Venture Capital puzzles, solved step by step

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.

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.

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.

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.

20% if Rs 200 crore is the pre-money, 25% if it is the post-money. Pre-money is the value before the cheque, so post-money is 200 plus 50, Rs 250 crore, and 50 over 250 is 20%. If Rs 200 crore already includes the cheque, investors own 50 over 200, which is 25%, and the pre-money was only Rs 150 crore. One unstated word moves five points of the company.

What do pre-money and post-money actually mean?

Two friends own a food stall worth Rs 2,00,000. A third friend puts in Rs 50,000 for a new oven. The stall is now worth Rs 2,50,000 and the new friend owns a fifth of it, because the Rs 50,000 is inside the new total. Pre-money is the value before the new money arrives, post-money is pre-money plus the new money, and the investor's share is always the cheque divided by post-money. The only question is which of the two numbers the founder quoted.

Why does the post-money reading cost the founder more?

If Rs 200 crore is post-money, the pre-money is only Rs 150 crore: the founder sold Rs 50 crore of shares against a company valued Rs 50 crore lower. 25% against 20% is a quarter more of the company for the same cheque, and that extra slice is diluted alongside everything else in every later round. Check both readings the same way: 20% of 250 is 50, and 25% of 200 is 50. Both pass, which is exactly why the sentence alone cannot settle it.

Headlines tend to quote whichever number sounds bigger, and a term sheet settles it by stating the pre-money and the fully diluted share count. Some convertible instruments quote a post-money cap instead, so the habit of asking which one carries straight into later work.

Faster than 33.3% a year; at exactly one third her stake's value stands still. Each round leaves her 75% of her previous ownership, so her stake's value changes by 0.75 times one plus the valuation growth. That equals 1 when growth is 1 over 0.75 minus 1, a third. At 20% growth her stake loses 10% of its value every year, even while the company grows.

Why is the break-even growth a third and not a quarter?

A shop sells an item at a 25% discount and wants its revenue back to where it was: it needs a third more units, not a quarter more, because 75 x 1.333 is 100. After giving up a quarter, she holds three quarters, and three quarters of anything must grow by a third to get back to the whole. This is the same asymmetry as recovering from a loss: the recovery is measured on a smaller base, so it needs a bigger percentage.

What happens at 20% and at 50% growth?

At 20%, each year multiplies her stake's value by 0.75 x 1.2 = 0.9. After five rounds the company is worth 2.5 times as much, and her stake is worth only 59% of what it was. At 50%, each year multiplies it by 1.125, and five rounds take it to 1.80 times. Same dilution, opposite outcomes, decided entirely by whether growth clears one third.

Why would an investor ask this?

Because it is the test every round must pass for existing holders. With a quarter sold, post-money growth of a third is the same as the new round's pre-money equalling the last round's post-money. A round only makes existing holders richer if the new pre-money beats the old post-money, which is what an up round means. Say that link and the puzzle becomes a point about pricing, not just arithmetic.

On these numbers, no: waiting is worth Rs 79 crore on average against a certain Rs 80 crore. Weight each outcome by its chance: half of 110 is 55, three tenths of 80 is 24, and the no-deal branch adds nothing. Waiting loses a crore of expected value and adds a one in five chance of having no round at all, which for a company that needs the money can be far worse than zero.

How do you compare a sure thing with a gamble?

A shop offers you Rs 800 for your old phone today, or you can try an online sale that might fetch Rs 1,100, might fetch Rs 800, or might not sell at all. Put a number on the gamble by weighting each outcome by its chance and adding, then compare that expected value with the sure offer. Here waiting gives 0.5 x 110 + 0.3 x 80 + 0.2 x 0, which is Rs 79 crore of pre-money on average, against Rs 80 crore she can sign today.

Why is the expected value not the whole answer?

