Explanation:
This is a currency swap valuation problem where we need to calculate the value of the swap to the financial institution at the end of year 3.
Using the interest rate parity formula with continuous compounding:
F = S × exp[(r_USD - r_EUR) × T]
Where:
F = 1.044 × exp[(0.02 - 0.03) × 1] = 1.044 × exp[-0.01] = 1.044 × 0.99005 = 1.0336 USD/EUR
Receipts (EUR):
Payments (USD):
Receipts in USD:
Using continuous compounding with r_USD = 2.0%:
Net value to financial institution = USD 0.366 million - USD 7.8112 million = USD -7.4452 million
The negative value indicates this is a liability to the financial institution at the end of year 3.
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A US financial institution entered into a 4-year currency swap contract with an industrial company located in France. Under the terms of the swap, the financial institution receives interest at 3% per year in EUR and pays interest at 2% per year in USD. The principal amounts are EUR 50 million and USD 60 million, and interest payments are exchanged once at the end of each year. Immediately before cash flow payments and receipts are exchanged at the end of year 3, the exchange rate is USD 1.044 per EUR 1, the 1-year risk-free rate in France is 3.0%, and the 1-year risk-free rate in the US is 2.0%. Assuming continuous compounding, what is the value of the swap to the financial institution at the end of year 3?
A
USD –7.603 million
B
USD –7.445 million
C
USD –7.068 million
D
USD –6.921 million