Venture Capital puzzles, solved step by step

Puzzles: 100
Traced to a firm: 7
Topics: 12
Hard: 30

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016A company has 1 crore shares outstanding and 20 lakh vested options with a strike price of Rs 50. The shares are worth Rs 200 each. How many shares does the treasury stock method count as fully diluted, and how many does counting every option as a share give?Dilution and ownership riddlesCoreGrowth equitySeries A to C VC
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How many new shares do the options add under the treasury method?
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The treasury method gives 1.15 crore shares; counting every option gives 1.20 crore. Exercising 20 lakh options at Rs 50 brings in Rs 10 crore, and at Rs 200 a share that cash buys back 5 lakh shares. So the options add a net 15 lakh, not 20 lakh. Counting all 20 lakh ignores the strike money the option holders pay.
Why does the strike price reduce the dilution?
Suppose five friends own a flat together and a sixth may join by paying Rs 50 lakh towards a share worth Rs 2 crore. The newcomer dilutes the others, but the Rs 50 lakh he brings in offsets a quarter of that. An option holder pays the strike to get a share, and that cash is worth something to the existing owners, so only the part of the share's value not covered by the strike is true dilution. Here each option pays Rs 50 for a Rs 200 share, so three quarters of each option is real dilution, and 20 lakh x 0.75 is 15 lakh.
How does the treasury method count it?
It pretends every in-the-money option is exercised and the company spends the strike cash buying its own shares at today's price. Rs 10 crore of strike cash at Rs 200 a share buys back 5 lakh shares, so the share count rises by 20 lakh and falls by 5 lakh, ending at 115 lakh, or 1.15 crore. Counting every option as a full share gives 1.20 crore, which overstates the dilution by the 5 lakh shares the strike money pays for.
The relationship
$\text{FD} = 100 + 20 - \frac{20 \times 50}{200} = 100 + 20 - 5 = 115 \text{ lakh}$
100 basic shares outstanding, lakh
20 vested options, lakh
50 strike price, Rs
200 share price, Rs
What it says in wordsAdd every option, then take off the shares the strike money could buy back at the current price.
Counting every option as a share gives 120 lakh shares, but the Rs 10 crore paid on exercise buys back 5 lakh at Rs 200, so the treasury method's fully diluted count is 115 lakh.
How do you check that the treasury count is right?
Price the company both ways. At Rs 200 a share, 115 lakh shares is an equity value of Rs 230 crore. A buyer paying Rs 200 for all 120 lakh shares would pay Rs 240 crore but collect Rs 10 crore of strike money back, a net Rs 230 crore. The two routes agree, which is the proof that the treasury method counts exactly what the options are worth, not more. Counting all options without the cash would value the company Rs 10 crore too high.
Where candidates lose it
The quick wrong answer is 1.2 crore shares, counting every option as a share. It forgets that option holders pay Rs 50 each, and the interviewer will ask where that Rs 10 crore went.
The other slip is ignoring the options entirely because they are not yet exercised. Vested in-the-money options are a claim on the company today; say they are counted and show the buyback.
What the interviewer asks next
If the share price falls to Rs 40, how many shares do the options add?
Should unvested options be counted in a fully diluted share count for an acquisition?
How does a convertible note enter a fully diluted count?

027A company has 10 lakh shares and a Rs 50 crore pre-money valuation, and raises Rs 12.5 crore. The investor insists that a new option pool of 1.5 lakh shares be created inside the pre-money. What is the price per share, and how many new shares does the investor get?Dilution and ownership riddlesCoreSeed and early-stage VCIndia VC

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Before you calculate: what does putting the pool inside the pre-money do to the price per share?

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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.

The relationship

\text{price} = \frac{\text{pre-money}}{\text{existing} + \text{pool}} = \frac{50{,}00{,}00{,}000}{11{,}50{,}000} = 434.78 \qquad \text{new shares} = \frac{12{,}50{,}00{,}000}{434.78} = 2{,}87{,}500

pre-money	the agreed value of the company before the new money, Rs 50 crore
existing + pool	the 10 lakh shares already issued plus the 1.5 lakh pool shares counted before the round
new shares	what the Rs 12.5 crore cheque buys at that price

What it says in wordsDivide the pre-money by every share that exists before the round, including the new pool, and that is the price the investor pays.

