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Mergers and acquisitions - the arithmetic of deal math

Purchase price and consideration

The enterprise-to-equity bridge, cash-free debt-free, the working capital peg, and every contingent piece of the price.

The headline number in a press release is one of at least four different prices, and they differ by amounts large enough to change whether a deal is good. Enterprise value is what the business costs; equity value is what the shareholders receive; the amount actually paid at closing is adjusted for working capital, cash and debt as measured on the closing date; and the amount ultimately paid includes or excludes earnouts, escrow releases, and ticking fees that resolve months or years later. This section states each bridge explicitly. The worked target throughout: 96.0 basic shares, options on 8.0 shares struck at 12.00, offer price 24.00 per share, total debt 600.0, cash and equivalents 150.0, preferred stock with a 50.0 redemption value, and non-controlling interests carried at 25.0.

Enterprise value to equity value bridge

Read downward to build enterprise value from an offer per share; read upward to solve the offer price from an enterprise value. Both directions use the same signs, reversed.

LineAmountRunning total
Offer price per share 24.00 x fully diluted shares 100.02,400.02,400.0 = equity value
Plus total debt (all interest-bearing, including finance leases)+600.03,000.0
Plus preferred stock at redemption value+50.03,050.0
Plus non-controlling interests+25.03,075.0
Less cash and cash equivalents-150.02,925.0 = enterprise value
Memo: net debt = 600.0 - 150.0450.0-
Reverse check: 2,925.0 - 450.0 - 50.0 - 25.0-2,400.0

Treasury stock method, diluted share count

Options in the money at the offer price are treated as exercised, with the strike proceeds used to repurchase shares at the offer price. Offer price 24.00.

StepCalculationShares
Basic shares outstandinggiven96.0
Options exercised (strike 12.00, in the money)given+8.0
Option proceeds8.0 x 12.00 = 96.0-
Shares repurchased with proceeds96.0 / 24.00-4.0
Fully diluted shares96.0 + 8.0 - 4.0100.0
Net dilution from options8.0 x (1 - 12.00/24.00)4.0

Working capital true-up scenarios

Base purchase price 500.0 on a cash-free debt-free basis. Peg (target normalised net working capital) 60.0. Collar of plus or minus 2.5 around the peg, with the full difference payable once the collar is breached.

Closing NWCRaw differenceInside collar?Adjustment appliedAdjusted price
68.0+8.0No+8.0508.0
62.0+2.0Yes0.0500.0
61.5+1.5Yes0.0500.0
57.0-3.0No-3.0497.0
52.0-8.0No-8.0492.0

Earnout payout schedule

Base consideration 500.0. Earnout of up to 100.0 on year-one EBITDA, zero below 60.0, straight-line between 60.0 and 70.0, capped at 100.0. Payout = 100.0 x (Actual - 60.0)/10.0, floored at 0 and capped at 100.0.

Year-1 EBITDAEarnout payoutTotal considerationMarginal payout per unit of EBITDA
58.00.0500.00.0
60.00.0500.010.0
63.030.0530.010.0
66.060.0560.010.0
70.0100.0600.00.0
75.0100.0600.00.0

Entries

Enterprise value to equity value bridge

The identity connecting the value of the operating business to the value of its common equity. Every claim on the enterprise that ranks ahead of common stock is added, and every non-operating asset is deducted.

FieldValue
FormulaEV = E + D + preferred + NCI - C; equivalently E = EV - ND - preferred - NCI
Worked, upward2,400.0 + 600.0 + 50.0 + 25.0 - 150.0 = 2,925.0
Worked, downward2,925.0 - 450.0 - 50.0 - 25.0 = 2,400.0
Implied per share from EV(2,925.0 - 450.0 - 50.0 - 25.0) / 100.0 = 24.00
  • The bridge is only as reliable as the completeness of the claims list. Items routinely missing: unfunded pension obligations, asset retirement obligations, deferred and contingent consideration owed on the target's own prior acquisitions, tax indemnity liabilities, off-balance-sheet factoring, and management incentive plan payouts triggered by the sale.
  • Operating leases capitalised under ASC 842 sit on the balance sheet as liabilities but are excluded from net debt by most practitioners because the corresponding right-of-use asset is an operating asset and lease expense is already in EBITDA. Including them without moving to an EBITDAR basis double-counts. State which convention is being used.
  • Non-controlling interests should be added at fair value, not book value, if the multiple being applied is derived from consolidated EBITDA that includes the subsidiary in full. Adding NCI at book while valuing 100 percent of consolidated earnings is internally inconsistent.
  • Cash is not automatically deductible in full. Cash trapped in a jurisdiction with a repatriation cost, cash required as a regulatory minimum, and cash that is really customer float are not available to the buyer and should be excluded from the deduction.

