Answer: USD -7.445 million

The correct answer to the question is B, which is USD -7.445 million. The explanation for this answer is as follows: 1. **Forward Exchange Rate Calculation**: The forward exchange rate for the end of year 3 is calculated using the formula \( F = S \times e^{(r_{USD} - r_{EUR}) \times T} \), where \( S \) is the current exchange rate, \( r_{USD} \) and \( r_{EUR} \) are the risk-free rates in USD and EUR respectively, and \( T \) is the time to maturity in years. Plugging in the values, we get \( F = 1.044 \times e^{(0.02 - 0.03) \times 1} = 1.0336 \) (USD per EUR for Year 4 FX rate). 2. **Expected Cash Flows Calculation**: The expected cash flows are calculated for both receipts and payments at the end of year 3 and year 4: - **Year 3 Receipts**: EUR 50 million * 0.03 = EUR 1.5 million. - **Year 4 Receipts**: EUR 50 million * 0.03 + EUR 50 million = EUR 51.5 million. - **Year 3 Payments**: USD 60 million * 0.02 = USD 1.2 million. - **Year 4 Payments**: USD 60 million * 0.02 + USD 60 million = USD 61.2 million. 3. **Conversion of EUR Cash Flows to USD**: The cash flows in EUR are converted to USD using the current and forward exchange rates: - **Year 3 Receipts in USD**: (EUR 1.5 million) * 1.0440 = USD 1.566 million. - **Year 4 Receipts in USD**: (EUR 51.5 million) * 1.0336 = USD 53.2304 million. 4. **Net Cash Flows**: The net cash flows are calculated by subtracting the payments from the receipts for each year: - **Year 3 Net**: USD 1.566 million - USD 1.2 million = USD 0.366 million. - **Year 4 Net**: USD 53.2304 million - USD 61.2 million = USD -7.9696 million. 5. **Discounting and Summing Cash Flows**: The cash flows are discounted back to the present value at the end of year 3. However, the discounting factors and the final calculation steps are not provided in the file content. Assuming the standard discounting process, one would use the risk-free rates to discount the cash flows and sum them to find the present value of the swap to the financial institution. The final step in the explanation seems to be truncated, and the exact discounting process is not detailed. However, based on the steps provided, the calculation of the value of the swap to the financial institution at the end of year 3 would involve discounting the net cash flows from Year 4 back to Year 3 and adding the net cash flow from Year 3. The correct answer, as stated in the file content, is USD -7.445 million, which would be the result of this discounted cash flow analysis.

Author: LeetQuiz Editorial Team