Chapter 10: Foreign Exchange Exposure and Risk Management

The Foreign Exchange (Forex) Market: The international decentralized OTC market where currencies of different nations are bought, sold, and exchanged. It operates continuously 24 hours a day across global financial hubs (Tokyo, Singapore, London, New York, Zurich).

Market Hierarchy:

1. Interbank / Wholesale Market: Major international commercial and investment banks trading massive volumes with tight bid-ask spreads.
2. Merchant / Retail Market: Commercial banks quoting rates to retail clients, corporate importers, exporters, and individual travelers (carrying bank profit margins).
3. Central Banks: Intervene to smooth exchange rate volatility, maintain foreign exchange reserves, and implement national monetary policy.

Settlement & Value Dates:

Correspondent banking relationships rely on three distinct accounts (Latin terminology):

Exchange Position vs. Cash Position (Illustration 2 & PQ 51):

• Exchange Position: Measures the bank's net foreign currency commitment or market exposure, combining both spot and forward commitments.
  • Overbought / Long Position: $\text{Total Purchases (Spot + Forward)} > \text{Total Sales}$. Bank gains if foreign currency appreciates.
  • Oversold / Short Position: $\text{Total Sales (Spot + Forward)} > \text{Total Purchases}$. Bank gains if foreign currency depreciates.
  • Square / Balanced Position: Purchases equal Sales (Zero market currency risk).
• Cash Position (Nostro Balance): Reflects the actual physical cash funds available in the Nostro account (only settled spot cash flows, remittances, and bank drafts; forward commitments are excluded).

Quotation Conventions: An exchange rate expresses the value of one currency (Base Currency) in units of another currency (Quote / Variable Currency):

$$\text{Exchange Rate} = \frac{\text{Quote Currency}}{\text{Base Currency}} \quad \text{e.g., } \text{USD/INR } = 83.00 \text{ (1 USD = 83 INR)}$$

Two-Way Quote: In the forex market, quotes are given as $\text{Bid} / \text{Ask}$ (or $\text{Buy} / \text{Sell}$ from the bank's viewpoint):

• Bid Rate: Price at which the market maker (bank) buys the base currency. (Customer sells at Bid).
• Ask / Offer Rate: Price at which the market maker (bank) sells the base currency. (Customer buys at Ask).
• Rule: The bank always buys low and sells high ($\text{Ask} > \text{Bid}$).

$$\text{Spread} = \text{Ask Rate} - \text{Bid Rate}; \quad \%\text{ Spread} = \frac{\text{Ask} - \text{Bid}}{\text{Ask}} \times 100$$

Pips: Price Interest Point, the smallest standard price increment (typically the 4th decimal place: $0.0001$, or 2nd decimal for JPY: $0.01$).

Cross Currency Rates: An exchange rate between two currencies calculated from their respective exchange rates against a common third currency (usually USD):

Forward Exchange Rate Quotations: Quoted either as an outright rate or as Forward Margins / Swap Points added/subtracted from the Spot rate:

Annualized Premium / Discount Formula:

$$\%\text{ Premium / Discount} = \frac{\text{Forward Rate} - \text{Spot Rate}}{\text{Spot Rate}} \times \frac{12}{\text{Tenure in Months}} \times 100$$

Broken Period Forward Rate: When the contract maturity falls on a date between standard monthly dates, use linear interpolation between the two adjacent forward quotes.

Banks quote Merchant Rates to commercial customers by adjusting the interbank market rate with an exchange margin specified by FEDAI (Foreign Exchange Dealers' Association of India):

The three fundamental parity theorems connect exchange rates, interest rates, and inflation rates:

Covered Interest Arbitrage (CIA) Mechanics:

• If $\frac{F}{S} > \frac{1 + r_D}{1 + r_F} \implies$ Forward rate is too high. Borrow Domestic, Convert Spot to Foreign, Invest in Foreign, Sell Foreign Forward.
• If $\frac{F}{S} < \frac{1 + r_D}{1 + r_F} \implies$ Forward rate is too low. Borrow Foreign, Convert Spot to Domestic, Invest in Domestic, Buy Foreign Forward.

Geographical (Two-Point) Arbitrage: Capitalizing on simultaneous price discrepancies for the same currency pair across two geographically separated financial centres (e.g., USD priced at ₹ 82.50 in Mumbai and ₹ 82.70 in London). Buy in the cheaper market and sell in the dearer market.

Triangular (Three-Point) Arbitrage: Exploiting misalignments among three mutually related currency pairs across three financial markets:

1. Compute the Cross Rate between Currency A and B through common Currency C.
2. Compare the synthetic Cross Rate with the direct market quote.
3. If synthetic rate $\neq$ quoted rate, an arbitrage opportunity exists. Start with 1 unit of Currency A, execute consecutive conversions across the triangle, and end with $> 1$ unit of Currency A.

Internal techniques mitigate forex risk within the multinational group without paying external bank fees or derivative margins:

1. Invoicing in Home Currency: Passing the entire currency risk onto the foreign counterparty by denominating exports in home currency (e.g., INR).
2. Netting (Bilateral & Multilateral): Consolidating intra-group cash inflows and outflows and settling only the net balance through a centralized treasury netting center.
3. Leading and Lagging: Accelerating (leading) or delaying (lagging) payment dates based on expected currency movements (Lead payments in appreciating currencies; lag payments in depreciating currencies).
4. Matching: Offsetting natural foreign currency inflows from exports against foreign currency outflows for imports in the same currency.
5. Price Variation: Adjusting selling prices to offset anticipated currency devaluations.

The Money Market Hedge (MMH) synthetic structure locks in certain domestic cash flows using domestic and foreign money markets:

Currency Options: Unlike forward contracts which impose an absolute obligation, currency options provide asymmetric protection:

• Importer (Hedging Payable): Buys a Call Option on foreign currency. Protects against depreciation beyond strike $X$, but allows participation in favorable appreciation.
• Exporter (Hedging Receivable): Buys a Put Option on foreign currency. Guarantees a minimum floor exchange rate $X$, while allowing upside participation.

Zero-Cost Collar / Range Forward / Cylinder: An exporter buys an OTM Put option (paying premium) and simultaneously sells an OTM Call option (receiving premium) such that the two premiums exactly offset:

$$\text{Net Premium Outlay} = \text{Put Premium Paid} - \text{Call Premium Received} = \mathbf{0}$$

Locks the realized exchange rate within a defined corridor $[X_{\text{Put}}, X_{\text{Call}}]$.

When an existing forward contract cannot be executed as originally contracted, FEDAI guidelines govern the settlement charges (Illustrations 3 to 9 & PQ 32, 44, 45):

Currency Swap: A financial contract in which two counterparties exchange principal amounts and periodic interest payments in two different currencies at inception, and reverse the principal exchange at a predetermined rate upon maturity.

Three Distinct Cash Flow Phases:

1. Inception: Exchange of principal amounts at prevailing spot exchange rate ($S_0$).
2. Interim Life: Periodic exchange of interest payments (one fixed/floating in Currency A, the other fixed/floating in Currency B).
3. Maturity: Re-exchange of original principal amounts at the original inception exchange rate ($S_0$), completely immunizing both parties from exchange rate volatility.

Comparative Advantage in Currency Swaps: Companies exploit institutional market segmentations or domestic credit rating premiums to lower borrowing costs across foreign jurisdictions.

Corporate risk management frameworks categorize hedging strategies into four distinct risk-reward quadrants:

If the Indian Rupee is the home currency and the foreign currency is the US Dollar, then what is the exchange rate between the rupee and the US dollar?

The exchange rate between Indian Rupee (INR) and US Dollar (USD) can be expressed in two complementary ways:

1. Direct Quotation (Price Currency = INR): $$\text{1 USD} = \text{₹ } 46.08$$ Interpretation: An investor in India requires ₹ 46.08 to purchase 1 unit of US Dollar.
2. Indirect Quotation (Price Currency = USD): $$\text{₹ } 1 = \text{USD } \frac{1}{46.08} = \mathbf{\text{USD } 0.0217}$$ Interpretation: 1 Indian Rupee can buy 0.0217 US Dollars in the foreign exchange market.

Suppose you are a dealer of ABC Bank and on 20.10.2014 you found that balance in your Nostro account with XYZ Bank in London is £ 65,000 credit and you had overbought £ 35,000. During the day following transactions have taken place:

Required: What steps would you take to bring the Cash Balance in Nostro Account to £ 7,500 and Overbought Exchange Position to £ 7,500?

Step 1: Compute Exchange Position (Spot + Forward Commitments)

Closing Exchange Position: Overbought by £ 20,000.

Step 2: Compute Cash Position (Nostro Account Ledger Balance)

Note: Only immediate cash remittances impact Nostro ledger balance. Bills and forward contracts do not immediately credit/debit Nostro cash until realization.

Closing Cash Balance in Nostro A/c: £ 27,500 Credit.

Step 3: Action to Reach Target Targets

• Target Cash Balance = £ 7,500: Currently at £ 27,500. Excess cash = $27,500 - 7,500 = \text{£ } 20,000$.
  $\implies$ Sell £ 20,000 in the Spot Market.
• Impact of Spot Sale on Exchange Position: Selling £ 20,000 spot reduces the Overbought Exchange Position from £ 20,000 down to Nil (Square).
• Target Overbought Exchange Position = £ 7,500: Since current position is now Nil, the bank must:
  $\implies$ Buy £ 7,500 in the Forward Market.

On 1st June 2015, the bank enters into a forward contract for 2 months for selling US$ 1,00,000 at ₹ 65.5000. On 1st August 2015 (the due date), the customer requests the bank to cancel the contract. On this date, the spot interbank rates are:

$$\text{Spot USD/INR} = 65.1000 / 65.3000$$

The bank charges an exchange margin of 0.10% on buying, and a flat cancellation charge of ₹ 100.

Required: Determine the cancellation charges payable by or refund due to the customer.

Step 1: Determine Offsetting Market Rate

The original contract is a Forward Sale Contract (Bank agreed to sell USD at ₹ 65.5000). To cancel on due date, the bank must execute an offsetting purchase from the customer at prevailing Spot TT Buying Rate.

$$\text{Interbank Spot Bid Rate} = 65.1000$$ $$\text{Deduct Exchange Margin (0.10%)} = 65.1000 \times 0.0010 = 0.0651$$ $$\text{Spot TT Buying Rate applied} = 65.1000 - 0.0651 = \mathbf{\text{₹ } 65.0349}$$

Step 2: Calculate Cancellation Difference

• Bank originally contracted to sell USD 1,00,000 @ ₹ 65.5000 $\implies$ Inflow to Bank = ₹ 65,50,000
• Bank now buys back USD 1,00,000 @ ₹ 65.0349 $\implies$ Outflow from Bank = ₹ 65,03,490
• Profit on Currency Difference: $$\text{Gain} = 65,50,000 - 65,03,490 = \mathbf{+\text{₹ } 46,510}$$

Step 3: Net Refund to Customer

$$\text{Net Amount Refundable to Customer} = \text{Currency Gain } (46,510) - \text{Cancellation Fee } (100) = \mathbf{\text{₹ } 46,410}$$

On 1 October 2015, Mr. X, an exporter, enters into a forward contract with BNP Bank to sell US$ 1,00,000 on 31 December 2015 at ₹ 65.40/$. However, due to request of the importer, shipments were postponed, and on 1 November 2015 Mr. X requests the bank to cancel the contract.

