Venture Capital puzzles, solved step by step

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  1. 004A founder owns 100% before a seed round that sells 20%. At the Series A the investor buys 25% and a 10% option pool is created, both measured post-money and both diluting existing holders. If the founder wants to keep at least 50% after the Series B, what is the most the Series B can sell?Dilution and ownership riddlesHardSeed and early-stage VCSeries A to C VC

    Try it first

    What does the founder own going into the Series B?

    Show the worked solution

    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.

    The Series A leaves the founder at 52%, so only 2 points of room remain100%Start80.0%After seed52.0%After Series A50.0%After Series B50%floorFounderSeedSeries APoolSeries BSeries B can sellat most 3.85%1 - 50/52Every stage shrinks all existing holders by the same factor: 0.80, then 0.65, then 0.9615.
    The founder falls from 100% to 80% at the seed and to 52% at the Series A, when the investor's 25% and the 10% pool come out together; a Series B selling 3.85% takes the founder to exactly 50%.

    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.

    The relationship
    0.80×0.65×(1−x)≥0.50  ⇒  x≤1−0.500.52≈3.85%0.80 \times 0.65 \times (1 - x) \ge 0.50 \;\Rightarrow\; x \le 1 - \frac{0.50}{0.52} \approx 3.85\%
    0.80what the founder keeps after the seed round
    0.65what existing holders keep after the Series A and the pool
    xthe share of the company the Series B sells
    What it says in wordsMultiply the keep-factors of every round and require the product to stay at or above one half.

    Where candidates lose it

    The classic loss is subtracting: 100 minus 20 minus 25 minus 10 leaves 45%, so the founder is already below 50% and there is no answer. The interviewer wants to see you multiply.

    The quieter loss is chaining the investor and the pool as if they were separate rounds, which gives 54% and a Series B limit of 7.4%. Read how the pool is measured before you calculate.

    What the interviewer asks next

    • If the pool had been created before the seed round, what would the founder hold after the Series A?
    • The Series B sells 20%. What does the founder own, and what would a pool top-up of 5% do on top?
    • Why do founders negotiate for the option pool to be counted in the pre-money?
  2. 085A founder has two offers, each raising Rs 25 crore. Offer A is Rs 90 crore pre-money and requires a new option pool of 20% of the post-money, created inside the pre-money. Offer B is Rs 80 crore pre-money with a 10% pool on the same basis. Which leaves the founders more, and what is each offer's effective pre-money?Dilution and ownership riddlesHardSeries A to C VCIndia VC

    Try it first

    Which offer leaves the founders the larger share of the company?

    Show the worked solution

    Offer B leaves the founders 66.2% against 58.3% under Offer A, and its effective pre-money is Rs 69.5 crore against Rs 67.0 crore. A pool created inside the pre-money is paid for by the existing holders. Offer A's 20% pool is Rs 23 crore of a Rs 115 crore post-money, so the founders' shares are really valued at Rs 67 crore. Offer B's 10% pool costs only Rs 10.5 crore.

    Why does a pool inside the pre-money lower the real price?

    A flat sold for Rs 90 lakh, where the seller must also leave Rs 23 lakh of new furniture for the buyer, really sold for Rs 67 lakh. A pool created inside the pre-money is paid for entirely by the existing holders, so the effective pre-money is the headline pre-money minus the pool's value. Offer A: post-money is 90 + 25 = Rs 115 crore, the pool is 20% of that, Rs 23 crore, and the founders' shares are worth 90 - 23 = Rs 67 crore. Offer B: post-money Rs 105 crore, pool Rs 10.5 crore, effective pre-money Rs 69.5 crore.

    The lower headline offer leaves the founders more once the pool is countedOffer ARs 90 crore pre, 20% poolFounders 58.3%Rs 67.0 crPool 20.0%Rs 23.0 crInvestor 21.7%Rs 25.0 crPost-money Rs 115 crore. Effective pre-money = 90 - 23.0 = Rs 67.0 croreOffer BRs 80 crore pre, 10% poolFounders 66.2%Rs 69.5 crPool 10%, Rs 10.5 crInvestor 23.8%Rs 25.0 crPost-money Rs 105 crore. Effective pre-money = 80 - 10.5 = Rs 69.5 croreFounders keep 66.2% under B against 58.3% under A: the pool is paid for by the existing holders
    Offer A's Rs 115 crore post-money splits into 21.7% investor, 20% pool and 58.3% founders, while Offer B's Rs 105 crore splits into 23.8% investor, 10% pool and 66.2% founders, so the lower headline leaves the founders more.

    What share do the founders keep under each offer?

    Take the investor's share and the pool off the whole. The founders keep one minus the investor's share minus the pool: 58.3% under Offer A and 66.2% under Offer B. The investor gets a smaller share under A, 21.7% against 23.8%, which is why the headline looks better; the extra 10 points of pool more than cancel it. This assumes the founders own everything before the round and there is no existing pool.

    The relationship
    f=1−IPre+I−pfA=1−25115−0.20=58.3%fB=1−25105−0.10=66.2%f = 1 - \frac{I}{\text{Pre} + I} - p \qquad f_A = 1 - \frac{25}{115} - 0.20 = 58.3\% \qquad f_B = 1 - \frac{25}{105} - 0.10 = 66.2\%
    fshare the founders keep
    Inew money, Rs 25 crore
    ppool as a share of post-money
    What it says in wordsWhatever the investor and the new pool take comes out of the founders' share.

    What would you push back on?

    The pool size, not the headline. A pool should be sized to the hires planned before the next round, not to a round number. If the founder can show that 10% covers the hiring plan, Offer A's pool falls to Rs 11.5 crore, its effective pre-money rises to Rs 78.5 crore and the founders keep 68.3%, better than either offer as written.

    Where candidates lose it

    Comparing headline pre-money is the whole trap: Rs 90 crore beats Rs 80 crore, so candidates pick Offer A. The pool is a second price term hidden inside the first, and the interviewer set the numbers so that it flips the answer.

    The second slip is computing the pool as a share of pre-money, 20% of 90, which gives Rs 18 crore rather than Rs 23 crore. Read which base the term sheet uses before you multiply.

    What the interviewer asks next

    • How high must Offer A's headline pre-money go before its effective pre-money matches Offer B's?
    • Why do investors want the pool inside the pre-money rather than the post-money?
    • The company already has a 5% unallocated pool. How does that change the comparison?