The hundred points

A worked explainer built on Cap Table 101 by Ramy Adeeb, 1984 Ventures Founders Handbook. Every figure below is generated by a numpy script and checked against 2,000 randomised cases — none is typed by hand. Educational use only; not legal, tax, or investment advice.

Cap table arithmetic defeats people who can price a bond in their head. The reason is structural, and it is worth naming before we touch a number.

Percentages are defined on a base that the transaction itself changes. If you want to give a new hire five percent of the company, you cannot simply take five percent of today's share count and issue it — because issuing those shares enlarges the company, and your new hire now owns five percent of a smaller thing. The answer depends on itself. That recursion is the whole difficulty, and it shows up again, disguised, in the option pool.

The second difficulty is a category error. A financing round has two outputs: a valuation, which is a headline, and an ownership split, which is a legal fact. First-time founders negotiate the headline. Experienced ones negotiate the split. By the end of this piece you will be able to show that the same investor cheque can produce a bigger headline and a worse outcome — and to compute exactly how much worse.

Two founders incorporate and take 1,000,000 shares each — a fifty-fifty split, 2,000,000 shares in issue. A seed fund offers $2M at an $8M pre-money valuation. We will price it as a priced equity round, because a priced round makes every mechanic visible. (Most real seed money arrives as a SAFE, which defers this arithmetic rather than avoiding it — more on that at the end.)

Three steps, in strict order. Each one feeds the next.

Dilution is a multiplier, not a subtraction

This is the single most common modelling error, and it costs people real money in later rounds. Dilution is the share of the post-transaction company represented by the newly issued stock: 500,000 / 2,500,000 = 20.00%. It does not get subtracted from your stake. It gets multiplied into it.

Each founder keeps 0.80 of whatever they had. Hold onto that retention factor — in Section Six we multiply four of them together and the result surprises most people.

The company lands its first engineer and offers her five percent. There is no option pool, so the board must authorise and issue fresh shares. How many?

The instinct is 2,500,000 × 5% = 125,000. That is wrong, and it is wrong in a specific direction — it shortchanges the employee. Issue 125,000 shares and she ends up with 4.762%, not five percent, because her own shares enlarged the denominator she is measured against. Solving the recursion gives 131,579 shares — 6,579 more than the naive answer.

The highlighted row is why option pools exist. The investor bought twenty points and now holds 19.00%, and will lose another slice with every subsequent hire. No fund will sign up to open-ended dilution from a hiring plan it cannot see. So the investor asks for the hiring plan to be priced into the round.

The fix is an option pool: a reserved block of authorised-but-unissued shares, typically ten to fifteen percent of the post-round company, sitting on the cap table as its own line. Grants to employees come out of the pool rather than being newly issued, so the fully diluted share count does not move and nobody is diluted by a hire.

That much is uncontroversial and genuinely useful. The consequential part is a question the term sheet answers in a single clause: whose points does the pool come out of?

Run it. The investor wants 20.00% and a 10.00% pool, so the founders' 2,000,000 shares must represent the remaining 70.00%. That fixes the fully diluted count, and everything else follows.

The pool has quietly repriced the round. The investor still writes $2M and still receives 20.00% — but at $3.50 per share instead of $4.00, a 12.5% discount. The $8M pre-money on the term sheet is not the price at which the founders' stock changed hands.

The number the term sheet does not print

Ask what the founders' existing stock is actually being valued at, and the fog clears. Multiply their shares by the real price per share: 2,000,000 × $3.50 = $7M. There is a general form, and it is the most useful single line in this piece:

Nothing here is underhanded. The pool is a real cost of building the company, and someone has to bear it; investors argue, reasonably, that hires made after their money arrives create value they have already paid for. But it is a price term dressed as an administrative one, and it is negotiable along two axes: the size of the pool, and which side of the money it sits on.

Now the pool does its job

Hire the same engineer at five percent. Her 142,857 shares move out of the pool rather than being issued fresh. Fully diluted shares stay at 2,857,143. The investor is still at 20.00%, the founders still at 35.00% each, and the pool drops to 5.00%. Nobody was diluted by the hire — because the founders already paid for it, in advance, in Section Four.

One tidy postscript. If the company is acquired with pool shares still unissued, those shares are typically cancelled and everyone else's ownership rises. The size of that rise is routinely misstated. With 5.00% of the pool unallocated, each founder goes from 35.00% to 36.84% — a gain of 1.84 percentage points, which is a 5.26% relative increase. "Everyone gains five percent" is true only in the relative sense, and it is the kind of ambiguity that ends up in a distribution schedule.

Everything above is one path through a three-variable space. Move the variables. The bar at the top of the page redraws as you go, and the readouts give you the numbers you would need to argue your case in the room.

Two experiments worth running deliberately. First, set the pool to zero: effective pre-money equals headline pre-money exactly, which is the only configuration in which the term sheet's front page tells the truth about price. Second, hold the pool at ten percent and push the pre-money up: the gap between headline and effective widens in absolute dollars, because a fixed percentage carve costs more when the company is worth more.

Here is the payoff. Two funds bid for the same $2M round. Fund A offers $8M pre-money with a 10% pool. Fund B offers $7.5M — half a million lower — with a 5% pool. Every founder's instinct, and most founders' actual behaviour, is to take Fund A.

Fund B's headline is $0.5M lower and it leaves the founders 3.95 percentage points better off. Those points are not static, though — they get diluted alongside everything else in the rounds that follow, so their eventual worth needs carrying forward. Push the company through the Series A, B and C in the next section and the seed-round gap survives at 0.4918 of its original size.

Follow Founder A from incorporation to a $500M exit through a conventional financing path. Each round has an investor stake and a pool top-up; together they define a retention factor, and the retention factors compound.

The four retention factors are 0.70 × 0.75 × 0.79 × 0.83 = 0.3442. Founder A keeps 34.4% of her starting ownership — 17.21% of the company, down from fifty. Now compare that with the additive intuition. Adding the dilutions gives 30 + 25 + 21 + 17 = 93%, which would imply she is left with just 3.5%. She actually holds 17.21% — 4.92× what that arithmetic predicts.

Both directions of this matter in a negotiation. Founders who add the dilutions panic early and raise too little. Founders who ignore compounding entirely are surprised at Series C to find their combined stake below the threshold where their votes decide anything.

Everything above treats a percentage of the company as a claim on that percentage of an exit. It is not. The model here is the right first model, and it is incomplete in ways that reverse conclusions rather than merely refining them.

The source this piece is built on is a good one — clear, honest, and written by someone who prices these rounds for a living. It also contains errors, which is normal for anything with arithmetic in it and is the reason auditing is a skill rather than an insult. Three candidate defects follow. One of them is not a defect. Identify which, and quantify the other two.