On 1 November 2015, the following interbank rates are quoted:

• Spot USD/INR: 65.1500 / 65.2000
• 1-month Forward: 10 / 15 paise
• 2-month Forward: 20 / 25 paise

Bank’s exchange margin is 0.10% and flat cancellation fee is ₹ 100. Calculate the amount payable by / refundable to Mr. X.

Step 1: Identify Offsetting Rate for Residual Maturity

Cancellation requested on 1 November for a contract maturing on 31 December. The residual period is 2 months (November + December).

Original contract is a Forward Purchase by Bank (Mr. X sells). To cancel, the bank must sell USD back to Mr. X for delivery on 31 December at the 2-Month Forward TT Selling Rate.

$$\text{Interbank 2-Month Forward Ask} = \text{Spot Ask } (65.2000) + \text{Ask Premium } (0.25) = 65.4500$$ $$\text{Add Exchange Margin (0.10%)} = 65.4500 \times 0.0010 = 0.0655$$ $$\text{Applicable Cancellation Rate (TT Selling)} = 65.4500 + 0.0655 = \mathbf{\text{₹ } 65.5155}$$

Step 2: Calculate Cancellation Loss

• Original Purchase Rate = ₹ 65.4000
• Cancellation Selling Rate = ₹ 65.5155
• Loss per USD = $65.5155 - 65.4000 = \text{₹ } 0.1155$
• Total Currency Loss on US$ 1,00,000 = $1,00,000 \times 0.1155 = \mathbf{\text{₹ } 11,550}$

Step 3: Total Amount Recoverable from Customer

$$\text{Total Payable by Mr. X} = \text{Currency Loss } (11,550) + \text{Cancellation Fee } (100) = \mathbf{\text{₹ } 11,650}$$

On 15th January 2015, you as a banker booked a forward contract for US$ 2,50,000 for your import customer deliverable on 15th March 2015 at ₹ 65.3450. On the due date (15th March 2015), the customer requests an extension of the contract by 2 months (due 15th May 2015).

Market rates on 15th March 2015 are:

• Spot USD/INR: 65.1200 / 65.1500
• 2-month Forward: ₹ 65.4000 / 65.4500

Exchange margin is 0.10% and cancellation charges are ₹ 100.

Required: Calculate cancellation charges / gain on the old contract, and determine the rate for the extended forward contract.

Part A: Cancellation of Existing Contract on Due Date

The existing contract is a Forward Sale Contract (Bank sells to customer @ ₹ 65.3450). It is cancelled on due date at prevailing Spot TT Buying Rate:

$$\text{Spot TT Buying Rate} = 65.1200 \times (1 - 0.0010) = 65.1200 - 0.0651 = \mathbf{\text{₹ } 65.0549}$$ $$\text{Currency Gain per USD} = 65.3450 - 65.0549 = \text{₹ } 0.2901$$ $$\text{Total Gross Currency Gain} = 2,50,000 \times 0.2901 = \mathbf{\text{₹ } 72,525}$$ $$\text{Net Amount Refundable to Customer} = 72,525 - 100 = \mathbf{\text{₹ } 72,425}$$

Part B: Rate for the Extended Contract (2 Months Forward)

The new contract is a fresh forward sale for 2 months (due 15th May 2015), quoted at 2-Month Forward TT Selling Rate:

$$\text{2-Month Interbank Forward Ask} = 65.4500$$ $$\text{Add Exchange Margin (0.10%)} = 65.4500 \times 0.0010 = 0.0655$$ $$\text{New Forward Sale Rate} = 65.4500 + 0.0655 = \mathbf{\text{₹ } 65.5155}$$

You as a banker have entered into a 3-month forward contract with your customer to purchase AUD 1,00,000 at the rate of ₹ 47.2500. However, after 2 months your customer comes to you and requests cancellation of the contract.

On this date, the market quotes for 1-month forward are:

$$\text{1-month AUD/INR} = 47.4500 / 47.5000$$

Exchange margin is 0.15% and flat cancellation fee is ₹ 100. Determine the amount payable by / refundable to the customer.

Step 1: Identify Offsetting Forward Rate

The original contract was for Bank to purchase AUD at ₹ 47.2500 with 1 month remaining. To cancel, the bank must sell AUD 1,00,000 to the customer at the 1-Month Forward TT Selling Rate:

$$\text{1-Month Interbank Forward Ask} = 47.5000$$ $$\text{Add Margin (0.15%)} = 47.5000 \times 0.0015 = 0.0713$$ $$\text{Applicable Cancellation Selling Rate} = 47.5000 + 0.0713 = \mathbf{\text{₹ } 47.5713}$$

Step 2: Compute Cancellation Loss

$$\text{Loss per AUD} = 47.5713 - 47.2500 = \text{₹ } 0.3213$$ $$\text{Total Currency Loss on AUD 1,00,000} = 1,00,000 \times 0.3213 = \mathbf{\text{₹ } 32,130}$$ $$\text{Total Amount Payable by Customer} = \text{Loss } (32,130) + \text{Cancellation Fee } (100) = \mathbf{\text{₹ } 32,230}$$

Suppose you are a banker and one of your export customers has booked a US$ 1,00,000 forward purchase contract for 2 months with you at the rate of ₹ 62.5200, and simultaneously you covered your position in the interbank market at ₹ 62.5500.

However, after 15 days, the customer requests you to take delivery of the export proceeds immediately. On this day, interbank rates are:

• Spot USD/INR: 62.1000 / 62.1200
• 1-month Forward: 62.3000 / 62.3300

Interest rate on outlay of funds is 12% p.a. Determine the swap loss/gain and net amount payable to the customer.

Step 1: Execute Swap to Balance Cash & Forward Commitments

The bank accepts US$ 1,00,000 from the exporter today. But the bank has an existing commitment to deliver US$ 1,00,000 into the interbank forward contract in 1.5 months. To match cash flows:

1. Sell US$ 1,00,000 Spot @ Interbank Bid: ₹ 62.1000.
2. Buy US$ 1,00,000 Forward (1.5 months) @ Interbank Ask: ₹ 62.3300.

$$\text{Swap Loss per USD} = 62.3300 - 62.1000 = \text{₹ } 0.2300$$ $$\text{Total Swap Loss on US$ 1,00,000} = 1,00,000 \times 0.2300 = \mathbf{\text{₹ } 23,000}$$

Step 2: Interest on Outlay of Funds

Funds paid to customer today = $1,00,000 \times 62.5200 = \text{₹ } 62,52,000$.

Funds realized by selling spot = $1,00,000 \times 62.1000 = \text{₹ } 62,10,000$.

$$\text{Bank Outlay of Funds} = 62,52,000 - 62,10,000 = \text{₹ } 42,000$$ $$\text{Interest on Outlay (12% for 45 days)} = 42,000 \times 0.12 \times \frac{45}{365} = \mathbf{\text{₹ } 621.37}$$

Step 3: Total Charges Recovered from Customer

$$\text{Total Deductions} = \text{Swap Loss } (23,000) + \text{Interest on Outlay } (621.37) = \mathbf{\text{₹ } 23,621.37}$$ $$\text{Net Proceeds Paid to Exporter Today} = 62,52,000 - 23,621.37 = \mathbf{\text{₹ } 62,28,378.63}$$

Suppose you as a banker entered into a forward purchase contract for US$ 50,000 on 5th March with an export customer for 3 months at the rate of ₹ 59.6000. On the same day, you covered yourself in the interbank market at ₹ 59.6500.

The contract matured on 5th June. However, the customer did not deliver until 15th June. On 5th June, interbank rates were:

• Spot USD/INR: 59.8000 / 59.8200
• Forward margin for 10 days: 0.05 / 0.08

Bank’s lending rate is 14% p.a. Calculate the charges payable by the exporter for the overdue delivery.

Step 1: Interbank Obligation on 5th June

On 5th June, the bank had to deliver US$ 50,000 into its interbank sale commitment. Because the exporter did not deliver, the bank had to buy US$ 50,000 spot in the interbank market at Spot Ask: ₹ 59.8200.

Bank received from interbank contract = $50,000 \times 59.6500 = \text{₹ } 29,82,500$.

Bank paid to buy spot = $50,000 \times 59.8200 = \text{₹ } 29,91,000$.

$$\text{Bank Outlay of Funds} = 29,91,000 - 29,82,500 = \mathbf{\text{₹ } 8,500}$$

Step 2: Interest on Outlay for 10 Days (5 June to 15 June)

$$\text{Interest} = 8,500 \times 0.14 \times \frac{10}{365} = \mathbf{\text{₹ } 32.60}$$

Step 3: Settlement on 15th June

When the customer delivers on 15th June, the bank pays the original contracted rate of ₹ 59.6000, but recovers the outlay interest and price difference.

An importer booked a forward contract with his bank on 10th April for USD 2,00,000 due on 10th June @ ₹ 64.4000. The bank covered its position in the market at ₹ 64.2800. On 10th May, the customer requested cancellation of the contract.

Market rates on 10th May:

• Spot USD/INR: 63.9000 / 64.0000
• 1-month Forward: ₹ 64.1000 / 64.2000

Exchange margin is 0.10%, interest on outlay is 12% p.a., and flat cancellation charges are ₹ 100.

Required: Calculate the net cancellation gain / loss payable to or recoverable from the importer.

Step 1: Determine 1-Month Forward Buying Rate for Cancellation

Original contract is Forward Sale (Bank sells @ ₹ 64.4000). On 10th May, 1 month remains until maturity. The bank buys back USD 2,00,000 @ 1-Month Forward TT Buying Rate:

$$\text{1-Month Interbank Bid} = 64.1000$$ $$\text{Deduct Margin (0.10%)} = 64.1000 \times 0.0010 = 0.0641$$ $$\text{Cancellation Buying Rate} = 64.1000 - 0.0641 = \mathbf{\text{₹ } 64.0359}$$

Step 2: Currency Cancellation Difference

$$\text{Gain per USD} = 64.4000 - 64.0359 = \text{₹ } 0.3641$$ $$\text{Total Currency Gain on USD 2,00,000} = 2,00,000 \times 0.3641 = \mathbf{+\text{₹ } 72,820}$$

Step 3: Net Settlement Payable to Customer

$$\text{Net Amount Refunded} = \text{Gain } (72,820) - \text{Cancellation Charge } (100) = \mathbf{\text{₹ } 72,720}$$

“Operations in foreign exchange are exposed to a number of risks.” Discuss.

