37  International arbitrage; Multinational capital budgeting

37.1 Concept of Arbitrage

Arbitrage is the simultaneous purchase and sale of the same asset in two or more markets to profit from a price discrepancy. By definition, arbitrage is risk-free and self-financing — opportunities exist briefly because trading by arbitrageurs eliminates them, ensuring the law of one price. In international finance, arbitrage operates across currencies and interest rates and is the mechanism enforcing parity conditions (PPP, IRP) and uniform pricing in global markets. Capital budgeting in multinational corporations (MNCs) extends domestic NPV/IRR to foreign currency, country risk, tax, blocked funds and exchange-rate uncertainty.

37.2 Three Types of International Arbitrage

37.2.1 1. Locational (Spatial) Arbitrage

Profit from a difference in the spot rate of the same currency pair across two locations. Example: if USD/INR is 83.00 in Mumbai and 83.05 in Singapore — buy in Mumbai, sell in Singapore.

37.2.2 2. Triangular Arbitrage

Profit from inconsistencies among three cross-rates. If quoted rates between A/B, B/C and C/A do not satisfy the no-arbitrage condition, riskless profit is possible.

TipTriangular Arbitrage Example
  • USD/INR = 83
  • USD/GBP = 0.80
  • GBP/INR quoted in market = 110
  • Implied cross from above two = 83 / 0.80 = 103.75
  • Market quotes 110 — sell GBP in market, buy GBP through USD-INR route, lock in profit.

37.2.3 3. Covered Interest Arbitrage

If Interest Rate Parity (IRP) does not hold — i.e., the forward premium differs from the interest-rate differential — profit can be made by borrowing in one currency, converting at spot, investing at the higher rate abroad, and locking in the forward rate.

\[\text{Arbitrage exists if} \quad \frac{F - S}{S} \neq \frac{i_H - i_F}{1 + i_F}\]

37.3 Triangular No-Arbitrage Condition

For three currencies A, B, C with cross-rates: \[S_{A/B} \times S_{B/C} \times S_{C/A} = 1\]

Any deviation invites triangular arbitrage.

37.4 Covered vs Uncovered Interest Parity

TipCIP vs UIP
Parity Statement Hedged?
Covered Interest Parity (CIP) Forward premium = interest-rate differential Yes — via forward
Uncovered Interest Parity (UIP) Expected change in spot = interest-rate differential No — based on expectations

37.5 Multinational Capital Budgeting

The MNC capital budgeting decision is more complex than domestic because of:

TipChallenges in MNC Capital Budgeting
  • Multiple currencies — exchange-rate risk on inflows and outflows.
  • Tax regimes — host country, home country, double-tax treaties.
  • Political risk — expropriation, capital controls, blocked funds.
  • Country risk premia — different discount rates by host country.
  • Transfer pricing — internal pricing of inter-affiliate flows.
  • Subsidised financing — sometimes available from host government.
  • Exchange controls — restrict repatriation.
  • Different inflation rates in different countries.

37.6 Two Perspectives — Parent vs Subsidiary

TipParent vs Subsidiary Perspectives
Aspect Parent perspective Subsidiary perspective
Relevant cash flows Cash flows received by parent in home currency All cash flows generated by project locally
Tax Home + host country Host country only
Currency Convert at expected exchange rates Keep in local currency
Risk Sovereign and FX risk to parent Local commercial risk
Discount rate Parent’s WACC + risk premium Local cost of capital

The general consensus: parent’s perspective is appropriate for shareholder-wealth maximisation, because shareholders care about cash flows they eventually receive.

37.7 Estimating Cash Flows

TipCash-Flow Steps in MNC Capital Budgeting
  1. Forecast project cash flows in host-country currency.
  2. Apply host-country tax to get post-tax cash flows.
  3. Forecast exchange rates over project life (using IRP, PPP, forward rates).
  4. Convert to home currency.
  5. Apply home-country tax (less foreign-tax credit, if any).
  6. Adjust for blocked funds, transfer pricing, royalties, management fees.
  7. Compute terminal value (asset sale, working capital recovery).
  8. Discount at parent’s risk-adjusted WACC.

37.8 Adjusted Present Value (APV)

In MNC settings, the Adjusted Present Value (APV) is often preferred to plain NPV:

\[APV = \text{Base NPV (all-equity)} + \sum \text{PV of side effects}\]

Side effects include: tax shield from debt; subsidised loans; cost of issue; lost depreciation tax shield from currency translation; etc.

37.9 Risk Adjustment

TipAdjusting for Country and FX Risk
  • Country-specific WACC with sovereign-spread add-on.
  • Adjust cash flows directly with probability-weighted scenarios.
  • Forward exchange rates for FX conversion (most common).
  • Sensitivity analysis across exchange-rate paths.
  • Real options for political-risk flexibility.

