Venture Capital puzzles, solved step by step

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.

Rs 5 crore, which is 10% of the round. Selling 25% for Rs 50 crore values the company at Rs 200 crore after the round. If you sit out, your 10% becomes 7.5%. To get back to 10% you need another 2.5% of a Rs 200 crore company, which costs Rs 5 crore. The general rule: to hold your stake, take the same share of the round as you own of the company.

Why does your stake fall to 7.5% if you sit out?

Think of a pizza cut into ten slices, one of them yours. If the owner adds enough new pizza that the old one becomes three quarters of the total, your slice is unchanged in size but now a smaller share of the whole. A new round does not take shares away from you; it adds shares for someone else, so every existing holder is scaled down by the same factor, here 0.75. Ten per cent times 0.75 is 7.5%, and the other holders' 90% becomes 67.5%.

Why is the answer exactly 10% of the round?

Do the sum, then see the pattern. The round sells 25% for Rs 50 crore, so the post-money is Rs 200 crore and 2.5% costs Rs 5 crore. Taking 10% of the round gives you 10% of the new shares, and you already hold 10% of the old ones, so you hold 10% of everything. This is what a pro rata rightA right, usually written into the investment terms, that lets an existing investor buy a share of a new round equal to its current ownership, so its stake is not diluted. gives an investor: the option to take its ownership share of each new round. It works the same at any round size.

When would a fund choose not to take its pro rata?

The arithmetic says what it costs; it does not say it is worth paying. Rs 5 crore at a Rs 200 crore post-money is a new investment decision at a higher price, and a seed fund with limited reserves may prefer to back a new company instead. The limitation of the clean answer is that it assumes the round stays at Rs 50 crore with your cheque inside it. If your money comes on top of a Rs 50 crore round from others, the round grows and you need slightly more to hold 10%.