Venture Capital puzzles, solved step by step

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.

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.