37.10 Blocked Funds

When host countries restrict profit repatriation, MNCs employ: - Re-invoicing centres — shift cash through intermediate entities. - Royalty and management-fee payments — to bring back cash. - Transfer-pricing (within arm’s-length norms). - Parallel loans — back-to-back lending between parent groups in different countries.

flowchart TB
  A[International Arbitrage] --> L[Locational]
  A --> T[Triangular]
  A --> C[Covered Interest]
  M[MNC Capital Budgeting] --> P[Parent Perspective]
  M --> S[Subsidiary Perspective]
  M --> APV[APV =<br/>Base NPV + side effects]
    classDef default fill:#003366,color:#ffffff,stroke:#ffcc00,stroke-width:3px,rx:10px,ry:10px;

NoteDistractor warning

PYQs ask: arbitrage is risk-free and self-financing. If a strategy requires capital investment and bears risk, it is not arbitrage. Covered interest arbitrage uses forwards to eliminate FX risk; uncovered interest arbitrage (speculation) is risky.

37.11 Practice Questions

Q 01 Arbitrage Easy

Arbitrage is:

  • ARisky speculation
  • BRiskless, self-financing profit from price differentials
  • CTax evasion
  • DLong-term investment
View solution
Correct Option: B
Arbitrage — riskless profit from price discrepancies; restores the *law of one price*.
Q 02 Types Medium
View solution
Correct Option: A
Three types — locational, triangular, covered interest.

Which is **not** a type of international arbitrage?

  • ADividend arbitrage
  • BLocational
  • CTriangular
  • DCovered interest
Q 03 Locational Medium

USD/INR = 83.00 in Mumbai, 83.20 in Singapore. The arbitrageur should:

  • ABuy USD in Mumbai, sell in Singapore
  • BBuy USD in Singapore, sell in Mumbai
  • CDo nothing
  • DHold USD long-term
View solution
Correct Option: A
USD cheaper in Mumbai (83 INR) than Singapore (83.20 INR) → buy where cheap, sell where dear.
Q 04 Triangular Hard

For three currencies A, B, C with cross-rates, the no-arbitrage condition is:

  • AS_{A/B} × S_{B/C} × S_{C/A} = 1
  • BS_{A/B} − S_{B/C} = S_{C/A}
  • CAll three cross-rates equal
  • DCross-rates are independent
View solution
Correct Option: A
Product of the three rates around the triangle = **1** — else arbitrage exists.
Q 05 CIP Medium

Covered Interest Parity (CIP) involves:

  • ASpeculative FX exposure
  • BLocking the forward rate to eliminate FX risk
  • CGovernment intervention
  • DOption-based hedging only
View solution
Correct Option: B
CIP — risk eliminated via forward; UIP — uncovered.
Q 06 UIP Hard

Uncovered Interest Parity (UIP) states:

  • AForward premium = interest-rate differential
  • BExpected change in spot = interest-rate differential
  • CSpot = Forward
  • DCapital flows are zero
View solution
Correct Option: B
UIP — *expected* spot change matches interest-rate differential.
Q 07 MNC Medium

Which is **not** an additional challenge in MNC capital budgeting (vs domestic)?

  • AExchange-rate risk
  • BPolitical / country risk
  • CBlocked funds
  • DUse of double-entry book-keeping
View solution
Correct Option: D
Double-entry book-keeping is universal — not MNC-specific.
Q 08 Perspective Medium

For MNC project appraisal, the *appropriate* perspective is:

  • ASubsidiary's perspective
  • BParent company's perspective
  • CAverage of both
  • DHost country's tax authority
View solution
Correct Option: B
Shareholders are at the parent — wealth maximisation requires parent perspective.
Q 09 APV Hard

In MNC capital budgeting, APV is computed as:

  • ABase NPV minus tax shield
  • BBase NPV (all-equity) plus PV of side effects (tax shields, subsidies, etc.)
  • CCash flow ÷ Cost of capital
  • DSum of dividends
View solution
Correct Option: B
**APV = Base NPV (all-equity) + Σ PV of side effects** — preferred in complex financing situations.
Q 10 Blocked Medium

MNCs can repatriate cash from countries with exchange controls via:

  • ARoyalty and management-fee payments
  • BRe-invoicing centres
  • CParallel loans
  • DAll of the above
View solution
Correct Option: D
All three methods help mitigate blocked-fund problems.
Q 11 Country risk Medium

In MNC capital budgeting, *country risk premium* is typically:

  • AAdded to the discount rate or deducted from cash flows
  • BIgnored
  • CSet to zero in all cases
  • DTreated as negative
View solution
Correct Option: A
Adjust either the discount rate (risk-adjusted) or the cash flows (probability-weighted).
Q 12 FX forecast Medium

For projecting future spot rates in MNC capital budgeting, the most common technique is to use:

  • AForward rates / Interest Rate Parity
  • BRandom walk
  • CAverage historical rate
  • DGovernment-set targets
View solution
Correct Option: A
**Forward rates** (derived via IRP) are the most-used unbiased predictors.
Q 13 Self-financing Medium

"Self-financing" in arbitrage means:

  • ANo initial capital investment is required
  • BLarge equity
  • CCrowdfunded
  • DGovernment-financed
View solution
Correct Option: A
Pure arbitrage requires no net capital outlay.
Q 14 Worked CIA Hard

If 3-month spot is INR 80/USD, 3-month forward 81; Indian 3-month interest is 6 %, US is 2 % (annualised). Covered interest arbitrage:

  • ABorrow USD, invest INR
  • BBorrow INR, invest USD
  • CNo arbitrage
  • DInsufficient data
View solution
Correct Option: A
3-month forward premium on USD = (81 − 80)/80 = 1.25 % → 5 % annualised; this *exceeds* the i_H − i_F = 4 % → borrow USD (cheap), invest INR, sell INR forward; covered arbitrage profit.
Q 15 Parallel loan Hard

A "parallel loan" arrangement to overcome exchange controls involves:

  • ATwo parent companies in different countries lending to each other's subsidiaries in their local currencies
  • BA swap with a central bank
  • CAn ECB
  • DIssuing GDRs
View solution
Correct Option: A
**Parallel / back-to-back loans** sidestep exchange controls between two countries.
Q 16 Tax Medium

In MNC capital budgeting, the *foreign tax credit* mechanism:

  • ADoubles the tax burden on the project
  • BAvoids double taxation by crediting host-country taxes against home tax liability
  • CEliminates all taxes
  • DApplies only to dividend
View solution
Correct Option: B
**Foreign tax credit** under DTAA prevents double taxation.
Q 17 Transfer pricing Medium

MNCs use transfer pricing to:

  • AManage internal pricing of inter-affiliate transactions; subject to arm's-length norms
  • BSet retail prices
  • CPay dividends
  • DIssue shares
View solution
Correct Option: A
Transfer pricing of intra-group transactions — must be at arm's-length (§92 Income-tax Act in India).
Q 18 Country risk Hard

"Country risk" in MNC capital budgeting typically includes:

  • APolitical risk and expropriation
  • BCurrency convertibility risk
  • CRegulatory and tax-policy changes
  • DAll of the above
View solution
Correct Option: D
Country risk = political + regulatory + currency + macro.
Q 19 Match Medium

Match each arbitrage type with its description:

Type Description
(i) Locational (a) Inconsistencies among three cross-rates
(ii) Triangular (b) Forward premium ≠ interest-rate differential
(iii) Covered Interest (c) Same pair, different price across centres
  • A(i)-(c), (ii)-(a), (iii)-(b)
  • B(i)-(b), (ii)-(c), (iii)-(a)
  • C(i)-(a), (ii)-(b), (iii)-(c)
  • D(i)-(c), (ii)-(b), (iii)-(a)
View solution
Correct Option: A
Locational — same pair across centres; Triangular — three cross-rates; CIA — forward vs interest differential.
Q 20 Law of one price Medium

Arbitrage in efficient markets ensures the:

  • ALaw of Many Prices
  • BLaw of One Price
  • CPersistence of price differentials
  • DGovernment control of prices
View solution
Correct Option: B
**Law of One Price** — identical assets sell at the same price after adjustment for transport / tax.

37.12 Quick Recall

ImportantQuick recall
  • Arbitrage — riskless, self-financing profit; restores law of one price.
  • Three types: Locational (same pair, different centres), Triangular (three cross-rates), Covered Interest (CIA, when IRP violated).
  • Triangular no-arbitrage: \(S_{A/B} \times S_{B/C} \times S_{C/A} = 1\).
  • CIP — hedged with forwards; UIP — unhedged, based on expectations.
  • MNC capital budgeting — adds multi-currency, country risk, blocked funds, transfer pricing, tax layers.
  • Parent perspective is appropriate — shareholders are at parent.
  • Cash-flow steps: forecast in foreign currency → host tax → convert via forward → home tax/credit → adjust for blocked/transfer → discount at parent WACC + country premium.
  • APV = Base NPV (all-equity) + PV of side effects (tax shields, subsidies, etc.) — preferred for complex financing.
  • Repatriation tools: royalty/management fees, re-invoicing, transfer pricing, parallel loans.