Explanation:
The value of the currency swap to the American Dream Bank (AD) is the present value of the USD cash flows it receives minus the present value of the GBP cash flows it pays, converted into USD.
Using continuous compounding:
1. Present Value of USD received:
Interest = 10% of $120 million = $12 million.
PV(USD) = $12M * e^(-0.055 * 1) + $132M * e^(-0.055 * 2)
PV(USD) = $12M * 0.94648 + $132M * 0.89583 = $11.36M + $118.25M = $129.61 million.
2. Present Value of GBP paid: Interest = 8% of GBP 80 million = GBP 6.4 million. PV(GBP) = £6.4M * e^(-0.068 * 1) + £86.4M * e^(-0.068 * 2) PV(GBP) = £6.4M * 0.93426 + £86.4M * 0.87284 = £5.98M + £75.41M = £81.39 million.
3. Value of the Swap in USD:
Convert the PV of GBP to USD: £81.39M * 1.26 = $102.55 million.
Swap Value = PV(USD) - Converted PV(GBP) = $129.61M - $102.55M = $27.06 million.
(Note: The result of ~27.06 million makes option C the closest standard answer provided due to potential differences in intermediate rounding or discrete vs. continuous compounding methods.)
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Q.30 Two banks, the American Dream Bank (AD) and the British Royal Bank (BR), have entered into a 2-year currency swap agreement with annual payments, where AD agreed to pay 8% in British pound (GBP) on the principal amount of GBP 80 million to BR. In addition, BR agreed to pay 10% to AD on the principal of $120 million. The exchange rate is USD 1.26 per GBP. Suppose that the interest rate in the United States and Great Britain are flat at 5.5% and 6.8%, respectively, determine the value of the currency swap to American Dream Bank in USD.
A
USD 30.45 million.
B
USD 21.69 million.
C
USD 26.39 million.
D
USD 20.40 million.