36 International Arbitrage and Multinational Capital Budgeting
37 Part A — International Arbitrage
37.1 Meaning of Arbitrage
Arbitrage is the simultaneous purchase and sale of an asset (or sets of assets) in two or more markets to exploit a price discrepancy and earn a risk-free profit (vij2021?; apte2020?). Three working features distinguish arbitrage from speculation and hedging:
- Risk-free. No directional bet; the offsetting trades lock the gain.
- Self-financing. No initial investment needed (in the textbook idealisation).
- Self-destroying. Arbitrage activity closes the price gap that created it; arbitrage opportunities are therefore fleeting in efficient markets.
In international finance, arbitrage takes three classical forms — locational, triangular and covered interest arbitrage — each enforcing a corresponding parity condition.
| Type | Mechanism | Parity enforced |
|---|---|---|
| Locational / Spatial | Buy a currency where it is cheaper, sell where it is dearer | Single price across geographic centres |
| Triangular | Exploit inconsistencies between three exchange rates | Cross-rate consistency |
| Covered Interest | Borrow in low-rate currency, invest in high-rate currency, lock the conversion via a forward | Covered Interest Rate Parity |
37.2 Locational Arbitrage
If USD/INR is quoted at ₹83.00 in Mumbai and ₹83.10 in London at the same moment, an arbitrageur buys USD in Mumbai (cheap) and simultaneously sells USD in London (dear), pocketing ₹0.10 per USD. The activity raises the Mumbai rate and lowers the London rate, restoring equality.
Locational arbitrage is enforced by competition, telecommunications speed and dealer networks; in modern wholesale markets, gaps are detected and closed in milliseconds.
37.3 Triangular Arbitrage
Triangular arbitrage exploits inconsistencies between three exchange rates. The cross rate implied by two currency pairs must equal the direct quote of the third pair; if not, an arbitrage profit exists.
37.3.1 Worked example
Suppose the market quotes:
- USD/INR = 83.00
- USD/EUR = 0.92 (i.e. 1 USD buys 0.92 EUR)
- EUR/INR = 91.00 (direct quote)
The cross rate of EUR/INR implied by the USD pairs is \(83.00 / 0.92 = 90.22\). But the market is quoting EUR/INR at 91.00 — higher than the cross-rate.
The arbitrageur therefore: starts with INR 1,00,000 → buys USD at ₹83.00, getting USD 1,204.82 → buys EUR at the USD/EUR rate, getting EUR 1,108.43 → sells EUR for INR at ₹91.00, getting INR 1,00,867. Profit ≈ ₹867 per ₹1,00,000, before transaction costs.
The activity raises the cross-rate-implied EUR/INR and lowers the directly quoted EUR/INR until they coincide.
37.4 Covered Interest Arbitrage
Covered interest arbitrage (CIA) earns a risk-free return by borrowing in a low-interest-rate currency, investing in a high-interest-rate currency, and covering the future conversion via a forward contract. The arbitrage continues until Covered Interest Rate Parity (IRP) is restored:
\[ \dfrac{F}{S} = \dfrac{1 + i_{\text{home}}}{1 + i_{\text{foreign}}} \]
When the equation does not hold, a riskless profit exists. The currency of the high-interest-rate country trades at a forward discount; the currency of the low-interest-rate country trades at a forward premium.
37.4.1 Worked example
USD interest rate = 2 % p.a.; INR interest rate = 7 % p.a.; USD/INR spot = 83.00; six-month forward = 84.50.
The IRP-consistent forward = \(83.00 \times (1 + 0.07/2) / (1 + 0.02/2) = 83.00 \times 1.035 / 1.01 = 85.05\).
The market forward (84.50) is below the IRP-consistent forward (85.05). An Indian investor can therefore borrow INR at 7 %, convert to USD at spot, invest USD at 2 %, and cover via the 6-month forward — locking a riskless gain.
37.5 International Parity Conditions
International finance rests on a small set of parity conditions that, in equilibrium, link spot rates, forward rates, interest rates and inflation rates (apte2020?).
| Condition | Statement |
|---|---|
| Purchasing Power Parity (PPP) | \(\dfrac{\Delta S}{S} \approx \pi_h - \pi_f\) — exchange rate adjusts to inflation differential |
| Covered Interest Rate Parity | \(\dfrac{F - S}{S} \approx i_h - i_f\) — forward premium equals interest differential |
| Uncovered Interest Rate Parity | \(\dfrac{E(S_t) - S}{S} \approx i_h - i_f\) — expected spot change equals interest differential |
| Fisher Effect | \(i = r + \pi^e\) — nominal rate equals real rate plus expected inflation |
| International Fisher Effect | \(\dfrac{\Delta S}{S} \approx i_h - i_f\) — high-interest-rate currency depreciates |
A useful mental picture: in equilibrium, forward premium ≈ interest differential ≈ inflation differential ≈ expected exchange-rate change.
