Question

Please show all work.

Suppose the U.S. yield curve is flat at 6% and the euro yield curve is flat at 4%. The current exchange rate is $1.3 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 2.7 million euros for a given number of dollars in each year.

Answer 1

Forward Exchange Rate = Spot Rate * (1+US Yield Curve)^n / (1+Euro Yield Curve)^n
Spot Rate = $1.30/€
US Yield Curve = 6%
Euro Yield Curve = 4%
n = No of Years
Forward Exchange Rate for Year 1
Forward Exchange Rate = Spot Rate * (1+US Yield Curve)^n / (1+Euro Yield Curve)^n
= $1.30 * (1+6%)^1 / (1+4%)^1
= $1.30 * (1.06) / (1.04)
= $1.30 * 1.019231
= $1.3250
Forward Exchange Rate for Year 2
Forward Exchange Rate = Spot Rate * (1+US Yield Curve)^n / (1+Euro Yield Curve)^n
= $1.30 * (1+6%)^2 / (1+4%)^2
= $1.30 * (1.06)^2 / (1.04)^2
= $1.30 * 1.1236 / 1.0816
= $1.30 * 1.038831
= $1.3505
Forward Exchange Rate for Year 3
Forward Exchange Rate = Spot Rate * (1+US Yield Curve)^n / (1+Euro Yield Curve)^n
= $1.30 * (1+6%)^3 / (1+4%)^3
= $1.30 * (1.06)^3 / (1.04)^3
= $1.30 * 1.191016 / 1.124864
= $1.30 * 1.058809
= $1.3765
Now,
Amount Delivered in Year 1
= Exchange Amount * Forward Exchange Rate of Year 1
= €2,700,000 * $1.3250
= $3,577,500
Amount Delivered in Year 2
= Exchange Amount * Forward Exchange Rate of Year 2
= €2,700,000 * $1.3505
= $3,646,350
Amount Delivered in Year 3
= Exchange Amount * Forward Exchange Rate of Year 3
= €2,700,000 * $1.3765
= $3,716,550
To Calculate no of dollars each year we need to calculate present value.
No of Dollars each year
= [Present Value @ 6% of Amount delivered] / No of Years
= [$3,577,500/(1+6%)^1 + $3,646350/(1+6%)^2 + $3,716,550/(1+6%)^3] / 3
= [$3,577,500/(1.06)^1 + $3,646350/(1.06)^2 + $3,716,550/(1.06)^3] / 3
= [$3,577,500/1.06 + $3,646350/1.1236 + $3,716,550/1.191016] / 3
= [$3,375,000 + $3,245,238.52 + $3,120,487.05] / 3
= $9,740,725.57 / 3
= $3,246,908.52