Venture Capital puzzles, solved step by step

The preference is about Rs 73.47 crore, and conversion wins only above an exit of about Rs 293.9 crore. Rs 50 crore compounding at 8% for five years is 50 x 1.08 to the power 5. Converting gives 25% of the exit, which beats Rs 73.47 crore only when the exit exceeds 73.47 divided by 0.25. Without the dividend the break-even would be Rs 200 crore.

How does an unpaid dividend change the preference?

Think of a loan where the interest is not paid each year but added to what you owe, so next year's interest is charged on the bigger amount. A cumulative dividend that accrues instead of being paid works the same way: each year's 8% is added to the preference, and the next year's 8% is charged on the larger figure. After one year the preference is Rs 54 crore, after two Rs 58.32 crore, and after five Rs 73.47 crore, about 47% more than was invested.

What happens between Rs 200 crore and Rs 294 crore?

In that band the investor takes the preference rather than converting, and the founders and common holders feel it. At an exit of Rs 250 crore, a plain 1x preference holder would convert and take Rs 62.5 crore; with the accrued dividend the investor takes Rs 73.47 crore instead, and the extra comes out of the common holders' share. The accrued dividend is a return on the investment that is paid whether or not the company has grown, which is why founders negotiate hard against it or ask for it to be non-cumulative.

Name the assumptions. The answer takes the dividend as forfeited on conversion, which is the usual drafting, and the preference as non-participating. If the dividend were also paid on conversion, the investor would convert at a lower exit; read the actual terms before trusting any break-even.

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.

Contribution is Rs 90 crore, a 75% margin on revenue, and the company is valued at 8.3x revenue and 11.1x contribution. A 12% take rate on Rs 1,000 crore of GMV is Rs 120 crore of revenue. Payment costs of Rs 20 crore and refunds of Rs 10 crore leave Rs 90 crore. The 1x GMV headline is the same price as 8.3x revenue.

Why is GMV not the company's revenue?

A property broker who helps sell a Rs 1 crore flat does not earn Rs 1 crore; she earns her commission. GMVGross merchandise value: the total value of goods or services sold through a marketplace, before the platform takes its cut. is the value flowing through the platform, and only the take rate, here 12%, is the platform's revenue. On Rs 1,000 crore of GMV that is Rs 120 crore. The other Rs 880 crore belongs to sellers, so a multiple of GMV prices something the company never keeps.

What is left after the costs that scale with every order?

Payment processing costs 2% of GMV, Rs 20 crore, and refunds the platform absorbs cost 1%, Rs 10 crore. Both are charged on GMV but paid out of revenue, so a 3% cost on GMV eats a quarter of a 12% take rate. Contribution is Rs 90 crore: 75% of revenue, but only 9% of GMV. This is the money available to pay for marketing, salaries and offices, and eventually profit.

What would you say about the valuation?

That the headline multiple flatters the price, and the real question is what the contribution can grow into. Paying 11.1x contribution is reasonable only if contribution grows fast or the take rate can rise without losing sellers. Two marketplaces at 1x GMV can be wildly different prices: one with a 25% take rate is valued at 4x revenue, one with a 5% take rate at 20x. Always convert GMV multiples into revenue and contribution before comparing companies.

About 45%, below a coin flip. Exactly two pilots convert in three ways: pilots 1 and 2 only, 0.6 x 0.5 x 0.7 = 0.21; pilots 1 and 3 only, 0.6 x 0.5 x 0.3 = 0.09; pilots 2 and 3 only, 0.4 x 0.5 x 0.3 = 0.06. All three convert with probability 0.09. Adding the four gives 0.45.

How do you make sure you count every way to survive?

Think of a cricket team that needs two of its three openers to score fifty. You would list who scores and who does not, because each opener's failure matters to the case where the other two succeed. List the outcomes that satisfy the condition, write each as a product of the chance each pilot converts or does not, and add them. At least two out of three means exactly two, which can happen three ways, or all three.

Why do the quick shortcuts fail?

Multiplying the two best pilots, 0.6 x 0.5, gives 30% and forgets that pilots 1 and 3, or 2 and 3, also keep the company alive. Adding the three pair products, 0.30 + 0.18 + 0.15, gives 63% and makes the opposite error. Each pair product already includes the case where the third pilot converts too, so the all-three outcome is counted three times and must be taken off twice: 0.63 minus 2 x 0.09 is 0.45. That correction gives the same answer as the list, which is a useful check in the room.

What would you tell the investment committee?

That three pilots which each sound promising still leave the company more likely to fail than survive. The answer also depends heavily on independence: if the pilots share a buyer type or a product gap, they tend to succeed or fail together, and the real survival chance could be noticeably higher or lower. Ask what the pilots have in common before trusting the 45%.

Total dilution is 48.8%, not 60%. Each round takes 20% of whatever the holder owns going into it, so the holder keeps 80% each time and the keeps multiply. 0.8 x 0.8 x 0.8 is 0.512, so a founder who started with 100% holds 51.2% after three rounds. The rounds compound in the founder's favour compared with simple adding.

