Valuation and pricing

The post-money identity

Post-money valuation is pre-money valuation plus the money. That single identity generates the investor's ownership, the existing holders' retention, and the dilution, and it holds exactly as long as nothing else is issued in the same transaction.

Field	Value
Formula	POST = PRE + R; investor ownership q = R/POST; existing holders retain PRE/POST; dilution = 1 - PRE/POST = R/POST
Worked	PRE = 8,000,000 and R = 2,000,000: POST = 10,000,000; q = 20.000 percent; existing holders retain 80.000 percent
Solving backwards	An investor targeting q = 20.000 percent with R = 2,000,000 is proposing POST = 10,000,000, hence PRE = 8,000,000

• The identity fails the moment anything else is issued at the same closing - a new option pool inside the pre-money count, or converting SAFEs and notes. In those rounds the investor still holds R/POST, but the existing holders retain materially less than PRE/POST.
• That is the single most useful diagnostic on a term sheet. Compute PRE/POST, compare it to the founder ownership in the closing cap table, and the gap is the total cost of everything else being issued in the round.
• Because the identity is exact, any two of PRE, POST and R determine the third. A negotiation conducted in two of them and then reopened on the third is a negotiation reopened on nothing.

Also described at: Wikipedia · Wikidata

Solving for the pre-money from an ownership target

Investors with an ownership target and a cheque size are not proposing a pre-money valuation - they are solving for one. Reading the pre-money as the primary variable inverts the causality and makes the negotiation harder than it is.

Field	Value
Formula	PRE = R*(1 - q)/q and POST = R/q. Equivalently, for a given PRE, R = PRE*q/(1 - q)
Worked, q = 0.20	R = 2,000,000: POST = 2,000,000/0.20 = 10,000,000; PRE = 10,000,000 - 2,000,000 = 8,000,000
Worked, q = 0.15	Same cheque: POST = 2,000,000/0.15 = 13,333,333; PRE = 11,333,333
Cross-check	PRE = 2,000,000*0.85/0.15 = 11,333,333
Sensitivity	Moving the ownership target 5 points moves the pre-money by 3,333,333 on an unchanged cheque

• PRE is hyperbolic in q, so ownership concessions are much more expensive at low q than at high q. Going from 25 to 20 percent on a 2,000,000 cheque moves PRE by 2,000,000; going from 15 to 10 percent moves it by 6,666,667.
• The productive lever is usually the cheque size, not the valuation. Raising less at the same ownership target is the same economic outcome as raising the valuation, and it is a much shorter conversation.
• Any argument about pre-money valuation that does not name the fully diluted denominator is incomplete, because the same PRE at a larger FD is a lower price per share.

Also described at: Wikipedia · Wikidata

Why the absolute share count is arbitrary

Multiplying every share count by the same factor changes no ownership percentage, no payout, and no preference amount. It divides the price per share by that factor and nothing else. Price per share therefore carries no information on its own.

Field	Value
Formula	Multiplying all share counts by k leaves every ownership percentage and every waterfall payout unchanged, and sets price = PRE/(k*FD)
Worked	PRE = 8,000,000 on FD = 9,411,765 gives 0.8500. After a 10:1 forward split, FD = 94,117,650 and the price is 0.0850
Unchanged	Ownership percentages, exit proceeds, preference amounts, and every formula in this corpus that is expressed in p rather than in shares

• The count is chosen for two practical reasons only: a strike price granular enough to grant small slices to employees, and a per-share number that reads as normal to them. Neither is an economic term.
• It follows that a comparison of price per share between two companies, or between two rounds with different share counts, is meaningless. Compare valuations and ownership.
• Splits do matter to thresholds expressed as absolute share numbers - major-holder definitions, board-appointment minimums, protective-provision minimums. Well-drafted documents restate those after any split; check that they were.

A SAFE cap is not a valuation

A valuation cap determines how many shares a given amount will buy when a priced round eventually happens. It does not price a share, does not establish a post-money valuation, and does not make the company worth the cap at any point.

