Accretion and dilution

Pro forma EPS

Combined net income divided by combined share count, adjusted for every earnings and share effect of the transaction. The construction, not the concept, is where deals are won and lost in a board presentation.

Field	Value
Formula	EPS_pf = (NI_A + NI_T + Syn*(1-tau) - Cash*r_d*(1-tau) - AmortStepUp*(1-tau) + OtherAdj) / (S_A + Stock/P_A)
Worked, all cash	(500.0 + 100.0 + 0 - 2,400.0*0.06*0.75) / 250.0 = (600.0 - 108.0)/250.0 = 492.0/250.0 = 1.9680
Worked, all stock	(500.0 + 100.0) / (250.0 + 2,400.0/30.00) = 600.0 / 330.0 = 1.8182
Standalone	500.0 / 250.0 = 2.0000

• Pro forma financial information filed with the SEC follows Regulation S-X Article 11, which distinguishes transaction accounting adjustments from management's adjustments for synergies and requires the latter to be disclosed separately. A board deck that folds synergies silently into the numerator is not following the standard investors will see.
• Target net income must be re-based to the acquirer's tax rate and capital structure before it is added. Adding a target's as-reported net income when the target had a different effective tax rate double-counts or omits tax that the deal changes.
• Stub periods are a common quiet error. A deal closing mid-year contributes a partial year of target earnings and a partial year of interest, and the weighted average share count uses the issuance date. First-year accretion computed on a full-year basis is not what will be reported.

Source: Regulation S-X, Article 11

Accretion or dilution percentage

The percentage change in the acquirer's EPS caused by the transaction. Positive is accretive, negative is dilutive. The sign, not the magnitude, is what most boards react to, which is why the sign is worth deriving in closed form rather than reading off a model.

Field	Value
Formula	Accretion = EPS_pf / EPS_A - 1
Worked, all cash	1.9680 / 2.0000 - 1 = -0.0160 = -1.60%
Worked, all stock	1.8182 / 2.0000 - 1 = -0.0909 = -9.09%
Worked, all cash with 40.0 synergies	2.0880 / 2.0000 - 1 = +0.0440 = +4.40%

• Accretion is not value creation. Buying earnings at a lower P/E than your own is accretive whether or not the business is worth what you paid, and issuing stock at a low multiple to buy a better business at a higher one is dilutive and can be correct.
• The metric is exquisitely sensitive to the acquirer's own share price, which the acquirer does not control. A stock deal that is accretive at a 30.00 share price is dilutive at 24.00 for reasons that have nothing to do with the target.
• First-year dilution followed by year-three accretion is the standard shape of an integration-heavy deal. Quote the year in which the number is measured or the number is meaningless.

Exchange ratio

In a stock deal, the number of acquirer shares issued per target share. A fixed exchange ratio fixes the number of shares and lets the value float with the acquirer's price; a floating ratio fixes the value and lets the share count float.

Field	Value
Formula	Fixed ratio: ER = P_offer / P_A. Floating ratio: ER_at_close = P_offer / P_A,close
Worked	ER = 24.00 / 30.00 = 0.80 acquirer shares per target share
New shares issued	0.80 * 100.0 = 80.0
Target holders' pro forma ownership	80.0 / 330.0 = 24.24%

• Under a fixed exchange ratio the target's shareholders bear the acquirer's price risk between signing and closing, which can be many months in a regulated deal. Under a floating ratio the acquirer bears the dilution risk instead. That single choice reallocates more economic risk than most of the rest of the agreement.
• A collar is the middle case: fixed ratio inside a price band, floating outside it, or the reverse. Collars are where fixed and floating disputes are usually settled, and they introduce a discontinuity in the payoff that both sides' models frequently smooth over.
• In a stock-for-stock merger the ownership split is the real deal term. Quoting a premium to the target's unaffected price and quoting a pro forma ownership percentage are two views of the same number, and they can be made to sound very different.

Breakeven P/E rule, stock consideration

In an all-stock deal with no synergies and no other adjustments, the transaction is accretive if and only if the P/E paid for the target is below the acquirer's own P/E. The breakeven is exact and requires no model.

