Explanation:
To calculate the value of the currency swap, we need to find the present value of the cash flows in each currency and convert them to a common currency (USD).
Given:
$10,000,000$15,000,000Step 1: Calculate annual cash flows
$10,000,000 × 2.75% = $275,000$15,000,000 × 3.75% = $562,500Step 2: Calculate present values Using continuous compounding: PV = CF × e^(-r×t)
USD side:
$275,000 × (e^(-0.04×1) + e^(-0.04×2) + e^(-0.04×3))$10,000,000 × e^(-0.04×3)CAD side:
$562,500 × (e^(-0.05×1) + e^(-0.05×2) + e^(-0.05×3))$15,000,000 × e^(-0.05×3)Step 3: Convert CAD present value to USD Divide CAD present value by spot rate (1.52)
Step 4: Calculate swap value Value = PV(USD cash flows received) - PV(CAD cash flows paid in USD)
After performing these calculations:
$10,131,967$10,000,000$131,967Therefore, the value of the swap is $131,967, which corresponds to option C.
Ultimate access to all questions.
Consider the following 3-year currency swap, which involves exchanging annual interest of 2.75% on 10 million US dollars for 3.75% on 15 million Canadian dollars. The spot rate is 1.52 CAD per USD. The term structure is flat in both countries. Calculate the value of the swap in USD if interest rates (continuous compounding) in Canada are 5% and in the United States are 4%. Round to the nearest dollar.
A
$152,000
B
$145,693
C
$131,967
D
$127,818
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