Why can you not add the percentages?

A shop that cuts a price by 20% three times does not sell the item at 40% of the original; each cut is taken on an already reduced price, so it ends at 0.8 x 0.8 x 0.8, 51.2%. Dilution works the same way: each round takes 20% of the stake you hold at that moment, and that stake is smaller every time, so the keeps multiply. After the first round you hold 80%; the second round takes 20% of that, 16 points, leaving 64%; the third takes 12.8 points, leaving 51.2%.

Where does this matter in a real cap table?

Everywhere a founder plans ahead. Because dilution compounds, each later round takes fewer percentage points than the one before even at the same rate: 20 points, then 16, then 12.8. It also means a founder's stake shrinks more slowly than the headline numbers suggest, which is why a founder can raise several rounds and still hold a meaningful share: at 20% a round it takes 7 rounds to fall below a quarter. Rounds of different sizes multiply the same way: a 20% round followed by a 25% round is a total dilution of 40%, not 45%.

One honest caveat: this assumes every holder is diluted equally. Option pool top-ups, anti-dilution protection and investors taking up their pro rata rights all change who absorbs each round, so a real cap table should be built line by line.

About 23.7% after five years and about 5.6% after ten. Each year the company survives with probability 0.75, and the years are independent, so the chances multiply: 0.75 to the fifth is 0.237. Ten years is that number squared, 0.237 x 0.237, about 0.056. Half the companies are gone before the end of year three.

Why do you multiply survival rather than add up the deaths?

Think of a batch of 100 phones, each with a one in four chance of breaking in every year you own it. In year one about 25 break and 75 are left. In year two the 25% applies to those 75, not to the original 100, so about 19 break and 56 are left. A yearly death rate only acts on the companies still alive, so survival shrinks by the same factor each year instead of falling by the same amount. Adding 25% five times gives 125%, and a probability above 100% is the sign you are using the wrong operation.

How do you get 0.75 to the fifth in your head?

Build it from squares. 0.75 squared is 0.5625, call it 0.56. Squared again, 0.56 x 0.56 is about 0.316, which is year four. One more 0.75 takes 0.316 to 0.237 for year five. Year ten is year five squared, so once you have 0.237 the second answer is one step: 0.237 x 0.237 is about 0.056. Saying the squaring route out loud shows the interviewer a method rather than a memorised number.

What does a flat death rate mean for a seed portfolio?

Two more numbers fall out of the same 25%. The average company lives four years, one over the yearly death rate, and half are gone within about 2.4 years, where 0.75 to the n crosses one half. A seed fund of 30 companies with this death rate expects only about 1.7 of them alive at year ten, which is why seed funds are sized for most companies failing. Say the limitation too: real death rates are not flat. They are highest in the first two years and fall for companies that find a market, so a flat 25% overstates late deaths and understates early ones.

The price is Rs 434.78 a share and the investor gets 2,87,500 new shares. The Rs 50 crore pre-money is divided across 11.5 lakh shares, the 10 lakh existing plus the 1.5 lakh pool, so each is worth Rs 434.78. Rs 12.5 crore buys 2,87,500 shares, 20% of the 14,37,500 after the round. With the pool left out of the pre-money the price would be Rs 500.

Why does the pool change the price but not the headline valuation?

Picture four friends agreeing that a flat is worth Rs 1 crore, and then agreeing, inside that same Rs 1 crore, to set aside a fifth room for a flatmate who has not arrived yet. The value of the flat has not moved, but each friend's share of it is smaller. A pool created inside the pre-money is paid for entirely by the existing holders, because the fixed pre-money value is spread across more shares before the new money comes in. This is the option pool shuffleSetting the size of the employee option pool inside the pre-money valuation, so the dilution from the pool falls on existing shareholders rather than on the new investor., and the price falls from Rs 500 to Rs 434.78 even though the term sheet still says Rs 50 crore.

What is the founders' real pre-money, and what does each party own?

Value the shares the founders actually hold. 10 lakh shares at Rs 434.78 is Rs 43.48 crore, so the founders have in effect accepted a pre-money of Rs 43.48 crore, not Rs 50 crore. The Rs 6.52 crore gap is the pool, valued at the round price. A 2.5 lakh pool on the same terms would cut their real pre-money to Rs 40.00 crore, which is why founders negotiate the pool size as hard as the headline.

Then give the ownership table, because the interviewer will ask for it. After the round there are 14,37,500 shares: founders hold 69.6%, the pool 10.4% and the investor 20.0%. The investor's 20% is fixed by Rs 12.5 crore over a Rs 62.5 crore post-money; the pool only decides who inside the other 80% gives it up. Had the same pool been created after the round, the investor would share the dilution: founders 71.4%, investor 17.9%, pool 10.7%.