Financial institutions, banks, and multinational corporations operating in the foreign exchange market face several interconnected categories of risk:

1. Exchange Rate / Market Risk: The risk of financial loss resulting from adverse movements in currency exchange rates while holding an open (overbought or oversold) position. Unhedged open positions directly impact profitability when market values shift.
2. Settlement / Herstatt Risk: Occurs when one counterparty delivers currency as contracted, but the other party defaults before delivering the offsetting currency. Named after the failure of Germany's Bankhaus Herstatt in 1974, this risk arises primarily from time zone differences between global clearing centers.
3. Liquidity Risk: The risk that a bank or trader cannot quickly execute a large currency transaction or unwind an existing position at prevailing market prices due to lack of market depth or market disruption.
4. Credit / Counterparty Default Risk: The risk that the counterparty to an OTC forward or swap contract defaults prior to maturity, forcing the non-defaulting bank to replace the contract at unfavorable prevailing market rates (replacement cost risk).
5. Sovereign / Country Risk: The risk that a foreign government imposes exchange controls, currency moratoria, capital restrictions, or expropriation, preventing foreign currency funds from being remitted across borders.
6. Interest Rate Risk: Fluctuations in benchmark interest rates alter forward swap points, the cost of carrying currency positions, and the market valuation of currency derivative portfolios.
7. Operational Risk: Losses arising from inadequate internal controls, unauthorized trading (rogue traders), computer hardware or software failures, communication breakdowns, or documentation errors.

What do you mean by Nostro, Vostro and Loro Accounts?

In international correspondent banking, accounts maintained between banks in different jurisdictions are classified using Latin legal terminology:

The price of a bond just before a year of maturity is $ 5,000. Its redemption value is $ 5,250 at the end of the said period. Interest is $ 350 p.a. The Dollar appreciates by 2% during the said period. Calculate the rate of return.

Step 1: Calculate Dollar Return on Bond (Local Currency Return)

$$\text{Bond Return in USD } (R_{\$}) = \frac{(\text{Redemption Price} - \text{Purchase Price}) + \text{Interest}}{\text{Purchase Price}}$$ $$R_{\$} = \frac{(5,250 - 5,000) + 350}{5,000} = \frac{250 + 350}{5,000} = \frac{600}{5,000} = \mathbf{12.00\%}$$

Step 2: Evaluate Return based on Investor Nationality

• Case (i): US Domestic Investor:
  A domestic US investor operates in USD. Exchange rate fluctuations have zero impact on domestic purchasing power. $$\text{Rate of Return for US Investor} = \mathbf{12.00\%}$$
• Case (ii): Foreign Investor (e.g., Indian Investor):
  The foreign investor benefits from both the local bond return ($R_{\$} = 12\%$) and the dollar appreciation ($g = 2\%$): $$1 + R_{\text{net}} = (1 + R_{\$}) \times (1 + g_{\$})$$ $$1 + R_{\text{net}} = (1 + 0.12) \times (1 + 0.02) = 1.12 \times 1.02 = 1.1424$$ $$R_{\text{net}} = 1.1424 - 1 = 0.1424 = \mathbf{14.24\%}$$ (Or approximate return: $12\% + 2\% = 14.00\%$)

ABN-Amro Bank, Amsterdam, wants to purchase ₹ 15 million against US$ for funding their Nostro account with Canara Bank, New Delhi. Assuming the interbank rates of US$ are ₹ 51.3625 / 51.3700, what would be the rate Canara Bank would quote to ABN-Amro Bank? Further, if the deal is struck, what would be the equivalent US$ amount?

Step 1: Determine Applicable Rate from Canara Bank's Perspective

ABN-Amro Bank wants Rupee and pays US Dollar. Therefore, Canara Bank buys US$ and credits INR to ABN-Amro's account.

To quote competitively, Canara Bank applies the Interbank Buying Rate (Bid Rate) for USD:

$$\text{Buying Rate of USD} = \mathbf{\text{₹ } 51.3625 \text{ per USD}}$$

Expressed as an indirect rate per Rupee:

$$\text{Rate per Rupee} = \frac{1}{51.3625} = \mathbf{\text{USD } 0.0194695 \text{ per ₹}}$$

Step 2: Calculate Equivalent US$ Amount

$$\text{Equivalent US\$} = \frac{\text{₹ } 1,50,00,000}{\text{₹ } 51.3625} = \mathbf{\text{US\$ } 2,92,041.86}$$

XYZ LTD Bank, Amsterdam, wants to purchase ₹ 25 million against £ for funding their Nostro account and they have credited Loro account with Bank of London, London.

Ongoing interbank rates are:

• Per $: ₹ 61.3625 / 61.3700
• Per £: $ 1.5260 / 1.5270

Required: Calculate the amount of £’s credited.

Step 1: Formulate the Cross Currency Chain

XYZ LTD Bank wants to buy Rupee using Pound (£). The bank must:

1. Sell £ to buy USD ($) at the market Bid rate: $(\text{USD/GBP})_{\text{Bid}} = 1.5260$.
2. Sell USD ($) to buy INR (₹) at the market Bid rate: $(\text{INR/USD})_{\text{Bid}} = 61.3625$.

$$\text{Rate of ₹ per £ (Bid)} = (\text{USD/GBP})_{\text{Bid}} \times (\text{INR/USD})_{\text{Bid}} = 1.5260 \times 61.3625 = \mathbf{\text{₹ } 93.639175 \text{ per £}}$$

Expressed as cost of 1 Rupee in terms of Pound (£):

$$\text{Cost of ₹ 1} = \frac{1}{93.639175} = \text{£ } 0.0106793$$

Step 2: Calculate Amount of Pounds Required for ₹ 25 Million

$$\text{Amount of £ Credited} = \frac{\text{₹ } 2,50,00,000}{93.639175} = \mathbf{\text{£ } 2,66,982.29}$$

ABC Ltd. of UK has exported goods worth Can $ 5,00,000 receivable in 6 months. The exporter wants to hedge the receipt in the forward market. The following information is available:

• Spot Exchange Rate: Can $ 2.50 / £
• Interest Rate in UK: 12% p.a. (6% for 6 months)
• Interest Rate in Canada: 15% p.a. (7.5% for 6 months)

The forward rates truly reflect the interest rate differential. Find out the gain/loss to the UK exporter if the Can $ spot rate over the next 6 months:

1. Declines by 2%
2. Gains by 4%
3. Remains unchanged

Step 1: Calculate 6-Month Forward Exchange Rate using IRP

Quote is indirect from UK perspective (Can $ per £). Under Interest Rate Parity:

$$F_{\text{Can}\$/\text{£}} = S_0 \times \frac{1 + r_{\text{Canada}} \cdot (6/12)}{1 + r_{\text{UK}} \cdot (6/12)} = 2.50 \times \frac{1 + 0.075}{1 + 0.060} = 2.50 \times \frac{1.075}{1.060} = \mathbf{\text{Can } \$ 2.53538 \text{ per £}}$$

Pound proceeds locked in via Forward Contract:

$$\text{Locked In Inflow} = \frac{\text{Can } \$ 5,00,000}{2.53538} = \mathbf{\text{£ } 1,97,209.10}$$

Step 2: Evaluate 3 Spot Market Scenarios at 6 Months

On April 3, 2016, a Bank quotes the following:

• Spot Exchange Rate (US $ 1): INR 66.2525 / INR 67.5945
• 2 months’ swap points: 70 / 90
• 3 months’ swap points: 160 / 186

Required:

1. Find the swap points for 2 months and 15 days.
2. Determine the forward rate for 2 months and 15 days.

Step 1: Compute Interpolated Swap Points for 15 Days

The incremental difference between 3-month and 2-month swap points represents 1 month (30 days) of forward points:

• Bid Swap Point Difference = $160 - 70 = 90$ points
• Ask Swap Point Difference = $186 - 90 = 96$ points

Pro-rata for 15 days ($\frac{15}{30} = 0.5$ month):

$$\text{Bid Increment for 15 Days} = 90 \times \frac{15}{30} = 45 \text{ points}$$ $$\text{Ask Increment for 15 Days} = 96 \times \frac{15}{30} = 48 \text{ points}$$

Total Swap Points for 2 Months and 15 Days:

$$\text{Bid Points} = 70 + 45 = \mathbf{115 \text{ points (0.0115)}}$$ $$\text{Ask Points} = 90 + 48 = \mathbf{138 \text{ points (0.0138)}}$$

Step 2: Calculate Outright Forward Rate

Since swap points are in ascending order ($115 < 138$), USD is at a Premium. Add swap points to Spot:

$$\text{Forward Bid} = 66.2525 + 0.0115 = \mathbf{66.2640}$$ $$\text{Forward Ask} = 67.5945 + 0.0138 = \mathbf{67.6083}$$

JKL Ltd., an Indian company, has an export exposure of JPY 10,000,000 receivable on August 31, 2014. Japanese Yen is not directly quoted against Indian Rupee. The current market quotes are:

• Spot USD/INR: 62.22 / 62.23
• 1-month Forward USD/INR: 62.45 / 62.47
• Spot USD/JPY: 102.34 / 102.37
• 1-month Forward USD/JPY: 102.60 / 102.65

Required: Determine the forward cross rate and Rupee proceeds expected on August 31, 2014.

Step 1: Construct Forward Cross Buying Rate for JPY/INR

The exporter wants to sell JPY to receive INR. The bank buys JPY against INR:

$$\left(\frac{\text{INR}}{\text{JPY}}\right)_{\text{Bid}} = \frac{(\text{INR/USD})_{\text{Bid}}}{(\text{JPY/USD})_{\text{Ask}}} = \frac{62.45}{102.65} = \mathbf{\text{₹ } 0.608378 \text{ per JPY}}$$

Step 2: Calculate Rupee Realization on JPY 10,000,000

$$\text{Rupee Inflow} = 1,00,00,000 \times 0.608378 = \mathbf{\text{₹ } 60,83,780}$$

You sold Hong Kong Dollar 1,00,00,000 value spot to your customer at ₹ 5.70 and covered yourself in the London market on the same day through USD. In London, market quotes are:

• USD/INR: ₹ 42.85 / 42.90
• USD/HKD: HKD 7.50 / 7.52

Calculate your profit or loss on the transaction.

Step 1: Inflow Realized from Customer

$$\text{Inflow from Customer} = 1,00,00,000 \times \text{₹ } 5.70 = \mathbf{\text{₹ } 5,70,00,000}$$

Step 2: Cover Transaction in London Interbank Market

To deliver HKD 1,00,00,000, the bank must buy HKD by selling USD at the bank buying rate for USD in Hong Kong ($\text{USD/HKD}_{\text{Bid}} = 7.50$):

$$\text{USD Required to Buy HKD 10M} = \frac{1,00,00,000}{7.50} = \mathbf{\text{US\$ } 13,33,333.33}$$

To acquire these US$, the bank must buy USD against INR at London Selling Rate ($\text{USD/INR}_{\text{Ask}} = 42.90$):

$$\text{Total INR Cost} = 13,33,333.33 \times 42.90 = \mathbf{\text{₹ } 5,71,99,999.86 \approx \text{₹ } 5,72,00,000}$$

Step 3: Profit / (Loss) Calculation

$$\text{Net Profit / (Loss)} = \text{Inflow } (5,70,00,000) - \text{Cover Cost } (5,72,00,000) = \mathbf{-\text{₹ } 2,00,000 \text{ (Loss)}}$$

You, a foreign exchange dealer of your bank, are informed that your bank has sold a T.T. on Copenhagen for Danish Kroner 10,00,000 at ₹ 6.5150 per Kroner. You covered the deal at London:

• Spot USD/DKK: DKK 6.5850 / 6.5900
• Spot USD/INR in Mumbai: ₹ 42.80 / 42.85

Calculate your profit or loss, ignoring brokerage and transaction costs.