37.6 Random Walk Hypothesis
A complementary view holds that the spot exchange rate follows a random walk — the best forecast of tomorrow’s spot is today’s spot. Empirically, this hypothesis often beats more complex models over short horizons (Meese-Rogoff 1983 finding).
38 Part B — Multinational Capital Budgeting
38.1 Meaning
Multinational capital budgeting is the process of evaluating long-term investment projects that cross national borders — typically a foreign-direct-investment (FDI) decision by a parent firm to set up or acquire a subsidiary abroad. The basic principles of capital budgeting (NPV, IRR, PI) carry over, but several layers of complexity are added (shapiro2020?; vij2021?).
38.2 How It Differs from Domestic Capital Budgeting
| Issue | Domestic | Multinational |
|---|---|---|
| Cash-flow currency | Single currency | Multiple currencies; need translation |
| Tax regime | One | Two — host and home |
| Inflation | One | Two — host and home |
| Political risk | Low | Significant |
| Repatriation | Free | May be restricted by host country |
| Regulatory framework | Single | Two or more, often conflicting |
| Cost of capital | Domestic WACC | Project-specific, with country-risk premium |
| Subsidised financing | Rare | Common (host-country export-promotion subsidies) |
| Cash-flow perspective | Firm = parent | Parent vs subsidiary distinction |
38.3 Parent vs Subsidiary Cash Flows
The single most-tested idea in this topic: cash flows from a foreign project must be evaluated from the parent’s perspective, not the subsidiary’s, because the parent is the entity actually deploying the capital (shapiro2020?).
The two views can differ for several reasons:
- Withholding tax on dividends remitted to the parent.
- Blocked funds — host-country restriction on remittance.
- Differential tax rates between host and home.
- Inflation differentials affecting future remittance values.
- Exchange-rate movement between project cash flows and the parent’s home currency.
- Subsidised host-country financing not available domestically.
A project viable from the subsidiary’s standpoint may fail from the parent’s; in international finance, the parent’s NPV is decisive.
38.4 Cash-Flow Estimation in Foreign Projects
| Step | Action |
|---|---|
| 1 | Estimate subsidiary’s after-tax cash flows in local currency |
| 2 | Apply withholding-tax rates on remittances |
| 3 | Apply tax-treaty credits and parent’s home-country tax |
| 4 | Convert remittable cash flows to parent’s currency at expected future spot rates |
| 5 | Discount the parent-currency cash flows at the project’s risk-adjusted cost of capital |
The terminal value must reflect what the parent could realistically realise — sale of subsidiary, accumulated retained earnings net of remittance restrictions, or transfer-of-business value.
38.5 Cost of Capital for Foreign Projects
The discount rate for a foreign project is not the parent’s home WACC. It must reflect:
- Country risk — sovereign and political risk in the host.
- Exchange-rate risk not hedged in cash flows.
- Project-specific business risk.
- Local financing benefits — subsidised host-country loans lower the project cost of capital but do not change intrinsic business risk.
A common formulation: project required return = home-country WACC + country-risk premium + project-specific premium.
38.6 Adjusted Present Value (APV) Approach
The Adjusted Present Value (APV) approach — developed by Stewart Myers (1974) — separates the project’s value into three additive components:
\[ \text{APV} = \text{NPV}_{\text{ungeared}} + \text{PV(tax shield from financing)} + \text{PV(side effects)} \]
In an international setting, side effects may include:
- PV of subsidised loans (host-country export incentives).
- PV of foreign-tax credits and withholding-tax saved.
- PV of remittance restrictions or blocked funds.
- PV of political-risk insurance premium.
The APV approach is preferred over WACC-based NPV when the financing of the foreign project is unusual or has identifiable, separable benefits.
