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Mergers and acquisitions - the arithmetic of deal math

Accretion / dilution calculator

One division problem: pro forma net income over pro forma share count, against standalone EPS. Every consideration structure changes the numerator, the denominator, or both, and each has a closed-form breakeven that gives the answer before a model is built. Every input is encoded in the URL.

Assumptions

Result

Deal terms

Pro forma earnings bridge

Breakevens

Breakeven conditions by funding source

Pro forma EPS against the stock share of consideration

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The formulas

Standalone and offer arithmetic

EPS_A = NI_A / S_A P/E_A = P_A / EPS_A Price = P_offer * S_T offer equity value P/E_offer = Price / NI_T ER = P_offer / P_A shares issued per target share

Pro forma EPS

Cash = cash% * Price Stock = Price - Cash NewDebt = Cash - BalanceSheetCash NewShares = Stock / P_A S_pf = S_A + NewShares EPS_pf = ( NI_A + NI_T + Syn*(1-tau) - NewDebt*r_d*(1-tau) - BalanceSheetCash*y*(1-tau) - Amort*(1-tau) ) / S_pf Accretion = EPS_pf / EPS_A - 1

Target net income is assumed already re-based to the acquirer's tax rate. Cash funded from the balance sheet costs the after-tax yield foregone rather than the cost of debt. Cost to achieve is a one-time item and is excluded from run-rate pro forma EPS by construction; it is reported separately below as an after-tax amount and as a payback against after-tax synergies.

Exchange ratio and ownership

ER = P_offer / P_A NewShares = ER * S_T Target ownership = NewShares / S_pf

Under a fixed exchange ratio the target's holders bear the acquirer's price risk between signing and closing; under a floating ratio the acquirer bears the dilution risk instead.

Breakeven P/E by funding source

All stock neutral when P/E_offer = P/E_A All new debt neutral when NI_T / Price = r_d*(1-tau) so breakeven P/E = 1 / (r_d*(1-tau)) All balance-sheet neutral when NI_T / Price = y*(1-tau) cash so breakeven P/E = 1 / (y*(1-tau)) Mixed, cash share c breakeven P/E = 1 / ( c*k + (1-c)/(P/E_A) ) where k is the after-tax cost of the cash portion

The mixed case is a harmonic weighting of the component conditions, not an arithmetic one, because each source contributes a cost per unit of price rather than a multiple. Set synergies and amortisation to zero to see the pure rule; the maximum EPS-neutral price reported above is solved numerically over the full expression, so it also holds when they are not zero.

Maximum EPS-neutral offer price and breakeven synergies

Max neutral price per share solves EPS_pf(P_offer) = EPS_A found by bisection on P_offer, all else held Syn_breakeven = [ EPS_A * S_pf - NI_pf_before_synergies ] / (1 - tau) where NI_pf_before_synergies = NI_A + NI_T - interest - foregone - Amort*(1-tau)

Breakeven synergies are the most testable number in an accretion analysis, because they convert a return claim into an operating claim. Expressed as a share of the target's EBITDA or cost base they become falsifiable; the raw amount hides the scale.

Amortisation and cash EPS

EPS drag = Amort*(1-tau) / S_pf Cash EPS = EPS_pf + drag

Goodwill is not amortised; only identifiable intangibles with finite lives are, so the allocation between the two sets the size of the drag. Cash EPS is a fair adjustment for a charge with no cash effect and an unfair one when it is used to make an expensive deal look cheap.

The worked cases

Acquirer: net income 500.0, 250.0 diluted shares, so EPS 2.00; share price 30.00, so P/E 15.0x. Target: net income 100.0, 100.0 shares, so EPS 1.00; offer 24.00 per share, so offer equity value 2,400.0 and offer P/E 24.0x. Tax 25 percent. New debt at 6.0 percent pre-tax, so 4.50 percent after tax. Run-rate pre-tax synergies where used are 40.0, which is 30.0 after tax. These are the defaults above, with synergies at zero.

ConsiderationNew sharesPro forma sharesAfter-tax interestAfter-tax synergiesPro forma net incomePro forma EPSAccretion
100% stock80.0330.00.000.0600.01.8182-9.09%
100% stock + synergies80.0330.00.0030.0630.01.9091-4.55%
50% cash / 50% stock40.0290.054.000.0546.01.8828-5.86%
50/50 + synergies40.0290.054.0030.0576.01.9862-0.69%
100% cash (debt funded)0.0250.0108.000.0492.01.9680-1.60%
100% cash + synergies0.0250.0108.0030.0522.02.0880+4.40%
All stock: 600.0 / (250.0 + 2,400.0/30.00) = 600.0 / 330.0 = 1.8182 -> -9.09% All cash: (600.0 - 2,400.0*0.06*0.75) / 250.0 = 492.0 / 250.0 = 1.9680 -> -1.60% 50/50: (600.0 - 1,200.0*0.045) / 290.0 = 546.0 / 290.0 = 1.8828 -> -5.86% Breakeven P/E, all stock = 15.00x -> max neutral price 15.00 per share Breakeven P/E, all new debt = 1 / 0.0450 = 22.22x -> 22.22 per share Breakeven P/E, all b/s cash = 1 / 0.0225 = 44.44x -> 44.44 per share Breakeven synergies, all stock: 2.00*330.0 = 660.0 required, 600.0 held 60.0 after tax / 0.75 = 80.0000 pre-tax Breakeven synergies, all cash: 2.00*250.0 = 500.0 required, 492.0 held 8.0 after tax / 0.75 = 10.6667 pre-tax

URL parameters

Every parameter is optional; omitted parameters take the worked-case default. Percentages are entered as numbers, so 6 means 6 percent. All computation happens in the browser and no request leaves the page.

ParameterMeaningDefault
acqniAcquirer standalone net income to common500
acqshAcquirer fully diluted shares250
acqpxAcquirer share price; sets the P/E and the stock issue price30
tgtniTarget net income, re-based to the acquirer's tax rate100
tgtshTarget fully diluted shares at the offer price100
offerOffer price per target share; offer equity value is offer x tgtsh24
cashpctCash share of the consideration, percent; the remainder is stock at acqpx100
ratePre-tax cost of the incremental debt, percent6
cashonhandAmount of the cash consideration funded from existing cash0
cashyieldPre-tax yield foregone on that cash, percent3
taxMarginal tax rate, percent25
synergiesRun-rate pre-tax synergies0
ctaOne-time pre-tax cost to achieve those synergies; excluded from run-rate EPS0
amortAnnual pre-tax intangible amortisation under purchase accounting0

All-stock at a 24.0x offer P/E:
https://m-a.wiki/calc/accretion/?acqni=500&acqsh=250&acqpx=30&tgtni=100&tgtsh=100&offer=24&cashpct=0&tax=25

The same price funded entirely with 6 percent debt, plus 40.0 of run-rate synergies:
https://m-a.wiki/calc/accretion/?acqni=500&acqsh=250&acqpx=30&tgtni=100&tgtsh=100&offer=24&cashpct=100&rate=6&tax=25&synergies=40

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Related: accretion and dilution · LBO returns math · LBO returns calculator · purchase price bridge · valuation cross-checks

A simplified model. It computes a full-year run-rate figure with no stub period, no weighted average share count for a mid-year issuance, no synergy phasing, no transaction costs expensed at close, no debt repayment schedule, no changes in the acquirer's share price between signing and closing, no election or proration mechanics, and no interest deduction limitation. Accretion is not value creation: buying earnings below your own multiple is accretive whether or not the price was worth paying.

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.

Text and data under CC BY 4.0. Reviewed 2026-08-27.