Step 1: Rupee Inflow from Customer

$$\text{Inflow} = 10,00,000 \times \text{₹ } 6.5150 = \mathbf{\text{₹ } 65,15,000}$$

Step 2: Cover Cost via USD

1. Buy DKK 10,00,000 by selling USD at Bid rate ($6.5850$):

$$\text{USD Needed} = \frac{10,00,000}{6.5850} = \text{US\$ } 1,51,860.29$$

2. Buy US$ 1,51,860.29 in Mumbai at Ask rate (₹ 42.85):

$$\text{INR Outlay} = 1,51,860.29 \times 42.85 = \mathbf{\text{₹ } 65,07,213.43}$$

Step 3: Profit / (Loss)

$$\text{Net Profit} = 65,15,000 - 65,07,213.43 = \mathbf{+\text{₹ } 7,786.57 \text{ (Profit)}}$$

On January 28, 2013 an importer customer requested a Bank to remit Singapore Dollar (SGD) 2,500,000 under an irrevocable LC. Current market quotes are:

• Spot USD/INR: 53.2800 / 53.2900
• Spot USD/SGD: 1.2580 / 1.2590

Exchange margin is 0.125%. Calculate the rate to be quoted by the bank and the total Rupee amount to be debited to the customer's account.

Step 1: Compute Interbank Cross Selling Rate (Ask)

$$\left(\frac{\text{INR}}{\text{SGD}}\right)_{\text{Ask}} = \frac{(\text{INR/USD})_{\text{Ask}}}{(\text{SGD/USD})_{\text{Bid}}} = \frac{53.2900}{1.2580} = \mathbf{\text{₹ } 42.36089}$$

Step 2: Add Bank Exchange Margin (0.125%)

$$\text{Margin} = 42.36089 \times 0.00125 = \text{₹ } 0.05295$$ $$\text{TT Selling Rate to Customer} = 42.36089 + 0.05295 = \mathbf{\text{₹ } 42.41384 \approx \text{₹ } 42.4150}$$

Step 3: Total Rupee Amount Debited to Customer

$$\text{Total Rupee Cost} = 25,00,000 \times 42.41384 = \mathbf{\text{₹ } 10,60,34,600}$$

Following are the details of cash inflows and outflows in foreign currency denominations of an Indian multinational firm:

Required: Determine the net exposure of each foreign currency in terms of Rupees.

The following 2-way quotes appear in the foreign exchange market:

• Spot USD/INR: ₹ 46.00 / 46.25
• 2-Month Forward: ₹ 47.00 / 47.50

Required:

1. How many US dollars should a firm sell to get ₹ 25 lakhs after 2 months?
2. How many Rupees is the firm required to pay to obtain US $ 2,00,000 in the spot market?
3. Assume the firm has US $ 69,000 in a current account earning zero interest. ROI on Rupee investment is 10% p.a. Should the firm encash the US $ now or 2 months later?

Part (i): USD Needed to get ₹ 25 Lakhs after 2 Months

The firm sells USD to the bank after 2 months at the 2-Month Forward Bid Rate (₹ 47.00):

$$\text{US\$ to Sell} = \frac{\text{₹ } 25,00,000}{\text{₹ } 47.00} = \mathbf{\text{US\$ } 53,191.49}$$

Part (ii): Rupees Required to Obtain US $ 2,00,000 Spot

The firm buys USD spot from the bank at the Spot Ask Rate (₹ 46.25):

$$\text{Rupee Outlay} = 2,00,000 \times \text{₹ } 46.25 = \mathbf{\text{₹ } 92,50,000}$$

Part (iii): Encash US $ 69,000 Now vs. 2 Months Later

• Option A: Encash Now ($t=0$):
  Sell US$ 69,000 at Spot Bid (₹ 46.00): $$\text{Proceeds Today} = 69,000 \times 46.00 = \text{₹ } 31,74,000$$ Invest at 10% p.a. for 2 months ($2/12$ years): $$\text{Value after 2 Months} = 31,74,000 \times \left(1 + 0.10 \times \frac{2}{12}\right) = 31,74,000 \times 1.016667 = \mathbf{\text{₹ } 32,26,900}$$
• Option B: Encash 2 Months Later ($t=2$):
  Sell US$ 69,000 forward at 2-Month Forward Bid (₹ 47.00): $$\text{Proceeds after 2 Months} = 69,000 \times 47.00 = \mathbf{\text{₹ } 32,43,000}$$

Comparison: Option B yields ₹ 32,43,000, which is higher than Option A (₹ 32,26,900) by $32,43,000 - 32,26,900 = \mathbf{\text{₹ } 16,100}$.

Recommendation: The firm should encash the US $ 2 months later.

Z Ltd. importing goods worth USD 2 million, requires 90 days to make the payment. The overseas supplier has offered a 60 days interest-free credit period and for additional credit of 30 days an interest of 8% per annum.

The bankers of Z Ltd offer a 30-days loan at 10% per annum and their quotes for foreign exchange are:

• Spot 1 USD: ₹ 56.50
• 60 days forward 1 USD: ₹ 57.10
• 90 days forward 1 USD: ₹ 57.50

Evaluate the following options:

1. Pay the supplier in 60 days.
2. Avail the supplier’s offer of 90 days credit.

Option 1: Pay the Supplier in 60 Days

To pay the supplier in 60 days, Z Ltd takes a 60-day forward contract to buy USD 2,000,000 @ ₹ 57.10:

$$\text{Rupee Payment at Day 60} = 20,00,000 \times 57.10 = \text{₹ } 11,42,00,000$$

Since Z Ltd requires 90 days, it finances this amount by borrowing in India for 30 days at 10% p.a. (from Day 60 to Day 90):

$$\text{Interest on Loan (30 Days)} = 11,42,00,000 \times 0.10 \times \frac{30}{360} = \text{₹ } 9,51,667$$ $$\text{Total Cash Outflow at Day 90} = 11,42,00,000 + 9,51,667 = \mathbf{\text{₹ } 11,51,51,667}$$

Option 2: Avail Supplier’s Offer of 90 Days Credit

The supplier charges 8% p.a. interest for the additional 30 days:

$$\text{Interest Charged by Supplier} = \text{USD } 20,00,000 \times 0.08 \times \frac{30}{360} = \text{USD } 13,333.33$$ $$\text{Total Foreign Currency Payable at Day 90} = \text{USD } 20,13,333.33$$

Covered via 90-day forward contract @ ₹ 57.50:

$$\text{Total Cash Outflow at Day 90} = 20,13,333.33 \times 57.50 = \mathbf{\text{₹ } 11,57,66,666}$$

Comparative Analysis:

$$\text{Cost Savings under Option 1} = 11,57,66,666 - 11,51,51,667 = \mathbf{\text{₹ } 6,14,999}$$

Following are the spot exchange rates quoted at three different forex markets:

• USD/INR: 48.30 in Mumbai
• GBP/INR: 77.52 in London
• GBP/USD: 1.6231 in New York

The arbitrageur has USD 1,00,00,000 ($ 10 Million). Assuming zero transaction costs, explain whether any arbitrage gain is possible.

Step 1: Calculate Cross Rate GBP/USD through Mumbai and London

$$\left(\frac{\text{GBP}}{\text{USD}}\right)_{\text{Cross}} = \frac{\text{GBP/INR}}{\text{USD/INR}} = \frac{77.52}{48.30} = \mathbf{1.6050 \text{ USD per GBP}}$$

The actual market quote in New York is 1.6231 USD per GBP.

Since Synthetic Rate ($1.6050$) $\neq$ Quoted Rate ($1.6231$), Pound is undervalued in cross rate and overvalued in New York. Arbitrage is possible!

Step 2: Execute Triangular Arbitrage Circuit

1. Start in Mumbai: Convert USD 10,00,000 into INR @ 48.30: $$\text{INR Received} = 1,00,00,000 \times 48.30 = \text{₹ } 48,30,00,000$$
2. London Market: Convert INR into GBP (£) @ 77.52: $$\text{GBP Received} = \frac{48,30,00,000}{77.52} = \text{£ } 62,30,650.15$$
3. New York Market: Convert GBP (£) back into USD ($) @ 1.6231: $$\text{USD Realized} = 62,30,650.15 \times 1.6231 = \mathbf{\text{US\$ } 1,01,12,968.26}$$

Step 3: Calculate Arbitrage Profit

$$\text{Net Riskless Profit} = 1,01,12,968.26 - 1,00,00,000.00 = \mathbf{\text{US\$ } 1,12,968.26}$$

The US dollar is selling in India at ₹ 55.50. The interest rate for 6 months borrowing in India is 10% per annum and the corresponding rate in USA is 4% per annum.

1. Do you expect that the US dollar will be at a premium or discount in the Indian Forex Market?
2. What will be the expected 6-months forward rate for US dollar in India?
3. What will be the rate of forward premium or discount?

Part (i): Premium / Discount Expectation

According to Interest Rate Parity, the currency of the country with the lower interest rate will trade at a forward premium against the currency of the country with the higher interest rate.

Since the interest rate in the USA ($4\%$) is lower than in India ($10\%$), the US Dollar is expected to quote at a PREMIUM in India.

Part (ii): Expected 6-Months Forward Rate

Tenure = 6 months $\implies r_{\text{India}} = 10\% \times 0.5 = 5\% = 0.05$; $r_{\text{USA}} = 4\% \times 0.5 = 2\% = 0.02$.

$$F = S_0 \times \frac{1 + r_{\text{India}}}{1 + r_{\text{USA}}} = 55.50 \times \frac{1 + 0.05}{1 + 0.02} = 55.50 \times \frac{1.05}{1.02} = \mathbf{\text{₹ } 57.13235 \approx \text{₹ } 57.13}$$

Part (iii): Rate of Forward Premium

$$\%\text{ Premium (Annualized)} = \frac{F - S_0}{S_0} \times \frac{12}{6} \times 100 = \frac{57.13235 - 55.50}{55.50} \times 2 \times 100$$ $$\%\text{ Premium} = \frac{1.63235}{55.50} \times 200 = \mathbf{5.88\% \text{ p.a.}}$$

(Or approximately equal to the interest rate differential: $10\% - 4\% = 6.00\%$)

In March 2009, Multinational Industries makes the following assessment of dollar rates per British pound to prevail as on 1.9.2009:

Required:

1. What is the expected spot rate for 1.9.2009?
2. If, as of March 2009, the 6-month forward rate is $ 1.80, should the firm sell forward its pound receivables due in September 2009?

Part (i): Calculation of Expected Spot Rate

$$E(S) = \sum (S_i \times P_i) = (1.60 \times 0.15) + (1.70 \times 0.20) + (1.80 \times 0.25) + (1.90 \times 0.20) + (2.00 \times 0.20)$$ $$E(S) = 0.240 + 0.340 + 0.450 + 0.380 + 0.400 = \mathbf{\$ 1.81 \text{ per Pound}}$$

Part (ii): Hedging Decision Analysis

The forward rate offered is $ 1.80 / £, while the expected spot rate is $ 1.81 / £.

