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Answer: $131,967
To value the currency swap: 1. **Calculate present value of USD cash flows:** - Principal: $10,000,000 - Annual interest: 2.75% × $10,000,000 = $275,000 - Discount rate: 4% continuous compounding - PV(USD) = $275,000 × (e^(-0.04) + e^(-0.08) + e^(-0.12)) + $10,000,000 × e^(-0.12) 2. **Calculate present value of CAD cash flows:** - Principal: CAD 15,000,000 - Annual interest: 3.75% × CAD 15,000,000 = CAD 562,500 - Discount rate: 5% continuous compounding - PV(CAD) = CAD 562,500 × (e^(-0.05) + e^(-0.10) + e^(-0.15)) + CAD 15,000,000 × e^(-0.15) 3. **Convert CAD to USD:** - Spot rate: 1.52 CAD/USD - PV(CAD in USD) = PV(CAD) / 1.52 4. **Swap value = PV(USD received) - PV(USD paid)** - Since we're receiving CAD and paying USD, value = PV(CAD in USD) - PV(USD) After calculations, the value is approximately $131,967.
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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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