Outside investors should cut the chance the company is good from 50% to 12.5%. Take 200 seed companies: 100 good and 100 bad. The fund backs 90 good and 30 bad ones, and passes on 10 good and 70 bad. A pass therefore comes from a good company 10 times out of 80. An insider investing, by contrast, lifts the chance to 75%.

Why does one fund's decision carry so much information?

Imagine a restaurant owner who eats at her own restaurant nearly every day, and then one week stops. Regulars notice, because she knows the kitchen better than anyone. An existing investor has a board seat, the monthly numbers and a view of the team, so its choice to follow on or not is a signal from the best-informed party in the room. This is the signalling riskThe damage to a startup's fundraising when a well-informed existing investor declines to invest again, because outsiders read the decision as bad news. founders weigh when they take seed money from a large multi-stage fund.

How do you turn the percentages into the answer without a formula?

Use counts, not probabilities; they are harder to get wrong under pressure. Start with 200 companies because it makes every branch a whole number. Of 200, the fund passes on 10 good and 70 bad companies, so a pass is compatible with a good company only 10 times in 80. The same tree answers the mirror question for free: of the 120 companies it backs, 90 are good, so an insider investing lifts the chance from 50% to 75%.

When is the insider's pass weaker evidence than this?

Say the limit before the interviewer does. The numbers assume the fund passes only for reasons of quality. A fund that has run out of reserves, or whose cheque size no longer fits the round, passes for reasons unrelated to the company, and the fall from 50% should then be much smaller. That is why a good outside investor asks why the insider passed before reading the pass as a verdict, and why founders prefer insiders who state their follow-on policy in advance.

190 one-to-ones in all, and 150 of those pairs never meet if talk stays within tables. Each of 20 founders pairs with 19 others, 380 counted from both sides, so 190 pairs. A table of five holds 5 x 4 / 2 = 10 pairs, and four tables hold 40. That leaves 190 minus 40, or 150 pairs, about 79% of all possible meetings, unmet.

Why do you divide by two?

Think of handshakes at a wedding. If you asked every guest how many hands they shook and added up the answers, each handshake would be counted twice, once by each person in it. A pair is one meeting seen from two sides, so the number of pairs among n people is n times (n minus 1), halved. For twenty founders that is 20 x 19 / 2, which is 190.

How many pairs does the seating leave out, and why is it more than three quarters?

Count what the tables allow, then subtract. A table of five holds 10 pairs, so four tables hold 40. Splitting a group into four tables does not cut the meetings to a quarter; it cuts them to about a fifth, because pairs grow with the square of group size. 40 out of 190 is 21%, so 150 pairs never meet. Check it from one founder's seat: each founder meets 4 people and misses 15, and 20 x 15 / 2 is also 150.

Why would a venture interviewer ask about pairs?

Pair counting sits under network effects. A marketplace with n users has about n squared over two possible connections, which is why tripling users multiplies the possible connections roughly ninefold. It is also why platform teams at funds run founder dinners in rotating rounds: moving people between tables is the cheapest way to raise the share of pairs that meet. Say the limit as well: a possible connection is not a valuable one, and most of the 190 pairs would have little to discuss.

About 1.97 and about 0.48. For the first, the rule of 72 says 7% doubles money in about 10.3 years, so ten years gives just under 2. For the second, ln 0.93 is about minus 0.0725, ten years of it is minus 0.725, and e to that is about 0.48. They are not reciprocals because 0.93 is not 1 over 1.07: undoing a 7% rise takes only a 6.5% fall.

How do you get each number without a calculator?

Start with the one you know. The rule of 72A shortcut for compounding: money growing at r per cent a year doubles in roughly 72 divided by r years. says money growing at r% doubles in about 72 over r years, so at 7% it doubles in about 10.3 years and ten years leaves you just short of 2. For the fall, work in natural logs, which turn compounding into adding. ln(1 minus x) is about minus x minus half of x squared, so ln 0.93 is about minus 0.07 minus 0.00245, which is minus 0.0725. Ten years gives minus 0.725. e to minus 0.693 is exactly one half, and minus 0.725 is a little further down, so the answer is a shade under a half: about 0.48.

Why are the two answers not mirror images?

Everyday version first: a shirt marked up 7% and then marked down 7% ends below its starting price, because the markdown is taken on the higher price. The x squared term in the log has the same sign whichever way the rate goes, so it drags both paths down: the up path gains a little less than 7% a year in log terms and the down path loses a little more. The true mirror of a 7% rise is a 6.5% fall. Put the two paths together and 1.07 x 0.93 is 0.9951 a year, so ten years of each leaves 0.952: a round trip that still loses about 5%.

Then say why a growth investor cares. Swings cost compound growth even when the average yearly change is zero. A company whose revenue alternates between up 7% and down 7% averages zero change but ends smaller, losing roughly half the square of the swing every year. The limit is that this is a small effect at 7%; it becomes large at the 30% and 50% swings early-stage revenue can show.