CA Final · Advanced Financial Management

International Financial Management: formula sheet

Full chapter guide

Key formulas

Forecast exchange rate (PPP): S₁ = S₀ × (1 + i_home) ÷ (1 + i_foreign); Rates quoted as ₹ per unit of foreign currency. Use for expected future spot rates when inflation rates are given.
Forward rate (IRP): F = S₀ × (1 + r_home) ÷ (1 + r_foreign); Use interest rates, not inflation rates, when the question asks for forward-based rates.
Fisher relation: (1 + nominal rate) = (1 + real rate) × (1 + inflation); Use to convert between real and nominal discount rates.
NPV of foreign project (home currency method): NPV = Σ [CF_foreign,t × S_t ÷ (1 + k_home)^t] − I₀ × S₀; CF must be the cash flow available to the parent, not just the project's operating cash flow.
NPV (foreign currency method): NPV₍₎ = [Σ CF_foreign,t ÷ (1 + k_foreign)^t − I₀] × S₀; Convert once at spot. k_foreign must be consistent with k_home and expected depreciation.
Discount rate parity: (1 + k_home) = (1 + k_foreign) × (S₁ ÷ S₀); Links the two rates when the exchange rate moves as forecast.
APV: APV = Base-case NPV (all-equity) + PV of financing side effects; Side effects: interest tax shield (interest × tax rate), subsidised loan benefit, less issue costs.
Risk-adjusted cash flow: Expected CF = CF × probability of survival (or Σ p × CF); Preferred way to include political risk.
Cost of foreign currency debt (before tax): Kd = [I + (RV − NP) ÷ n] ÷ [(RV + NP) ÷ 2]; Approximate method for a plain bond. I = annual interest, RV = redemption value, NP = net proceeds, n = years. Exact cost is the IRR where NP = PV of interest and redemption.
After-tax cost of debt: Kd after tax = Kd × (1 − t); Apply only if interest is tax deductible. Use the tax rate given in the question.
Rupee cost of a foreign currency loan: (1 + rupee cost) = (1 + foreign cost) × (1 + depreciation of ₹ per year) − 1; Equivalent: (1 + Kf) × (Forward or expected rate ÷ spot rate) − 1 for one year. Rupee depreciation raises your cost.
Conversion ratio: Conversion ratio = Face value of bond in rupees (face value in foreign currency × stated exchange rate) ÷ Conversion price in rupees; Number of shares per bond. Always convert the foreign currency face value to rupees at the stated rate before dividing by the rupee conversion price.
Conversion value: Conversion value = Conversion ratio × Market price per share (at the time); Compare with the redemption value, with both in the same currency. Holder converts if conversion value is higher.
Conversion premium: Premium = (Conversion price − Current market price) ÷ Current market price × 100; Shows how much the share must rise before conversion becomes worthwhile. Use both prices in rupees.
Cost of FCCB (exact): Net proceeds = Σ Interest ÷ (1 + k)^t + Terminal flow ÷ (1 + k)^n, where t = 1 to n; Net proceeds are the issue proceeds after expenses, received at time 0. Interest and the terminal flow are the company's outflows, discounted at k. Terminal flow is the redemption value if not converted, or the conversion value if converted. Solve k by trial and interpolation.
Net position of a unit: Net = Total receivables from all units − Total payables to all units; Positive means net receiver, negative means net payer. The sum of all net positions is zero before charges.
Bilateral netting: Net payment = Larger amount − Smaller amount (payment by the unit owing more); Convert both amounts into one currency first, at the rate given for netting.
Saving from netting: Saving = (Gross transfers − Net transfers) × transaction cost %; Gross transfers are the sum of all inter-company payments. Net transfers are the sum of net payments only.
Cost of early or late payment: Interest effect = Amount × interest rate × days ÷ 365 (or 360 as the question states); Use the day-count basis given. Compare this with the exchange gain or loss.
Forward premium or discount (annualised): (Forward − Spot) ÷ Spot × 12 ÷ months × 100; Use to judge whether leading or lagging beats hedging.
Effective cost of foreign currency loan (in ₹): [(1 + r_f) × (S1 ÷ S0)] − 1; r_f is the foreign interest rate for the period, S0 is spot at borrowing, S1 is spot at repayment, both in ₹ per unit of foreign currency.
Relative PPP (forecast of spot rate): S₁ = S₀ × (1 + Ih) ÷ (1 + If); S is in units of home currency per one unit of foreign currency (for example ₹ per $). Ih and If are inflation rates for the same period. Home inflation goes on top.
Absolute PPP: S = Ph ÷ Pf; Price of the same basket at home divided by its price abroad. Holds only if there are no transport costs, barriers or taxes.
Interest rate parity (forward rate): F = S₀ × (1 + ih × n) ÷ (1 + if × n); ih and if are annual rates, n is the period in years (for example 0.5 for six months). Use compounding instead if the question says so. Same quote direction as S₀.
Forward premium or discount (annualised): (F − S₀) ÷ S₀ × (12 ÷ months); A positive result means the foreign currency is at a forward premium. A negative result means a discount.
Fisher equation: (1 + i) = (1 + r) × (1 + π); i is the nominal rate, r is the real rate and π is expected inflation. The shortcut i ≈ r + π is only an approximation.
International Fisher effect (forecast of spot rate): S₁ = S₀ × (1 + ih) ÷ (1 + if); Uses nominal interest rates for the same period. Assumes equal real rates in both countries.