Because the outcomes are not equally painful. A one crore gap in expected value understates the case against waiting, because the 20% branch is not a lower valuation but no round at all. A company with six months of cash that misses a round may have to cut staff or raise on much worse terms later. Even if waiting were worth slightly more on average, a founder who cannot survive the bad branch should still sign. Turn it round to show the margin: holding the no-deal chance at 20%, waiting only beats signing if the chance of Rs 110 crore rises above 53.3%; holding the 50% upside, the no-deal chance must fall below 18.75%.

What would you ask before trusting the probabilities?

Where the 50% comes from. Founders tend to overrate the chance of a better offer because the meetings that went well are the ones they remember. Ask how many investors are past a partner meeting, and whether the current lead would return at the same price after being turned down, which this puzzle quietly assumes. A pre-money figure is also not the founder's wealth: the stake she keeps depends on how much she raises as well.

About 30.6% a year, not 36%; and 10% a year needs monthly churn of about 0.87%. Each month keeps 97% of the customers still there, so a year keeps 0.97 to the power 12, which is 69.4%. Going the other way, 90% retention a year means a monthly retention of 0.9 to the power one twelfth, about 99.13%, so monthly churn of 0.87%. This counts one starting group of customers and ignores new sign-ups.

Why is it not simply twelve times 3%?

A water tank that loses 3% of what is in it every hour loses less each hour, because there is less water to lose. Monthly churn is a share of the customers still there, so it compounds on a shrinking base: the yearly survival rate is the monthly survival rate raised to the twelfth power. After six months 0.97 to the sixth leaves 83.3%, and after twelve 69.4%. Twelve times 3% would be right only if each month lost 3% of the original group, which nobody measures.

How do you get the monthly rate for 10% a year without a calculator?

Dividing 10% by 12 gives 0.83%, and it is close because small rates compound gently. The exact figure is slightly higher, 0.87%, because the monthly losses come out of a shrinking base and so each month must lose a touch more to reach 10% in total. Say the division as a first estimate, then the correction. For large rates the gap grows: 3% a month gives 30.6% a year, against 36% by multiplication.

Why does an investor care which convention a company used?

Because companies quote whichever looks better. A business that reports 3% monthly churn and 30.6% annual churn is internally consistent; one that reports 3% monthly and 25% annual is either measuring different customers or counting new sign-ups against losses. Ask what base the churn is measured on and whether it counts logos or revenue, since revenue churn can be much lower when the customers who leave are the small ones.

150 decks. Reduce everything to one unit first: 4 associates working 3 hours is 12 associate-hours, and 60 decks over 12 is 5 decks per associate-hour. Six associates for five hours is 30 associate-hours, so 30 x 5 = 150. As a check, scale the original: 60 x 6/4 x 5/3 is also 150. This assumes everyone works at the same steady rate.

Why reduce to a rate per associate-hour?

If 2 cooks make 40 rotis in an hour, one cook makes 20 an hour, and any kitchen size or shift length follows from that one number. Work problems become simple once you find the output of one worker in one unit of time, because the total is then that rate times workers times hours. Here 60 decks came from 4 x 3 = 12 associate-hours, so the rate is 5 decks per associate-hour. Everything else is multiplication.

How do you avoid the slip under time pressure?

Ask which way each change pushes the answer before you multiply. More associates and more hours both raise output, so both ratios must be greater than one: 6/4 and 5/3, never 4/6 or 3/5. The fast wrong answer, 90, applies the 6/4 and stops. On a timed test the danger is not hard arithmetic but a missed step, so a five-second check that the answer moved in the right direction by roughly the right amount is worth it: one and a half times the people for two thirds more time should give about two and a half times the output, and 60 x 2.5 is 150.

Where would this break down in a real deal team?

The model assumes every associate screens at the same steady pace and that output scales with hours. Real screening slows late in a long day, and a bigger team spends time coordinating and avoiding duplicate work. Saying so is unnecessary on the test itself, but it is the right instinct if the same question comes up in an interview: the arithmetic answer is the ceiling, and the real number is usually lower.