IAI Actuarial Core Principles · Business Finance

Corporate growth, restructuring and divestment: formula sheet

Full chapter guide

Key formulas

Value created by an acquisition: Gain = Value of combined firm − (Value of acquirer + Value of target); Gain is the value of synergies before any premium. Positive gain is needed for the deal to be worthwhile.
Net gain to acquirer: Net gain to acquirer = Synergy gain − Premium paid; Premium = price paid − market value of target before the bid. If premium exceeds synergies, the acquirer's shareholders lose.
Net gain to target shareholders: Gain to target = Premium paid; Target shareholders gain the premium over their pre-bid market value.
Synergy value: Synergy = V(AB) − [V(A) + V(B)]; V(AB) is the value of the combined firm. A deal adds value only if synergy is positive.
Acquisition premium: Premium = Price paid − Target's standalone value; The premium is what the bidder hands to target shareholders.
Net gain to bidder: Net gain to bidder = Synergy − Premium; Positive only if synergy exceeds the premium paid. If the premium is higher, the bidder's shareholders lose.
Gain to target shareholders: Gain to target = Premium; Using standalone value as the starting point.
P/E valuation of target: Target value = Target earnings × P/E ratio; Use a P/E from comparable firms. Use maintainable earnings, not one-off peaks.
Earnings per share: EPS = Earnings attributable to ordinary shareholders ÷ Number of ordinary shares; After a deal, use combined earnings and the new total number of shares.
DCF value of target: Value = Σ FCFt ÷ (1 + r)^t, plus terminal value discounted; Use a discount rate that reflects the target's risk, not the bidder's.
Gain to bidder: Bidder gain = (Standalone value of target + Synergies) − Price paid − Deal costs; If positive, the bid creates value for the bidder's shareholders.
Premium: Premium = (Offer price − Market price) ÷ Market price; Express as a percentage of the pre-bid price.
Share exchange: New shares issued = Target shares × Exchange ratio; Exchange ratio = bidder shares offered per target share.
Post-deal EPS: Combined EPS = (Bidder earnings + Target earnings + after-tax synergies − after-tax financing costs) ÷ (Bidder shares + New shares issued); Include interest on new debt after tax in a cash offer funded by debt.
Gearing (debt-to-equity): Gearing = Debt ÷ Equity; Use book or market values as the question states. Some texts use Debt ÷ (Debt + Equity). State your definition.
Interest cover: Interest cover = Profit before interest and tax ÷ Interest expense; Low cover signals financial distress. LBOs need adequate cover to service heavy debt.
Value of a restructuring versus liquidation: Restructure if: PV of expected cash flows from continuing > Net realisable value on liquidation; Core decision rule for creditors and the board in a turnaround.
Debt-for-equity swap effect: New equity = Old equity + Debt converted; New debt = Old debt − Debt converted; Total capital is unchanged. Gearing falls and interest burden falls.
LBO equity cheque: Equity required = Purchase price + Costs − New debt raised; Higher debt means less equity for the buyers, so higher gearing and higher return on equity if the deal works.
Divestment decision rule: Divest if sale proceeds (or separate value) > value of the unit to the group if retained; Value to the group means the present value of its future after-tax cash flows, including any synergies that would be lost.
Gain on sale: Gain = Sale proceeds − Carrying amount (book value) of the unit's net assets; This is an accounting gain. Tax on the gain, if any, is separate and reduces the cash kept.
Net cash from sale: Net cash = Sale price − Tax on gain − Selling costs − Debt transferred or repaid; Use this figure when asking how much the parent can reinvest or return to shareholders.
Value before and after a demerger: Value of parent before = Value of parent after + Value of demerged company (shares received by shareholders); Ignoring costs and market reaction, shareholder wealth is unchanged by the mechanics. Any gain comes from improved performance or better pricing.
Carve-out proceeds: Proceeds = Number of new shares sold × Issue price per share (less issue costs); Parent's retained stake = 1 − (shares sold ÷ total shares of the unit).

Quick revision

Organic growth comes from a company's own resources; inorganic growth comes from acquiring or combining with other businesses.
Inorganic growth is usually faster but carries integration and price risk.
A merger combines companies; an acquisition or takeover means one company gains control of another.
Common M&A motives: economies of scale, market power, access to new markets or skills, diversification and synergy.
Synergy means the combined value is expected to exceed the sum of the separate values.
A deal creates value for the buyer only if the benefits exceed the premium paid.
Value a target from its expected cash flows, discounted at a rate that reflects its risk.
Payment can be cash, shares or a mix, and the choice affects gearing and ownership dilution.
Restructuring changes a company's structure, operations or finances to improve performance.
A divestment is a sale of part of a business; a demerger splits a company into separate companies.
In a spin-off, shareholders receive shares in the new separate company.
Always state assumptions and name who gains or loses: shareholders, managers, lenders and employees.

Common mistakes

Treating all inorganic growth as the same. Fix: Separate them by ownership and control: acquisition means full or majority control, joint venture means a shared separate entity, alliance means a contract without a new entity.
Saying growth always increases shareholder value. Fix: State that growth adds value only if returns exceed the cost of capital after allowing for premium and risk.
Mixing up vertical and conglomerate deals. Fix: Ask if the two firms are linked in one supply chain. If yes, it is vertical. If they have no link, it is conglomerate.
Claiming diversification always benefits shareholders. Fix: Say that investors can diversify cheaply themselves, so company-level diversification adds value only if it brings something investors cannot get alone.
Treating higher EPS as proof that the deal creates value. Fix: State that EPS is an accounting measure. Check price paid against value, and consider risk and gearing.
Forgetting to deduct tax-adjusted interest in a debt-financed cash bid. Fix: Subtract interest × (1 − tax rate) from combined earnings before dividing by shares.
Treating all restructuring as financial restructuring. Fix: Split every answer into financial, operational and ownership changes, then say which applies.
Saying an MBO and an LBO are the same thing. Fix: An MBO is defined by who buys (managers). An LBO is defined by how it is funded (mainly debt). A deal can be both.
Saying a demerger raises cash for the company. Fix: In a demerger or spin-off, shares go to existing shareholders for no payment. The company gets no cash. Only a sale or carve-out brings cash in.
Treating carve-out and spin-off as the same. Fix: Check who receives the shares. Spin-off: existing shareholders, free. Carve-out: new investors, who pay. The parent often keeps control in a carve-out.

Exam tips

Always give both advantages and disadvantages when a question asks you to evaluate a route.
Use case facts (cash, speed, market knowledge) to justify your recommendation. Generic lists earn fewer marks.
For acquisition numbers, show synergy, premium and net gain separately.
In MCQs, check ownership and control wording to tell joint ventures from alliances.
Mention agency motives such as empire-building when a case suggests growth for its own sake.
Always classify the deal type first when a scenario is given, and justify it with one phrase from the scenario.
In evaluation questions, give both sides: motives for the deal and reasons it may not add value.
Show the synergy, premium and net gain steps separately in numerical questions, as method marks are given.