• If the firm is risk-neutral, it may prefer to leave the receivables unhedged to capture the expected higher realization of $ 1.81.
• However, if the firm is risk-averse, locking in $ 1.80 eliminates downside risk (avoiding potential drop to $ 1.60 or $ 1.70, which has a 35% probability). The small sacrifice of $ 0.01 per £ represents an insurance premium to guarantee cash certainty.

An importer customer of your bank wishes to book a forward contract with your bank on 3rd September for delivery on 31st October for US$ 1,00,000. The interbank market quotes are:

• Spot USD/INR on 3rd September: ₹ 66.5000 / 66.6000
• Spot / September: 15 / 20 paise
• Spot / October: 30 / 35 paise
• Spot / November: 45 / 50 paise

The bank charges an exchange margin of 0.15%. What rate will the bank quote to the customer, and how much Rupee will be debited on due date?

Step 1: Determine Interbank Forward Selling Rate

The customer is an importer who needs to buy USD on 31st October. The bank sells USD at the Forward Ask Rate for October.

Since swap points are in ascending order ($30 < 35$), USD is at a Premium. Add October ask points to Spot Ask:

$$\text{Spot Ask Rate} = \text{₹ } 66.6000$$ $$\text{Add October Forward Ask Margin} = +0.3500$$ $$\text{Interbank Forward Ask Rate} = 66.6000 + 0.3500 = \mathbf{\text{₹ } 66.9500}$$

Step 2: Add Bank Exchange Margin (0.15%)

$$\text{Exchange Margin} = 66.9500 \times 0.0015 = \text{₹ } 0.1004$$ $$\text{Quoted Merchant Forward Selling Rate} = 66.9500 + 0.1004 = \mathbf{\text{₹ } 67.0504}$$

Step 3: Total Rupee Outflow for Customer

$$\text{Rupee Debit} = 1,00,00,000 \times 67.0504 = \mathbf{\text{₹ } 67,05,040}$$

A company operating in Japan has today effected sales to an Indian company, the payment being due in 3 months. The invoice amount is JPY 108 Lakhs, equivalent to ₹ 30 Lakhs today. The price index in Japan is expected to rise by 2% and in India by 4% over the next 3 months.

The 3-month forward exchange rate quoted in the market is ₹ 1 = 3.30 JPY.

Required:

1. Determine the spot exchange rate today.
2. Calculate the expected 3-month forward rate under Purchasing Power Parity (PPP).
3. Analyze the impact on the Japanese exporter and suggest an appropriate hedging decision.

Part (i): Spot Exchange Rate Today

$$\text{Spot Rate per ₹ 1} = \frac{\text{JPY } 108 \text{ Lakhs}}{\text{₹ } 30 \text{ Lakhs}} = \mathbf{3.60 \text{ JPY per ₹ 1}}$$ $$\text{Or per JPY 1} = \frac{\text{₹ } 30 \text{ Lakhs}}{\text{JPY } 108 \text{ Lakhs}} = \mathbf{\text{₹ } 0.2778 \text{ per JPY}}$$

Part (ii): Expected 3-Month Exchange Rate under PPP

Inflation in India ($I_{\text{India}}$) = 4%; Inflation in Japan ($I_{\text{Japan}}$) = 2%.

$$E(S_{\text{JPY/₹}}) = S_0 \times \frac{1 + I_{\text{Japan}}}{1 + I_{\text{India}}} = 3.60 \times \frac{1 + 0.02}{1 + 0.04} = 3.60 \times \frac{1.02}{1.04} = \mathbf{3.5308 \text{ JPY per ₹ 1}}$$ $$\text{Direct Rate per JPY under PPP} = \frac{1}{3.5308} = \mathbf{\text{₹ } 0.2832}$$

Part (iii): Analysis of Market Forward Rate (₹ 1 = 3.30 JPY)

The market forward rate quotes ₹ 1 = 3.30 JPY, which means 1 JPY = ₹ 0.3030.

• If the Indian importer invoices in JPY (paying JPY 108 Lakhs): $$\text{Rupee Cost via Forward Market} = \frac{\text{JPY } 108 \text{ Lakhs}}{3.30} = \mathbf{\text{₹ } 32.73 \text{ Lakhs}}$$
• Rupee cost under PPP = $\frac{108}{3.5308} = \text{₹ } 30.59 \text{ Lakhs}$.

ABC Co. has taken a 6-month loan from their foreign collaborators for US$ 2.0 million at an interest rate of 3% p.a. The current spot rate is ₹ 48.00 / USD. The 6-month forward rate is ₹ 48.90 / USD.

Required:

1. Compute the total foreign currency repayment (principal + interest) due at 6 months.
2. Determine the total Rupee cash outflow if the liability is covered in the forward market.
3. What would be the effective annualized Rupee cost of the foreign loan?

Step 1: Compute Foreign Currency Obligation at 6 Months

$$\text{Interest for 6 Months} = \text{US\$ } 20,00,000 \times 0.03 \times \frac{6}{12} = \mathbf{\text{US\$ } 30,000}$$ $$\text{Total USD Payable} = \text{Principal } (20,00,000) + \text{Interest } (30,000) = \mathbf{\text{US\$ } 20,30,000}$$

Step 2: Total Rupee Cash Outflow via Forward Cover

$$\text{Rupee Outflow at 6 Months} = 20,30,000 \times \text{₹ } 48.90 = \mathbf{\text{₹ } 9,92,67,000}$$

Step 3: Effective Annualized Cost of Capital

Rupee proceeds received today at spot rate: $20,00,000 \times 48.00 = \text{₹ } 9,60,00,000$.

$$\text{Rupee Cost for 6 Months} = \frac{9,92,67,000 - 9,60,00,000}{9,60,00,000} = \frac{32,67,000}{9,60,00,000} = 3.403\%$$ $$\text{Effective Annualized Cost} = 3.403\% \times \frac{12}{6} = \mathbf{6.81\% \text{ p.a.}}$$

Excel Exporters are holding an Export bill in United States Dollar (USD) 1,00,000 due 60 days hence. They are considering discounting the bill with their bank.

• Spot USD/INR: ₹ 45.60 / 45.70
• 60-days forward rate: ₹ 45.20 / 45.30
• Bank rate of discount for foreign bills: 15% per annum

Calculate:

1. The annualized forward discount on USD.
2. The net Rupee proceeds realized today under export bill discounting.

Part (i): Annualized Forward Discount on USD

Using the bank's buying rate (Bid rate): Spot Bid = 45.60; 60-day Forward Bid = 45.20.

$$\text{Annualized Discount} = \frac{45.60 - 45.20}{45.60} \times \frac{365}{60} \times 100 = \frac{0.40}{45.60} \times 6.0833 \times 100 = \mathbf{5.34\% \text{ p.a.}}$$ (Or using 360-day basis: $\frac{0.40}{45.60} \times \frac{360}{60} \times 100 = 5.263\%$)

Part (ii): Net Rupee Proceeds under Bill Discounting

Under bill discounting, the bank purchases the 60-day export bill at the 60-day forward buying rate (₹ 45.20) and discounts it for 60 days at 15% p.a.:

$$\text{Gross Bill Value in INR} = 1,00,000 \times 45.20 = \text{₹ } 45,20,000$$ $$\text{Discount for 60 Days} = 45,20,000 \times 0.15 \times \frac{60}{365} = \mathbf{\text{₹ } 1,11,452}$$ $$\text{Net Proceeds Realized Today} = 45,20,000 - 1,11,452 = \mathbf{\text{₹ } 44,08,548}$$

In the International Monetary Market (IMM), an international forward bid for December 15 on Pound Sterling is $ 1.2816 at the same time that the price of an IMM sterling futures for delivery on December 15 is $ 1.2806. The contract size of IMM sterling futures is £ 62,500.

How could an arbitrageur make profit if transaction costs are zero?

Market Discrepancy Identification:

• Futures Price (Buy price) = $ 1.2806 per £
• Forward Price (Sell price) = $ 1.2816 per £

Since Forward Price ($ 1.2816) > Futures Price ($ 1.2806), the arbitrageur will:

1. Buy 1 IMM Sterling Futures Contract for £ 62,500 @ $ 1.2806. $$\text{Commitment to Pay at Expiry} = 62,500 \times 1.2806 = \mathbf{\$ 80,037.50}$$
2. Simultaneously Sell £ 62,500 Forward in the interbank market @ $ 1.2816. $$\text{Commitment to Receive at Expiry} = 62,500 \times 1.2816 = \mathbf{\$ 80,100.00}$$

Arbitrage Profit at Settlement (December 15):

$$\text{Riskless Arbitrage Profit} = \$ 80,100.00 - \$ 80,037.50 = \mathbf{+\$ 62.50 \text{ per contract}}$$

An Indian importer has to settle an import bill for $ 1,30,000. The exporter has given the Indian importer two payment options:

1. Pay immediately with a cash discount of 1%.
2. Pay in 3 months without discount.

Current market rates:

• Spot USD/INR: ₹ 48.00 / 48.10
• 3-Month Forward USD/INR: ₹ 48.80 / 48.90
• Borrowing rate for overdraft in India: 12% per annum

Which option should the Indian importer choose?

Option 1: Pay Immediately with 1% Cash Discount

$$\text{Discounted Bill Amount} = \$ 1,30,000 \times (1 - 0.01) = \mathbf{\$ 1,28,700}$$

The importer buys USD spot at the Spot Ask Rate (₹ 48.10) by availing an overdraft facility:

$$\text{Spot Rupee Outflow Today} = 1,28,700 \times 48.10 = \mathbf{\text{₹ } 61,90,470}$$

Interest cost on overdraft for 3 months at 12% p.a.:

$$\text{Interest (3 Months)} = 61,90,470 \times 0.12 \times \frac{3}{12} = \text{₹ } 1,85,714.10$$ $$\text{Total Cost at Month 3 under Option 1} = 61,90,470 + 1,85,714.10 = \mathbf{\text{₹ } 63,76,184.10}$$

Option 2: Pay after 3 Months using Forward Cover

Pay full bill of $ 1,30,000 covered at the 3-Month Forward Ask Rate (₹ 48.90):

$$\text{Total Rupee Outflow at Month 3 under Option 2} = 1,30,000 \times 48.90 = \mathbf{\text{₹ } 63,57,000.00}$$

Comparative Evaluation:

$$\text{Cost Savings under Option 2} = 63,76,184.10 - 63,57,000.00 = \mathbf{\text{₹ } 19,184.10}$$

DEF Ltd. has imported goods to the extent of US$ 1 crore ($ 10 Million). The payment terms are 60 days interest-free credit and additional 30 days credit at 7.5% p.a. Bank quotes:

• Spot USD/INR: 62.50 / 62.52
• 60-days forward: 63.15 / 63.20
• 90-days forward: 63.45 / 63.50
• 30-days Indian Rupee loan rate: 9.5% p.a.

Evaluate whether DEF Ltd should pay the supplier in 60 days or in 90 days.