38.7 Risk in Foreign Projects
| Risk | Working content | Mitigation |
|---|---|---|
| Political risk | Expropriation, war, sanctions, regime change | Political-risk insurance (MIGA), host-country diplomacy |
| Country / Sovereign risk | Default on sovereign obligations; capital controls | Country-risk rating, local borrowing |
| Exchange-rate risk | Adverse currency moves on cash flows | Forward, options, money-market hedge, natural hedges |
| Inflation differential risk | Persistent local inflation erodes real cash flows | Indexed pricing, indexation clauses |
| Repatriation risk | Blocked funds; withholding tax | Inter-company loans, royalties, transfer pricing within arm’s length |
| Cultural risk | Mismatch between corporate and local practices | Joint ventures, local partners |
38.8 Tools to Quantify Risk
| Tool | Working content |
|---|---|
| Sensitivity analysis | Vary one input (FX rate, inflation) and observe NPV |
| Scenario analysis | Best, base, worst (peg break, expropriation) |
| Monte Carlo simulation | Stochastic distributions of FX, prices, inflation |
| Decision tree | Sequential decisions and probabilistic outcomes |
| Real-options analysis | Recognise option to expand, abandon, switch (Myers 1977) |
| Risk-adjusted discount rate | Add country-risk premium to discount rate |
| Certainty-equivalent | Discount certainty-equivalent cash flows at risk-free rate |
38.9 Worked Example — Parent vs Subsidiary NPV
A US parent considers a project in India that costs ₹100 crore. Local cash flows of ₹15 crore per year for 8 years. Host-country tax 25 %, withholding tax 10 % on dividends; India has a tax treaty with the USA preventing double taxation. Spot ₹83 / USD; INR expected to depreciate at 4 % p.a. against USD. Required return for the parent project = 12 %.
Outline of computation:
- Subsidiary view: discount ₹15 crore × 8 years at INR cost of capital. NPV in INR.
- Parent view: convert each year’s after-tax remittable cash flow (post-withholding) to USD at expected future spot rate (\(S_t = 83 \times 1.04^t\)); discount at 12 % USD rate.
The parent NPV will typically be lower than the subsidiary NPV because (i) withholding tax reduces remittable amounts and (ii) USD-equivalent flows fall as INR depreciates. The decision must rest on the parent NPV.
38.10 Exam-Pattern MCQs
View solution
| Type | Parity | ||
| (i) | Locational arbitrage | (a) | Cross-rate consistency |
| (ii) | Triangular arbitrage | (b) | Single price across geographic centres |
| (iii) | Covered interest arbitrage | (c) | Covered Interest Rate Parity |
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| Condition | Statement | ||
| (i) | Purchasing Power Parity | (a) | Forward premium ≈ interest-rate differential |
| (ii) | Covered Interest Rate Parity | (b) | Exchange rate change ≈ inflation differential |
| (iii) | International Fisher Effect | (c) | Expected change in spot ≈ interest differential |
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| Risk | Mitigation | ||
| (i) | Political risk | (a) | Forwards, options, money-market hedge |
| (ii) | Exchange-rate risk | (b) | MIGA insurance; local partnerships |
| (iii) | Repatriation risk | (c) | Royalties, inter-company loans within arm's length |
| (iv) | Cultural risk | (d) | Joint ventures with local partners |
View solution
- Arbitrage — risk-free, self-financing, self-destroying.
- Three types of international arbitrage: locational, triangular, covered interest — each enforces a parity condition.
- Locational arbitrage → single price across centres; Triangular arbitrage → cross-rate consistency; Covered interest arbitrage → CIRP.
- CIRP: \(F/S = (1 + i_h) / (1 + i_f)\). High-interest currency trades at forward discount.
- Five parity conditions: PPP, Covered IRP, Uncovered IRP, Fisher Effect, International Fisher Effect.
- Equilibrium chain: forward premium ≈ interest differential ≈ inflation differential ≈ expected exchange-rate change.
- Multinational capital budgeting differs from domestic in: multiple currencies, two tax regimes, two inflation rates, political risk, repatriation, regulation, cost of capital, financing subsidies, parent-subsidiary perspective.
- Decision rule: project evaluated from parent’s perspective, not subsidiary’s.
- 5-step parent CF estimation: subsidiary CFs → withholding tax → home tax → convert at expected future spot → discount at parent’s risk-adjusted rate.
- APV (Myers 1974) = ungeared NPV + PV(tax shield) + PV(side effects).
- Risks: political, country/sovereign, exchange-rate, inflation, repatriation, cultural. Tools: sensitivity, scenario, Monte Carlo, decision tree, real options, RADR, certainty-equivalent.