Field	Value
Formula	A post-money cap fixes ownership = I/cap of the capitalisation before new money. The company's implied post-money at conversion is the round price multiplied by the post-round share count, which can be above or below the cap
Worked	I = 1,000,000 at an 8,000,000 post-money cap fixes 12.500 percent of the pre-new-money capitalisation
What the round actually says	The priced round closes at PRE = 12,000,000 and R = 3,000,000, so POST = 15,000,000. The company was never valued at 8,000,000 on any date
What the holder ends with	1,142,857 shares at a round price of 1.3125 = 1,500,000 of value on 1,000,000 invested, a 1.50x

• No security is issued when the instrument is signed, so there is no price and no valuation event. Describing a capped instrument as a raise 'at an 8,000,000 valuation' is a category error that then propagates into every subsequent model.
• A SAFE is not a priced preferred issuance, so it does not supply the evidence of fair market value that a closed preferred round does. Expecting it to reset a 409A analysis on its own is a common and expensive misreading.
• The cap is a ceiling on the conversion price, not a floor on ownership and not a floor on price. In a round priced below the cap the instrument converts at a worse price than the new money pays.

Also described at: Wikipedia · Wikidata · Y Combinator: the SAFE

The 409A gap between common and preferred

Option strike prices are set to the fair market value of common stock, determined under section 409A. Preferred stock carries a liquidation preference, protective provisions and other rights that common does not, so the fair market value of common is set below the price paid for preferred in the same round.

Field	Value
Formula	Discount to the preferred price = 1 - (common fair market value / preferred price). The level is an appraisal output, not a rule
Worked	Preferred price 0.8500 with a common fair market value of 0.2550: discount = 1 - 0.30 = 70.0 percent
Worked, a narrower gap	Same preferred price with a common value of 0.5100: discount = 1 - 0.60 = 40.0 percent
What drives it	The size of the aggregate preference relative to enterprise value, the probability weighting across exit scenarios, and marketability

• The gap is a direct consequence of the preference overhang, so it narrows as the company grows into its stack and widens when a large new preference is added. It is the same arithmetic as the dead zone, expressed as a valuation input rather than as a payout.
• Timing matters more than most grantees realise: a grant made before a 409A refresh that follows a strong round carries a lower strike than the identical grant made after it. That is a scheduling decision, not a compensation decision.
• Two different numbers are correct at the same time - the preferred price and the common fair market value - and quoting either as 'the' share price will mislead somebody. Always say which one.
• The appraisal is an independent determination. Do not model a target discount and back into the value; the direction of the arithmetic is the point of the rule.

Source: IRC section 409A

Also described at: Wikipedia · Wikidata · 26 CFR 1.409A-1 (definitions and covered plans)

Ownership percentage is not a claim on the exit price

Multiplying ownership by exit value gives the right answer only above the conversion indifference point. Below it, the preference comes off the top first and the residual is shared among a smaller group, so the naive calculation overstates common proceeds.

Field	Value
Formula	Founder proceeds = (E - preferences of non-converting series - carve-out) * s_founder/(s_common + s_converting), which equals p*E only for E >= E* = x*I/p
Setup	Post-round FD 11,764,706 shares: founders 8,000,000 (68.000 percent), pool 1,411,765 (12.000 percent), preferred 2,352,941 (20.000 percent) carrying 1x on 2,000,000
Worked at E = 5,000,000	Preferred takes max(2,000,000, 0.20*5,000,000) = 2,000,000. Residual 3,000,000 to 9,411,765 common and pool shares: founders 8,000,000/9,411,765 * 3,000,000 = 2,550,000; pool 450,000
The naive figure	0.68 * 5,000,000 = 3,400,000, overstating founder proceeds by 850,000 - 25.0 percent too high
Where it becomes correct	E* = 2,000,000/0.20 = 10,000,000; at and above that the preferred converts and ownership times exit value is exact

• The error is largest in the exit range that is most likely, which is what makes it consequential. Above E* the naive calculation is exactly right and nobody needs it; below E* it is wrong and everybody uses it.
• The residual is shared with the option pool, including unallocated shares in many structures. Founders modelling their own outcome frequently divide by the common they know about rather than by the full residual group.
• Run any ownership figure through the waterfall at three exit values - below the aggregate preference, between it and E*, and above E* - before treating the percentage as a number that means anything.