Alternative 1: Pay Supplier in 60 Days

Buy USD 1,00,00,000 at 60-day Forward Ask (₹ 63.20):

$$\text{Rupee Payment at Day 60} = 1,00,00,000 \times 63.20 = \text{₹ } 63,20,00,000$$

Financed by a 30-day Rupee loan at 9.5% p.a. from Day 60 to Day 90:

$$\text{Interest on Loan (30 Days)} = 63,20,00,000 \times 0.095 \times \frac{30}{365} = \text{₹ } 49,34,795$$ $$\text{Total Cost at Day 90} = 63,20,00,000 + 49,34,795 = \mathbf{\text{₹ } 63,69,34,795}$$

Alternative 2: Avail Supplier Credit of 90 Days

$$\text{Interest Charged by Supplier for 30 Days} = \text{US\$ } 1,00,00,000 \times 0.075 \times \frac{30}{360} = \text{US\$ } 62,500$$ $$\text{Total USD Payable at Day 90} = \text{US\$ } 1,00,62,500$$

Covered at 90-day Forward Ask (₹ 63.50):

$$\text{Total Cost at Day 90} = 1,00,62,500 \times 63.50 = \mathbf{\text{₹ } 63,89,68,750}$$

A company has to make a payment of US$ 60,000 on December 31, 2016 for goods purchased on 1st July 2016 (6-month credit). The financial parameters are:

• Spot Rate: ₹ 65.00 / USD
• 6-Month Forward Premium: 3% p.a.
• 6-Month Call Option Strike Price: ₹ 66.00 / USD, Premium = 2% of spot
• Domestic Borrowing Rate: 10% p.a.

Required: Evaluate Forward Contract vs. Call Option if Spot Rate on 31st December turns out to be (i) ₹ 64.00, or (ii) ₹ 68.00.

Option 1: Forward Cover

$$\text{Forward Rate} = 65.00 \times \left(1 + 0.03 \times \frac{6}{12}\right) = 65.00 \times 1.015 = \mathbf{\text{₹ } 65.975 / \text{USD}}$$ $$\text{Locked-In Rupee Outflow} = 60,000 \times 65.975 = \mathbf{\text{₹ } 39,58,500}$$

Option 2: Call Option Cover ($X = 66.00$)

$$\text{Call Premium per USD} = 2\% \times 65.00 = \text{₹ } 1.30$$ $$\text{Total Premium Paid Today} = 60,000 \times 1.30 = \text{₹ } 78,000$$ $$\text{Future Value of Premium at 10% for 6 Months} = 78,000 \times (1 + 0.05) = \text{₹ } 81,900 \text{ (₹ 1.365/USD)}$$

• If Spot falls to ₹ 64.00: Call is OTM. Lapse call, buy spot @ ₹ 64.00. $$\text{Total Outflow} = (60,000 \times 64.00) + 81,900 = 38,40,000 + 81,900 = \mathbf{\text{₹ } 39,21,900}$$
• If Spot rises to ₹ 68.00: Call is ITM. Exercise call @ ₹ 66.00. $$\text{Total Outflow} = (60,000 \times 66.00) + 81,900 = 39,60,000 + 81,900 = \mathbf{\text{₹ } 40,41,900}$$

AKC Ltd. exports electronic components on 90-day credit terms. Receivables due in 90 days are:

• Japan: JPY 78,00,000
• USA: US$ 1,02,300
• Europe: EUR 95,920

Relevant quotes (90-day forward):

• USD/INR: ₹ 67.50 / 67.80
• USD/JPY: 108.50 / 108.80
• EUR/USD: 1.1200 / 1.1230

Required: Calculate the total Rupee realization if all foreign exchange risk is hedged using forward contracts.

1. Realization on US$ 1,02,300:

$$\text{Inflow} = 1,02,300 \times 67.50 = \mathbf{\text{₹ } 69,05,250}$$

2. Realization on JPY 78,00,000:

$$\text{Forward Cross Buying Rate } (\text{INR/JPY}) = \frac{(\text{INR/USD})_{\text{Bid}}}{(\text{JPY/USD})_{\text{Ask}}} = \frac{67.50}{108.80} = \text{₹ } 0.620404$$ $$\text{Inflow} = 78,00,000 \times 0.620404 = \mathbf{\text{₹ } 48,39,151}$$

3. Realization on EUR 95,920:

$$\text{Forward Cross Buying Rate } (\text{INR/EUR}) = (\text{USD/EUR})_{\text{Bid}} \times (\text{INR/USD})_{\text{Bid}} = 1.1200 \times 67.50 = \text{₹ } 75.60$$ $$\text{Inflow} = 95,920 \times 75.60 = \mathbf{\text{₹ } 72,51,552}$$

Total Combined Rupee Realization:

$$\text{Total Inflow} = 69,05,250 + 48,39,151 + 72,51,552 = \mathbf{\text{₹ } 1,89,95,953}$$

EFD Ltd. is an Indian export business house. The company has an export receivable of USD 10,000,000 ($ 10 Million) due in 6 months. Market quotes are:

• Spot Rate: USD 0.016129 / ₹ (i.e. ₹ 62.00 / USD)
• 6-Month Forward: USD 0.016129 / ₹ (₹ 62.00)
• 6-Month Interest Rates: India = 8% p.a.; US = 5% p.a.
• 6-Month Put Option Strike Price: ₹ 62.00, Premium = 2.5%

Evaluate Forward Contract vs. Money Market Hedge vs. Currency Put Option.

Option 1: Forward Contract

$$\text{Rupee Proceeds at Month 6} = \frac{\$ 10,000,000}{0.016129} = \mathbf{\text{₹ } 62,00,01,240}$$

Option 2: Money Market Hedge (MMH)

1. Borrow USD for 6 months at 5% p.a. (2.5% for 6 months): $$\text{USD Borrowed} = \frac{\$ 10,00,000}{1 + 0.025} = \text{US\$ } 97,56,097.56$$
2. Convert borrowed USD to INR at Spot: $$\text{INR Realized Today} = 97,56,097.56 \times 62.00 = \text{₹ } 60,48,78,049$$
3. Invest INR in India at 8% p.a. for 6 months (4%): $$\text{INR at Month 6} = 60,48,78,049 \times (1 + 0.04) = \mathbf{\text{₹ } 62,90,73,171}$$

Option 3: Put Option

$$\text{Premium Paid Today} = 2.5\% \times \text{₹ } 62.00 \times 10,000,000 = \text{₹ } 1,55,00,000$$ $$\text{Future Value of Premium at 8% for 6 months} = 1,55,00,000 \times 1.04 = \text{₹ } 1,61,20,000$$ $$\text{Net Guaranteed Inflow at Strike ₹ 62} = 62,00,00,000 - 1,61,20,000 = \mathbf{\text{₹ } 60,38,80,000}$$

Spot rate: 1 US $ = ₹ 48.0123. 180-day interest rates: India = 12% p.a., US = 8% p.a. An Indian firm has a receivable of US$ 86,644 in 180 days. Show the exact mechanical steps to execute a complete Money Market Hedge.

1. Borrow USD Today: Discount US$ 86,644 at 8% p.a. for 180 days ($4\%$): $$\text{USD Borrowed} = \frac{86,644}{1 + 0.04} = \mathbf{\text{US\$ } 83,311.54 \approx \text{US\$ } 83,312}$$
2. Convert Spot: Sell US$ 83,312 at spot rate ₹ 48.0123: $$\text{Rupees Realized Today} = 83,312 \times 48.0123 = \mathbf{\text{₹ } 40,00,000}$$
3. Invest in India: Deposit ₹ 40,00,000 at 12% p.a. for 180 days ($6\%$): $$\text{Proceeds at Day 180} = 40,00,000 \times (1 + 0.06) = \mathbf{\text{₹ } 42,40,000}$$
4. Repayment: The export customer pays US$ 86,644, which automatically pays off the foreign currency borrowing plus interest.

Given the following information:

• Spot Exchange Rate: Can $ 0.665 per DM
• 3-Month Forward Rate: Can $ 0.670 per DM
• 3-Month Interest Rate in Canada: 9% p.a.
• 3-Month Interest Rate in Germany: 7% p.a.

Determine whether covered interest arbitrage is possible and outline the arbitrage strategy.

Step 1: Compute Annualized Forward Premium on DM

$$\text{Annualized Premium} = \frac{0.670 - 0.665}{0.665} \times \frac{12}{3} \times 100 = \frac{0.005}{0.665} \times 400 = \mathbf{3.01\% \text{ p.a.}}$$

Step 2: Compare with Interest Rate Differential

$$\text{Interest Rate Differential } (r_{\text{Canada}} - r_{\text{Germany}}) = 9\% - 7\% = \mathbf{2.00\% \text{ p.a.}}$$

Since Forward Premium on DM ($3.01\%$) > Interest Differential ($2.00\%$), DM is overvalued forward. Covered Interest Arbitrage is possible!

Arbitrage Execution Steps:

1. Borrow Canadian Dollars at 9% p.a.
2. Convert Can $ to DM at Spot (0.665).
3. Invest DM in Germany at 7% p.a.
4. Sell DM forward at Can $ 0.670.
5. Net arbitrage gain = $3.01\% - 2.00\% \approx \mathbf{1.01\% \text{ p.a.}}$

An Indian exporting firm, Rohit and Bros., would be covering itself against a likely depreciation of Pound Sterling. Receivables are £ 5,00,000 due in 6 months. The bank’s forward contract desk is temporarily closed due to market turmoil. Outline the steps to hedge using the money market.

1. Borrow in UK: Borrow discounted amount of £ 5,00,000 in London at the UK lending rate for 6 months.
2. Convert Spot: Convert borrowed Pounds into Indian Rupees at the prevailing spot bid rate.
3. Invest in India: Place Rupee proceeds in a fixed deposit in India at the domestic deposit rate.
4. Close Out: At month 6, customer's £ 5,00,000 remittance directly liquidates the UK bank loan.

An exporter is a UK-based company. Invoice amount is $ 3,50,000 due in 3 months. Market data:

• Spot Rate: $ 1.5800 / £
• 3-Month Forward Rate: $ 1.6000 / £
• UK Interest Rate: Borrowing = 10% p.a., Deposit = 8% p.a.
• US Interest Rate: Borrowing = 6% p.a., Deposit = 4% p.a.

Evaluate Forward Contract vs. Money Market Hedge.

Option 1: Forward Cover

$$\text{Pound Proceeds at Month 3} = \frac{\$ 3,50,000}{1.6000} = \mathbf{\text{£ } 2,18,750.00}$$

Option 2: Money Market Hedge (MMH)

1. Borrow USD at 6% p.a. for 3 months (1.5%): $$\text{USD Borrowed} = \frac{\$ 3,50,000}{1 + 0.015} = \text{US\$ } 3,44,827.59$$
2. Convert to GBP at Spot ($ 1.5800): $$\text{Pound Today} = \frac{3,44,827.59}{1.5800} = \text{£ } 2,18,245.31$$
3. Invest in UK at 8% p.a. for 3 months (2%): $$\text{Pound Proceeds at Month 3} = 2,18,245.31 \times 1.02 = \mathbf{\text{£ } 2,22,610.22}$$

The rate of inflation in India is 8% per annum and in the USA it is 4% per annum. The current spot rate is ₹ 48.00 / USD. Determine the expected spot rate at the end of Year 1, Year 2, and Year 3 using Purchasing Power Parity.

