Rounds, structures and bridges

A bridge prices off a round that has not happened yet

A bridge converts at a discount to the next round's price, and its own shares are inside the pre-money count used to set that price. The two facts make the calculation simultaneous, and they mean the bridge holder's return depends on the next round being priced well - which is the opposite of the protection a bridge investor thinks it is buying.

Field	Value
Formula	S = FD / (1 - amount / ((1 - discount) * PRE)). Round price = PRE/S, conversion price = (1 - discount)*PRE/S, bridge shares = amount divided by that conversion price
Setup	5,000,000 bridge at a 20 percent discount, on the post-Series B ledger of 19,607,844 shares. The next round raises 30,000,000
At PRE = 120,000,000	S = 20,685,198, round price 5.8012, conversion price 4.6410, bridge shares 1,077,354 = 4.167 percent after the round
At PRE = 60,000,000	Round price 2.7412, conversion price 2.1930, bridge shares 2,279,982 = 6.944 percent
At PRE = 180,000,000	Bridge shares 705,318 = 2.976 percent
Bridge value at the round price	At 120,000,000: 6,250,000 on 5,000,000 advanced, a multiple of 1.25 - which is 1/(1 - discount) at every price
Effect on the round price	Without the bridge the price would be 120,000,000/19,607,844 = 6.1200; with it, 5.8012

• The discount delivers a fixed multiple of 1/(1 - discount) regardless of the round price, so a 20 percent discount is a 1.25x on the money and nothing more. A bridge investor taking equity risk for a 1.25x is being paid a debt return for an equity position.
• That is why bridges are usually written with a cap as well as a discount, converting at the better of the two. The discount sets the floor return and the cap provides the upside if the round prices well above where the bridge was written.
• The bridge shares depress the round price, which the new investor is indifferent to - its percentage is R/POST either way. The cost lands on the pre-money holders, exactly as with a pool or a converting instrument.
• A bridge with no cap and no discount is a loan, and it should be documented and priced as one. Convertibility with no economic term attached gives the holder the downside of equity and the upside of debt.

An extension round is a flat price at a later date

An extension sells more of the same series at the same price, months after the original closing. In valuation terms it is a flat round; in economic terms it is a down round if the business is worth more than it was, and an up round if it is worth less. Nothing in the documents records which.

Field	Value
Formula	Shares = amount / the original round price. Implied pre-money = original price * the current fully diluted count, which rises as the count rises even though the price has not moved
Setup	5,000,000 added to the Series B at its 5.1000 price, on a count of 19,607,844 shares
Shares issued	980,392, taking the count to 20,588,236
Implied pre-money	5.1000 * 19,607,844 = 100,000,004, equal to the Series B post-money up to share-count rounding
Dilution to existing holders	4.762 percent; founders move from 40.800 to 38.857 percent
Aggregate preference	Rises from 30,000,000 to 35,000,000, so the first dollar to common moves up 5,000,000
Anti-dilution	Not triggered, because the price has not fallen. That is the main documentary attraction of an extension

• An extension is the cheapest financing to document because it uses the existing charter and the existing series. It needs no new anti-dilution analysis, no new protective provisions and often no new consents, which is why it is reached for under time pressure.
• It is also the financing that most reliably understates what happened. A company that has doubled its revenue and extends at the old price has taken a real down round in economic terms, and the cap table records a flat one.
• Check whether the extension shares carry the original series' terms including the original accrual start date for any cumulative dividend. Same series, later money, older dividend clock is a combination worth reading.
• Where an extension is being used to avoid triggering anti-dilution, the honest alternative is a priced down round with a negotiated reset. The extension defers the reset rather than avoiding it, and the deferral is paid for by the common.

An inside round has no external price, so the price is the conflict

When the existing investors fund the round, the people setting the price are on both sides of it. The arithmetic of the transfer is simple and computable, which is what makes the process protections around an inside round worth running rather than assuming.

Field	Value
Formula	Extra shares to the insider from pricing at PRE_low rather than PRE_high = R*FD*(1/PRE_low - 1/PRE_high). Their value at the higher price is R*(PRE_high/PRE_low - 1)
Setup	20,000,000 from existing holders on the post-Series C ledger of 24,509,805 shares
Priced at PRE = 120,000,000	Price 4.8960, shares 4,084,968, insider holds 14.286 percent of the enlarged company
Priced at PRE = 90,000,000	Price 3.6720, shares 5,446,623, insider holds 18.182 percent
Extra shares from the lower price	1,361,656, worth 6,666,667 at the higher price
Formula check	20,000,000 * (120,000,000/90,000,000 - 1) = 6,666,667
Process protections	Approval by directors without an interest in the financing; an independent valuation; and a rights offering giving every holder the chance to invest on the same terms