Net debt

Total interest-bearing debt less cash and cash equivalents. A defined term in the purchase agreement whose scope is negotiated line by line, not an accounting quantity that can be read off the balance sheet.

FieldValue
FormulaND = D - C, where the contents of D and C are as defined in the agreement
Worked600.0 - 150.0 = 450.0
Usually in DBank debt, notes, finance leases, drawn revolver, accrued but unpaid interest, prepayment premiums
Frequently disputedShareholder loans, deferred consideration, pension deficit, factored receivables, seller transaction expenses, change-of-control bonuses
  • Every item argued into net debt reduces the equity price one for one. On a deal with a fixed enterprise value, the net debt definition is a direct transfer of price, and it is negotiated after the headline number has been agreed and announced.
  • The debt-like items list is where most post-LOI price erosion happens. A seller who agrees an enterprise value without simultaneously agreeing the net debt and working capital definitions has agreed to a number, not a price.
  • Net debt is measured at closing, not at signing or at the last audited balance sheet date. A seller that draws its revolver to fund operations between signing and closing has reduced its own proceeds.

Treasury stock method

The standard convention for converting basic shares into a fully diluted count for valuation purposes. In-the-money options and warrants are assumed exercised, and the strike proceeds are assumed used to buy back shares at the offer price.

FieldValue
FormulaNet new shares = N_options * (1 - K / P_offer), for K < P_offer; zero otherwise
Worked8.0 * (1 - 12.00/24.00) = 8.0 * 0.50 = 4.0 net new shares; FD = 96.0 + 4.0 = 100.0
CircularityNet new shares depend on the offer price, which depends on FD shares if solving from an EV - iterate or solve algebraically
At a 15.00 offer8.0 * (1 - 12.00/15.00) = 1.6 net new shares; FD = 97.6
  • Dilution from options is a function of the offer price, so the fully diluted count rises with the price. Solving for an offer price from a fixed enterprise value is therefore circular; the closed-form solution is P = (EV - ND - pref - NCI + sum of K_i*N_i) / (S_basic + sum of N_i) over the tranches that end up in the money.
  • The method understates dilution where options are settled in cash at the spread rather than exercised for shares, because the cash outflow reduces equity value directly and no repurchase offsets it. In a change-of-control cash settlement, treat the payout as a use of funds instead.
  • Restricted stock units carry no strike and are fully dilutive - add them at face count, not through the treasury method. Performance share units accelerating on a change of control frequently vest at maximum, not target, which is a real and commonly missed increase in the count.
  • ASC 260 governs diluted EPS reporting and uses the same mechanic with the average market price rather than an offer price. The two produce different counts and are not substitutes.

Source: ASC 260

Cash-free debt-free

A pricing convention, standard in private M&A, in which the agreed price is the enterprise value: the seller keeps the cash and settles the debt, and the buyer acquires the operating business with a normalised balance sheet.

FieldValue
FormulaSeller proceeds = EV_agreed - D_at_close + C_at_close +/- NWC adjustment - transaction expenses
WorkedEV 500.0, debt at close 80.0, cash at close 20.0. Seller proceeds = 500.0 - 80.0 + 20.0 = 440.0
With a +8.0 NWC true-up500.0 + 8.0 - 80.0 + 20.0 = 448.0
Equivalent statementBuyer pays EV for the business; the balance sheet is settled at actual closing-date amounts
  • The convention exists because the buyer is pricing an operating business, not a cash pile. It also means the seller has no incentive to hoard cash and every incentive to argue about what counts as debt, which is why the debt-like items list is longer in a cash-free debt-free deal than anywhere else.
  • Cash-free debt-free removes the cash and debt distortion but not the working capital distortion, which is exactly what the peg exists to address. Without a peg, a seller can convert working capital to cash before closing and keep both.
  • In a locked box structure the balance sheet is fixed at an earlier reference date and the buyer takes the economic risk and benefit from that date forward, usually with an interest-style ticking payment to the seller. Locked box and cash-free debt-free with a completion true-up are alternatives, not complements - a deal should use one.

Working capital peg

The normalised level of net working capital the business is expected to be delivered with, agreed in advance. Delivering above the peg increases the price; delivering below it reduces the price.