Under Relative PPP, the expected spot rate at year $t$ is:

$$S_t = S_0 \times \left(\frac{1 + I_{\text{India}}}{1 + I_{\text{USA}}}\right)^t = 48.00 \times \left(\frac{1.08}{1.04}\right)^t = 48.00 \times (1.03846)^t$$

On April 1, 3-months interest rates are: UK £ = 7.5% p.a., US $ = 3.5% p.a. Current spot rate is £ 1 = $ 1.6000. The 3-month forward rate quoted in the market is £ 1 = $ 1.5800.

Determine whether Covered Interest Arbitrage is feasible and show the arbitrage cash flows starting with £ 10,00,000.

Step 1: Check Theoretical Forward Rate under IRP

$$F_{\text{theoretical}} = 1.6000 \times \frac{1 + 0.035 \times 0.25}{1 + 0.075 \times 0.25} = 1.6000 \times \frac{1.00875}{1.01875} = \mathbf{\$ 1.5843 / \text{£}}$$

Actual market forward rate = $ 1.5800. Actual forward rate < Theoretical forward rate. Pound is undervalued forward.

Step 2: Arbitrage Execution Starting with £ 10,00,000

1. Borrow USD or invest in UK:
   Invest £ 10,00,000 in UK @ 7.5% for 3 months ($1.875\%$): $$\text{Pound Proceeds at Month 3} = 10,00,000 \times 1.01875 = \mathbf{\text{£ } 10,18,750}$$
2. Simultaneously sell USD forward / borrow in US: $$\text{Arbitrage Profit} \approx \mathbf{\text{£ } 2,750}$$

An importer requests his bank to extend a forward contract for US$ 20,000 which is due for execution on 30-10-2010 for a further period of 3 months. The original contract was booked @ ₹ 45.5000.

On 30-10-2010, market quotes are:

• Spot USD/INR: ₹ 44.8000 / 44.9000
• 3-Month Forward: ₹ 45.2000 / 45.3500

Exchange margin is 0.10% and cancellation charges are ₹ 100.

Calculate cancellation gain/loss and rate for the extended forward contract.

Part (i): Cancellation of Existing Forward Sale Contract

Cancelled at prevailing Spot TT Buying Rate:

$$\text{Spot TT Buying Rate} = 44.8000 \times (1 - 0.0010) = \mathbf{\text{₹ } 44.7552}$$ $$\text{Currency Gain per USD} = 45.5000 - 44.7552 = \text{₹ } 0.7448$$ $$\text{Total Currency Gain} = 20,000 \times 0.7448 = \mathbf{\text{₹ } 14,896}$$ $$\text{Net Amount Refundable} = 14,896 - 100 = \mathbf{\text{₹ } 14,796}$$

Part (ii): Rate for Extended Contract (3-Month Forward Sale)

$$\text{3-Month Forward TT Selling Rate} = 45.3500 \times (1 + 0.0010) = \mathbf{\text{₹ } 45.3954}$$

XYZ Ltd., an Indian firm, will need to pay Japanese Yen (JPY) 5,00,000 on 30th June. Current quotes on 1st April:

• Spot Rate: ₹ 1 = JPY 2.00 (i.e. ₹ 0.50 / JPY)
• 3-Month Forward Rate: ₹ 1 = JPY 1.95 (i.e. ₹ 0.5128 / JPY)
• Call Option on JPY: Strike Price = ₹ 0.50 / JPY, Premium = ₹ 0.02 / JPY

Evaluate Forward Cover vs Call Option if Spot Rate on 30th June is: (i) ₹ 1 = JPY 1.90, or (ii) ₹ 1 = JPY 2.05.

Option 1: Forward Cover

$$\text{Rupee Cost} = \frac{\text{JPY } 5,00,000}{1.95} = \mathbf{\text{₹ } 2,56,410}$$

Option 2: Call Option ($X = \text{₹ } 0.50$, Premium = ₹ 0.02)

$$\text{Premium Paid} = 5,00,000 \times 0.02 = \text{₹ } 10,000$$

• Scenario (i): Spot = ₹ 1 = JPY 1.90 (₹ 0.5263 / JPY):
  Since market rate (0.5263) > Strike (0.50), Exercise Call: $$\text{Total Cost} = (5,00,000 \times 0.50) + 10,000 = 2,50,000 + 10,000 = \mathbf{\text{₹ } 2,60,000}$$
• Scenario (ii): Spot = ₹ 1 = JPY 2.05 (₹ 0.4878 / JPY):
  Since market rate (0.4878) < Strike (0.50), Lapse Call, buy spot: $$\text{Total Cost} = (5,00,000 \times 0.4878) + 10,000 = 2,43,902 + 10,000 = \mathbf{\text{₹ } 2,53,902}$$

ABC Technologic is expecting to receive a sum of US$ 4,00,000 after 3 months. The company decides for futures market hedging. The contract size is US$ 1,000 on the NSE currency derivatives segment.

Current market rates:

• Spot Rate: ₹ 62.40 / USD
• 3-Month Futures Rate: ₹ 62.80 / USD

Required: Determine the number of futures contracts to be traded, and calculate the net proceeds if the spot rate at 3 months is (i) ₹ 62.00, or (ii) ₹ 63.50, assuming futures prices converge to spot at expiry.

Step 1: Determine Futures Position & Contract Count

Since the company has an export receivable (inflow of USD), it faces the risk of USD depreciation. To hedge, the company must Sell (Short) USD Futures Contracts.

$$N = \frac{\text{Exposure Amount}}{\text{Contract Size}} = \frac{\text{US\$ } 4,00,000}{\text{US\$ } 1,000} = \mathbf{400 \text{ Futures Contracts (Sell)}}$$

Step 2: Payoff Simulation under Two Market Scenarios

Gibralater Limited has imported 5,000 bottles of shampoo at a landed cost in Mumbai of USD 80 per bottle (Total US$ 4,00,000) payable in 3 months. Financial data:

• Spot USD/INR: ₹ 65.50
• 3-Month Forward Rate: ₹ 66.20
• 3-Month Call Option: Strike Price = ₹ 66.00, Premium = ₹ 0.80 / USD
• Borrowing Rate: 10% p.a.

Evaluate: (i) Forward Contract, and (ii) Call Option, if the spot rate on due date is ₹ 65.00, ₹ 66.00, or ₹ 67.50.

Option I: Forward Cover

$$\text{Locked-In Rupee Cost} = 4,00,000 \times \text{₹ } 66.20 = \mathbf{\text{₹ } 2,64,80,000}$$

Option II: Call Option ($X = 66.00$)

$$\text{Premium Paid Today} = 4,00,000 \times 0.80 = \text{₹ } 3,20,000$$ $$\text{Future Value of Premium at 10% for 3 Months} = 3,20,000 \times (1 + 0.025) = \text{₹ } 3,28,000 \text{ (₹ 0.82/USD)}$$

An American firm is under obligation to pay interest of Can $ 10,00,000 in 6 months. The financial parameters are:

• Spot Rate: Can $ 1.2600 / US $ (i.e. US $ 0.7937 / Can $)
• 6-Month Forward: Can $ 1.2700 / US $ (i.e. US $ 0.7874 / Can $)
• 6-Month Canadian Deposit Rate: 8% p.a. (4% for 6 months)
• 6-Month US Borrowing Rate: 6% p.a. (3% for 6 months)

Compare: Forward Market Cover vs. Money Market Cover.

Option 1: Forward Market Cover

$$\text{USD Outflow at 6 Months} = \frac{\text{Can } \$ 10,00,000}{1.2700} = \mathbf{\text{US\$ } 7,87,401.57}$$

Option 2: Money Market Cover (MMH)

1. Deposit Canadian Dollars today to accumulate Can $ 10,00,000 at 4%: $$\text{Can \$ to Deposit} = \frac{10,00,000}{1 + 0.04} = \text{Can } \$ 9,61,538.46$$
2. Convert Can $ 9,61,538.46 to USD at Spot (1.2600): $$\text{USD Borrowed Today} = \frac{9,61,538.46}{1.2600} = \text{US\$ } 7,63,125.76$$
3. Repay US borrowing with interest at 3%: $$\text{USD Outflow at 6 Months} = 7,63,125.76 \times 1.03 = \mathbf{\text{US\$ } 7,86,019.53}$$

Comparison: Money Market Hedge saves $7,87,401.57 - 7,86,019.53 = \mathbf{\text{US\$ } 1,382.04}$.

Zaz plc, a UK company, is negotiating an order amounting to € 2.8 million with a European customer on 6-month credit terms. Three proposals are considered:

• Proposal A: Invoice in Euro (€ 2.8M) with forward cover. (Spot GBP/EUR = 1.1660 / 1.1680; 6-Month Forward = 1.1820 / 1.1850).
• Proposal B: Invoice in US$ ($ 3.6M) with forward cover. (Spot GBP/USD = 1.4820 / 1.4850; 6-Month Forward = 1.4920 / 1.4960).
• Proposal C: Invoice in GBP (£ 2.35M) with no currency risk to Zaz plc.

Evaluate which proposal yields the highest net receipt in GBP.

Columbus Surgicals Inc. based in the US has imported surgical instruments from the UK for £ 1,00,000 payable in 3 months. Market data:

• Spot Rate: $ 1.5500 / £
• 3-Month Forward Rate: $ 1.5700 / £
• 3-Month Call Option Strike Price: $ 1.5600 / £, Premium = $ 0.02 / £
• US Borrowing Rate: 8% p.a.

Advise Columbus Surgicals on the best hedging alternative.

Option 1: Forward Cover

$$\text{Locked-In Dollar Outflow} = 1,00,000 \times 1.5700 = \mathbf{\$ 1,57,000}$$

Option 2: Call Option ($X = 1.5600$, Premium = $ 0.02)

$$\text{Future Value of Premium at 8% for 3 Months} = (1,00,000 \times 0.02) \times (1 + 0.02) = 2,000 \times 1.02 = \mathbf{\$ 2,040}$$ $$\text{Maximum Dollar Outflow under Call} = (1,00,000 \times 1.5600) + 2,040 = \mathbf{\$ 1,58,040}$$

Break-even exchange rate where Call Option cost equals Forward Cover ($ 1,57,000):

$$S_T + 0.0204 = 1.5700 \implies S_T = \mathbf{\$ 1.5496 / \text{£}}$$

XYZ Ltd., a US firm, will need £ 3,00,000 in 180 days. Market quotes:

• Spot Rate: $ 1.9600 / £
• 180-Day Forward Rate: $ 1.9700 / £
• 180-Day UK Lending Rate = 10% p.a.; UK Borrowing Rate = 12% p.a.
• 180-Day US Lending Rate = 8% p.a.; US Borrowing Rate = 9% p.a.
• Call Option Strike: $ 1.9800 / £, Premium = $ 0.035 / £

Evaluate all three alternatives and determine the best hedging choice.

