Venture Capital puzzles, solved step by step

About 2.03, not 1.6. ARR is one year of recurring revenue, so a Rs 8 crore contract spanning three years adds Rs 2.67 crore of ARR. Net new ARR falls from Rs 25 crore to Rs 19.67 crore, and Rs 40 crore of burn divided by that is 2.03. The company spends about Rs 2 of cash for every rupee of new annual revenue, not Rs 1.60.

What is the burn multiple actually measuring?

The burn multipleNet cash burned in a period divided by the net new annual recurring revenue added in that period. Lower is more efficient. asks how many rupees of cash a company spends to add one rupee of annual recurring revenue. Both halves have to be measured over the same year, so a contract that covers three years can only put one year's revenue in the denominator. A gym that sells a three-year membership for Rs 36,000 has not added Rs 36,000 of yearly revenue; it has added Rs 12,000 a year for three years.

How do you restate it in your head?

Split the Rs 25 crore into the part that was fine and the part that was not. Rs 17 crore came from ordinary annual contracts. The prepaid contract is Rs 8 crore over three years, which is Rs 2.67 crore a year. Restated net new ARR is 17 plus 2.67, or Rs 19.67 crore, and 40 divided by 19.67 is 2.03. A quick check: 40 over 20 would be exactly 2, and the denominator is a little under 20, so the answer sits a little above 2.

Why does the gap between 1.6 and 2.03 matter?

Many investors read a multiple under about 1.5 to 2 as efficient growth and anything much above 2 as expensive, though the cut-offs vary with stage and market. The restatement moves this company across that line, from efficient-looking to expensive. It also tells you what to ask next: how many other contracts are multi-year, and whether the sales team is paid on total contract value, which would explain why the number was booked this way.

About 3.85% of the company. Seed leaves the founder at 80%. The Series A investor and the new pool take 35% of the post-money together, so existing holders keep 65%, and the founder goes to 52%. To stay at 50%, the founder can keep no less than 50 over 52 of the Series B cap table, so the Series B can sell at most 1 minus 50/52, about 3.85%.

Why does dilution multiply rather than subtract?

Think of a pizza you own whole. Give a friend a fifth and you keep four fifths. If the pizza is then cut again and newcomers take a third of every slice, you lose a third of what you still hold, not a third of the original pizza. Each round shrinks every existing holder by the same factor, so the founder's stake is the product of the factors, not 100% minus the percentages sold. Subtracting 20, 25 and 10 from 100 gives 45% and is wrong for exactly this reason.

How do the Series A investor and the pool combine?

Both are measured on the post-money cap table of the same round, so they come out of the same pie at the same time. Existing holders keep 100% minus 25% minus 10%, which is 65%, and the founder goes from 80% to 52%. Had the terms said the pool was created after the investor bought in, you would chain them instead, 0.75 times 0.90, and the founder would hold 54%. Asking which way the pool is measured is the question that separates candidates here.

How big can the Series B be?

The Series B shrinks the founder by a factor of one minus whatever it sells. The founder stays at or above 50% only if 52% times (1 minus x) is at least 50%, which gives x of at most 1 minus 50/52, about 3.85%. That is a tiny round. In practice it tells you the founder's goal and a normal Series B, which often sells 15% to 25%, cannot both happen.

Rs 20 crore with the catch-up, and about Rs 10.6 crore without it. LPs first get their Rs 100 crore back plus an 8% compounding return, Rs 46.93 crore. The GP then takes the next Rs 11.73 crore until it holds 20% of the profit so far, and the last Rs 41.33 crore is split 80/20. Without the catch-up, only the Rs 53.07 crore above the hurdle is split, and the GP gets 20% of that.

What order does the money flow in?

A distribution waterfallThe agreed order in which a fund pays out cash: which party is paid first, how much, and when the next tier begins. is a queue at a buffet: each tier eats fully before the next is served. Tier one returns the LPs' capital, tier two pays them the hurdle, tier three is the GP's catch-up, and only then does the 80/20 split begin. The hurdle compounds, so after five years it is 1.08 to the power 5 minus 1, about 46.9% of capital, Rs 46.93 crore, not the Rs 40 crore that simple interest would give.

How big is the catch-up, and why does it stop where it does?