FieldValue
FormulaAdjustment = NWC_close - Peg, subject to any collar. Adjusted price = base price + adjustment
Worked, abovePeg 60.0, closing NWC 68.0: +8.0, price 500.0 to 508.0
Worked, belowPeg 60.0, closing NWC 52.0: -8.0, price 500.0 to 492.0
Worked, inside a 2.5 collarClosing NWC 61.5: raw +1.5, inside collar, no adjustment, price stays 500.0
  • The peg is normally set as an average of monthly net working capital over a trailing period, most commonly twelve months to neutralise seasonality. A peg set on a single month's balance sheet in a seasonal business is a coin flip on which side of the seasonal swing closing falls.
  • Two collar conventions exist and they are not equivalent. Under the version shown here the full difference is payable once the collar is breached; under the alternative only the excess beyond the collar is payable, so a closing NWC of 68.0 against a 60.0 peg with a 2.5 collar would produce an adjustment of 5.5 rather than 8.0. The agreement must say which.
  • The definition of net working capital in the agreement almost never matches the definition in the target's management accounts. Every included and excluded line - deferred revenue, accrued bonuses, income tax payable, current portion of debt - is a price term.
  • The most valuable protection for either side is an agreed sample calculation appended to the agreement, applying the definition to a historical month and showing the resulting number. Without it, the true-up is a dispute over accounting policy conducted after the money has moved.

Closing statement and true-up mechanics

The process by which the estimated closing adjustment paid at completion is replaced by the actual amount once closing accounts are prepared, with the difference settled in cash.

FieldValue
FormulaTrue-up payment = (actual adjustment - estimated adjustment); positive is payable by buyer to seller
WorkedEstimated NWC at close 64.0 (+4.0 paid). Actual determined at 68.0 (+8.0 owed). True-up = 4.0 from buyer to seller
Typical sequenceEstimated statement pre-closing, buyer-prepared closing statement post-closing, seller objection period, resolution period, independent accountant on unresolved items
  • Whoever prepares the closing statement has a structural advantage, because the other side must object within a fixed window on specified grounds. Sellers who concede preparation rights and accept a short objection window have given away more than they usually realise.
  • The independent accountant's mandate matters as much as their identity. An expert determination limited to the disputed items, deciding within the range the parties have each proposed, produces a very different distribution of outcomes from an unconstrained arbitration.
  • A true-up escrow sized to the plausible downside is the standard way to make a negative true-up collectible. Without it, a buyer owed money by a seller who has already distributed the proceeds has a claim, not a recovery.
  • The accounting hierarchy clause - agreement definitions first, then the specified sample calculation, then the target's historical policies, then GAAP - decides most true-up disputes before they start. Its ordering is a negotiated term and is frequently reversed by mistake.

Earnout

Contingent consideration payable after closing if the acquired business meets specified performance conditions. Economically a bridge across a valuation disagreement and a written option on the metric chosen.

FieldValue
FormulaPayout = min(Cap, max(0, Rate * (Actual - Threshold))), summed over any tiers
WorkedCap 100.0, threshold 60.0, full at 70.0, so Rate = 10.0 per unit. Actual 66.0: 10.0*(66.0-60.0) = 60.0
At 63.0 and 75.010.0*(63.0-60.0) = 30.0; and capped at 100.0 above 70.0
AccountingRecognised at fair value at the acquisition date under ASC 805 and remeasured through earnings each period until settled
  • An earnout is a written option, so its value depends on the volatility of the metric as well as its expected level. A cliff structure with a single threshold is a digital option and creates an enormous incentive to move revenue across the measurement date; a linear structure with a floor and a cap is a call spread and creates a smoother, weaker incentive.
  • Choose the metric for its manipulability, not its relevance. Revenue is the easiest to verify and the easiest to buy with margin. EBITDA is closer to value and fully exposed to allocation of shared costs. Non-financial milestones - a regulatory approval, a named contract signed - are the least gameable and the least connected to value.
  • The covenant package around an earnout is more important than the formula. Without an obligation to operate the business consistently, maintain the sales force, and refrain from reallocating customers or loading costs into the earnout entity, the buyer controls the outcome of the payment it owes.
  • Earnouts convert a price dispute into a post-closing litigation risk. Delaware courts read earnout provisions narrowly and generally do not imply an obligation to maximise the earnout absent express language, so what is not written is usually not owed.

Source: ASC 805

Escrow and holdback

A portion of the purchase price withheld at closing to secure the seller's post-closing obligations - most often indemnification and the working capital true-up. Escrow is held by a third party; a holdback is retained by the buyer.