Alternative A: Forward Contract

$$\text{Total Outflow at Day 180} = 3,00,000 \times 1.9700 = \mathbf{\$ 5,91,000.00}$$

Alternative B: Money Market Hedge (MMH)

1. Deposit GBP today to accumulate £ 3,00,000 at UK lending rate (10% p.a. = 5% for 180 days): $$\text{Pound to Deposit} = \frac{3,00,000}{1 + 0.05} = \text{£ } 2,85,714.29$$
2. Buy GBP Spot at $ 1.9600 by borrowing USD in the US at 9% p.a. (4.5%): $$\text{USD Borrowed Today} = 2,85,714.29 \times 1.9600 = \mathbf{\$ 5,60,000.00}$$
3. Repay US loan with interest at Day 180: $$\text{Total Outflow at Day 180} = 5,60,000 \times (1 + 0.045) = \mathbf{\$ 5,85,200.00}$$

Alternative C: Call Option ($X = 1.9800$, Prem = $ 0.035)

$$\text{Future Value of Premium at 9% for 180 Days} = (3,00,000 \times 0.035) \times (1 + 0.045) = 10,500 \times 1.045 = \mathbf{\$ 10,972.50}$$ $$\text{Maximum Outflow under Call Option} = (3,00,000 \times 1.9800) + 10,972.50 = \mathbf{\$ 6,04,972.50}$$

A Ltd. of U.K. has imported chemicals worth USD 3,64,897 from the USA. Credit period is 6 months. Quotations are given indirectly in London:

• Spot Rate: £ 1 = USD 1.5617 / 1.5659
• 6-Month Forward: £ 1 = USD 1.5455 / 1.5509

Required: Convert indirect quotes to direct quotes and determine the total Sterling cost to settle the invoice.

Step 1: Direct Quotes Conversion (GBP per USD)

$$\text{Direct Bid} = \frac{1}{\text{Indirect Ask}} = \frac{1}{1.5509} = \mathbf{\text{£ } 0.644787}$$ $$\text{Direct Ask} = \frac{1}{\text{Indirect Bid}} = \frac{1}{1.5455} = \mathbf{\text{£ } 0.647039}$$

Step 2: Total Sterling Cost

The UK importer buys USD from the bank at the Direct Ask Rate (£ 0.647039 per USD), or divides by Indirect Bid (1.5455):

$$\text{Sterling Cost} = \frac{\text{US\$ } 3,64,897}{1.5455} = \mathbf{\text{£ } 2,36,102.88}$$

Nitrogen Ltd, a UK company, is negotiating an export order with a foreign buyer under 3 invoicing alternatives: (i) USD 5 Million with 6-month forward cover, (ii) EUR 4.2 Million with 6-month forward cover, or (iii) GBP 3.2 Million direct invoice. Compare the receipts and advise Nitrogen Ltd.

Calculate net GBP realization for each proposal using applicable 6-month forward bid rates. Select the alternative that maximizes guaranteed Sterling cash inflows.

Sun Ltd. is planning to import equipment from Japan at a cost of 3,400 lakh Yen (¥ 340 Million). Two financing options are available:

• Option I (Domestic Rupee Loan): Pay supplier today. Finance by availing Rupee term loan at 18% per annum. Spot exchange rate is ₹ 100 = 240 Yen.
• Option II (Supplier Credit): Supplier offers 1-year credit at 6% per annum. 1-year forward quote is ₹ 100 = 222 Yen.

Evaluate both options and advise Sun Ltd.

Option I: Domestic Rupee Loan at 18% p.a.

Rupee required today to pay ¥ 3,400 Lakhs at Spot (¥ 2.40 / ₹):

$$\text{Principal Loan Amount Today} = \frac{3,400 \text{ Lakh Yen}}{2.40} = \mathbf{\text{₹ } 1,416.67 \text{ Lakhs}}$$

Repayment after 1 year with 18% interest:

$$\text{Total Outflow after 1 Year} = 1,416.67 \times (1 + 0.18) = \mathbf{\text{₹ } 1,671.67 \text{ Lakhs}}$$

Option II: Supplier Credit at 6% p.a. with Forward Cover

$$\text{Total Yen Payable after 1 Year} = 3,400 \times (1 + 0.06) = \mathbf{3,604 \text{ Lakh Yen}}$$

Covered at 1-year forward rate (¥ 2.22 / ₹):

$$\text{Total Outflow after 1 Year} = \frac{3,604 \text{ Lakh Yen}}{2.22} = \mathbf{\text{₹ } 1,623.42 \text{ Lakhs}}$$

Comparative Evaluation:

$$\text{Savings under Option II} = 1,671.67 - 1,623.42 = \mathbf{\text{₹ } 48.25 \text{ Lakhs}}$$

NP and Co. has imported goods for US $ 7,00,000 payable in 3 months. Market data:

• Spot USD/INR: ₹ 67.20
• 3-Month Forward Rate: ₹ 67.80
• 3-Month Call Option Strike: ₹ 67.50, Premium = ₹ 0.50 / USD

Evaluate Forward Contract vs. Call Option if the market rate at maturity moves to: (i) ₹ 66.80, (ii) ₹ 67.50, or (iii) ₹ 68.50.

1. Forward Market Cover: Fixed Outflow = $7,00,000 \times 67.80 = \mathbf{\text{₹ } 4,74,60,000}$.

2. Call Option Strategy: Premium Paid = $7,00,000 \times 0.50 = \text{₹ } 3,50,000$.

A customer with whom the Bank had entered into a 3-month forward purchase contract for Swiss Francs (CHF) 1,00,000 @ ₹ 27.25 requests cancellation of the contract 1 month before due date. The bank’s 1-month forward selling rate is ₹ 27.52. Flat cancellation charge is ₹ 100. Calculate the amount payable by the customer.

Bank originally contracted to buy CHF @ ₹ 27.25. On cancellation, the bank sells CHF back to the customer at the 1-month forward selling rate of ₹ 27.52:

$$\text{Loss per CHF} = 27.52 - 27.25 = \text{₹ } 0.27$$ $$\text{Total Currency Loss} = 1,00,000 \times 0.27 = \mathbf{\text{₹ } 27,000}$$ $$\text{Total Amount Payable by Customer} = 27,000 + 100 = \mathbf{\text{₹ } 27,100}$$

A bank enters into a forward purchase TT covering an export bill for Swiss Francs 1,00,000 at ₹ 32.40. On due date, the customer cancels the contract. Cross market rates on due date are quoted via USD. Calculate the cancellation loss recovered by the bank at the TT selling rate.

1. Compute the TT Selling Rate for CHF by combining USD/INR Ask and USD/CHF Bid plus exchange margin.
2. Calculate difference between cancellation selling rate and contracted purchase rate (₹ 32.40).
3. Recover net difference plus flat cancellation fee from the exporter.

Your forex dealer had entered into a cross-currency deal and bought EUR 10,00,000 against USD at 1.1250. Cover rates in the interbank market move. Calculate the net gain or loss in USD and INR.

Calculate the net settlement in USD, and convert into INR at the prevailing spot exchange rate.

You have following quotes from Bank A and Bank B:

Required: Determine the triangular cross rates and demonstrate how an arbitrageur can profit starting with 1 Million GBP.

1. Sell GBP for USD: Sell 1,000,000 GBP to Bank B at the higher Bid rate ($1.7650$): $$\text{USD Received} = 10,00,000 \times 1.7650 = \mathbf{\$ 17,65,000}$$
2. Buy CHF with USD: Sell USD for CHF with Bank B at Bid ($1.4660$): $$\text{CHF Received} = 17,65,00,0 \times 1.4660 = \mathbf{\text{CHF } 25,87,490}$$
3. Buy back GBP using CHF: Reconvert at cheaper synthetic rate.

M/s Omega Electronics Ltd. exports air conditioners to the USA. Selling price is $ 500 per unit. Cost of production is ₹ 20,000 per unit. Spot rate is ₹ 48.00 / USD. Calculate profit at current rate and analyze the impact if USD depreciates to ₹ 45.00 or appreciates to ₹ 52.00.

Your bank’s London office has surplus funds of USD 5,00,000 for 3 months. Two investment choices exist:

• London Deposit: Invest in USD deposit at 5% p.a.
• New York Arbitrage: Convert to Sterling (£) and invest in London at 8% p.a. with 3-month forward cover. (Spot GBP/USD = 1.5500; 3-Month Forward = 1.5400).

Advise the bank on the best deployment of funds.

Choice 1: Invest in USD in London at 5% p.a. (1.25% for 3 months)

$$\text{Proceeds after 3 Months} = 5,00,000 \times (1 + 0.0125) = \mathbf{\text{US\$ } 5,06,250.00}$$

Choice 2: Convert to Sterling, Invest at 8% p.a. (2% for 3 months) & Cover Forward

1. Convert USD to GBP at Spot ($ 1.5500): $$\text{Pound Invested} = \frac{5,00,000}{1.5500} = \text{£ } 3,22,580.65$$
2. Interest earned at 2%: $$\text{Pound Proceeds at Month 3} = 3,22,580.65 \times 1.02 = \text{£ } 3,29,032.26$$
3. Convert back to USD at 3-Month Forward Rate ($ 1.5400): $$\text{USD Proceeds at Month 3} = 3,29,032.26 \times 1.5400 = \mathbf{\text{US\$ } 5,06,709.68}$$

Gain from Arbitrage: Choice 2 yields $5,06,709.68 - 5,06,250.00 = \mathbf{\text{US\$ } 459.68}$ extra profit.

Drilldip Inc., a US-based company, has won a contract in India for drilling an oilfield requiring an initial outlay of ₹ 500 Crores. It can raise USD at 4% p.a. but faces high borrowing costs in India (11% p.a.). An Indian corporate, Bharat Petroleum, needs USD 60 Million to acquire overseas refinery assets and can borrow in India at 9% p.a. Structure a mutually beneficial currency swap.

1. Inception: Drilldip borrows USD in the US and swaps USD for INR with Bharat Petroleum at the current spot exchange rate.
2. During Tenure: Drilldip pays interest in INR at the agreed swap rate, and Bharat Petroleum pays interest in USD.
3. Maturity: Both companies reverse the principal swap at the initial spot rate, eliminating currency risk and sharing the comparative borrowing advantage.

You as a dealer in foreign exchange have the following position in Swiss Francs (CHF) on 31st October:

Nostro account opening balance was CHF 1,00,000 credit. Determine the closing Exchange Position and Nostro Cash Position, and specify the market deals required to square both positions.

Step 1: Compute Exchange Position

Exchange Position: Oversold by CHF 10,000.

Step 2: Compute Cash Position (Nostro Ledger Balance)

Nostro Cash Balance: Credit balance of CHF 1,10,000.

Step 3: Squaring Action

1. To square the Oversold Exchange Position of CHF 10,000:
   $\implies$ Buy CHF 10,000 in the Foreign Exchange Market.
2. To deploy surplus Nostro cash without creating an open exchange position:
   $\implies$ Execute a Buy-and-Sell Swap or place CHF 1,10,000 in a short-term interbank money market deposit.