• The rights offering is the protection that does the most work, because it converts a price dispute into a choice. A holder that thinks the price is too low can buy at it, and a holder that declines has accepted the price by conduct.
• A disinterested director committee is the standard second protection, and it requires that such a director exists. On a board of two founders and three investors all of whom are funding the round, it does not.
• The arithmetic above is the entire transfer, and it is worth computing and circulating before the round rather than after. A 30,000,000 difference in pre-money on a 20,000,000 round is 6,666,667 of value moving between existing holders.
• Delaware review of a self-interested transaction is a matter of process and price together. Nothing in this corpus is legal advice, but the structural point is uncontroversial: the record of how the price was set is part of the transaction.

Source: Delaware General Corporation Law section 144 (interested director transactions)

Sizing a pay-to-play bridge across the stack

A pay-to-play bridge is offered pro rata to the existing preferred, with conversion to common as the penalty for declining. Sizing it means allocating the amount across the series in proportion to their holdings, and the allocation is what determines who is being asked for what.

Field	Value
Formula	Series j's pro rata share of a bridge of B = B * p_j / p_class, where p_class is the preferred's aggregate ownership. A holder that declines converts its preferred to common and gives up x_j*I_j of preference
Setup	A 6,000,000 bridge offered pro rata across the four-series preferred, which holds 61.600 percent of the company
Allocation	Seed 935,065, Series A 1,558,442, Series B 1,558,442, Series C 1,948,052
Check	6,000,000 total
Cost of declining, Seed	A 935,065 cheque against a 2,000,000 preference, a ratio of 2.14 to 1
Cost of declining, Series C	A 1,948,052 cheque against a 30,000,000 preference, a ratio of 15.40 to 1
Preference protected per dollar of bridge	Seed 2.14 to 1, Series A 5.13 to 1, Series B 12.83 to 1, Series C 15.40 to 1
Why the ratios differ	The pro rata allocation follows ownership and the preference at risk follows invested capital. The later series has far more preference per dollar of ownership, so the clause bites hardest on it

• The clause is written as a penalty and functions as a pricing mechanism: it sets the cost of not funding equal to the whole existing position, which is what makes an insider bridge happen when no outside price exists.
• The ratios above are the real content. The Seed holder is being asked for a small cheque to protect a small preference and the Series C holder for a larger cheque to protect a much larger one, so the same clause produces very different decisions around the table.
• It also concentrates the cap table exactly when the company can least afford a governance fight, because holders that convert lose their consent rights at the same moment.
• From the holder's side the decision is not the cheque against the position's book value. It is the cheque against the position's value in the outcomes that made the bridge necessary.

Every structured term can be quoted as a number of dollars taken from common

Multiples, participation, caps and ratchets are argued as structures and settle as amounts. Fixing an exit value and running the waterfall converts each proposal into a single figure, which is the only form in which they can be compared with each other or with a lower price.

Field	Value
Formula	Cost to common of a structure = common's proceeds under a clean 1x non-participating alternative, less its proceeds under the structure, both measured at the same E
Reference case	Clean 1x Series C at 150,000,000: Series C 30,000,000, common and pool 57,600,000
2x non-participating	Series C 60,000,000, common and pool 42,000,000 - a cost of 15,600,000
1x full participating	Series C 53,809,524, common and pool 45,714,286 - a cost of 11,885,714
1.5x participating capped at 2x	Series C 60,000,000, common and pool 42,000,000 - the same 15,600,000, by a different route
3x non-participating	Series C 90,000,000, common and pool 24,000,000 - a cost of 33,600,000
At a lower exit of 90,000,000	The clean case pays common 24,000,000; a 2x pays it 0; a 3x pays it 0

• Two structures that look nothing alike can cost the same. A 2x non-participating and a 1.5x participating capped at 2x both deliver Series C exactly 60,000,000 at this exit, because both are binding at the cap. Which is worse depends entirely on the exit value chosen.
• That is the reason to price a structure at three exit values rather than one: below the aggregate preference every structure costs common nothing, and far above the caps they converge again. The differences live in the middle.
• Once the cost is a number, it can be traded against the pre-money. A structure that costs common 15,600,000 at the likely exit is worth conceding only if the alternative clean price costs more than that.
• Structured terms also carry a second cost that does not appear in the waterfall: they widen the gap between the preferred price and the common fair market value, which lowers option strikes and raises the 409A discount. That is a benefit to employees and a signal to everyone else.

