ACCA Strategic Professional · Advanced Financial Management

International investment and financing decisions: formula sheet

Full chapter guide

Key formulas

Purchasing power parity forecast rate: Home per foreign: S₁ = S₀ × (1 + inflation home) ÷ (1 + inflation foreign). Foreign per home: S₁ = S₀ × (1 + inflation foreign) ÷ (1 + inflation home); Pick the line that matches the quote. For a quote of home currency per unit of foreign currency, home inflation goes on top. For a foreign per home quote (as in the worked example, Z per $), foreign inflation goes on top. For year t, raise the ratio to the power t.
Interest rate parity forward rate: Home per foreign: F₀ = S₀ × (1 + interest rate home) ÷ (1 + interest rate foreign). Foreign per home: F₀ = S₀ × (1 + interest rate foreign) ÷ (1 + interest rate home); Same structure as PPP, but uses interest rates. The currency with the higher interest rate trades at a forward discount. Use it when the question gives interest rates, not inflation.
Foreign discount rate: (1 + foreign rate) = (1 + home rate) × (1 + foreign inflation) ÷ (1 + home inflation); Used in the foreign currency method. Gives the same NPV as the home currency method if the assumptions match.
Home currency NPV: NPV = Σ [foreign cash flow t ÷ S_t] ÷ (1 + home rate)^t; Convert each year's remittable, after-tax foreign cash flow at the forecast rate for that year, then discount.
Top-up tax on remittance: Extra home tax = (home tax rate − foreign tax rate) × taxable profit, if the home rate is higher; Applies where a credit is given for foreign tax paid. If the foreign rate is higher, usually no extra tax and no refund. Follow the question's tax rules.
APV: APV = Base case NPV + PV of financing side effects; Accept the project if APV > 0. Side effects can be negative, for example issue costs.
Base case NPV: Base case NPV = PV of all-equity after-tax cash flows at Keu − initial investment; Exclude all interest and financing flows from these cash flows.
Ungeared cost of equity (with tax): Keu = [E × Ke + D(1 − T) × Kd] ÷ [E + D(1 − T)]; Use a proxy company's market values E and D, its cost of equity Ke, its pre-tax cost of debt Kd and tax rate T. This assumes debt is risk-free-like, as the exam normally does. Use the form given in your exam formulae sheet if it differs.
Tax shield on permanent debt: PV of tax shield = D × T; For debt that stays constant for ever, discounted at the pre-tax cost of debt. For finite debt, calculate each year's interest × T and discount at the pre-tax cost of debt.
Value of a subsidised loan: Benefit = Loan amount − PV of after-tax interest and repayments, discounted at the market (pre-tax) cost of debt; Use the actual subsidised interest rate to calculate the tax relief.
Forecast exchange rate (PPP): Future spot (foreign per $1) = Spot × (1 + foreign inflation) ÷ (1 + $ inflation); Apply it year by year, using the inflation rates for each year. Foreign currency per one unit of home currency.
Issue costs: Include as a negative PV at time 0; Deduct tax relief on them only if the question says they are tax deductible.
Purchasing power parity (forecast spot): S1 = S0 × (1 + hc) ÷ (1 + hb); S0 and S1 are quoted as units of currency c per 1 unit of currency b (the base). hc is the inflation rate in the quoted currency country and hb is the inflation rate in the base currency country. Check which currency is the base before you start.
Interest rate parity (forward rate): F0 = S0 × (1 + ic) ÷ (1 + ib); Same quotation rule as PPP. ic and ib are the nominal interest rates for the period to the forward date, not necessarily annual rates. Adjust annual rates for periods under a year.
Interest rate for part of a year: Period rate = annual rate × months ÷ 12; Use the simple pro-rata rate unless the question gives compound rates or tells you otherwise.
International Fisher effect: (1 + ic) ÷ (1 + ib) = (1 + hc) ÷ (1 + hb); Links interest rate differences to expected inflation differences. You can use it to find an unknown inflation rate from interest rates, or the reverse.
Fisher effect (single country): (1 + i) = (1 + r) × (1 + h); Nominal rate = real rate combined with inflation. Use it to separate real and money rates.
Expectations theory: Expected future spot ≈ forward rate; The forward rate is treated as an unbiased predictor of the future spot rate. This is a theory and does not always hold.