Step-up and price step are the same number only when nothing else is issued

A round's step-up is usually quoted as this pre-money against the last post-money. The number that actually determines whether existing holders gained is the price per share. They agree only when no shares beyond the round itself were issued in between.

Field	Value
Formula	Step-up = PRE_n / POST_(n-1). Price step = (PRE_n/FD_(n-1)) / (PRE_(n-1)/FD_(n-2)). The two are equal when FD_(n-1) = FD_(n-2) + shares issued in round n-1 and nothing else
Series A	PRE 24,000,000 on a prior POST of 10,000,000: step-up 2.40. Price 0.8500 to 2.0400: price step 2.40
Series B	PRE 80,000,000 on a prior POST of 32,000,000: step-up 2.50. Price 2.0400 to 5.1000: 2.50
Series C	PRE 120,000,000 on a prior POST of 100,000,000: step-up 1.20. Price 5.1000 to 6.1200: 1.20
With a 5 percent pool refresh at Series A	The pre-money count used to price rises to 12,605,042, so the price is 1.9040 and the price step is 2.24 against an unchanged 2.40 step-up
The wedge	Any share issued between the two rounds - a pool refresh, a converting instrument, a warrant exercise - makes the price step smaller than the step-up, and only the price step is felt by existing holders

• A round can be announced as a 2.4x step-up while the price per share rises by less, and both statements are true. Ask for the price per share; it is the only figure that is directly comparable between rounds on the same cap table.
• The reverse is possible too. A buyback or a reverse split raises the price without raising the valuation, which is why price per share cannot be compared between companies at all.
• Step-ups reported across a portfolio are almost always pre-money against prior post-money, because that is the pair available from public announcements. Treat them as a valuation series and not as a return series.
• For an existing holder the only figures that matter are its own retention factor PRE/POST and the price at which any new shares were sold. Both are in the closing documents and neither is in the announcement.

The pre-money cap that is equivalent to a post-money cap

A pre-money cap and a post-money cap are the same term measured against different capitalisations, and the conversion between them is exact. For one instrument the equivalent pre-money cap is simply the post-money cap less the amount raised. For a stack it is a single expression in the committed fraction.

Field	Value
Formula	For a stack of post-money instruments with committed fraction w = sum of I_k/cap_k and total raised sum I_k, the pre-money cap issuing the same total share count is cap_pre = (sum I_k)*(1 - w)/w
One instrument	1,000,000 at an 8,000,000 post-money cap: cap_pre = 1,000,000*0.87500/0.12500 = 7,000,000, which is the post-money cap less the amount raised
A two-instrument stack	1,000,000 at 8,000,000 and 750,000 at 12,000,000: w = 18.750 percent on 1,750,000 raised
Equivalent pre-money cap	1,750,000 * 0.81250/0.18750 = 7,583,333
Check, post-money route	S = 8,000,000/(1 - 0.18750) = 9,846,154, and w*S = 1,846,154 conversion shares
Check, pre-money route	1,750,000 * 8,000,000/7,583,333 = 1,846,154 conversion shares

• Converting a pre-money term sheet onto a post-money template without moving the cap is a price change, not a documentation cleanup. The difference is the amount raised on the instruments, which is a number both sides already know.
• The formula shows why the gap widens as more is raised on instruments: cap_pre falls away from cap_post by the whole amount raised, so the same nominal cap becomes progressively more generous to the holder as the stack grows.
• It also gives a clean way to compare instruments signed on different templates. Restate every cap as a pre-money cap on the same FD, and the stack becomes a single ordered list of prices.
• The identity holds only for capped instruments with no discount and no interest. Anything that makes the conversion price depend on the round price breaks it, and there is no closed form left.

