Question

Suppose the U.S. yield curve is flat at 4% and the euro yield curve is flat at 3%. The current exchange rate is $1.45 per euro. What will be the swap rate on an agreement to exchange currency over a 3-year period? The swap will call for the exchange of 2.3 million euros for a given number of dollars in each year. (Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places.)

Answer 1

Current Exchange Rate 1 Euro = $1.45

Size of Exchange = 2,300,000 Euros

US Yield = 4%

Euro Yield = 3%

Calculation of Forward Price at end of Year 1

Forward Rate = Current Rate * [(1+US interest rate) / (1+Euro interest rate)]1

= $1.45 * [(1+0.04) / (1+0.03)]1

= $1.464

Number of Dollars to be delivered = $1.464 * 2,300,000

= $3,367,200

Calculation of Forward Price at end of Year 2

Forward Rate = Current Rate * [(1+US interest rate) / (1+Euro interest rate)]2

= $1.45 * [(1+0.04) / (1+0.03)]2

= $1.478

Number of Dollars to be delivered = $1.478 * 2,300,000

= $3,399,400

Calculation of Forward Price at end of Year 3

Forward Rate = Current Rate * [(1+US interest rate) / (1+Euro interest rate)]3

= $1.45 * [(1+0.04) / (1+0.03)]3

= $1.492

Number of Dollars to be delivered = $1.492 * 2,300,000

= $3,431,600

Calculation of Swap rate

(F/1.04) + (F/1.042) + (F/1.043) = (1.464/1.04) + (1.478/1.042) + (1.492/1.043)

F = $1.477

Therefore, Swap Rate is 1 Euro = $1.477