ACCA Strategic Professional · Advanced Financial Management

Financing acquisitions and mergers: formula sheet

Full chapter guide

Key formulas

Offer value per target share (cash): Offer value = cash per share × number of target shares; Total cash needed. Add any transaction costs if the question gives them.
Offer value per target share (share exchange): Value per target share = exchange ratio × acquirer share price; For example, 1 for 2 means 0.5 acquirer shares per target share. Use the acquirer's price before the bid unless told otherwise.
New shares issued: New shares = target shares × exchange ratio; Add to the acquirer's existing shares to get the enlarged share count.
After-tax cost of new debt: Interest after tax = debt raised × interest rate × (1 − tax rate); Deduct from combined earnings in a cash offer funded by debt.
Post-deal EPS: EPS = (acquirer earnings + target earnings + after-tax synergies − after-tax interest on new debt) ÷ (existing shares + new shares); Use only the items that apply to the option you are testing.
Ownership split: Target holders' share = new shares ÷ (existing shares + new shares); Shows dilution and the loss of control for the acquirer's shareholders.
Gearing (market value basis): Gearing = debt ÷ equity, or debt ÷ (debt + equity), using market values; State which definition you use. Say what you assume about the share price after the deal.
Post-merger share price (value approach): Price = (value of acquirer + value of target + PV of synergies − cash paid) ÷ total shares after the deal; Use it to compare what each group of shareholders gains under each offer.
Earnings yield test: Earnings yield = 1 ÷ P/E = EPS ÷ share price; Compare with the after-tax cost of debt as a quick guide to which method boosts EPS.
Exchange ratio: Exchange ratio = bidder shares offered ÷ target shares held (e.g. 3 for 5 = 0.6); Always state which company's shares are on top. Read the offer wording carefully.
New shares issued: New shares = target shares in issue × exchange ratio; Add these to the bidder's existing shares to get total shares after the deal.
Value of offer per target share: Offer value per target share = exchange ratio × bidder's share price; Compare with the target's current price to find the premium or discount.
Premium: Premium = (offer value per target share − target market price) ÷ target market price; Use the target's price before the bid is announced.
Post-merger EPS: Post-merger EPS = (bidder earnings + target earnings + after-tax synergies − extra costs) ÷ total shares after the deal; Remember to add any new finance costs only if the deal also involves debt.
Post-merger share price (P/E method): Share price = post-merger EPS × assumed P/E ratio; State the P/E you assume. Bidder's P/E is common, but a weighted P/E may be more realistic.
Post-merger share price (value method): Share price = (bidder value + target value + PV of synergies − costs) ÷ total shares after the deal; Use market values before the bid. Make sure synergies are in present value terms.
Gain to each group: Gain = value of holding after the deal − value of holding before the deal; Target holding after = new shares received × post-merger price. Bidder gain = (new price − old price) × old shares.
Number of new shares needed: New shares = (Cash required + issue costs) ÷ issue price; Add issue costs to the cash required if the question says the issue costs are paid from proceeds.
Theoretical ex-rights price (TERP): TERP = [(N × cum-rights price) + (n × issue price)] ÷ (N + n); N is existing shares and n is new shares. Assumes no other information reaches the market.
Value of a right: Per new share = TERP − issue price; per existing share = (TERP − issue price) × n ÷ N; Use the per-existing-share figure when comparing against the shareholder's current holding.
After-tax cost of debt (approximate): Kd (1 − t) = pre-tax interest rate × (1 − tax rate); For an irredeemable bond. For redeemable debt use the IRR of the after-tax cash flows.
WACC: WACC = Ke × E ÷ (E + D) + Kd (1 − t) × D ÷ (E + D); Use market values of equity and debt, after the funding is raised.
Modigliani-Miller cost of equity (with tax): Ke(geared) = Ke(ungeared) + [Ke(ungeared) − Kd] × (1 − t) × D ÷ E; Use only when the question gives the ungeared cost of equity and assumes risk-free debt. Kd here is pre-tax.
