ACCA Strategic Professional · Advanced Financial Management

Management of international trade and finance: formula sheet

Full chapter guide

Key formulas

Annual cost of forgoing a cash discount: [(1 ÷ (1 − d))^(365 ÷ N) − 1], where d = discount rate and N = days of extra credit gained; Compare with the cost of short-term borrowing. If the cost of forgoing the discount is higher, take the discount.
Discount on a forfaited bill or discounted receivable (simple basis): Proceeds = Face value × (1 − discount rate × days ÷ 360 or 365); Use the day-count basis given in the question. Banks often quote on 360 days.
Effective annual cost of financing a receivable: (Face value ÷ Proceeds)^(365 ÷ days) − 1; Use this to compare factoring, discounting or forfaiting with an overdraft rate.
Foreign currency receivable in home currency: Home currency = Foreign amount ÷ spot rate (when the rate is quoted as foreign per 1 home) or × spot rate (when quoted as home per 1 foreign); Check the quote direction first. Use the bank's less favourable rate when converting.
Transaction exposure (net): Net exposure in a currency = Receipts in that currency − Payments in that currency over the same period; Offset inflows and outflows in the same currency first. Only the net amount needs external hedging.
Foreign receivable converted: Home currency receipt = Foreign amount ÷ Spot rate (if rate is quoted as foreign per 1 home); Check the quote direction first. If the rate is home per 1 foreign, multiply instead.
Translation of net assets: Home currency net assets = Foreign net assets ÷ Closing rate (foreign per 1 home); Net assets are translated at closing rate under IAS 21. Exposure is the net asset amount, not the profit alone.
Exposure change from rate move: Gain or loss = Net foreign exposure ÷ New rate − Net foreign exposure ÷ Old rate (foreign per 1 home); A positive net foreign receivable or net asset gains home value when the foreign currency strengthens and loses home value when it weakens. A net foreign payable does the opposite. Exchange differences on foreign-currency receivables and payables (transaction items) go to profit or loss under IAS 21. Translation differences on a foreign operation whose functional currency differs from the group's presentation currency go to other comprehensive income on consolidation. Establish the functional currency first.
Classification rule: Transaction = cash, short term, contractual. Translation = accounting, no cash. Economic = value and competitiveness, long term.; Use this as a quick label for any scenario.
Purchasing power parity (future spot rate): S1 = S0 × (1 + hc) ÷ (1 + hb); Rate is quoted as units of the counter currency per 1 unit of the base currency. hc is the inflation rate in the counter currency country. hb is the inflation rate in the base currency country.
Interest rate parity (forward rate): F0 = S0 × (1 + ic) ÷ (1 + ib); Same quoting convention. ic and ib are interest rates for the same period as the forward contract. Adjust for the time period, for example use 6/12 of the annual rate for six months.
International Fisher effect: S1 ÷ S0 = (1 + ic) ÷ (1 + ib); Uses nominal interest rates to forecast the expected future spot rate. Assumes equal real interest rates.
Fisher effect (closed economy): (1 + nominal rate) = (1 + real rate) × (1 + inflation rate); Use it to split a nominal rate into real rate and inflation.
Four-way equivalence link: (1 + ic) ÷ (1 + ib) = (1 + hc) ÷ (1 + hb) = F0 ÷ S0 = E(S1) ÷ S0; This is a theoretical set. In practice the links hold only approximately, and the forward and spot expectations usually differ.
Net position of a group company (in a common currency): Net position = Σ amounts to be received − Σ amounts to be paid; Convert every amount to one currency at the same agreed rate before you net. A positive result is a net receiver. A negative result is a net payer.
Check on a multilateral netting table: Σ net receipts = Σ net payments (all net positions add up to zero); If they do not add up to zero, you have made an arithmetic or conversion error. Check this before you go further.
Gross versus net settlement: Reduction in flows = Gross payments − Net payments; Bank charges and spreads are normally charged on the amounts converted. Fewer and smaller payments reduce the cost.
Benefit of leading (paying early): Benefit = Expected foreign currency cost at the later date − (Cost now × (1 + interest rate for the period)); Compare at the same date. Lead only if the benefit is positive and you accept that the exchange rate view could be wrong.
Matching rule: Exposure left = Foreign currency receipts − Foreign currency payments (same currency, similar date); Only this net amount needs hedging externally.
Which side of the quote: Bank buys the base currency at the lower rate and sells it at the higher rate; For a quote of $ per €1, you sell euros to the bank at the lower rate and buy euros from the bank at the higher rate. Always choose the rate that is worse for you.
Forward rate (interest rate parity): F = S × (1 + i home × t) ÷ (1 + i foreign × t); This form applies only when the quote is home currency per unit of foreign currency (for example $ per € for a US company). If the quote is the reverse (foreign currency per unit of home currency), invert the interest rate ratio: F = S × (1 + i foreign × t) ÷ (1 + i home × t). Use time t in years. This is used to estimate forwards or check them. In the exam the bank usually gives the forward rate.
Money market hedge: foreign payable: Foreign amount ÷ (1 + foreign deposit rate × t) = foreign currency to deposit now; Buy this at spot (offer side). If you need home currency to do so, borrow it at the home borrowing rate, then multiply by (1 + home borrowing rate × t) for the cost at the payment date. If you have surplus cash, use the home deposit rate as an opportunity cost.
Money market hedge: foreign receivable: Foreign amount ÷ (1 + foreign borrowing rate × t) = foreign currency to borrow now; Convert at spot (bid side). Deposit the home currency at the home deposit rate, multiplied by (1 + home deposit rate × t), to get the amount at the receipt date.
Futures contracts needed: Number of contracts = Exposure ÷ Contract size; Round to the nearest whole contract. Sell futures to hedge a receivable in the foreign currency. Buy futures to hedge a payable in the foreign currency. Check whether the futures price is quoted in the same direction as your exposure.
