Venture Capital puzzles, solved step by step

About 12% for 20 bets and 59% for 5 bets. In both strategies a single hit returns at least the whole fund: 20x on 5% is 1x, and 20x on 20% is 4x. So a strategy loses money only when every bet misses. Twenty bets all miss with chance 0.9 to the twentieth, 12.2%; five bets all miss with chance 0.9 to the fifth, 59.0%. Expected value is 2x either way.

When does each strategy lose money?

Buying one lottery ticket in each of twenty draws and buying four tickets in each of five draws can cost the same and win the same on average, yet the second leaves you empty-handed far more often. Find the outcome that loses money first: here one hit already pays back the whole fund in both strategies, so losing means getting no hits at all. With 20 bets each worth 5% of the fund, a hit returns 20 x 5% = 1x the fund, exactly the money back. With 5 bets of 20%, a hit returns 4x. Either way, zero hits is the only losing outcome.

If the expected value is the same, why does it matter?

Because a fund's investors live through one draw, not the average of many. Concentration leaves the expected multiple at 2x but stretches the outcomes: B loses money 59% of the time, yet also returns 4x or more 41% of the time, against 13% for A. A returns at least 3x 32% of the time and rarely does spectacularly. Neither is better in the abstract; the choice depends on how much the fund's investors can bear a blank.

What does the model leave out?

It assumes the bets are independent and identical. In practice a concentrated fund argues that it can pick better and support each company more, raising p; a diversified one argues that nobody can pick reliably at seed. Correlation also matters: if all twenty companies depend on the same funding climate, the 12% understates how often A has a blank decade. Say the result, then say which assumption you would test first.

Applied to every share, the offer implies Rs 720 crore, but it prices common shares, not the company. The Rs 1,200 crore figure was a price for preferred shares, which are paid back first in a sale and carry protections. Common is paid last, is illiquid and usually needs company consent to sell. A buyer discounts for all of that. Neither Rs 1,200 crore nor Rs 720 crore is the company's value.

Why do the two prices differ for the same company?

A first-class and a general ticket on the same train cost different amounts, but the fare gap says nothing about the train's speed. Preferred and common are different securities in the same company: preferred is paid back before common in a sale, so a rupee of preferred is worth more than a rupee of common whenever a weak exit is possible. Multiplying the preferred price by every share gives the headline Rs 1,200 crore; multiplying the common offer, 60% of that price, by every share gives Rs 720 crore. Both are prices of a security scaled up, not a measure of what the business is worth.

Where does the discount come from?

Take an illustration: preferred holders own 40% and are owed Rs 400 crore first in any sale. In a Rs 400 crore sale they take everything and common gets nothing; only above Rs 1,000 crore, where 40% of the sale beats Rs 400 crore, do the two classes share pro rata. Common holds the first loss in the bad outcomes. On top of that come illiquidity, the company's right to block or match a sale, and the lack of information rights. Each adds to the discount, and none says the company is worth less than at the last round.

When would a secondary price be a real markdown signal?

When the discount is to the same security, or much larger than the structure explains. A buyer offering a deep discount for preferred shares from the latest round is a stronger signal, because the security is identical to the one that set the headline. Ask which class is being sold, how big the preference stack is relative to the likely exit range, and how much stock is on offer; a small, forced sale tells you about the seller's need for cash as much as the company.

1.25 on the headline numbers, and 0.75 once the one-off services are removed. The magic number is the quarter's revenue increase, annualised, divided by the previous quarter's sales and marketing spend. Headline: Rs 5 crore x 4 = Rs 20 crore over Rs 16 crore is 1.25. But only Rs 3 crore will recur; Rs 12 crore over Rs 16 crore is 0.75. Two crore of services flattered the efficiency by two thirds.

What is the magic number measuring?

A coaching centre that spends Rs 1.6 lakh on advertising one month and signs students paying an extra Rs 50,000 a month in fees has bought Rs 6 lakh a year of fees for Rs 1.6 lakh. The magic number is the annualised increase in recurring revenue divided by the sales and marketing spend that produced it, usually the previous quarter's. It is a quick read on how efficiently a company turns sales spend into new revenue. Annualise because the spend buys a full year of revenue from each new customer, not just one quarter.

Why does the one-off revenue matter so much?

Because the measure is built on a small difference. A Rs 2 crore swing in a Rs 5 crore increase is 40% of the numerator, so a one-off item moves the magic number far more than it moves revenue. Read as recurring revenue, a magic number of 1 means a year of the new revenue repays the quarter's sales spend; 1.25 suggests about 9.6 months, but the true 0.75 means about 16 months, and that is before the cost of serving the customers. Some investors multiply by gross margin for that reason: at a 75% margin the recurring figure becomes 0.56.

Ask three things before trusting the number: is the revenue recurring, is the spend fully counted, including sales salaries and commissions, and is one quarter representative. A single strong quarter can follow a deal that slipped from the quarter before, so investors look at a rolling average across several quarters.