Gearing measures: Debt ÷ equity, or debt ÷ (debt + equity); Use the measure the question defines, and be consistent. Market or book values should match the data given.
Interest cover: Interest cover = profit before interest and tax ÷ interest; Recalculate with the new interest from acquisition debt and the target's earnings.
Conversion ratio: Conversion ratio = nominal value of loan stock ÷ conversion price; Gives the number of shares received per bond, for example ₹100 stock at a ₹50 conversion price gives 2 shares.
Conversion value: Conversion value = conversion ratio × current share price; Compare this with the redemption value to see whether conversion is likely.
Value of convertible bond: Value = higher of (present value of coupons and redemption at the straight-debt yield) and the conversion value, plus any option premium; The floor value is the straight debt value. The market price is normally above both.
Conversion premium: Conversion premium = market price of the bond − conversion value; Per share, divide by the conversion ratio to get premium per share.
Post-merger EPS: EPS = (combined earnings − after-tax interest on new debt) ÷ total shares after issue; For convertibles, show EPS before and after conversion (fully diluted).
Value of share-based offer: Offer value per target share = exchange ratio × bidder share price; Add any cash element to get the total value of a mixed offer.
Earn-out present value: PV of deferred payment = expected payment × discount factor, weighted by probability; Discount at a rate reflecting the risk of the target's performance.
Combined EPS: Combined EPS = (Acquirer earnings + Target earnings + synergies − after-tax finance cost) ÷ total shares after the deal; Use after-tax interest on new debt. Add new shares only for share-funded parts. Include synergies only if the question gives them.
After-tax interest: After-tax interest = Debt raised × interest rate × (1 − tax rate); Interest is tax-deductible in most questions. Check whether the question says otherwise.
Exchange ratio: New acquirer shares per target share = Offer price per target share ÷ Acquirer share price; For a stated ratio, multiply it by the number of target shares to get the new shares issued.
Offer price and premium: Premium = (Offer price − Pre-bid price) ÷ Pre-bid price; Compare the premium with the synergies per target share to judge who gains.
P/E test for EPS effect: Offer P/E = Offer price ÷ Target EPS. Compare with Acquirer P/E; In a pure share exchange with no synergies, EPS rises if offer P/E is below acquirer P/E and falls if it is above.
Gearing (market value): Gearing = Debt ÷ Equity (market value), or Debt ÷ (Debt + Equity); State which definition you use and keep to it. Use the one the question uses.
Ownership after share exchange: Old holders' share = Existing shares ÷ (Existing shares + New shares issued); The target holders own the rest. Compare with control thresholds that the question mentions.
Interest cover: Interest cover = Profit before interest and tax ÷ Interest; Useful financial risk measure after a debt-funded deal.
Bidder EPS after a share exchange: Combined EPS = (Bidder earnings + Target earnings + after-tax synergies) ÷ (Bidder shares + new shares issued); New shares issued = target shares × exchange ratio.
Bidder EPS after a cash offer funded by debt: Combined EPS = (Bidder earnings + Target earnings + after-tax synergies − after-tax interest on new debt) ÷ Bidder shares; Interest after tax = interest × (1 − tax rate).
Gain to bidder shareholders: Gain = (Value of target + synergies) − price paid; Price paid includes the premium. For a share offer, the target holders also share in the combined value.
Premium: Premium = Offer price − Pre-bid target market value; Compare it with the present value of synergies.
Gearing (debt to equity): Gearing = Debt ÷ Equity (or Debt ÷ (Debt + Equity)), stated using market or book values; State which definition you use and stay consistent.
Theoretical ex-rights price (TERP): TERP = (Number of old shares × cum-rights price + new shares × issue price) ÷ total shares after the issue; Useful if a rights issue funds the cash offer.

