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Explanation:
The value of the swap to the financial institution is the present value of the yen receipts minus the present value of the dollar payments, expressed in U.S. dollars.
The institution receives:
Discounting at the Japanese continuously compounded rate of 2%:
Convert to USD at ¥110 per USD:
The institution pays:
$1 million at the end of year 1$1 million + $10 million = $11 million at the end of year 2Discounting at the U.S. continuously compounded rate of 3%:
The nearest answer is A: $51,400.
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Q-723.3. Suppose that the term structure of risk-free interest rates is flat in both Japan and the United States. The Japanese interest rate is 2.0% per annum and the U.S. interest rate is 3.0% per annum (both with continuous compounding). A financial institution has entered into a currency swap in which it receives 15.0% per annum in yen (¥) and pays 10.0% per annum in dollars (10.0` million and ¥1,000.0 million yen. The swap will last only for another two years (i.e., there are only two remaining cash exchanges, although the final principal must be exchanged) and the current exchange rate is ¥110 yen per dollar.
| Assumptions | US | Yen |
|---|---|---|
| Principal | $10.00 | ¥1,000.0 |
| Swap (fixed) rates | 10.0% | 15.0% |
| Interest rate | 3.0% | 2.0% |
| FX exchange rate, USDJPY | $0.00909 | ¥110.0 |
| Base/Quote | JPYUSD | USDJPY |
Which is nearest to the current value of the swap to the financial institution, in U.S. dollars?
A
$51,400
B
$725,000
C
$11.33 million
D
$5.65 million