Leaving the pool out prices the round at Rs 500 a share; counting the 1.5 lakh pool shares inside the pre-money cuts the price to Rs 434.78, so the founders' 10 lakh shares are worth Rs 43.48 crore, their real pre-money.

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%.

Where candidates lose it

The common loss is dividing Rs 50 crore by the 10 lakh existing shares and answering Rs 500, as if the pool sat outside the pre-money. The question told you where the pool sits precisely to see whether you add it to the share count before you price.

The second loss is thinking the investor pays for the pool. The investor's 20% is set by the cheque and the post-money; the pool comes out of the founders' side, and saying so is the point of the question.

What the interviewer asks next

The founders push the pool out to after the round. What is the price now, and what does each party own?
What pool size inside the pre-money would leave the founders with exactly 70% after the round?
Why might an investor prefer a larger pool now to a smaller one topped up at the next round?

055A founder owns 40% of a company worth Rs 100 crore. It raises money at Rs 300 crore post-money, selling 20% of the company. A year later it raises again at Rs 250 crore post-money, selling another 20%. What is her stake worth after each round?Dilution and ownership riddlesCoreSeed and early-stage VCSeries A to C VC
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What is her stake worth after the second round?
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Rs 40 crore today, Rs 96 crore after the first round, Rs 64 crore after the second. Each round sells 20% of the company, so she keeps 80% of her stake: 40% becomes 32%, then 25.6%. Her rupees are that stake times the post-money value: 32% of Rs 300 crore is Rs 96 crore, and 25.6% of Rs 250 crore is Rs 64 crore. Dilution cut her percentage both times; only the down round cut her value.
Why does selling 20% leave her with 32%, not 20%?
Cut a pizza into ten slices and give four to a friend. If the host then takes a fifth of every plate for a late guest, the friend loses a fifth of her four slices, not two of them. A round that sells 20% of the company shrinks every existing holder by the same fifth, so her stake is multiplied by 0.8, not reduced by 20 points. 40% x 0.8 is 32%. The second round does it again: 32% x 0.8 is 25.6%.
Her ownership falls from 40% to 32% to 25.6% as each round takes a fifth of it, while her stake's rupee value rises from Rs 40 crore to Rs 96 crore through the up round and falls back to Rs 64 crore through the down round.
If her percentage fell both times, why did her wealth rise the first time?
Because the first round was priced well above today's value. A Rs 300 crore post-money with Rs 60 crore raised means a pre-money of Rs 240 crore, so the company was repriced from Rs 100 crore to Rs 240 crore before the new money arrived. Dilution is a smaller slice; whether it costs you money depends entirely on the price the new investor pays for the slice. The second round sold 20% at Rs 250 crore post-money, which is Rs 50 crore raised on a pre-money of Rs 200 crore, below the Rs 300 crore she was last marked at. Her percentage fell by the same fifth, and this time her value fell too, from Rs 96 crore to Rs 64 crore.
The relationship
$\text{Value} = s_0 (1-d_1)(1-d_2) \times \text{Post}_2 = 0.40 \times 0.8 \times 0.8 \times 250 = 64$
s_0 her starting stake, 40%
d_1, d_2 the share of the company sold in each round, 20%
Post_2 the post-money value after round two, Rs 250 crore
What it says in wordsHer stake shrinks by what each round sells; her wealth is that stake times the latest price.
One limit is worth stating. The Rs 64 crore is a paper value at the last round's price, and it assumes her shares are worth the same per share as the investors' preferred shares, which carry preferences hers do not. In a sale below the preferences, her real payout would be less.
Where candidates lose it
The classic slip is subtracting points: 40% minus 20% is 20%, then zero after the second round. It sounds absurd once said, but candidates rushing through it say it anyway.
The second trap is reading the percentage drop as the whole story. Say both numbers each time, percentage and rupees, and point out that the first round made her richer and the second made her poorer, even though both cost her the same fifth.
