Cap table math

What a cap table actually is

A cap table — short for "capitalization table" — is a structured record of who owns what fraction of a company. At its simplest, it's a list of holders and their shares, summing to the total. In practice, it gets more complex because companies have multiple classes of stock (common vs preferred, multiple preferred series), different categories of shares (issued vs reserved vs vested), and dilution events that change the math over time.

Before doing the math, get the vocabulary right. These distinctions trip up first-time founders and even some investors:

Founder ownership over time

The natural mental model is that founders start at 100% and get diluted from there. The cleaner model is: founders own a fixed number of shares, and their percentage decreases as the company issues more shares to other holders. Their share count doesn't change (unless they sell or have shares clawed back); the denominator grows. This framing helps with everything that follows.

The Pipework founders started with 10,000,000 shares between them (5,000,000 each). After all the dilution events we'll work through in this module, they still own exactly 10,000,000 shares. Their percentage drops because the total share count grows from 10 million to 25 million to whatever it eventually becomes. Once you internalize this, the dilution math becomes much less mysterious.

The basic per-share math

Everything in cap-table mechanics ultimately reduces to per-share math. The key relationships:

The third relationship is the one that converts a "valuation" into a "share count." If the company has 10 million pre-money shares and the pre-money valuation is $20M, then each existing share is worth $20M ÷ 10M = $2. When the new investor's money comes in at $2 per share, they get Investment ÷ $2 new shares.

A worked example — first priced round

Pipework's seed round: $2M raised at an $8M pre-money valuation, so $10M post-money. The founders own 10,000,000 shares between them. Walk through the math:

That's the full mechanic for a priced round without any option pool complications. The arithmetic is straightforward. The next section adds the wrinkle that almost every real term sheet has: the option pool.

The option pool shuffle, computed

Module 02 mentioned the option pool shuffle. Module 05 named it. Here is the full mechanic with numbers.

Most term sheets include a clause requiring the company to set up or expand an option pool before the new money goes in — that is, the pool is created pre-money. Why does this matter? Because the pool counts as part of the pre-money share count when calculating the new investor's price per share. Increasing the pre-money share count reduces the price per share, which means the new investor gets more shares for their money, which means the existing shareholders are more diluted.

The investor's actual position: "You and I agreed the company is worth $X pre-money. We also agreed there needs to be an option pool of Y% post-money. I'm not paying for that pool — you are. Set it up before my money comes in."

The same round, with a 12% option pool

Same Pipework seed round: $2M raised at an $8M pre-money valuation, $10M post-money, 20% investor ownership. Now add the requirement that a 12% option pool (measured post-money) be established pre-money. The new mechanics:

Comparison — without and with the pool

The full 12% of the pool comes out of the founders' percentage. The investor's 20% is unchanged. The pool's existence reduces the price per share (from $0.80 to $0.68), which means the investor gets more shares for the same $2M — but those additional shares dilute the founders, not the investor.

Dilution across multiple rounds

Now build up the full Pipework cap table across three rounds. The arithmetic is the same as Sections 02 and 03 applied repeatedly. At each round, we start with the prior post-money cap table, expand the option pool if required, calculate the price per share, and issue new shares to the new investor.

Round 1 — Seed ($2M at $10M post-money, 12% pool)

This is the round we just worked through in Section 03. The post-Round-1 cap table:

Round 2 — Series A ($15M at $75M post-money, pool refreshed to 12% post-money)

Pipework now has 14,705,882 shares outstanding. The Series A investor will take 20% of the post-money. The term sheet also requires the option pool to be refreshed to 12% of the post-money (the Round 1 pool has largely been granted out, so the company tops it back up to 12% to support continued hiring). Both the pool refresh and the new investor are priced at the same time.

The clean way to solve this is algebraically, in one pass — no mid-example corrections. Define the target post-money percentages, then solve for the one unknown.

Solving for the total in one step — fixed shares ÷ their target percentage — avoids any iteration. The pool refresh is built into the 68%/12%/20% split, so it comes out of the existing holders' percentages, not the new investor's. That is the option pool shuffle again, now at Series A.

The seed investor's percentage went from 20% to 15.5% — diluted by the option pool refresh and the Series A investor's 20%. This is exactly the math from the typical-founder-dilution table in Module 03: each round dilutes everyone existing in proportion to how much new equity is being issued.

The preference stack at exit

Module 05 introduced the concept of liquidation preferences; Module 03 showed a worked example at three exit prices. This section works through the underlying math.

The order of payments in a typical sale of a venture-backed company:

1. Preferred shareholders first, in reverse order of investment (most recent series first, oldest last). Each preferred series gets the greater of (a) their liquidation preference, or (b) what they would get by converting to common.
2. Common shareholders (founders, employees who exercised options) receive whatever remains after all preferences have been paid.

The "or" in step 1 is the optionality that makes preferred stock work as a security. Each preferred shareholder gets to choose, after seeing the deal price, whether to take their preference (the downside protection) or convert to common (the upside participation). They always pick whichever is better for them.

The break-even point

For a 1× non-participating preferred holder, there's a price at which their preference equals what they'd get from conversion. Below that price, they take the preference; above it, they convert.

For Pipework's Series A investor (the most recent round in our running example), the break-even is exactly the post-money valuation of their round — $75M. Below that, they take their $15M back. Above that, they convert and take 20% pro-rata. This is why post-money valuations matter to investors: a $75M post-money is the price below which the investor is "underwater" on the conversion-pro-rata path.