An IPO ratchet, and the shares it issues

A ratchet guarantees a holder a stated value at a public offering by issuing additional shares if the offering prices below a floor. The additional shares come from everyone else, and the number rises hyperbolically as the offering price falls.

Field	Value
Formula	Shares required = guaranteed value / offering price. Additional shares issued = max(0, that figure - shares already held). Every other holder is diluted by additional/(FD + additional)
Setup	Series C holds 4,901,961 shares from a 30,000,000 investment, with a 1x ratchet at a floor equal to its 6.1200 issue price
Offering at 6.1200	Shares required 4,901,961, already held 4,901,961, additional issued 0
Offering at 5.0000	Required 6,000,000, additional 1,098,039, count rises to 25,607,844, common and pool falls to 36.753 percent
Offering at 4.0000	Required 7,500,000, additional 2,598,039, count rises to 27,107,844, common and pool falls to 34.720 percent
Offering at 2.0000	Required 15,000,000 shares, more than half the pre-offering count
The asymmetry	The holder's value is fixed at 30,000,000 across every price above zero, and the entire variance is transferred to the other holders

• A ratchet is a put option on the offering price, written by the common. Priced as an option it is expensive, and it is negotiated as a technical condition rather than as the transfer of variance that it is.
• Because the share count is inversely proportional to the price, the ratchet is worthless in the outcome everyone is planning for and enormous in the outcome nobody is. That shape is what makes it hard to argue about with numbers taken from the plan.
• The countermeasures are a floor on the number of additional shares, a cap on the total, a sunset date, and a requirement that the ratchet lapse if the company achieves stated milestones. All four are arithmetic and all four are drafting.
• A ratchet also complicates the offering itself, because underwriters have to describe a share count that depends on the price they are setting. That practical friction is often a better argument against it than the economics.

Venture debt, warrant coverage and the dilution comparison

Venture debt is priced in interest and fees and dilutes through warrants. Warrant coverage is quoted as a percentage of the principal, which converts to a share count at the stated exercise price. Compared with equity for the same cash the dilution is far smaller, and the claim in an exit is far more senior.

Field	Value
Formula	Warrant shares = coverage * principal / exercise price. Dilution = warrant shares / (FD + warrant shares). Equity for the same cash issues amount/price shares
Setup	A 5,000,000 facility with 20 percent warrant coverage, exercise price at the Series B price of 5.1000, on a count of 19,607,844
Warrant shares	0.20000 * 5,000,000 / 5.1000 = 196,078 shares = 0.990 percent
Equity for the same 5,000,000	5,000,000/5.1000 = 980,392 shares = 4.762 percent
Ratio	Equity is 5.00 times as dilutive as the warrants for the same cash
Ranking	The principal is repaid before the waterfall runs, so it reduces E rather than adding to T. Debt is ahead of the entire preferred stack
Warrant value at a 10.2000 exit	1,000,000, against 1,000,000 of nominal coverage

• The dilution comparison is the part of the decision that is arithmetic, and it always favours debt. Everything that argues the other way - covenants, a material adverse change clause, an amortisation schedule that starts before revenue does, and a lender that can accelerate - is not in the comparison.
• Debt reduces the exit proceeds available to every equity holder, so it is senior to the entire stack including the most recent round. That makes an indebtedness threshold in the protective provisions one of the more consequential list entries.
• Facilities sized against a recent equity round rather than against cash flow are effectively lending against the next round happening. If the next round does not happen, the facility is what determines the timetable.
• Warrants are usually not in the fully diluted count used to price the next round unless someone asks, which is the same denominator question as everywhere else in this corpus - and worth roughly 1 percent of the price here.

Revenue-based financing - the cap is not the rate

A revenue-based facility advances cash against a fixed repayment cap, collected as a percentage of revenue. The cap looks like a multiple and behaves like a rate, because the same 1.4x repaid quickly is much more expensive than the same 1.4x repaid slowly. Speed is the whole cost.

Field	Value
Formula	Total repayment = cap * advance. Monthly payment = share * monthly revenue. Duration = total repayment / monthly payment. The implied rate solves sum of payment/(1+i)^t over the duration = advance
Setup	1,000,000 advanced, a 1.4x repayment cap, collected at 8 percent of a flat 500,000 of monthly revenue
Total repayment	1,400,000; monthly payment 0.08000 * 500,000 = 40,000
Duration	1,400,000/40,000 = 35.0 months
Implied rate	1.9996 percent a month, an effective annual rate of 26.82 percent
Same cap repaid over 18 months	Payment 77,778 a month: 3.8099 percent a month, 56.63 percent a year
The asymmetry	Growing faster repays sooner and costs more. A 1.4x cap on a company doubling revenue is roughly twice the annual rate of the same cap on a flat one

