Answer: USD -7.445 million

The value of the swap to the financial institution at the end of year 3 is calculated by following these steps: 1. **Forward Exchange Rate Calculation**: The 1-year forward exchange rate is calculated using the formula \( F = S \times e^{(r_{USD} - r_{EUR}) \times T} \), where \( S \) is the current spot rate (USD 1.044 per EUR 1), \( r_{USD} \) is the 1-year US Treasury rate (2.0%), \( r_{EUR} \) is the 1-year French risk-free rate (3.0%), and \( T \) is the time to maturity (1 year). Plugging in the values, we get \( F = 1.044 \times e^{(0.02 - 0.03) \times 1} = 1.0336 \) (USD per EUR). 2. **Expected Cash Flows Calculation**: The expected cash flows for both the financial institution and the French company are calculated for year 3 and year 4: - **Year 3**: The financial institution receives 3% of EUR 50 million and pays 2% of USD 60 million. - **Year 4**: In addition to the interest payments, the principal amounts are also exchanged. 3. **Currency Conversion**: Convert the EUR cash flows into USD using the current spot rate for year 3 and the forward rate for year 4: - **Year 3 Receipts**: \( 1.5 \text{ million EUR} \times 1.044 = 1.566 \text{ million USD} \) - **Year 4 Receipts**: \( 51.5 \text{ million EUR} \times 1.0336 = 53.2304 \text{ million USD} \) 4. **Net Cash Flows**: Calculate the net cash flows for each year by subtracting the payments from the receipts: - **Year 3**: \( 1.566 \text{ million USD} - 1.2 \text{ million USD} = 0.366 \text{ million USD} \) - **Year 4**: \( 53.2304 \text{ million USD} - 61.2 \text{ million USD} = -7.9696 \text{ million USD} \) 5. **Discounting and Summing Cash Flows**: Discount the net cash flows to the present value at the end of year 3 using the respective risk-free rates for each currency. However, the discounting step is not explicitly shown in the provided explanation. Assuming continuous compounding and using the risk-free rates, the present values would be calculated, and then the cash flows would be summed to find the total value of the swap to the financial institution. The correct answer provided is B, which is USD -7.445 million. This value represents the present value of the net cash flows, taking into account the time value of money and the exchange rates. The explanation provided in the file content does not include the discounting step explicitly, but it is implied that the present values of the cash flows have been calculated and summed to arrive at the final answer.

Author: LeetQuiz Editorial Team