Expected cash flow with probability of loss: Expected cash flow = Σ (probability × cash flow under each scenario); Use when the question gives a chance of expropriation or restriction. Probabilities must total 1.
Risk-adjusted NPV: NPV = Σ [expected cash flow ÷ (1 + r)^t] − initial investment; Here r may include a country risk premium. Do not adjust both cash flows and rate for the same risk without saying so.
Cash received by parent under a remittance cap: Remittable cash = lower of (cash available, permitted remittance); Blocked balance stays in the host country. Value it by reinvestment return or, if idle, at a delayed or nil value.
Present value of delayed remittance: PV = Blocked amount × (1 + local reinvestment return)^n ÷ (1 + r)^n; Use when funds are released after n years and can earn a return meanwhile.
CAPM cost of equity: Ke = Rf + β × (Rm − Rf); Use the risk-free rate and market premium for the market the beta is measured against. In an international CAPM that may be the world market.
Ungearing an equity beta (debt beta assumed zero): βa = βe × Ve ÷ [Ve + Vd(1 − T)]; Use market values and the proxy company's tax rate. If a debt beta is given, include it: βa = βe × Ve/(Ve + Vd(1−T)) + βd × Vd(1−T)/(Ve + Vd(1−T)).
Regearing to a target capital structure (debt beta zero): βe = βa × [1 + Vd(1 − T) ÷ Ve]; Use the project's or parent's target gearing and the tax rate that applies to the project.
After-tax cost of debt: Kd(1 − T); Use the relevant tax rate. Redeemable debt needs the IRR of its cash flows to get Kd.
WACC: WACC = Ke × Ve ÷ (Ve + Vd) + Kd(1 − T) × Vd ÷ (Ve + Vd); Weights are market values at the target gearing for the project.
Beta from correlation: β = ρ(i,m) × σi ÷ σm; ρ is the correlation between the project's returns and the market portfolio. A different market portfolio gives a different beta.
Two-asset portfolio variance: σp² = w1²σ1² + w2²σ2² + 2 × w1 × w2 × ρ × σ1 × σ2; A lower correlation ρ gives more diversification and lower portfolio risk.
Fisher relationship: (1 + nominal rate) = (1 + real rate) × (1 + inflation); Use it to move between real and nominal rates.
Foreign-currency discount rate from home rate: (1 + foreign rate) = (1 + home rate) × (1 + foreign inflation) ÷ (1 + home inflation); The same logic works with nominal interest rate differentials. Use it to discount foreign-currency cash flows consistently.
After-tax cost of debt (simple): Kd (after tax) = i × (1 − t); Use the tax rate of the country where interest is deductible. Applies to irredeemable debt; for redeemable debt find the IRR of the after-tax cash flows.
Effective home-currency cost of foreign borrowing: (1 + home cost) = (1 + foreign rate) × (1 + % change in foreign currency value against home currency); Use the forecast change in the value of the foreign currency in home terms. A rise in the foreign currency raises the cost. When rates are quoted as foreign units per one home unit, the % change in foreign currency value = S₀ ÷ S₁ − 1.
Interest rate parity: F₀ = S₀ × (1 + i foreign) ÷ (1 + i home); Rates are for the same period and quoted as foreign units per one home unit. Gives the forward rate. A lower foreign interest rate gives a lower F₀, which means fewer foreign units per home unit, so the foreign currency strengthens.
Purchasing power parity: S₁ = S₀ × (1 + h foreign) ÷ (1 + h home); h is the inflation rate. Rates are foreign units per home unit. Forecasts the future spot rate. A lower foreign inflation rate gives a lower S₁, which means fewer foreign units per home unit, so the foreign currency strengthens. Its % change in value = S₀ ÷ S₁ − 1.
Withholding tax effect on remittance: Net cash to parent = gross dividend − withholding tax − extra home tax, where extra home tax = max(0, home tax on grossed-up profit − (foreign corporate tax + withholding tax)); The gross dividend is the amount before withholding tax. The grossed-up profit is the foreign taxable profit before foreign corporate tax, so it includes both the foreign corporate tax and the withholding tax. Check the double tax treaty and whether credit is given for foreign tax paid, including withholding tax.
Extra home tax on foreign income with credit: Extra home tax = max(0, home tax on grossed-up profit − total creditable foreign tax); Total creditable foreign tax includes both foreign corporate tax and withholding tax on the same income. Credit is limited to the home-tax liability. If foreign tax is higher, the excess is usually not refunded.

