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Answer: USD -7.445 million
The value of the swap to the financial institution at the end of year 3 is calculated through a series of steps: 1. **Forward Exchange Rate Calculation**: The 1-year forward exchange rate is determined using the formula \( F = S \times \exp[(r_{usd} - r_{eur}) \times T] \), where \( S \) is the current spot rate (USD 1.044 per EUR 1), \( r_{usd} \) is the 1-year risk-free rate in the US (2.0%), \( r_{eur} \) is the 1-year risk-free rate in France (3.0%), and \( T \) is the time to maturity (1 year). This results in a forward rate of USD 1.0336 per EUR for Year 4. 2. **Expected Cash Flows Calculation**: The expected cash flows are calculated for both Year 3 and Year 4. For Year 3, the institution receives EUR 1.5 million from the industrial company and pays USD 1.2 million. For Year 4, the institution is expected to receive EUR 51.5 million (EUR 50 million principal plus EUR 1.5 million interest) and pay USD 61.2 million (USD 60 million principal plus USD 1.2 million interest). 3. **Currency Conversion**: The EUR cash flows are converted into USD using the current and forward exchange rates. For Year 3, EUR 1.5 million is converted to USD 1.566 million. For Year 4, the forward rate is used, converting EUR 51.5 million to USD 53.2304 million. 4. **Net Cash Flows**: The net cash flows are calculated by subtracting payments from receipts for each year. For Year 3, the net is USD 0.366 million. For Year 4, the net is USD -7.969 million. 5. **Discounting and Summing Cash Flows**: The cash flows are discounted back to the present value at the end of Year 3. The present value of Year 3's net cash flow is USD 0.366 million. For Year 4, the present value is calculated as USD -7.969 million discounted by the US risk-free rate, resulting in USD -7.8112 million. 6. **Net Value Calculation**: The net value of the swap to the financial institution is the sum of the present values of the cash flows, which is USD 0.366 million minus USD 7.8112 million, equating to a value of USD -7.4452 million. The correct answer is B, USD -7.445 million, as it correctly accounts for the forward exchange rate, expected cash flows, currency conversion, net cash flows, discounting, and summing of cash flows to determine the value of the swap at the end of year 3.
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A US-based financial institution has entered into a 4-year currency swap agreement with an industrial firm located in France. Under the terms of the agreement, the financial institution will receive an annual interest payment of 3% in euros and, in turn, will pay an annual interest of 2% in US dollars. The principal amounts involved are 50 million euros and 60 million US dollars. These interest payments are exchanged annually at the end of each year. As the end of the third year approaches, the current exchange rate is 1.044 US dollars per 1 euro. The 1-year risk-free rates are 3.0% in France and 2.0% in the United States, and it is assumed that these rates are continuously compounded. Determine the value of this swap to the financial institution at the end of the third year, given the aforementioned conditions.
A
USD-7.603million
B
USD -7.445 million
C
USD -7.068million
D
USD -6.921 million