Quick revision

Interest rate parity links the forward rate to the spot rate and the interest rate difference between the two currencies.
With the rate quoted as home currency per foreign unit: Forward = Spot × (1 + home rate) ÷ (1 + foreign rate), for the same period.
Purchasing power parity links expected spot rate to inflation difference, with the rate quoted as home currency per foreign unit: Expected spot = Spot × (1 + home inflation) ÷ (1 + foreign inflation).
Fisher relationship: (1 + nominal rate) = (1 + real rate) × (1 + inflation).
International Fisher effect: the interest rate difference points to the expected change in the spot rate.
Under interest rate parity, the currency with the lower interest rate trades at a forward premium against the currency with the higher interest rate.
In foreign project NPV, cash flows and discount rate must be in the same currency.
Home currency approach: convert forecast foreign cash flows at forecast rates and discount at the home rate. Foreign currency approach: discount in foreign currency and convert the NPV at spot.
The two approaches give the same NPV only when the exchange rate forecasts and the home and foreign discount rates follow the same parity relationship.
Include project-specific items such as taxes, blocked funds, and remittance limits when the case gives them.
ADRs and GDRs are depository receipts representing shares of an issuer; FCCBs are foreign currency bonds convertible into shares.
Netting reduces the number of cross-border payments by settling only the net amount; leading and lagging change payment timing to suit expected rate moves.
For institutions, remember the purpose of each: what it lends or regulates, and who it serves.

Common mistakes

Discounting the project's cash flows instead of the parent's cash flows Fix: Always ask what reaches the parent. Show a line for remittable cash flow before converting.
Using the spot rate for all years Fix: Forecast each year's rate by PPP or use the rates given. Only the initial outlay is converted at spot.
Treating ADR and GDR as the same thing Fix: State the market: ADR is for the US market, GDR is issued across several countries, usually in Europe. Add the regulatory difference: ADRs listed on US exchanges (Level II and III) follow SEC disclosure norms, while Level I and Rule 144A ADRs have lighter requirements.
Using the coupon as the cost of an FCCB Fix: Cost includes the redemption premium or conversion value, and issue expenses. Compute the IRR of all cash flows.
Netting amounts in different currencies without converting. Fix: Convert every cell to the settlement currency at the stated rate before any subtraction.
Net positions do not add to zero and the student carries on. Fix: Always add the nets. If the total is not zero, recheck the matrix before moving on.
Thinking the Euro currency market deals only in euros or only in Europe. Fix: Define it as deposits and loans in a currency held outside its home country, in any location.
Mixing up the roles of the IMF and the World Bank. Fix: Link the IMF to balance of payments and monetary stability, and the World Bank to long-term development projects.
Putting the foreign rate on top and the home rate below. Fix: Always write the quote as home currency per one unit of foreign currency first. Then home rate goes on top. Check the sign afterward: the higher-rate currency must weaken.
Using the full annual interest rate for a three-month or six-month forward. Fix: Multiply the annual rate by n (months ÷ 12) before using it, unless the question specifically gives a compound rate for the period.

Exam tips

Write the quote direction (₹ per unit of foreign currency) at the top of your working. Many marks are lost on inverted rates.
Show the parent cash flow as a separate line. The examiner's marking scheme usually gives marks for tax, fees and blocked funds.
If the question gives both inflation and interest rates, use inflation for forecast spot rates (PPP) and interest rates for forward rates (IRP), as the question words it.
For APV, keep base-case NPV, tax shield and issue cost as three clearly labelled lines so you score even if one line is wrong.
Close with a one-line decision and a short comment on exchange or political risk. Case-scenario MCQs often test exactly this judgement.
In theory questions, write ADR vs GDR as short points under fixed heads: market, listing, regulator, investors, disclosure, and cost.
In FCCB numericals, always check whether the question wants cost if converted or if redeemed. Show both when unsure and state which one holders would choose.
Show the IRR trial with two rates and interpolation, since marks go for the method even if the final value differs slightly.