Corporate Restructuring: formula sheet

Key formulas

Spin-off distribution

Subsidiary shares received = Parent shares held × distribution ratio

Pro rata and no cash received. Parent shareholders own both firms afterwards.

Split-off share exchange

Subsidiary shares received = Parent shares tendered × exchange ratio

Voluntary exchange. Parent share count falls by the shares tendered.

Carve-out proceeds

Cash raised = Shares sold to public × offer price

Cash goes to the subsidiary or the parent depending on the terms. Parent usually keeps a controlling stake.

Parent ownership after carve-out

Parent % = Parent shares retained ÷ Total subsidiary shares outstanding

Include newly issued shares in the denominator if the subsidiary issues them.

Value test for the acquirer

Gain to acquirer = Synergies − Premium paid

Premium = price paid − target's pre-announcement standalone value. Synergies must exceed the premium for acquirer shareholders to gain.

Gain to target shareholders

Gain to target = Premium = Price paid − Target's standalone value

The target's shareholders gain the premium regardless of whether synergies are ever realized.

Total value created

Gain to acquirer + Gain to target = Synergies

Assumes the deal has no other costs. Synergies are the total value created, split by the price paid.

Integration types

Horizontal = same business; Vertical = supply chain (backward or forward); Conglomerate = unrelated

Classify by the relationship between the two firms' operations.

Form of deal

Statutory merger, subsidiary merger, consolidation; stock purchase vs asset purchase

Stock purchase: buy shares, target liabilities come along. Asset purchase: buy chosen assets, acquirer can avoid unwanted liabilities.

Takeover premium (TP)

TP = Price paid for target − Target's pre-announcement market value

Often shown as % of the pre-announcement market price. The price paid is per-share offer or total offer value.

Premium percentage

Premium % = (Offer price ÷ Pre-announcement price) − 1

Use the undisturbed price before rumours or the announcement.

Gain to the target

Gain to target = Takeover premium = P_T − V_T

V_T is the target's stand-alone value, if the question defines it that way; otherwise use market value.

Gain to the acquirer

Gain to acquirer = Synergies − Premium = S − (P_T − V_T)

Equals the acquirer's NPV for a cash deal.

Value of the combined firm

V_A+T = V_A + V_T + S

Synergies S are the present value of the incremental cash flows from combining.

Acquirer NPV, cash deal

NPV to acquirer = V_T + S − Cash paid

Positive means the acquirer's shareholders gain.

Acquirer NPV, stock deal

NPV to acquirer = (Acquirer's share of combined firm × V_A+T) − V_A

Ownership share = acquirer shares ÷ (acquirer shares + new shares issued). Combined value must include synergies.

Exchange ratio

Exchange ratio = offer price per target share ÷ acquirer share price

Shares issued = exchange ratio × number of target shares. Offer price is the price you read from the vignette, not the target's current price.

Post-merger EPS (stock deal)

EPS = (acquirer earnings + target earnings + after-tax synergies) ÷ (acquirer shares + new shares issued)

Use net income figures, not EBIT. Add synergies only if the vignette gives them.

Post-merger EPS (cash deal)

EPS = (acquirer earnings + target earnings + after-tax synergies − after-tax financing cost) ÷ acquirer shares

After-tax financing cost = cash paid × rate × (1 − tax rate). The rate is the borrowing rate, or the forgone interest rate on cash.

Target holders' ownership in combined firm

Ownership = new shares issued ÷ (acquirer shares + new shares issued)

This is the share of combined value and synergies that target holders receive in an all-stock deal.

Premium paid

Premium = offer price − target standalone price; premium % = premium ÷ target standalone price

This is the target shareholders' gain in a cash deal.

Gain split

Acquirer gain = synergies − premium paid; target gain = premium paid (cash deal)

In a stock deal, target gain = ownership share × combined value − target standalone value.

Accretion test (stock deal)

EPS accretive if acquirer P/E > offer price ÷ (target EPS + after-tax synergies per target share)

Equivalent to the target's earnings yield at the offer price exceeding the acquirer's earnings yield. With no synergies, the denominator is just target EPS. With synergies, you must add the after-tax synergies per target share to target EPS, or the test is wrong. If in doubt, recompute EPS in full.

Accretion test (cash deal)

EPS accretive if (target earnings + after-tax synergies) ÷ cash paid > after-tax financing rate

Target earnings yield at the price paid versus the after-tax cost of funds. With no synergies, use target earnings alone.

Pre-offer vs post-offer test

Typically in place before a bid arrives → pre-offer; adopted or used in response to a live bid → post-offer

Poison pills, poison puts, staggered boards and supermajority rules are standard pre-offer defenses. Greenmail, white knight, Pac-Man, crown jewel and leveraged recapitalization are post-offer. If the vignette says a normally pre-offer tool was adopted only after a bid appeared, treat that action as post-offer.