Quick revision

Foreign project appraisal starts with incremental cash flows, not accounting profit.
Convert foreign cash flows using forecast exchange rates, then discount at a consistent rate.
Purchasing power parity links expected inflation differences to expected exchange rate changes.
Interest rate parity links interest rate differences to the forward rate.
Parity-based forecasts are estimates and can differ from actual future rates.
Consider remittance limits, withholding taxes and timing of cash to the parent.
APV = base-case NPV + present value of financing side effects.
In APV, discount the base case at an all-equity rate suited to the project's risk.
Discount the tax shield on debt at a rate that reflects its risk, as the question indicates.
Use a rate that matches the project's risk, not automatically the parent's existing cost of capital.
Political risk can reduce cash flows through expropriation, blocked funds or changes in tax.
Match the currency of borrowing to the currency of project cash flows to reduce exposure.

Common mistakes

Discounting foreign cash flows at the home-currency rate without converting them Fix: Always state the currency of every column. Convert at forecast rates first, or use a foreign discount rate derived from Fisher.
Using the spot rate for all years Fix: Forecast the rate each year using PPP or IRP unless the question says the rate is fixed. Currencies with higher inflation usually weaken.
Discounting the base case flows at the WACC instead of the ungeared cost of equity. Fix: In APV the base case has no debt. Always use Keu, which you may need to calculate from a proxy company.
Including interest payments in the base case cash flows. Fix: Keep operating cash flows free of financing. Interest only enters through the tax shield and subsidy calculations.
Inverting the ratio so the answer moves the wrong way Fix: Always identify the base currency first. The quoted-currency rate goes on top. Then check that the higher-rate country's currency has weakened.
Using PPP to find a forward rate or IRP to forecast a spot rate Fix: Remember: inflation gives future spot (PPP), interest gives forward (IRP). Look at which rate data the question supplies.
Listing generic risks without using the scenario. Fix: Tie every point to a case fact, such as the sector, the host country's history or the funding structure.
Treating blocked funds as a loss of all the profit. Fix: Value the blocked cash at its delayed or reinvested value, and list legal routes such as royalties, fees and loan repayments.
Using the parent's WACC for the overseas project without comment. Fix: Use it only if the project has similar business risk and financing. Otherwise build a proxy-based rate, or explain why the parent's rate is acceptable.
Regearing a proxy's equity beta directly without ungearing first. Fix: Always ungear to the asset beta first. Then regear to the project's gearing.

Exam tips

Show the layout clearly: a table with currency labels and a year row. Markers can follow your working and award method marks even if a number is wrong.
Always state your assumptions, for example PPP holds, tax is paid in the same year, no working capital changes. Unstated assumptions lose marks.
Read for the traps: blocked funds, withholding tax, royalties, transfer prices and lost sales elsewhere in the group. Each one usually has marks.
Leave time for commentary. Link points to the scenario, such as the host country's political stability, and recommend a clear decision. This is where professional skills marks come from.
Be ready to explain why the home and foreign currency methods agree, and when you might prefer one over the other.
Show the three headings (base case NPV, side effects, APV) clearly. Markers give marks for correct method even if one number is wrong.
If the question gives you proxy company data, expect to ungear the cost of equity. Learn the formula and when to use pre-tax Kd. Check your exam formulae sheet.
Always state your assumption on discount rates for tax shields and loans. A one-line statement picks up marks if the question is ambiguous.