Multi-stack waterfalls

Things get more complex when there are multiple preferred series. Each series has its own preference. The waterfall computes payouts in order, with each series taking the better of their preference or their pro-rata conversion. The conversion calculation for one series depends on what other series have done, because their conversion shares get added to the denominator.

In practice, the waterfall is solved iteratively: assume all preferred convert, compute the pro-rata payouts, check whether each preferred series would have done better by taking their preference instead, flip any that would, recompute the conversion math with the remaining preferred holders. Repeat until stable. Modern cap-table tools (Carta, Pulley, Capdesk) do this automatically; the manual version is doable but tedious for more than two preferred series.

For the Pipework example with one seed series and one Series A, the calculation is manageable by hand. We'll work through it in Section 08.

The participating-preferred case

A 1× non-participating preferred holder gets the greater of preference-or-conversion. A 1× participating preferred holder gets both: they get their preference back AND then participate pro-rata in whatever's left. This is the "double-dip" — and it materially worsens founder economics at every exit price.

Participating preferred math

Consider an investor who put in $15M for 20% of the company on a 1× participating basis. Suppose the company sells for $200M.

The participating-preferred holder takes 26% of total exit proceeds vs. their 20% nominal ownership. The common shareholders (founders, employees) get 74% rather than 80%. That 6-percentage-point shift toward the investor is the cost of participation rights.

Why this gets worse at higher exit prices

Counterintuitively, participating preferred matters more in good exits than in bad ones — because in bad exits, the preference dominates anyway. Walk through a few price points:

In every case at or above break-even, the participating investor's "extra" over the non-participating outcome is exactly $12M. That is not a general law — it is specific to this example, where the participation percentage (20%) and the preference ($15M) are both fixed: the extra equals the preference times the share that flows back out to common, $15M × (1 − 20%) = $12M, the same at every price above break-even. Change the ownership percentage or the preference and the constant changes. What is general: above break-even, participation transfers a fixed dollar amount to the investor, so its percentage bite on common shrinks as the exit grows even though the dollars stay the same. Below break-even, the preference dominates and participation adds nothing.

Weighted-average anti-dilution

Module 05 distinguished weighted-average broad-based anti-dilution from full ratchet. This section works through the math of the broad-based weighted-average mechanism — the standard for early-stage rounds.

Anti-dilution adjusts the conversion price of the prior preferred series when a future round prices below their original price. The "weighted-average" part means the adjustment is sized in proportion to how big the new (down) round is relative to the existing capitalization. A tiny down round triggers a small adjustment; a large down round triggers a bigger one. This is fairer than full ratchet (which adjusts all the way to the new low price regardless of round size) and is the industry standard.

A worked example

Anti-dilution protects a prior preferred series when a later round prices below that series' conversion price. So the example needs a prior series with a high conversion price and a later down round beneath it. Use Pipework's Series A as the prior preferred — its conversion price is $3.94 per share (from Section 04) — and suppose the company later raises a $20M Series B at $2.00 per share, well below the Series A price. (The seed, at $0.68, sits below $2.00 and so is not triggered; only the Series A is.)

The Series A holder's conversion price dropped from $3.94 to $3.27 — a 17% reduction. With full ratchet, it would have dropped to $2.00 (the Series B price), a 49% reduction. The weighted-average mechanism is roughly a third as harsh in this example. The protection scales with the size of the down round: a much larger Series B would have produced a larger adjustment, closer to the full-ratchet result; a much smaller Series B would have produced almost no adjustment.

The Pipework exit waterfall — full math at four prices

The capstone. Take the Pipework post-Series-A cap table from Section 04 — both preferred series have 1× non-participating preferences — and compute the actual exit waterfall at four price points: $30M, $75M, $250M, and $1B. The investor amounts and ownership:

• Seed investor: $2M invested, 15.5% ownership, $2M preference
• Series A investor: $15M invested, 20.0% ownership, $15M preference
• Option pool (granted to employees): 12.0%
• Asha + Marco (common): 52.5% combined

Exit 1 — $30M (below combined preferences)

The waterfall is solved in order of preference seniority, with each preferred holder taking the better of its preference or its pro-rata conversion. At $30M:

At $30M, the founders each take home about $4.9M. The Series A investor recovered their full $15M; the seed investor made a modest return on conversion.

Exit 2 — $75M (at the Series A break-even)

$75M is exactly the Series A post-money valuation. This is the indifference point: Series A investor's preference ($15M) equals their pro-rata share (20% × $75M = $15M). Below this price they take preference; above they convert. At the break-even, the result is the same.

Exit 3 — $250M (good outcome)

At $250M, both preferred series convert (both have pro-rata above their preferences). All payouts are pure pro-rata.

Exit 4 — $1B (big outcome)

Same proportional split — at $1B exit, all preferred convert, and the math is just pro-rata × $1B. Each founder takes home about $263M.

What the four scenarios show

The breakdown across exit prices reveals the structural logic of preferred stock. At low prices, preferences dominate and common takes very little. As prices rise above the largest preference, preferred investors increasingly convert, and the payouts converge toward pure pro-rata ownership percentages. The founders' share rises non-linearly: from $4.9M each at $30M exit, to $19.7M at $75M, to $65.7M at $250M, to $262.7M at $1B. The first dollar above the preferences is much more valuable to common holders than dollars below them.

Test your understanding

Six questions on the cap-table math and exit waterfalls. The arithmetic is straightforward; the conceptual point of each question is to make sure you can see what's actually happening rather than just plugging numbers into a formula.