Flip-in poison pill effect

Bidder's percentage ownership falls as other holders buy new shares at a discount

The bidder is excluded from the discounted purchase. This dilutes the bidder's stake and raises its cost.

Herfindahl-Hirschman Index (HHI)

HHI = Σ (market share in % )² across all firms

A merger raises HHI by 2 × share of firm A × share of firm B. A larger rise in a concentrated market draws more antitrust scrutiny.

Takeover premium

Premium = (Offer price − Target's undisturbed price) ÷ Target's undisturbed price

Use the price before the deal news leaked. This is the main gain to target shareholders.

Acquirer gain

Acquirer gain = Synergies − Premium

Premium here means the total premium paid in money (premium per share × shares). Positive only if synergies exceed the premium.

Target gain

Target gain = Premium paid (in money)

Target shareholders keep the premium, whatever the later outcome.

Sponsor equity

Sponsor equity = Purchase price + Fees − New debt raised

Equity is the plug after debt is set.

Equity value at exit

Exit equity = Exit enterprise value − Net debt at exit

Exit EV is often exit EBITDA × exit multiple.

Money multiple and IRR

Multiple = Exit equity ÷ Sponsor equity; IRR = Multiple^(1 ÷ n) − 1 (single inflow and outflow, no interim payouts)

n is the holding period in years.

Quick revision

• Expansion happens through mergers and acquisitions; contraction happens through divestitures, spin-offs, split-offs and equity carve-outs.
• Name the form of a deal by its structure: a merger absorbs the target, while an acquisition may leave the target as a subsidiary.
• Synergies can be operating, such as cost savings or revenue gains, or financial, such as lower financing costs.
• Value created for the target holders is the premium: price paid minus the target's pre-deal market value.
• Gain to the acquirer = (target stand-alone value + synergies) − (price paid to target + transaction costs). For a stock deal, the cost depends on the target holders' share of the combined firm.
• Cash deals give the target holders a fixed amount; stock deals make them share in the combined firm's risks and outcomes.
• The exchange ratio is the number of acquirer shares given per target share; use it to find new shares issued and ownership split.
• Pre-offer defenses are set up beforehand; post-offer defenses are used once a bid arrives.
• Regulators review deals mainly for effects on competition, and review can delay or block a transaction.
• A leveraged buyout uses a large amount of debt to buy a company, and returns rely on cash flow, debt paydown and exit value.
• In every vignette, take the numbers from the exhibit first and check which party the question asks about.

Common mistakes

• Treating a carve-out as a full sale of the unit. Fix: A carve-out sells only a minority stake and the parent keeps control. A divestiture transfers control.
• Confusing spin-off with split-off. Fix: Spin-off is automatic and pro rata. Split-off needs shareholders to tender parent shares in exchange.
• Calling a deal vertical because the two firms are in the same industry. Fix: Same activity and often competitors is horizontal. Vertical means one firm supplies or buys from the other.
• Mixing up backward and forward integration. Fix: Backward means towards suppliers (inputs). Forward means towards customers or distribution (outputs).
• Using comparable company multiples and expecting them to include a control premium. Fix: Comparable multiples come from minority trading prices. Add a control premium or use precedent transactions if control is being acquired.
• Subtracting the premium from the target's stand-alone value instead of from synergies when finding the acquirer's gain. Fix: Acquirer gain in a cash deal = synergies − premium. Write it down before computing.
• Using the target's current price instead of the offer price when computing the exchange ratio. Fix: The ratio is offer price ÷ acquirer price. Use the current target price only to compute the premium.
• Using pre-tax interest in a cash deal funded by debt. Fix: Always multiply financing cost by (1 − tax rate) when adjusting net income.
• Classifying a poison pill as a post-offer defense. Fix: The curriculum lists poison pills as pre-offer defenses because they are typically adopted beforehand and triggered later. Only a pill the vignette says was adopted in response to a live bid would be a post-offer action.
• Confusing a white knight with a white squire. Fix: A white knight bids to acquire the target. A white squire buys a large stake without taking control.

Exam tips

• Decide the type from the mechanics described, not from the label the vignette uses.
• Check three things in order: cash received, control retained, shareholder choice.
• Motive questions usually reward the answer tied to the facts, such as focus after a conglomerate discount or a cash need.
• In ownership arithmetic, include new shares in the denominator and read whether the unit issues them or the parent sells existing ones.
• Practise labelling deals in three ways: integration, form and consideration. Vignettes often hide each label in a different sentence.
• Whenever a premium and a synergy appear together, do the subtraction. The question usually tests who captures the gain.
• Read motive statements critically. Pure diversification or empire building is a weak motive for shareholders.
• Link this topic to target valuation and deal financing, since items often continue from classification into pricing in one item set.