FieldValue
FormulaCash at close = purchase price - escrow - holdback; released per the release schedule less claims
WorkedPrice 500.0, indemnity escrow 10% = 50.0, separate NWC escrow 1.0% = 5.0. Cash at close = 445.0
ReleaseNWC escrow on final determination of the closing statement; indemnity escrow at the general survival date, less the amount of pending claims
Where escrow sitsThird-party escrow agent under a separate escrow agreement, with interest usually to the seller
  • An escrow that is the exclusive remedy caps the buyer's recovery at the escrow amount regardless of the size of the loss. An escrow that is merely the first source of recovery leaves the seller exposed above it. Those are radically different deals with nearly identical documents.
  • A buyer holdback is cheaper to administer and much worse for the seller than a third-party escrow, because collection depends on the buyer's willingness to release rather than on an instruction to an agent.
  • Escrow size and indemnity cap are separate terms that are often confused. A 10 percent cap with a 5 percent escrow means half the cap is unsecured; a 10 percent escrow with a 5 percent cap means half the escrow must be released.
  • Representations and warranties insurance has largely displaced the large indemnity escrow in mid-market and larger deals, reducing escrow to a true-up mechanism only. Where insurance is used, the escrow question becomes whether it also covers the retention under the policy.

Contingent value right

A transferable or non-transferable instrument issued to target shareholders entitling them to a payment if a specified future event occurs. The public-company analogue of an earnout, used where a discrete binary outcome dominates value.

FieldValue
FormulaCVR value = probability-weighted payout, discounted: sum of p_i * Payout_i / (1+r)^t_i
WorkedSingle milestone paying 3.00 per share, estimated probability 0.40, expected 3 years out, r = 10%: 0.40*3.00/1.10^3 = 0.9016 per share
Headline vs deliverableAn offer of 24.00 cash plus a 3.00 CVR is a 27.00 headline and 24.90 of present value on those assumptions
  • The gap between the headline sum and the present value is the point of a CVR: it lets an acquirer announce a larger number and pay a smaller one in expectation. Both sides know this, and target boards use it to bridge a gap they cannot bridge in cash.
  • Milestone definition is where the value actually sits. A payment on regulatory approval by a fixed date is a clean condition. A payment on cumulative net sales exceeding a threshold hands the acquirer control of the trigger through pricing, launch sequencing, and revenue recognition.
  • Tradeable CVRs are securities and require registration or an exemption; non-tradeable CVRs avoid that but leave holders with no way to monetise, which reduces the value they will ascribe to the instrument at the vote.
  • CVRs are most common where a single asset dominates value and the parties disagree about one probability rather than about the whole business. Outside that fact pattern they add complexity without resolving anything.

Ticking fee

An increase in the purchase price accruing at a stated rate for each day closing is delayed beyond a specified date, compensating the seller for the time value of proceeds held up in a long regulatory or financing process.

FieldValue
FormulaPrice_t = Price_0 * (1 + rate * days / 365); per share: P_t = P_0 + P_0*rate*days/365
WorkedP_0 = 24.00, rate 5.0% per annum, accrual from day 180. Daily accrual = 24.00*0.05/365 = 0.0032877 per share
After 60 days of accrual0.0032877 * 60 = 0.1973 per share, so P = 24.1973; aggregate on 100.0 shares = 19.73
DirectionUsually payable by buyer to seller; a reverse ticking fee reducing the price for seller-caused delay also exists
  • A ticking fee reprices delay but does not allocate blame for it. Whether it accrues during a delay caused by the seller's own failure to satisfy a condition depends entirely on the drafting, and the default reading is usually that it accrues regardless.
  • The rate is a negotiated number and functions as the seller's compensation for holding an unhedged position, not as an interest rate. Comparing it to a cost of funds misses that the seller also bears the deal-break risk during the same period.
  • Ticking fees and outside dates interact. A generous ticking fee with a distant outside date is a very different risk profile from no fee with a near outside date, and the combination is what determines the seller's real exposure to a long antitrust review.
  • In a locked box structure the equivalent mechanism is interest on the locked box price from the reference date to closing, which serves the same economic purpose through a different route.

Reference data. Reviewed 2026-08-27. Machine-readable: /purchase-price.json. Corpus manifest: /llms.txt.

Published and maintained by · [email protected]. A reference published by the wallstreet.wiki network. Every figure is stated as a formula and recomputed from it, every convention names the authority that sets it, and corrections are versioned and dated. About this reference.

Reference information only. Not legal, tax, or investment advice. Acquisition agreements, credit documents, and tax structures vary materially between transactions and jurisdictions; the mechanics described here are common patterns, not the terms of any particular deal. Worked examples use assumed inputs chosen to make the arithmetic verifiable, not to represent market levels. Consult counsel.