Field	Value
Formula	Accretive if P/E_offer < P/E_A. Maximum EPS-neutral price per share = P/E_A * EPS_T
Worked	P/E_A = 30.00/2.00 = 15.0x. Max neutral price = 15.0 * 1.00 = 15.00 per share
Check at 15.00	New shares = 1,500.0/30.00 = 50.0. EPS_pf = 600.0/300.0 = 2.0000. Exactly neutral.
At the 24.00 offer	24.0x paid against 15.0x owned, so dilutive - confirmed at -9.09%

• The rule is a statement about relative multiples, not about quality. A high-multiple acquirer can buy almost anything accretively in stock, which is why multiple-driven roll-ups are structurally stock-funded and why the strategy stops working the moment the acquirer's own multiple compresses.
• The rule inverts cleanly: a low-multiple acquirer buying a high-multiple target in stock is mathematically guaranteed to be dilutive before synergies. If such a deal is being pitched as accretive, the accretion is in the synergy line and should be interrogated there.
• Because the acquirer's P/E is measured at a market price and the target's at an offer price, the comparison silently includes the premium. The relevant test is the offer P/E, not the target's unaffected trading P/E.

Breakeven rule, cash and debt consideration

A debt-funded cash deal is accretive if the target's after-tax earnings yield on the purchase price exceeds the after-tax cost of the debt raised to pay it. Expressed as a multiple, the breakeven P/E is the reciprocal of the after-tax funding cost.

Field	Value
Formula	Accretive if NI_T / Price > r_d*(1-tau); equivalently if P/E_offer < 1 / (r_d*(1-tau))
After-tax cost of debt	0.06 * (1 - 0.25) = 0.0450 = 4.50%
Breakeven P/E	1 / 0.0450 = 22.22x, i.e. a maximum neutral equity price of 2,222.22 or 22.22 per share
Target yield at the offer	100.0 / 2,400.0 = 4.1667%, below 4.50%, so dilutive
Check at 22.22 per share	Interest = 2,222.22*0.06*0.75 = 100.00; NI_pf = 500.0 + 100.0 - 100.0 = 500.0; EPS = 2.0000. Neutral.

• Funding with surplus balance-sheet cash rather than debt replaces the cost of debt with the after-tax yield foregone. At a 3.0 percent pre-tax yield that is 2.25 percent, a breakeven P/E of 44.44x, and the same 24.0x offer flips from dilutive to accretive - the pro forma EPS becomes 546.0/250.0 = 2.184, or +9.20 percent.
• That flip is the single most misleading fact in accretion analysis. When the funding cost is near zero, almost any acquisition is accretive, and accretion stops carrying any information about whether the deal is good.
• The rule also explains why cash deals look better than stock deals in low-rate conditions and why the ranking reverses when rates rise, with no change in the underlying businesses.
• Deductibility matters: if the incremental interest is disallowed under IRC section 163(j), the after-tax cost is the full 6.0 percent, the breakeven P/E falls to 16.67x, and the deal is materially more dilutive.

Source: IRC s.163(j)

Synergies net of cost to achieve

Run-rate synergies are the recurring annual benefit; cost to achieve is the one-time spend required to realise them. Both belong in the analysis, but they belong in different places, and conflating them is the most common way a synergy case is overstated.

Field	Value
Formula	Run-rate EPS effect = Syn*(1-tau) / S_pf. Value effect = Syn*(1-tau)/r - CTA*(1-tau), for a perpetual synergy
Worked, run-rate	40.0 pre-tax = 30.0 after tax. All-cash: 522.0/250.0 = 2.0880, +4.40%. All-stock: 630.0/330.0 = 1.9091, -4.55%
Worked, capitalised value	At r = 8.9%: 30.0 / 0.089 = 337.08 of value, against a one-time after-tax cost of, say, 45.0, for a net 292.08
Phasing	A synergy reaching run-rate in year 3 contributes roughly one third of run-rate in year 1, which is where first-year dilution comes from

• Cost to achieve is a one-time item and therefore does not appear in run-rate pro forma EPS, but it is real cash and it appears in full in the value calculation. A deal justified on run-rate accretion alone has been justified with the cost removed.
• Cost synergies and revenue synergies do not deserve the same discount rate treatment in practice. Cost actions are largely under the acquirer's control; revenue synergies require customers to behave in a new way. Presenting both at the same probability is the standard optimism.
• The share of synergies paid away in the premium is the honest test. If the premium over the unaffected price is 600.0 and the capitalised net synergy value is 292.08, the acquirer has paid the target for more than all of the value the deal creates.
• Dis-synergies exist and are almost never modelled: customer overlap loss, attrition of revenue-generating staff, and the management attention consumed by integration.

Breakeven synergies

The run-rate synergy amount at which the transaction is exactly EPS-neutral. This is the most testable number in an accretion analysis because it converts a return claim into an operating claim someone can be held to.