A down round is a price cut, and the price cut is exact

A round priced below the last one is described in valuation terms and felt in price terms. The ratio of the two prices is the number that drives anti-dilution, the 409A analysis and every existing holder's mark, and it is not the ratio of the two valuations.

Field	Value
Formula	Price ratio = (PRE_n/FD_(n-1)) / (PRE_(n-1)/FD_(n-2)). Existing holders retain PRE_n/POST_n regardless of whether the round is up or down
Setup	After Series C the ledger is 24,509,805 shares at a 6.1200 price. A Series D raises 20,000,000 at PRE = 90,000,000
Price	90,000,000/24,509,805 = 3.6720, against 6.1200 - a price ratio of 0.6000 and a cut of 40.000 percent
Valuation comparison	PRE 90,000,000 against the prior POST of 150,000,000 is a step-down of 0.60, a different number
Shares and ownership	20,000,000/3.6720 = 5,446,623 shares; POST = 110,000,000; the new investor holds 18.182 percent
Existing holders retain	90,000,000/110,000,000 = 81.818 percent, so founders move from 32.640 to 26.705 percent
Anti-dilution input	The 0.6000 price ratio is what a full ratchet resets Series C to; a weighted average uses it together with the share count issued

• The price ratio and the valuation ratio differ whenever the share count changed between the rounds, and after a round of financing it always has. Quote the price.
• A flat round - the same price, not the same valuation - is the boundary case. Priced at 6.1200 on the same ledger it would be a 150,000,000 pre-money, which is a step-up in valuation terms and a flat round in price terms.
• A down round is what triggers anti-dilution, and anti-dilution is the reason a down round takes longer to close than an up round of the same size: the adjustment has to be computed, and usually waived or reset, before anyone can sign.
• The 409A analysis moves too, in both directions. A lower preferred price lowers the ceiling on the common value, which lowers the strike on new grants - one of the few compensating effects available in a down round.

Return on invested capital is entry ownership times the retained fraction

An investor's multiple at exit is not its entry ownership multiplied by the exit value. It is its exit ownership multiplied by the exit value, and exit ownership is entry ownership multiplied by the product of the later rounds' retention factors.

Field	Value
Formula	p_exit = p_entry * product of PRE_i/POST_i over all subsequent rounds. Multiple on invested capital = p_exit*E/I, provided E is above the holder's conversion flip point
Seed	Entry 20.000 percent, retained 0.75000*0.80000*0.80000 = 0.48000, exit 9.600 percent
Series A	Entry 25.000 percent, retained 0.80000*0.80000 = 0.64000, exit 16.000 percent
At E = 250,000,000	Seed 24,000,000 on 2,000,000 = 12.00x; Series A 40,000,000 on 8,000,000 = 5.00x
Series B and C	Series B 2.00x; Series C 1.67x
Aggregate	60,000,000 invested returns 154,000,000 = 2.57x across the stack
Per-share check	250,000,000/24,509,805 = 10.2000 a share, against entry prices of 0.8500, 2.0400, 5.1000 and 6.1200

• The per-share check is the fastest way to compute every holder's multiple at once: divide the exit value by the fully diluted count and divide the result by each round's price. On these numbers that is 12.00x, 5.00x, 2.00x and 1.67x, with no ownership arithmetic at all.
• It also makes the dependence explicit. An investor's multiple is set by the price it paid and the exit price per share; its ownership percentage is a derived quantity that happens to be easier to talk about.
• The formula holds only above the holder's conversion flip point. Below it the holder takes a preference and the multiple is x*I/I, capped at the multiple in the charter, which is why a preference is a floor on return rather than a claim on value.
• Aggregate returns across a stack are dominated by the earliest cheque, which is the smallest. That asymmetry, not the size of the later rounds, is what makes early ownership worth negotiating for.