times; only the down round cut her value.

Why does selling 20% leave her with 32%, not 20%?

Cut a pizza into ten slices and give four to a friend. If the host then takes a fifth of every plate for a late guest, the friend loses a fifth of her four slices, not two of them. A round that sells 20% of the company shrinks every existing holder by the same fifth, so her stake is multiplied by 0.8, not reduced by 20 points. 40% x 0.8 is 32%. The second round does it again: 32% x 0.8 is 25.6%.

If her percentage fell both times, why did her wealth rise the first time?

Because the first round was priced well above today's value. A Rs 300 crore post-money with Rs 60 crore raised means a pre-money of Rs 240 crore, so the company was repriced from Rs 100 crore to Rs 240 crore before the new money arrived. Dilution is a smaller slice; whether it costs you money depends entirely on the price the new investor pays for the slice. The second round sold 20% at Rs 250 crore post-money, which is Rs 50 crore raised on a pre-money of Rs 200 crore, below the Rs 300 crore she was last marked at. Her percentage fell by the same fifth, and this time her value fell too, from Rs 96 crore to Rs 64 crore.

One limit is worth stating. The Rs 64 crore is a paper value at the last round's price, and it assumes her shares are worth the same per share as the investors' preferred shares, which carry preferences hers do not. In a sale below the preferences, her real payout would be less.

Rs 8 crore of expected profit against Rs 6.5 crore, so the choice is worth Rs 1.5 crore. A good round turns Rs 5 crore into Rs 25 crore, a Rs 20 crore profit; a bad one leaves Rs 2.5 crore, a Rs 2.5 crore loss. Forced to invest, you expect 0.4 x 20 minus 0.6 x 2.5, or Rs 6.5 crore. With the right you pass on bad rounds, so you expect 0.4 x 20, or Rs 8 crore. The Rs 1.5 crore gap is the price of the bad branch you no longer have to take.

Why is a right worth more than an obligation to do the same thing?

A season ticket that lets you skip any match you like is worth more than one that forces you to sit through the washed-out ones, even though the matches are the same. A right is worth exactly the losses it lets you refuse, so its value is the expected loss on the branches you would walk away from. Here the bad branch costs Rs 2.5 crore 60% of the time, an expected Rs 1.5 crore, and the right lets you skip all of it. The good branch is the same Rs 20 crore profit either way, so it adds nothing to the difference.

Where does this simple answer overstate the right in real life?

The question lets the round's pricing tell you for certain whether it is good. In practice the signal is noisy, so a pro rata right is worth less than Rs 1.5 crore here: you will sometimes pass on a good round and sometimes take a bad one. If your read were no better than a coin, the choice would be worth nothing, because you could not tell the branches apart. Two more limits: a hot round may leave you no allocation even with the right, and a fund must hold reserves to exercise it, and that cash earns nothing while it waits.

This is why seed funds fight for pro rata rights and why the best later investors try to cut them back. The value sits with whoever gets to look before deciding, and it grows with how far apart the good and bad outcomes are. Say that last point in the room: a wider spread between good and bad rounds makes the right worth more, exactly as a wider spread makes any option worth more.

A score of 25 today, and a margin of minus 10% to reach 40 at 50% growth. The Rule of 40 adds revenue growth and free cash flow margin: 70 plus minus 45 is 25. If growth slows to 50 and the burn stays at minus 45, the score falls to 5. To get back to 40 the margin must rise to minus 10, a 35 point improvement in a year when growth is also slowing.

What does adding growth to margin actually measure?

A cricket team can win on runs scored or on runs saved; a selector looks at the margin of victory, not either number alone. The Rule of 40A rough test for software companies: revenue growth % plus free cash flow margin % should reach at least 40. treats growth and cash generation as substitutes, so a company may burn cash only to the extent that its growth pays for the burn. Today this company grows 70 and burns 45, for a score of 25: it is spending more than its growth justifies. A company growing 20 with a 20% margin also scores 40 and passes, which is the point: the test does not care which mix you choose.