Field	Value
Formula	Syn_breakeven = [EPS_A * S_pf - (NI_A + NI_T - Cash*r_d*(1-tau))] / (1 - tau)
Worked, all stock	Required NI_pf = 2.00 * 330.0 = 660.0. Have 600.0. Shortfall 60.0 after tax, so 60.0/0.75 = 80.0 pre-tax
Worked, all cash	Required NI_pf = 2.00 * 250.0 = 500.0. Have 492.0. Shortfall 8.0 after tax, so 8.0/0.75 = 10.6667 pre-tax
As a share of target EBITDA	If target EBITDA is 160.0, the all-stock breakeven of 80.0 is 50% of it; the all-cash breakeven of 10.67 is 6.7%

• Expressing the breakeven as a percentage of the target's cost base or EBITDA is what makes it falsifiable. A breakeven that requires half of the target's EBITDA in synergies is a different proposition from one requiring 7 percent, and the raw dollar figure hides that.
• The all-stock and all-cash breakevens differ by almost 8x in this example on the same purchase price. Consideration mix is therefore a bigger driver of the required synergy case than the price itself.
• A breakeven synergy figure larger than the target's total addressable overhead is a proof that the deal cannot be neutral on cost synergies alone, whatever the model shows.

Intangible amortisation drag and cash EPS

Purchase accounting steps acquired identifiable intangibles up to fair value, and the resulting amortisation is a non-cash charge that reduces reported pro forma EPS without reducing cash. Acquirers therefore report both GAAP EPS and a cash EPS excluding the charge.

Field	Value
Formula	Annual pre-tax amortisation = intangible step-up / useful life. EPS drag = amort*(1-tau) / S_pf
Worked	Step-up 400.0 over 10 years = 40.0 pre-tax, 30.0 after tax. All-cash EPS falls from 1.9680 to 462.0/250.0 = 1.8480
Accretion impact	1.8480 / 2.0000 - 1 = -7.60%, against -1.60% before the charge
Cash EPS	Adds the 30.0 back: 492.0/250.0 = 1.9680, i.e. the pre-amortisation figure

• Goodwill is not amortised under ASC 350; only identifiable intangibles with finite lives are. The allocation between goodwill and finite-lived intangibles therefore determines the size of the drag, and that allocation is a valuation exercise completed after signing, often after the accretion analysis was presented.
• Cash EPS is a legitimate adjustment for a charge that has no cash effect and an illegitimate one when it is used to make an expensive deal look cheap. The test is whether the intangible represents an asset that will need to be re-bought - customer relationships that must be re-won with real spend are an economic cost, not a bookkeeping one.
• Deals structured as asset purchases or IRC section 338(h)(10) elections generate tax-deductible amortisation of the step-up, which is a real cash benefit and is worth modelling separately from the book charge. In a stock purchase without an election there is usually no such deduction, so the book charge is a drag with no offsetting cash benefit.
• Inventory and fixed asset step-ups also produce charges, but they run through cost of sales and depreciation over shorter periods and are frequently missed entirely.

Source: ASC 805; IRC s.338(h)(10)

Mixed consideration and where the answer lands

A mixed cash-and-stock deal has an EPS effect that is a weighted blend of its components, weighted by the value of each component rather than by share count.

Field	Value
Formula	EPS_pf = (NI_A + NI_T + Syn*(1-tau) - c*Price*r_d*(1-tau)) / (S_A + (1-c)*Price/P_A), where c is the cash fraction
Worked, c = 0.50	Cash 1,200.0, stock 1,200.0. New shares 40.0, S_pf = 290.0. Interest 1,200.0*0.045 = 54.0. NI_pf = 546.0. EPS = 1.8828, accretion -5.86%
Bracketed by the pure cases	All stock -9.09%, mixed -5.86%, all cash -1.60%
With 40.0 synergies	NI_pf = 576.0, EPS = 1.9862, accretion -0.69%

• Consideration mix is usually driven by the target's tax position and the acquirer's rating headroom, not by the accretion answer. A target shareholder base seeking tax-deferred treatment needs a stock component large enough to qualify under IRC section 368(a); a rating-constrained acquirer needs the debt component small enough to hold its ratios.
• Those two constraints pull in opposite directions and the accretion number falls out of wherever they meet. Presenting the mix as chosen to optimise EPS inverts the actual causality in most deals.
• Election mechanics matter: where target holders may elect cash or stock subject to proration, the final mix is not known at signing and the accretion figure in the proxy is an estimate.

Source: IRC s.368(a)