Cap Table and Dilution: Method

Cap Table and Dilution: Conversion, Round Pricing, Option Pool, Anti-Dilution and the Exit Waterfall

Counting shares

The fully diluted capitalization counts every share of common stock, every option outstanding or promised, the unissued option pool and the preferred stock as converted to common stock. "Outstanding" leaves the unissued pool out. A holder's ownership is its as-converted shares over one of these two totals, and its dilution across a round is the fall of its fully diluted percentage as a fraction of the percentage before the round. This is ownership dilution. The dilution table of a prospectus (Regulation S-K, Item 506) is a different measure, the offering price against the net tangible book value per share, and is not computed here.

Safes and convertible notes

All safes and notes convert at the first priced round. Each converts at the price that gives its holder the most shares: the lowest of its cap price, its discounted price (round price × (1 − discount)) and the round price.

Post-money safe. The Safe Price is the Post-Money Valuation Cap divided by the Company Capitalization, which the Y Combinator user guide defines as the capital stock outstanding, the options outstanding and promised, the unissued option pool and all converting securities, without the pool increase of the round. Because the converting securities are in the count, a safe that converts at its cap receives purchase amount / cap of the Company Capitalization whatever the other safes do: CC = (shares before + shares of the instruments that do not convert at a post-money cap) / (1 − Σ amount / cap), and shares = CC × amount / cap. Whether a safe converts at its cap or at the round price depends on CC, and CC on those choices; the tool iterates CC = shares before + Σ max(CC × amount / cap, amount / price) to its fixed point, which is unique because the percentages sum to less than one.

Pre-money (original) safe. The cap is divided by the capitalization before the round plus the pool increase of the round, without the converting securities (the guide's table in Section B.4), so pre-money safes dilute one another and are not diluted by the new pool.

Convertible note. Principal plus simple interest, principal × (1 + rate × months / 12), converts on the pre-money safe basis. Notes differ in their capitalization definitions and interest conventions; this is one common reading, and the note itself governs.

An instrument that converts below the round price receives a shadow series (the guide's Safe Preferred Stock): the rights of the round's preferred stock with its own issue price, so its liquidation preference is the amount converted times the round's multiple.

Price per share of a round

Price = pre-money valuation / fully diluted shares before the new money. Those shares are the capitalization before the round, the conversion shares, the anti-dilution shares of earlier series and, when the pool is created before the money, the pool increase. New shares = amount raised / price, and the post-money valuation is the price times the fully diluted shares after the round. The conversion shares and the pool increase depend on the price (a safe converting at the round price, a pool sized as a percentage of the shares after the round), so the price P is the root of P × D(P) = pre-money valuation, D being the share count just described. P × D(P) does not fall as P rises, so the root is unique; the tool finds it by bisection. If the valuation is smaller than the value of the conversions and of the pool it must contain, no price exists and the tool says so.

With whole-share arithmetic the tool follows the guide: prices are rounded to four decimals, the conversion and pro rata share counts are cut to whole shares, the round's share count is rounded, and the calculation is repeated until the rounded price reproduces itself. The guide enters round numbers for its pool increases (1,695,000 shares for a 10 percent target); enter the increase in shares to follow it, or a target percentage to have the pool sized.

Option pool and effective pre-money valuation

The pool target is the unissued pool as a fraction t of the fully diluted shares after the round: increase = (t × (shares after conversion + new shares) − existing pool) / (1 − t), never negative. Created before the money, the increase sits inside the pre-money valuation and only the holders before the round pay for it; created after the money, it dilutes the new investors too. The table "What the pre-money valuation contains" values each block of pre-money shares at the round price. The first line, round price × the shares, options and pool that existed before the round, is the effective pre-money valuation: what the stated valuation leaves the existing holders after the conversions and the new pool are taken out of it.

Pro rata purchases

A safe holder with the pro rata side letter buys its percentage of the new shares, its conversion shares over the capitalization after the conversions (or an entered percentage). In a later round, "earlier investors pro rata" lets every holder of preferred stock buy its fully diluted percentage. The rest of the round goes to the new investors.

Anti-dilution

When a round is priced below the conversion price of an earlier series that carries protection, the conversion price falls and each share of that series converts into issue price / conversion price shares of common stock. The NVCA model charter gives the two forms. Broad-based weighted average: CP₂ = CP₁ (A + B) / (A + C), where A is the common stock outstanding before the issue, counting options outstanding and convertible securities as converted, B is the consideration received divided by CP₁ and C is the number of shares issued. Full ratchet: CP₂ is the price of the new issue. The tool takes the new money shares as the issue and counts the adjustment shares among the pre-money shares, so they dilute the unprotected holders and not the new investors.

Exit waterfall

The exit value is distributed over the final capitalization. Each series has a liquidation preference, shares × issue price × multiple, and a rank. Preferences are paid highest rank first; series of equal rank share pro rata to their preferences when the money runs short (the model charter's pari passu form is the case of one rank). The remainder is divided per as-converted share among the common stock, the options whose exercise price is below the per-share value, the series that have converted and the participating series. An option receives the per-share value less its exercise price; the exercise prices paid are added to the remainder (the cash method), so the per-share value p solves Σ common × p + Σ options × max(p − strike, 0) + Σ as-converted shares × p (capped for a capped participating series at its Maximum Participation Amount less the preference paid) = remainder. The left side is piecewise linear and rising in p, and is solved exactly segment by segment.

Conversion decisions. A non-participating series receives the greater of its preference and its as-converted amount; a capped participating series the greater of its capped amount and its as-converted amount; a fully participating series never needs to convert. The as-converted amount of one series depends on which others convert, the circularity the model charter's footnote describes. The tool looks for a set of decisions in which no series would receive more by changing its own decision while the others keep theirs: it tries the series in order of their entitlement per as-converted share, lets each take its better choice, and repeats until nothing changes; if that fails it enumerates every combination. The exit value at which a series starts to convert is found by bisection on this solution.

Safes outstanding at an exit. With no priced round, a safe receives the greater of its purchase amount and its as-converted amount at the Liquidity Price, the cap divided by the Liquidity Capitalization: stock and options outstanding and the safes that convert, without the unissued pool. A convertible note is repaid first as debt.

Checks

The four equity-financing scenarios and the liquidity scenarios of Appendix II of the Y Combinator guide are reproduced share for share (the examples are Y Combinator's). The exact arithmetic is compared with an independent implementation on twenty random capitalizations, where every exit point was found to have exactly one consistent set of conversion decisions.