Acquisitions and mergers versus other growth strategies: formula sheet

Key formulas

Value created by an acquisition

Value created = (Value of combined firm) − (Standalone value of acquirer + Standalone value of target) = Synergy value

Synergies are the source of any gain. Without them, a premium simply transfers value from the acquirer to the target's shareholders.

Gain to acquirer's shareholders

Gain to acquirer = Synergy value − Premium paid

Premium = Price paid − Target's standalone market value. If the premium exceeds synergies, the acquirer's shareholders lose.

Gain to target's shareholders

Gain to target = Premium paid

Gain to target and gain to acquirer add up to total synergy.

NPV of a growth option

NPV = Σ [Cash flow(t) ÷ (1 + r)^t] − Initial investment

Use the same test for organic projects, JVs, franchising or an acquisition: accept if the NPV is positive at a risk-adjusted rate.

Value of synergy

Synergy = V(A+B) − [V(A) + V(B)]

V(A+B) is the value of the combined firm. Positive synergy is the basic test for a worthwhile deal.

Net gain to acquirer's shareholders

Net gain = Synergy − Premium paid

Premium = price paid − target's standalone value. The acquirer gains only if synergy exceeds the premium, before deal costs.

Gain to target's shareholders

Gain to target = Premium paid

The target's shareholders keep the premium. Larger premium means more of the synergy goes to them.

Bootstrap effect (EPS)

Combined EPS rises if acquirer's P/E > target's P/E (in a share-for-share deal at market values)

This is an accounting effect and not real value unless the market ignores it. Do not present it as synergy.

Control versus commitment spectrum

Organic growth / acquisition (high control, high cost and risk) → JV → alliance / licensing / franchising (low control, low cost and risk)

Use it to rank options. Cost, risk and control generally move together, but this is a guide, not a rule.

Merger classification

Horizontal = same industry and stage; Vertical = supplier or customer; Conglomerate = unrelated

Name the type first, then give the matching motive and regulatory issue.

Synergy test

Value of combined firm > value of A + value of B

A deal creates value only if synergies exceed the premium paid plus costs.

Franchisor income (simple)

Franchisor annual income = initial fee (spread over term) + royalty % × franchisee sales − support costs

A simple way to compare franchising with owning outlets.

Gain to acquirer's shareholders

Gain = Value of synergies − Premium paid − Transaction and integration costs

Premium = price paid − standalone value of target. A positive gain means value is created for the acquirer.

Combined value check

Value of combined entity = Value of acquirer + Value of target + PV of synergies − costs

Use the same valuation basis for all parts, such as DCF or P/E.

Bid premium

Premium % = (Offer price − Pre-bid price) ÷ Pre-bid price × 100

Use the undisturbed share price from before bid rumours.

Maximum price the acquirer should pay

Maximum price = Standalone value of target + PV of synergies − costs

Paying more than this transfers all synergy value, and more, to target shareholders.

Share of synergies to each side

Target share = Premium ÷ Synergies; Acquirer share = 1 − Target share

Shows who captures the benefit of the deal.

Quick revision

• Organic growth is slower but gives more control and lower cost and risk than buying.
• External growth gives speed, immediate market share and access to skills, but costs more and is riskier.
• Synergy means the combined firm is worth more than the parts; it must be realistic and measurable.
• Common motives: economies of scale, market power, diversification, new markets, acquiring skills or technology, and tax or financial benefits.
• Diversification by a company is not always valuable, as shareholders can diversify themselves.
• Horizontal deals join competitors, vertical deals join supply chain stages, and conglomerate deals join unrelated businesses.
• A joint venture creates a shared entity; an alliance is looser; franchising lets others use your brand and system.
• Joint ventures and alliances share risk and local knowledge but reduce control and can cause disputes.
• Franchising allows fast growth with little capital but risks brand damage if quality slips.
• Deals fail from overpaying, poor integration, culture clash, weak due diligence and overestimated synergies.
• Competition authorities may block or add conditions to a deal that lessens competition.
• Always give a recommendation tied to the scenario, with the main risks.

Common mistakes

• Listing textbook advantages and disadvantages without using the scenario. Fix: Tie every point to a fact in the case, such as low cash, a short time window or a weak local market knowledge.
• Treating merger and takeover as clearly different in practice. Fix: State the definition, then note that most deals are acquisitions where one side controls the outcome, even if described as a merger.
• Listing generic motives without linking them to the scenario. Fix: Use the facts given. Name the company's markets, costs or cash position in every point.
• Claiming diversification always creates shareholder value. Fix: State that shareholders can diversify themselves at lower cost. Accept diversification only where there are real synergies or other stakeholder benefits.
• Calling any takeover of a competitor 'vertical' or any deal in a new country 'conglomerate'. Fix: Classify by the target's industry and position. Same industry and stage is horizontal. Supplier or customer is vertical. Unrelated is conglomerate.
• Treating JVs, alliances and franchising as the same thing. Fix: State the legal and control difference. A JV usually has shared ownership and often a separate entity. An alliance is a contract with no new entity. Franchising is a licensed business format with fees.
• Listing generic reasons for failure with no link to the scenario. Fix: Pick the reasons the scenario supports and quote its facts, such as a high premium or different cultures.
• Ignoring the premium and saying the deal is good because the target is profitable. Fix: Always compare premium and costs with synergies. A good business bought at too high a price still destroys value.

Exam tips

• AFM is a written exam with professional skills marks. Write in a clear, report-style way, give a recommendation and show commercial awareness.
• Always apply points to the scenario. Generic lists earn few marks.
• Where figures are given, do the calculation of synergy, premium or NPV first, then use it in the discussion.
• Cover regulation and risk for overseas options, including competition rules, political risk and exchange rates.
• End with a decision and the conditions attached to it, such as due diligence, a pilot or an exit clause.
• Always tie each motive to a fact in the scenario. Generic lists score poorly.
• Separate real value creation from accounting effects such as the bootstrap EPS gain, and say so explicitly.
• Where numbers are given, compute synergy and premium. Then say who benefits and by how much.