Futures gain or loss: Gain or loss = (Price movement) × Contract size × Number of contracts; Sold at the opening price and bought back at the closing price: gain if the price fell. A tick value equals tick size × contract size.
Basis and effective rate: Basis = Spot − Futures price. Effective rate ≈ Opening futures price + Closing basis; The futures price locks in the effective rate only if the basis is zero at closing. A change in basis changes the result.
Hedge efficiency: Hedge efficiency = Gain on futures ÷ Loss on the underlying exposure; Compare the gain on the futures with the loss on the exposure over the same period. A result of 100% is a perfect hedge.
Option type for a receipt: Receive foreign currency → buy a put on that currency; You want to sell the currency at a guaranteed minimum rate.
Option type for a payment: Pay foreign currency → buy a call on that currency; You want to buy the currency at a guaranteed maximum rate.
Premium cost: Total premium = premium per unit × amount hedged; Paid at the start. If asked, add interest to the date of the exposure.
Exercise decision (put, selling currency): Exercise if spot < strike; otherwise abandon and sell at spot; For a call (buying currency): exercise if spot > strike.
Effective rate with an option: Put: net rate ≈ strike − premium per unit (if exercised). Call: strike + premium per unit.; Premium and strike must be in the same currency terms. Ignores interest on the premium.
Number of exchange-traded contracts: Contracts = exposure ÷ contract size (round to whole contracts); Rounding leaves a small unhedged amount, which you settle at spot.
Black-Scholes call (currency, when foreign rate given): c = S × e^(−rf×T) × N(d1) − X × e^(−rd×T) × N(d2); S spot, X strike, rd domestic rate, rf foreign rate. Use it only if the question gives the inputs and expects it. If rf is ignored it reduces to the standard share formula.
d1 and d2: d1 = [ln(S ÷ X) + (rd − rf + σ²÷2) × T] ÷ (σ × √T); d2 = d1 − σ × √T; σ is the annualised volatility of the exchange rate.
Put-call parity (same inputs): p = c − S × e^(−rf×T) + X × e^(−rd×T); For European options. If rf = 0 it is the usual c − S + X × e^(−rT).
FRA quote notation: 3v9 FRA = starts in 3 months, ends in 9 months, covers a 6-month period; Take the bank's two-way quote. A borrower uses the higher rate. A depositor uses the lower rate.
FRA settlement (before discounting): Settlement = (Market rate − FRA rate) × Principal × months ÷ 12; If the market rate is above the FRA rate, the bank pays you. If it is below, you pay the bank. Interest is normally settled at the start of the period, so discount by 1 + (market rate × months ÷ 12).
Interest rate futures price: Futures price = 100 − implied interest rate (%); A borrower sells futures to hedge. A depositor buys futures. A rate rise lowers the price.
Tick value: Tick value = Contract size × 0.01% × contract months ÷ 12; For a 3-month contract of $1,000,000 the tick value is $25.
Number of futures contracts: Contracts = Principal ÷ Contract size × Hedge period ÷ Contract period; Use whole contracts. Match the contract expiry to the date the rate is fixed, not the end of the loan.
Futures hedge outcome: Method 1 (rate): Effective rate = (100 − opening futures price) ± basis adjustment. Method 2 (cash): Net interest cost = loan interest at actual rate − futures gain (or + futures loss); Gain or loss = ticks moved × tick value × contracts. Method 1 gives the lock-in rate: the implied rate at opening, adjusted for basis. Method 2 gives a cash cost, which you can convert back to a rate. Basis is the difference between the spot rate and the futures-implied rate. Basis risk means the hedge is rarely perfect.
Interest rate option (call and put on futures): Borrower buys a put on futures. Depositor buys a call on futures. Effective rate ≈ (100 − exercise price) adjusted for basis, plus the premium cost converted to a rate.; Exercise only if it beats the market. If you exercise, the futures position is closed out and the gain or loss on it, together with basis, moves your rate away from the strike. Before basis, the rate locked in is 100 − strike. If you do not exercise, you borrow at the market rate. Premium is paid upfront.
Cap, floor and collar: Cap = max rate. Floor = min rate. Collar = buy cap + sell floor (borrower).; Before premiums, the borrower's rate sits between the floor and cap strike rates. Premium received on the floor reduces the cap premium paid, so the net cost is the cap premium less the floor premium. An interest rate guarantee is a single-period OTC option, whereas a cap is a series of such options.
Swap net cost: Net cost = rate paid to lender + swap payment − swap receipt; Check both parties and the bank. The total gain from the swap equals the difference between the fixed-rate spread and the floating-rate spread, less any bank fee. With no bank, there is no fee to deduct.
Home tax payable on foreign income (credit method): Additional home tax = max(0, home tax rate × grossed-up foreign taxable profit − creditable foreign tax); The credit is capped at home tax on that income. For dividends, creditable foreign tax is the underlying corporate tax (on a grossed-up basis) plus any withholding tax, where the question or treaty gives credit for it. For interest and royalties, it is normally the withholding tax on the gross payment.
Withholding tax on a payment: Net cash received = gross payment × (1 − withholding tax rate); Applies to dividends, interest and royalties where the country imposes it. Use the treaty rate if given.
Effect of a payment on group tax: After-tax cost to payer = payment × (1 − payer's tax rate), if deductible; Dividends are not deductible. Interest, royalties and management charges usually are, subject to local rules.
Transfer price effect on tax: Group tax saving = change in profit shifted × (high tax rate − low tax rate); Compare tax rates in both countries. Check that the price remains within arm's length range.
Netting: Net payment = total owed by one company − total owed to it by the other; Multilateral netting reduces each company to one net receipt or payment, cutting transaction costs and spreads.
Group after-tax cash from a route: Cash to parent = dividend received net of any withholding tax − additional home tax, where additional home tax = max(0, home rate × grossed-up foreign profit − (underlying tax + withholding tax)); This formula is for dividends. The credit covers both the underlying tax and the withholding tax. For deductible payments such as interest, royalties and management charges, work out the local tax saved separately in a table, then compare routes.

