Valuation in Mergers and Acquisitions: formula sheet

Key formulas

Synergy

Synergy = Value of combined firm − (Value of A + Value of B)

A deal creates value only if synergy is positive after the premium paid and the costs of the deal.

Net gain to acquirer

Net gain = Synergy − Premium paid

Premium = Price paid for the target − Its stand-alone market value.

Classification rule

Same business = horizontal; different stages of one chain = vertical; unrelated businesses = conglomerate

Use the relationship between the firms, not their size.

Net asset value (NAV)

NAV = Fair value of assets − Outside liabilities (including preference capital)

Value per equity share = NAV available to equity ÷ number of equity shares. Exclude fictitious assets such as preliminary expenses.

Capitalisation of maintainable earnings

Value of business = Maintainable profit after tax ÷ Capitalisation rate

Capitalisation rate is the required rate of return. It equals 1 ÷ P/E multiple.

P/E based value

Equity value = Maintainable earnings × P/E multiple

Use the P/E of comparable companies, adjusted for the target's risk and size.

Enterprise value multiple

Enterprise value = EBITDA × EV/EBITDA multiple; Equity value = Enterprise value − Net debt

Net debt = Debt − Cash and cash equivalents.

Free cash flow to firm (FCFF)

FCFF = EBIT × (1 − t) + Depreciation − Capital expenditure − Increase in working capital

Discount FCFF at the WACC to get enterprise value.

Terminal value (growing perpetuity)

TV = FCFF(n+1) ÷ (WACC − g) = FCFF(n) × (1 + g) ÷ (WACC − g)

Valid only when g is less than WACC. Discount TV by the factor of year n.

DCF equity value

Equity value = PV of FCFF + PV of terminal value − Net debt

Divide by number of shares for value per share.

Synergy value

Synergy = V(AB) − [V(A) + V(B)]

V(AB) is the combined firm's value; A is the acquirer, B is the target. Positive synergy is the base for any merger gain.

Value of a perpetual synergy

Synergy value = Annual after-tax synergy cash flow ÷ r

Use r suited to the risk of the synergy. If the flow grows at g, use ÷ (r − g) with the first-year flow, and r must exceed g.

Premium paid

Premium = Price paid for target − Stand-alone value of target

If payment is in shares, value the shares at their post-merger worth or as the question directs.

Gain to target

Gain to target = Premium

Equals price paid minus the target's stand-alone value.

Gain to acquirer (cash deal)

Gain to acquirer = Synergy − Premium

Equivalent to V(AB) − V(A) − price paid, where V(AB) includes the effect of paying cash for the target.

Net present value of the merger

NPV to acquirer = Gain to acquirer

Accept the merger only if this is positive, subject to strategic factors.

Exchange ratio on market price

ER = Market price per share of target ÷ Market price per share of acquirer

Gives target holders the same market value, with no premium. Add any premium to the target price first.

Exchange ratio on EPS

ER = EPS of target ÷ EPS of acquirer

Equates earnings contribution per share. Use the same EPS basis for both.

Exchange ratio on book value

ER = Book value per share of target ÷ Book value per share of acquirer

Book value per share = Net worth available to equity ÷ Number of equity shares.

Weighted exchange ratio

ER = Σ (weight × ratio on each basis), with weights summing to 1

Use the weights given in the question. If none are given, state your assumption.

New shares issued

New shares = Target shares × ER

Total shares after merger = Acquirer shares + New shares.

EPS after merger

Merged EPS = (Earnings of acquirer + Earnings of target + synergy) ÷ Total shares after merger

Add synergy only if the question states it.

Market price after merger

Price = Merged EPS × P/E ratio assumed

The P/E is usually the acquirer's, or a stated combined P/E.

Equivalent EPS for target holder

Equivalent EPS = Merged EPS × ER

Compare with the target's old EPS to see the gain or loss per target share.

Purchase consideration

PC = Cash paid + (Shares issued × fair value per share) + fair value of other payments

Use fair value on the deal date. Payments made to the target's shareholders form the consideration.

Shares issued under an exchange ratio

New shares = Target shares × Exchange ratio

Exchange ratio is the number of acquirer shares given per target share.

Premium per share

Premium = Offer value per share − Unaffected market price per share

Use the price before the deal news leaked or was announced.

Premium percentage

Premium % = Premium per share ÷ Unaffected market price × 100

Total premium = premium per share × number of target shares.

Synergy

Synergy = V(combined) − V(acquirer) − V(target)

All values are standalone values before the deal. Synergy is the gain from combining.

Cost of a cash offer

Cost = Cash paid − V(target standalone)

Cost is the premium over standalone value.

Cost of a stock offer

Cost = (New shares ÷ Total shares after deal) × V(combined) − V(target standalone)

Total shares after deal = acquirer's old shares + new shares issued. Combined value includes synergy.

NPV of the merger to acquirer

NPV = Synergy − Cost

Positive NPV means acquirer's shareholders gain.

Goodwill on acquisition (Ind AS 103 style)

Goodwill = Consideration − Fair value of net identifiable assets acquired

A negative result is a bargain purchase, which needs separate treatment.