• The cap is the only term quoted and the duration is the term that sets the price, so the instrument is systematically cheaper-looking than it is. Compute the implied annual rate under the company's own revenue plan before comparing it with anything.
• The incentive is genuinely perverse: outperforming the plan accelerates collection and raises the effective rate, which is the opposite of every other financing instrument. A cap that steps down with duration fixes it and is rare.
• Collections scale with revenue, so the instrument is self-limiting in a downturn, which is its real attraction. It converts a fixed obligation into a variable one and prices the option accordingly.
• There is usually no dilution at all, which makes it directly comparable with the warrant coverage on a debt facility. On the numbers here, 1,400,000 of total cost against 1,000,000 advanced is a large price to avoid roughly 1 percent of the company.

SPV fee stacking - what two layers cost

A special purpose vehicle charges a management fee and a carried interest on top of whatever the underlying investment returns. Stack two vehicles and both layers charge on the same gross return, which converts a strong gross multiple into an ordinary net one.

Field	Value
Formula	Net multiple = [invested * gross - carry * (invested * gross - commitment)] / commitment, where invested = commitment * (1 - total management fee). Two layers apply the same transformation twice
Assumptions	A commitment of 100,000, a 2 percent annual management fee for five years drawn from the commitment, 20 percent carried interest over the commitment, and a 3.00x gross return on invested capital. All four are stated inputs
One layer	Fees 10,000, invested 90,000, gross return 270,000, carry 34,000, net 236,000 = 2.36x
Two layers, capital deployed	Feeder invests 90,000 into the vehicle, which invests 81,000 into the company
Two layers, distributions	Gross 243,000, vehicle carry 30,600, back to the feeder 212,400, feeder carry 22,480, net 189,920 = 1.90x
Cost of the second layer	2.36x becomes 1.90x - a loss of 0.46x on an unchanged 3.00x gross
Break-even gross	The gross multiple needed for a two-layer structure to return the one-layer net is materially higher, and it rises with the fee period

• Two layers cost about half a turn of multiple here on a 3.00x gross. On a 1.5x gross the same structure can return less than the commitment, because the fees are drawn whatever happens and the carry is only charged when there are gains.
• The management fee is the term that does the damage in a poor outcome and the carry is the term that does it in a good one. Both are quoted as small percentages and both are charged twice.
• Ask which layer's carry is charged over what. Carry over the commitment, over invested capital, or over a preferred return are three different numbers, and the difference is largest exactly where fees have reduced invested capital below the commitment.
• None of the figures above is a market observation; they are the arithmetic of one stated fee structure. The purpose is to show that the transformation is mechanical and can be computed before committing rather than reconciled afterwards.

The clean price that is equivalent to a structured round

A structured round at a high headline valuation and a clean round at a low one can leave the common in exactly the same position. Solving for the equivalent clean price turns a structural argument into a valuation argument, which is the argument founders are equipped to have.

Field	Value
Formula	Find PRE such that common's proceeds under a clean 1x round of R at PRE equal its proceeds under the structured round at a stated E. Solve numerically: lowering PRE raises the investor's share count and lowers common's ownership
The structured proposal	30,000,000 at a 120,000,000 pre-money with a 2x non-participating preference. At E = 150,000,000 common and pool receive 42,000,000
The equivalent clean round	30,000,000 at a pre-money of 43,750,000, 1x non-participating
Its arithmetic	Price 2.2312, Series C shares 13,445,379, fully diluted 33,053,223, common and pool 28.475 percent
Common and pool at E = 150,000,000	42,000,032, against 42,000,000 under the structure
What that means	At this exit value the 2x preference is worth the same to common as a 63.542 percent reduction in the pre-money valuation
Caveat	The equivalence holds at one exit value. At a different E the equivalent clean price is different, because a preference and a share count scale differently

• This is the single most useful calculation available in a structured negotiation, and it is almost never done. It reframes 'we need a 2x' as 'we are offering 43,750,000 pre-money, not 120,000,000' at the exit value both sides say they are underwriting.
• The equivalence is exit-dependent by construction, which is a feature: it forces the exit value into the conversation. Two parties who cannot agree on the equivalent clean price have not agreed on the exit range, and that is the disagreement worth having.
• A clean round at a lower price is better for common at high exit values and worse at low ones, because a share count participates without limit while a preference does not. Solve at the top and bottom of the credible range, not just the middle.
• The clean round is also better for everything downstream: a lower preferred price lowers the option strike, a smaller preference lowers the common break-even, and a simpler charter is cheaper to amend at the next round.