Quick revision

Transaction risk affects cash flows on committed deals; translation risk affects reported results; economic risk affects long-term competitiveness.
Internal methods first: netting, matching, leading and lagging, invoicing in home currency.
Purchasing power parity links expected spot movement to inflation differences.
Interest rate parity links the forward rate to interest rate differences between two currencies.
Forward contract: lock a rate today for a future date; certain outcome, no benefit from favourable moves.
Money market hedge: borrow or deposit now, convert at spot, and settle with the future flow.
Options give the right but not the obligation; the premium is paid upfront, so include it in your comparison.
Choose the correct bid or offer rate for the direction of each transaction.
A currency swap exchanges principal and interest in two currencies; an interest rate swap exchanges fixed and floating payments.
Forward rate agreements and interest rate futures or options fix or cap future borrowing or deposit rates.
Transfer pricing can shift profit between countries, but tax authorities and local rules limit it.
Always finish with a clear recommendation, a reason and one stated limitation.

Common mistakes

Saying a documentary collection guarantees payment. Fix: State that in a collection the banks only handle documents. Only a letter of credit carries a bank's promise to pay, and only if the documents comply.
Listing every export finance method without choosing one. Fix: Shortlist two or three methods that fit the scenario, compare them, and finish with a clear recommendation.
Treating translation exposure as a cash loss. Fix: State that no cash moves. The effect is on reported net assets, gearing and ratios, usually through other comprehensive income.
Confusing transaction and economic exposure. Fix: Transaction is tied to a specific contract with a known date. Economic is about future, uncertain cash flows and competitive position.
Putting the ratio upside down Fix: Label the quote first. The counter currency is the number you are forecasting, so its country's rate goes on top.
Using inflation rates for a forward rate or interest rates for a PPP spot forecast Fix: Remember: inflation gives PPP spot, interest gives IRP forward. The international Fisher effect gives a spot forecast but uses interest rates.
Netting amounts in different currencies without converting them to a common currency first. Fix: Convert every figure at the stated rate first and say which rate you used. Then net.
Confusing netting and matching. Fix: Netting works on intra-group balances owed in different directions. Matching offsets inflows and outflows in the same currency, and can involve outside parties. State this in one line in your answer.
Using the wrong side of the bid-offer spread Fix: Ask what the bank is doing. If you are buying the foreign currency, the bank sells and you use the higher rate for a $ per € quote. If you are selling it, use the lower rate. Write bid or offer next to each rate.
Using the annual interest rate for a part-year period Fix: Multiply the annual rate by the fraction of the year before you use it. Six months at 3% a year is 1.5%, not 3%.

Exam tips

Always tie the method to the scenario: the buyer's standing, the country, the size and length of the deal. Generic lists score poorly.
Show a number where you can. Even one effective-cost comparison gives credible support for your recommendation.
State drawbacks as well as benefits. Examiners look for balanced advice and commercial judgement.
Use the professional skills marks: write a clear structure, use a suitable tone for the board, and finish with a firm recommendation.
If sanctions, bribery or doubtful customers appear in the scenario, raise the ethical issue and say what you would do.
Always tie each exposure type to a fact in the scenario. A pure definition earns few marks.
Show the quote direction before any conversion, and write it in your working so the marker can follow.
When asked to discuss, give both the effect and a sensible response for each type, and then a conclusion.