Why is the slowdown the dangerous part of this question?

Growth rarely falls while the cost base shrinks on its own. When growth drops 20 points with the burn unchanged, the score falls from 25 to 5, and the company has to find 35 points of margin to make up for it. Those points come from cutting sales hiring and marketing, which is often what was producing the growth, so the cut can slow growth further. Say this in the room: the score is easy to compute, the hard part is whether the company can move margin that far without breaking the growth engine.

State the limits too. The rule is a rule of thumb from listed software companies; applied to an early company growing 200% it says little, because small numbers make growth rates swing. Which margin you use matters as well, free cash flow or EBITDA, and companies quote whichever flatters them, so ask which one is in the deck.

Ten tests, run at once. Number the statements and write each number in binary, ten digits long. Test pool 1 holds every statement whose first digit is 1, pool 2 every statement whose second digit is 1, and so on. A week later the ten results, read as positive equals 1, spell out the forged statement's number. Ten is the minimum because nine tests give only 512 possible result patterns, fewer than the 1,000 statements.

Why can you not just halve the pile and test again?

Halving is the right instinct when you can see each answer before asking the next question, like guessing a number with higher or lower clues. Here every result takes the full week, so all the testing has to be designed up front. When questions must be asked in parallel, each statement needs its own unique pattern of answers, and the puzzle becomes how many yes or no answers it takes to give 1,000 statements a distinct pattern each. Ten answers give 2 to the 10, or 1,024 patterns; that is enough.

How do you prove ten is the fewest?

Count the outcomes. Each test has two results, so n tests have at most 2 to the n distinct result patterns, and you need at least one pattern per possible forgery. Nine tests give 512 patterns for 1,000 suspects, so at least two statements would share a pattern and you could not tell them apart. Ten give 1,024, which is why 10 is both achievable and the minimum. One small detail: if you number the statements 1 to 1,000, the all-negative pattern is never used, which is fine because one statement is definitely forged.

Say where the trick breaks. It relies on exactly one forgery; with two forged statements, the positives are the union of two binary numbers and no longer name either one, so you would need more tests and a different design. It also assumes the test is perfectly sensitive in a pool of 500 statements. In real diligence a forger rarely fakes only one document, so the useful habit is the reasoning, counting outcomes before designing the checks.

The 12% deal made Rs 21 crore against Rs 1.5 crore, fourteen times as much. The quick flip shows a 32% IRR because 1.15x in six months annualises to 1.15 squared, about 1.32. But LPs spend rupees, not rates. If the Rs 11.5 crore then sat idle for the remaining nine and a half years, the deal is 1.15x over ten years, an IRR of about 1.4%. The ten-year deal's 3.1x is about 12% a year on the whole Rs 10 crore for the whole time.

How can a 32% IRR make less money than a 12% IRR?

A cab that charges a high rate per minute for a two-minute ride earns less than a modest-rate cab hired for the whole day. IRR is a rate per year while the money is out, so a short deal can post a huge IRR on a tiny rupee profit, and the rate says nothing about how long the capital earned it. On Rs 10 crore the flip made Rs 1.5 crore. The ten-year deal made Rs 21 crore, with a lower rate sustained over twenty times as long.

Why does it matter what the cash does after the exit?

The 32% assumes the Rs 11.5 crore can be put straight back to work at a similar rate. For an LP whose money was committed for ten years, cash returned early earns only what the LP can do with it next, and if that is nothing, the deal's true rate over the commitment is about 1.4%. This is why LPs read IRR beside the money multiple, and why a fund boasting a top-quartile IRR on a 1.3x fund gets hard questions. Some funds also time capital calls with credit lines to shorten the period the money counts as out, which flatters IRR without adding a rupee.

The fair limit: early cash is worth something if the LP really can reinvest it, and the reinvestment rate decides by how much. In the room, say both numbers for every deal, multiple and IRR, and say which one an LP banks.

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.