Quick revision

Share exchange: target holders share in future gains and risks; cash: they take value now and exit.
Combined value = bidder value + target value + synergies. Include synergies only if the question gives them or says they are expected; otherwise show results with and without them and state the assumption.
Value of a share offer depends on the bidder's post-deal share price, not only the current one.
Post-deal EPS = combined earnings ÷ total shares after issue, with earnings adjusted for synergies and financing cost.
Debt funding adds interest, which reduces earnings after tax at the stated tax rate.
A rights issue keeps control with existing holders who take up their rights (those who do not are diluted), and it raises equity so gearing does not rise as it would with debt funding.
Gearing in the combined entity includes the target's existing debt and the market value of the combined equity. A share exchange usually gives lower gearing than a debt-funded cash offer, but the result depends on how much debt the target already carries.
Convertibles give the holder a choice, and conversion dilutes ownership while redemption needs cash.
Vendor placing lets the target's holders receive shares and sell them to institutions for cash.
The bidder's shareholders gain if synergies (plus any undervaluation of the target) exceed the premium paid. If the premium exceeds the synergies, value transfers to the target's shareholders. In a share offer, the split of the gains also depends on post-deal ownership.
A higher EPS after a deal does not always mean higher shareholder wealth; check risk and price-earnings ratio.
End every answer with a clear recommendation, a reason and one risk.

Common mistakes

Deducting interest before tax, or forgetting to deduct it at all in a debt-funded cash offer. Fix: Always write 'interest × (1 − tax)' as its own line. Deduct it from combined earnings before dividing by shares.
Adding new shares in a cash offer, or ignoring new shares in a share exchange. Fix: Cash funded by debt issues no shares. Share exchange issues shares equal to target shares × exchange ratio. Check this before computing EPS.
Turning the exchange ratio upside down, for example using 5 ÷ 3 instead of 3 ÷ 5. Fix: Write 'bidder shares offered per target share' in the margin first. Then check that the new shares issued look sensible compared with the target's share count.
Valuing the offer using the bidder's price after the deal for the premium, or the target's price after the bid announcement. Fix: Use the bidder's current price and the target's pre-bid price to measure the premium. Use the post-merger price only to measure the actual gain or loss.
Using the issue price instead of the cum-rights price when computing TERP for the existing shares. Fix: Existing shares go in at the current market price. Only the new shares go in at the issue price.
Using book values of equity in WACC. Fix: Use market values of equity and debt unless the question says otherwise. State your assumption.
Treating convertible loan stock as ordinary debt only, or as equity only. Fix: Show both the debt floor and the conversion value. State what happens if holders convert and if they redeem.
Ignoring dilution after conversion when calculating EPS. Fix: Calculate EPS both before and after conversion. Add back after-tax interest saved and add the new shares.
Deducting the full interest instead of after-tax interest Fix: Always write interest × (1 − tax rate). Check the question for the tax rate and for any statement that interest is not deductible.
Adding new shares to a cash-and-debt option, or forgetting them in a share exchange Fix: Set up a column per option. Debt: no new shares. Share exchange: shares issued = offer value ÷ acquirer price (or the stated ratio × target shares).

Exam tips

Show a short comparison of each option on EPS, gearing and ownership. Then spend the remaining time on advice. Professional skills marks reward a clear, reasoned recommendation.
State your assumptions, such as share price unchanged after the bid or gearing on a market-value basis. Markers give credit for stated, sensible assumptions.
Apply the answer to the scenario. Use the company's tax position, debt covenants, shareholder base and the target's likely preferences, not generic points.
Advise both sides when the requirement allows. For example, explain what a target board might prefer and why.
If a rights issue or convertible is offered as funding, say how it changes gearing, dilution and timing compared with debt.
Show the exchange ratio, new shares and total shares as separate lines. Markers give method marks even if a later number is wrong.
Always finish with the gain or loss to both sets of shareholders. Questions often ask for it in a separate part, and the check that the gains equal the value created is quick.
State your assumption about the P/E ratio or the market's reaction. Then add a brief comment on whether it is realistic.