The catch-up pays the GP 100% of the next money until the GP holds 20% of all profit paid so far. If the catch-up is c, then c must equal 20% of the hurdle plus c. Solving gives c equal to the hurdle times 0.20 over 0.80, one quarter of Rs 46.93 crore, which is Rs 11.73 crore. At that point LPs hold 80% of profit and the GP holds 20%, so every later rupee split 80/20 keeps those shares fixed.

What is the catch-up worth to the GP here?

Without it, the GP earns 20% only of the Rs 53.07 crore above the hurdle, Rs 10.61 crore. The catch-up nearly doubles the GP's take, from about Rs 10.6 crore to Rs 20 crore, because it gives the GP its share of the hurdle profit back. The limit to say aloud: this is one distribution at year five. Real funds pay out over many years, and the hurdle runs on each rupee's own timing, which changes the numbers but not the order.

Series B takes its Rs 60 crore preference and Series A converts. Converting would give Series B at most Rs 45 crore, so it takes its money back. That leaves Rs 140 crore for Series A and common, who hold 20% and 60% of the shares; Series A's quarter is Rs 35 crore, beating its Rs 20 crore preference. Common receives Rs 105 crore.

How does a non-participating holder decide?

Think of a refund policy: you can take your money back, or keep the product and its resale value, but not both. A non-participating preferred holder takes the larger of its preference or what its shares are worth as common, never both. Two series holding the same 20% each face very different choices here, because Series B paid Rs 60 crore for its 20% and Series A paid Rs 20 crore. Series B's refund is worth three times as much, while their shares are worth the same.

Why does Series B not convert, whatever Series A does?

Test its best case. If Series A takes its preference, Series B converting would share Rs 180 crore with common, 20 parts of 80, which is Rs 45 crore. If Series A also converts, Series B would get 20% of Rs 200 crore, Rs 40 crore. Both are below Rs 60 crore, so Series B takes its preference however Series A behaves. That settles the order: take B's Rs 60 crore off the top first, then decide A.

Where are the break points if the sale price moves?

Series A converts once a quarter of what is left after Series B exceeds Rs 20 crore, which is any sale above Rs 140 crore. Series B converts only once 20% of the whole sale exceeds Rs 60 crore, above Rs 300 crore. Between Rs 140 crore and Rs 300 crore, the two series that own the same stake are treated differently, and Rs 200 crore sits inside that band. Below Rs 80 crore, pari passu means the two preferences share the proceeds in proportion to Rs 20 crore and Rs 60 crore, one part to three.

A proposes A Rs 98 crore, B nothing, C Rs 1 crore, D nothing and E Rs 1 crore. A needs three of five votes, its own and two more. If A were removed, B's winning plan would give C and E nothing, so Rs 1 crore each buys their votes. Working backwards from two partners up gives every step of the chain.

Where do you start a problem like this?

At the end, where the answer is obvious. A chess player thinks about the final position and works back to the move in front of her. Backward induction solves the smallest game first, then uses its answer as each partner's fallback in the next larger game. With only D and E left, D proposes Rs 100 crore for itself; its own vote is one of two, which is half, so it passes. E gets nothing, and everyone further up the table knows it.

How does each proposer buy votes as the table grows?

With three left, C needs two votes. E gets nothing if C is removed, so Rs 1 crore buys E: C 99, D 0, E 1. With four left, B needs two votes and D is the partner who would get nothing in C's plan, so Rs 1 crore buys D: B 99, C 0, D 1, E 0. Each proposer buys exactly the votes it needs from the partners whose fallback is lowest, paying one crore more than that fallback. With five left, A needs three votes; C and E get nothing in B's plan, so A pays them Rs 1 crore each and keeps Rs 98 crore.

What assumption is doing the work, and what does the puzzle say about real funds?

The tie rule matters. If an indifferent partner voted yes, A could offer C, D and E nothing and keep all Rs 100 crore, because they get nothing anyway. Stating how indifferent players vote is the step that separates a full answer from a lucky one. The real-world point is that self-interest plus a voting rule rewards whoever controls the agenda, which is why carry splits at real firms are set in writing, with vesting, rather than left to a vote among partners.

Committing now earns an expected Rs 2 crore; staging earns Rs 7.6 crore, so the option to stop is worth Rs 5.6 crore. Committing pays Rs 100 crore only 12% of the time, worth Rs 12 crore, against Rs 10 crore invested. Staging risks Rs 2 crore first and adds Rs 8 crore only after the milestone, so in the 70% of cases that fail it saves Rs 8 crore: 0.7 x 8 is Rs 5.6 crore.