What the interviewer asks next
What pre-money would the second round have needed for her value to stay at Rs 96 crore?
How would an option pool created in round one change her stake?
Why might she prefer a smaller round at a lower price to a bigger one at a higher price?
067A founder signs three post-money SAFEs before her first priced round: Rs 2 crore at a Rs 20 crore valuation cap, Rs 3 crore at a Rs 30 crore cap, and Rs 4 crore at a Rs 40 crore cap. Assume the priced round comes in above all three caps. What do the SAFE holders own just before that round, and why does the order of signing not matter?Dilution and ownership riddlesCoreSeed and early-stage VCIndia VC
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Together, the three SAFE holders own:
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30% together, 10% each, and the founder keeps 70%. A post-money SAFE converts into its amount divided by its cap, as a share of the company measured after all the SAFEs: Rs 2 crore over Rs 20 crore, Rs 3 crore over Rs 30 crore and Rs 4 crore over Rs 40 crore are each 10%. Because each percentage is fixed against that full capitalisation, a later SAFE cannot dilute an earlier one; only the founder is diluted, so the order does not matter.
What does 'post-money' fix that older SAFEs did not?
Three friends each promised a tenth of a home-cooked biryani know exactly what they get, however many friends were promised a share before them; the cook's portion is what shrinks. A post-money SAFEA simple agreement for future equity whose conversion stake is fixed as the amount invested divided by the post-money valuation cap, measured after all SAFEs convert. promises its holder a fixed percentage, amount over cap, of a company that already counts every SAFE, so SAFE holders never dilute one another and the founder carries all of it. 2/20, 3/30 and 4/40 are each 10%, and the founder goes from 100% to {founder67*100:.0f}%. Under the older pre-money SAFE, each holder's stake was measured before the other SAFEs converted, so they diluted each other and no one could read their percentage until the round.
Signed in either order, the three post-money SAFEs each take a fixed 10%, so together they own 30% before the priced round and the founder alone falls to 70%.
The relationship
$s_i = \frac{\text{amount}_i}{\text{cap}_i}: \quad \frac{2}{20} + \frac{3}{30} + \frac{4}{40} = 0.10 + 0.10 + 0.10 = 0.30$
s_i SAFE holder i's stake just before the priced round
amount_i what holder i invested
cap_i holder i's post-money valuation cap
What it says in wordsEach SAFE's stake is its own amount over its own cap, so the stakes simply add up and the founder keeps the remainder.
What happens at the priced round, and when does the 10% change?
The priced round then dilutes everyone, SAFE holders included. If the Series A sells 20% of the company, each SAFE holder goes from 10% to 8% and the founder from 70% to 56%. The cap is a ceiling on the price a SAFE converts at, so if the round is priced below a holder's cap, that holder converts at the round price and gets more than 10%, at the founder's expense again. That is why the question fixes the round above all three caps.
Two limits worth saying. The figures leave out an option pool, which is usually added before the round and also comes out of the founder's side. And the SAFE is a US instrument; Indian startups raise early money through structures such as compulsorily convertible preference shares or notes whose conversion terms vary, so read the actual conversion clause rather than assuming post-money SAFE mechanics.
Where candidates lose it
The common error is diluting each SAFE by the ones signed after it and arriving near 27%. That is how pre-money SAFEs behave; the question says post-money precisely to test whether you know the difference.
The second trap is forgetting who pays. The SAFE holders' 30% comes entirely out of the founder's stake, and founders who sign several SAFEs often discover this only when the round's cap table arrives.
What the interviewer asks next
If the Series A is priced at a Rs 25 crore post-money valuation, what does the Rs 30 crore cap holder get?
How would the answer change if these were pre-money SAFEs?
Where would a 10% option pool created before the round come from?