Debt-to-total funding in an LBO

Purchase price = Debt raised + Equity contributed (+ any seller finance)

Sources must equal uses. Uses include price paid, refinanced debt and fees.

Equity contributed

Equity = Total uses − Total debt

Equity is the balancing figure. Do not assume it is a fixed percentage.

Exit equity value

Exit equity = Exit enterprise value − Net debt at exit

Net debt = debt − cash. Debt repaid from cash flows raises exit equity.

Multiple of money (MoM)

MoM = Exit equity ÷ Equity invested

A simple return measure that ignores time.

IRR from a single exit

IRR = (Exit equity ÷ Equity invested)^(1 ÷ n) − 1

Use when there are no interim cash flows. n is the number of years held.

Interest cover

Interest cover = EBIT ÷ Interest expense

Lenders check this to see if debt is serviceable. Higher is safer.

Debt service capacity

Cash available for debt service ÷ (Interest + Principal repayment)

A value below 1 means the cash flow cannot meet scheduled payments.

Share entitlement in a demerger (pro rata)

New shares to a holder = Shares held in demerged company × Entitlement ratio

Example: ratio 1:2 means 1 resulting-company share for every 2 held. Fractions are usually rounded or settled in cash as per the scheme.

Value of demerged entity

Value of remaining business = Pre-demerger equity value − Value of undertaking demerged

Total shareholder wealth should be unchanged immediately before and after if both are valued fairly.

Open offer trigger and size (SEBI SAST)

Trigger: acquirer, with persons acting in concert, acquiring shares that take voting rights to 25% or more, or acquiring control. Minimum open offer = 26% of total shares of the target

State the thresholds exactly as the Regulations provide for the case, and note creeping acquisition rules separately.

Open offer price (principle)

Offer price = highest of the specified benchmarks (negotiated price, volume-weighted averages and other prescribed prices)

Do not use only the latest market price. Use the figures the question gives.

Post-restructuring value check

Value created = Sum of parts after restructuring − Value before restructuring

Positive only if standalone value of parts exceeds the conglomerate value, net of costs.

Quick revision

• Merger combines companies into one; acquisition is one company taking control of another.
• Horizontal deals join competitors, vertical deals join supply chain stages, conglomerate deals join unrelated businesses.
• Use more than one valuation method and explain why the chosen value is reasonable.
• Synergy = value of combined firm − (value of acquirer + value of target), both standalone.
• Synergy comes from revenue gains, cost savings, tax benefits and lower financing cost.
• Exchange ratio = shares of acquirer issued per share of target, based on the agreed value basis.
• Exchange ratio on market prices is target price ÷ acquirer price, when the deal is priced at market.
• Check the effect on EPS and market value per share for both sets of shareholders.
• Purchase consideration can be cash, shares, or a mix, and the form changes risk and tax for sellers.
• A leveraged buyout is financed mostly by debt, repaid from the target's own cash flows.
• Takeover defences include poison pill, white knight and buyback; know one line on each.
• A demerger transfers one undertaking into a separate company; know that the legal route needs approval under company law.

Common mistakes

• Treating merger and acquisition as the same thing in every case. Fix: State that in a merger the combining firms become one, while in an acquisition one firm gains control and the target may survive.
• Calling a deal vertical because the firms are in the same industry. Fix: Check whether the firms are at different stages. Same stage and same product is horizontal.
• Taking reported profit as maintainable profit without adjustment. Fix: Remove one-off gains and losses, adjust for tax, and then capitalise.
• Using book values in the asset-based method when fair values are given. Fix: Replace book values with the revalued figures and drop fictitious assets.
• Counting the target's stand-alone value as part of the synergy. Fix: Subtract both stand-alone values first. Synergy is only the extra over A + B.
• Treating the premium as a cost that reduces total synergy. Fix: The premium only transfers value to the target. Total synergy stays the same; it is split between the two parties.
• Dividing acquirer by target instead of target by acquirer. Fix: The ratio is acquirer shares per target share. Target value goes on top, acquirer value at the bottom.
• Using total earnings or total market value instead of per-share values. Fix: Convert to per share first. If you use totals, the ratio is a value ratio, not a share ratio.
• Measuring the premium against the current price after the announcement. Fix: Use the unaffected price before the news. If the question gives only one price, state your assumption.
• Valuing shares issued at face value in the consideration. Fix: For valuation questions use the fair or market value per share. Use face value only to split the amount between share capital and securities premium.

Exam tips

• In case questions, always name the type and give the reason from the facts. A bare label earns few marks.
• Write backward or forward whenever you say vertical.
• For motive questions, give four or five points with a one-line explanation each, not a list of words.
• Do not mix up the forms: a demerger is not a type of acquisition.
• Keep a short line on risks, such as integration problems and regulatory control, to make the answer balanced.
• Read the data first. The question usually hints at the method through the figures supplied.
• In MCQs, check whether the answer asks for enterprise value, equity value or per-share value.
• In written answers, show the formula, the working table and a closing comment on suitability.