Why is waiting worth anything if the payout is the same?

Think of booking a wedding venue with a small refundable deposit rather than paying in full a year out. If the engagement is called off, you lose the deposit, not the whole fee. Staging a cheque does not change what you win; it changes what you lose in the worlds where things go wrong, because you stop paying once you learn the milestone was missed. Here the milestone fails 70% of the time, and each of those times the staged route has spent Rs 2 crore instead of Rs 10 crore.

How do you work each route's expected profit?

Committing now: the company pays Rs 100 crore only if it passes both hurdles, 0.3 x 0.4, which is 12% of the time. That is worth Rs 12 crore against Rs 10 crore paid, an expected profit of Rs 2 crore. Staging: pay Rs 2 crore for sure, then in the 30% of worlds that hit the milestone, pay Rs 8 crore for a 40% shot at Rs 100 crore, which is worth Rs 32 crore at that point. Minus 2, plus 0.3 x 32, gives Rs 7.6 crore.

What would a founder say about this, and what is the limit?

A founder will rarely give you the same price for both tranches, because staging moves risk onto the company. The Rs 5.6 crore is the most it is worth paying for the right to stage, in a higher second-tranche price or a smaller stake. Staging also has costs the model ignores: a company that has to hit a milestone to get its money may be run for the milestone rather than for the business, and the uncertainty can scare off other investors.

The portfolio must distribute Rs 1,750 crore, 3.5x the fund, which is exactly five Rs 350 crore exits. LPs want Rs 1,500 crore: Rs 500 crore of capital plus Rs 1,000 crore of profit. Their profit is 80% of the total, so total profit is Rs 1,250 crore and gross is Rs 1,750 crore. At Rs 350 crore an exit that needs five exits, where ignoring carry suggests just over four.

How do you work back from net to gross?

Picture a sales agent who keeps a fifth of whatever the house sells for above the owner's purchase price. If the owner wants to walk away with Rs 1 crore of profit, the house has to make Rs 1.25 crore of profit, because the agent takes a fifth of it. Carry only touches profit, so gross up the LPs' profit by 0.8 and leave their capital alone. LPs need Rs 1,000 crore of profit on top of their Rs 500 crore, so total profit is 1,000 divided by 0.8, Rs 1,250 crore, and gross distributions are Rs 1,750 crore.

Why does the exit count matter more than the multiple?

Because exits come in whole companies. Forgetting carry gives Rs 1,500 crore, which looks like 4.3 exits and invites a partner to think four big outcomes plus some smaller ones will do; with carry it is exactly five, with nothing to spare. Each exit returning Rs 350 crore to the fund is itself rare: if the fund owns 10% at exit, each one is a Rs 3,500 crore company. Seen this way, a 3x net target is a statement about how many very large companies the fund must back and keep a meaningful stake in.

Say the simplifications. The rest of the portfolio is assumed to return nothing, which overstates the exits needed, while fees, which the question told you to ignore, would reduce the capital invested and raise the bar again. A real model would net the two.

The Series B follow-on, at 1.50x against 1.25x. Rs 10 crore at Rs 400 crore post buys 2.5%, worth Rs 50 crore in a Rs 2,000 crore exit; at a 30% chance that is Rs 15 crore expected. The seed buys 25%, halved to 12.5% by exit, worth Rs 250 crore; at 5% that is Rs 12.5 crore. The seed would need a 6% chance of the exit to draw level.

Why is the cheaper entry not automatically the better bet?

A lottery ticket costs very little and a fixed deposit costs a lot per rupee of payout, yet nobody thinks the ticket is the better deal just because it is cheap. What matters is the price multiplied by the chance of being paid. The expected multiple of a venture cheque is the chance of the exit times the stake you hold at exit times the exit value, divided by the cheque. The seed price is 10 times lower, so the stake starts 10 times bigger, but halving by dilution leaves it only 5 times bigger, and the odds are 6 times worse.

How do you compare them quickly in the room?

Compare the three ratios rather than the full sums. The seed stake at exit is 5 times the Series B stake, but its odds are 6 times lower, so its expected value is five sixths of the follow-on's. Five sixths of 1.5x is 1.25x. The same logic gives the break-even: the seed draws level only if its chance of the exit rises from 5% to 6%, or the Series B chance falls from 30% to 25%.

