Answer-first summary for fast verification
Answer: USD –7.445 million
## 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. ### Step 1: Calculate the 1-year forward exchange rate Using the interest rate parity formula with continuous compounding: F = S × exp[(r_USD - r_EUR) × T] Where: - S = 1.044 (current spot rate USD/EUR) - r_USD = 2.0% = 0.02 - r_EUR = 3.0% = 0.03 - T = 1 year F = 1.044 × exp[(0.02 - 0.03) × 1] = 1.044 × exp[-0.01] = 1.044 × 0.99005 = 1.0336 USD/EUR ### Step 2: Calculate expected cash flows at end of year 3 **Receipts (EUR):** - Year 3: EUR 50 million × 3% = EUR 1.5 million - Year 4: EUR 50 million × 3% + EUR 50 million principal = EUR 51.5 million **Payments (USD):** - Year 3: USD 60 million × 2% = USD 1.2 million - Year 4: USD 60 million × 2% + USD 60 million principal = USD 61.2 million ### Step 3: Convert EUR cash flows to USD **Receipts in USD:** - Year 3: EUR 1.5 million × 1.0440 = USD 1.566 million - Year 4: EUR 51.5 million × 1.0336 = USD 53.2304 million ### Step 4: Net cash flows per year - Year 3: USD 1.566 million - USD 1.2 million = USD 0.366 million - Year 4: USD 53.2304 million - USD 61.2 million = USD -7.9696 million ### Step 5: Discount to year 3 and sum Using continuous compounding with r_USD = 2.0%: - Year 3: Present value = USD 0.366 million (no discounting needed) - Year 4: Present value = USD -7.9696 million × exp(-0.02 × 1) = USD -7.9696 × 0.9802 = USD -7.8112 million **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.
Author: LeetQuiz .
Ultimate access to all questions.
No comments yet.
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