097A lead investor wants 20% of the company post-money, and insists on a new option pool of 10% of the post-money created before the round. The founder will not raise more than Rs 30 crore. If she raises the full Rs 30 crore, what post-money valuation does that set, what is the pre-money, and what share of the company do the existing holders keep?Dilution and ownership riddlesCoreSeries A to C VCIndia VC
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What share of the company do the existing holders keep?
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Post-money Rs 150 crore, pre-money Rs 120 crore, and existing holders keep 70%. The cheque sets the price: Rs 30 crore for 20% means the whole company after the round is 30 / 0.2 = Rs 150 crore, so the pre-money is Rs 120 crore. The pool is 10% of 150, Rs 15 crore, created inside the pre-money. Existing holders keep 70%, Rs 105 crore, which is their real price.
How does a cheque and a percentage set the valuation?
If Rs 30 buys a fifth of a pizza, the whole pizza costs Rs 150. Post-money is the cheque divided by the share it buys, and pre-money is post-money less the cheque. Rs 30 crore for 20% gives Rs 150 crore post-money and Rs 120 crore pre-money. The founder's cap on the raise works here as a cap on the valuation too: at 20%, raising only Rs 24 crore would set the post-money at Rs 120 crore.
Rs 30 crore for 20% sets a Rs 150 crore post-money; the new pool takes 10%, Rs 15 crore, inside the Rs 120 crore pre-money, so the existing holders keep 70% of the company, worth Rs 105 crore.
Where does the pool come from, and why does it matter?
The lead wants the pool created before its money arrives, so new shares for the pool are carved out of the pre-money. A pool inside the pre-money dilutes only the existing holders, so their shares are really valued at the pre-money less the pool: 120 - 15 = Rs 105 crore. The headline pre-money of Rs 120 crore is true for the company and flattering for the founders, which is why experienced founders negotiate the pool size as hard as the valuation.
The relationship
$\text{Post} = \frac{I}{s} = \frac{30}{0.20} = 150 \qquad e = 1 - s - p = 1 - 0.20 - 0.10 = 70\%$
I new money, Rs 30 crore
s lead investor's post-money share, 20%
p new pool as a share of post-money, 10%
e existing holders' share after the round
What it says in wordsThe cheque over the share it buys gives the post-money; everything not bought or set aside stays with existing holders.
One assumption to state: there is no existing unallocated pool. If there were, it would count towards the 10%, the new carve-out would be smaller, and the existing holders would keep more.
Where candidates lose it
The common slip is answering 80%, as if the investor's 20% were the only dilution. The pool is a second slice taken before the round, and the interviewer included it to see whether you count it.
The other loss is treating the pool as a percentage of what is left, which gives 72%. Read the base: here both percentages are of post-money, so they subtract directly.
What the interviewer asks next
If the pool were created after the round instead, from everyone pro rata, what would existing holders keep?
The company has 80 lakh shares before the round. What is the price per share?
The lead will accept 18% instead of 20% if the pool rises to 12%. Which is better for the founders?

100	basic shares outstanding, lakh
20	vested options, lakh
50	strike price, Rs
200	share price, Rs

s_i	SAFE holder i's stake just before the priced round
amount_i	what holder i invested
cap_i	holder i's post-money valuation cap

Try it first

Why does the strike price reduce the dilution?

How does the treasury method count it?

How do you check that the treasury count is right?

Where candidates lose it

What the interviewer asks next

Try it first

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

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

Where candidates lose it

What the interviewer asks next

Try it first

Why does selling 20% leave her with 32%, not 20%?

If her percentage fell both times, why did her wealth rise the first time?

Where candidates lose it

What the interviewer asks next

Try it first

What does 'post-money' fix that older SAFEs did not?

What happens at the priced round, and when does the 10% change?

Where candidates lose it

What the interviewer asks next

Try it first

How does a cheque and a percentage set the valuation?

Where does the pool come from, and why does it matter?

Where candidates lose it

What the interviewer asks next