What does the expected multiple leave out?

Say the limits before the interviewer does. The seed's 1.25x comes with a 95% chance of losing everything, against 70% for the follow-on, so the two bets carry very different risk even before you compare averages. Time matters too: a Series B company is closer to exit, so the same multiple earns a higher annual rate. Against that, a seed fund's strategy depends on owning large stakes in a few outliers, and a partner may accept a lower expected multiple for the bigger stake. The arithmetic decides the comparison only once those preferences are stated.

Blended LTV to CAC is 1.33x; the marginal ratio on the last 1,000 customers is 0.86x. Total spend is Rs 50 lakh plus Rs 80 lakh plus Rs 1.4 crore, Rs 2.7 crore for 3,000 customers, an average of Rs 9,000, and Rs 12,000 over Rs 9,000 is 1.33. The last cohort costs Rs 14,000 for Rs 12,000 of contribution, so it destroys Rs 20 lakh.

Why can a healthy average hide a losing cohort?

Think of picking mangoes from a tree. The low branches take seconds, the middle ones need a ladder, and the top ones need a long pole and ten minutes each. The average minutes per mango still looks fine long after the top branches stopped being worth the effort. Customer acquisition works the same way: each extra customer from a saturating channel costs more than the last, so the average lags behind the cost of the customer you are adding now. The blended 1.33x looks acceptable. The marginal LTV to CACThe lifetime contribution of the next customer divided by the cost of acquiring that customer, as opposed to the average across all customers acquired so far. on the third cohort is 0.86x.

How much value does each cohort create or destroy?

Turn the ratios into rupees, because a ratio cannot be added up. The first cohort creates Rs 7,000 a customer, Rs 70 lakh. The second creates Rs 4,000 a customer, Rs 40 lakh. The third loses Rs 2,000 a customer, Rs 20 lakh. Stopping at 2,000 customers leaves Rs 110 lakh of value against Rs 90 lakh for all 3,000, so the third cohort makes the company smaller. At 2,000 customers the blend would also read better, 1.85x.

Why does a venture investor care about the difference?

A growth plan funded by a new round usually means spending more in the same channels. The return on that new money is set by the marginal ratio, not the blended one, so a company quoting 1.33x may be raising money to buy customers at 0.86x. Ask for acquisition cost by month or by spend band, not the lifetime average. Say the limitation as well: here every customer brings the same Rs 12,000, but a saturated channel often brings weaker customers too, so the real marginal ratio is likely worse than 0.86x.

The price implies a free cash flow margin of about -7%, and the line gives Rs 312.5 crore at the actual minus 30%. Rs 600 crore over Rs 50 crore is 12x ARR; divided by 0.25 that is a score of 48; less 55 points of growth leaves -7%. At minus 30% the score is 25, the multiple 6.25x and the EV Rs 312.5 crore, so the price assumes a 23-point margin gain worth Rs 287.5 crore.

How do you run a peer line backwards?

If you know that flats in a building sell for Rs 10,000 a square foot and one sold for Rs 1.2 crore, you can tell its size without measuring it: 1,200 square feet. A peer line works the same way. When the market prices software companies at a fixed multiple of their Rule of 40A score for software companies: revenue growth rate plus free cash flow margin, both in per cent. Forty or more is the conventional bar for a healthy balance of growth and cash generation. score, any observed price tells you the score the market is assuming. Rs 600 crore over Rs 50 crore is 12x ARR, and 12x over 0.25 is a score of 48.

What is the price paying for that the company does not yet earn?

Run the line forwards with the actual numbers. Growth of 55 plus a margin of minus 30 is a score of 25, worth 6.25x ARR, or Rs 312.5 crore. The gap of Rs 287.5 crore is what the market pays today for the company moving its margin from minus 30% to -7%, a 23-point improvement, without giving up growth. An investor buying at Rs 600 crore should ask how plausible that improvement is and how soon it must arrive.

How far can you trust the line?

A ten-company scatter fitted with one slope is a rough guide. The line explains the middle of the peer set well and the edges badly, so a company at either extreme of growth or margin will often sit far from it for reasons the score does not capture. The score also weights a point of growth the same as a point of margin, which markets do not always do. Treat the implied margin as a question to put to management rather than a fact about the company.