答案中的1.0336的汇率是哪里来的，题目中并未提到

问题如下：

A financial institution entered into 4-year currency swap contract with a French industrial company.

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 a year. Suppose that it is exactly one year before expiration of the swap contract and just in time for the year 3 cash flow payments and receipts when the exchange rate is USD 1.044 per EUR 1, the 1-year French risk-free rate is 3.0% and the 1-year US Treasury rate is 2.0%. Assuming continuous compounding, what is the value of the swap to the financial institution at the end of year 3? (Practice Exam)

选项：

A.

USD -7.603 million

B.

USD -7.445 million

C.

USD -7.068 million

D.

USD -6.921 million

解释：

Step 1 - calculate the forward exchange rates as at the end of year 3:

1 year forward exchange rate (USD per EUR):

F = S*exp[(rusd–reur)*T] = 1.044*exp[(0.02–0.03)*1] = 1.0336 (i.e., Year 4 FX rate)

Step 2 - calculate the expected cash flows as at year 3:

Receipts:

Year 3: EUR 50mil*0.03 = EUR 1.5mil

Year 4: EUR 50mil*0.03 + EUR 50mil = EUR 51.5mil

Payments:

Year 3: USD 60mil*0.02 = USD 1.2mil

Year 4: USD 60mil*0.02 + USD 60mil = USD 61.2mil

Step 3 - convert the EUR cash flows into base currency, i.e. USD:

Receipts:

Year 3: (EUR 1.5mil)*1.0440= USD 1.566mil

Year 4: (EUR 51.5mil)*1.0336 = USD 53.2304mil

Step 4 - Net the cash flows per year:

Year 3: USD 1.566mil – USD 1.2mil = USD 0.366mil

Year 4: USD 53.230 – USD 61.2mil = USD -7.969mil

Step 5 - discount to year 3 and sum the cash flows in USD:

Year 3: Present value = USD 0.366mil

Year 4: Present value = USD -7.969*exp(-0.02*1) = USD -7.811mil

Net value to the financial institution = 0.366 – 7.811 = USD -7.445mil

A is incorrect. USD -7.603 million uses the appropriate exchange rates but does not discount back to year 3.

C is incorrect. USD -7.068 million uses the current USD per EUR rate (USD 1.044) to convert the EUR cash flows and does not discount back to year 3.

D is incorrect. USD -6.921 million uses the current USD per EUR rate (USD 1.044) to convert the EUR cash flows; however, it does discount back to year 3.