A 1-year, 4 percent euro denominated bond sells at par. A comparable risk 1-year, 5.5 percent euro/dollar dual-currency bond pays $1,500 at maturity per €1,000 of face value. It sells for €1,250. What is the implied $/€ exchange rate at maturity?

Question

Quizplus · Accepted Answer

Using the euro denominated bond:
Face Value = €1,000 
Coupon Rate = 4%
Coupon Payment = €1,000 x 4% = €40 
Maturity Value = €1,000 + €40 = €1,040

Using the euro/dollar dual-currency bond:
Face Value = €1,000 
Maturity Value = $1,500 
Exchange Rate = €1,250/€1,000 = $1.25/€1.00

To find the implied exchange rate, we need to calculate the dollar value of the euro-denominated bond at maturity:
Maturity Value of euro-denominated bond = €1,040 
Implied exchange rate = ($ amount received at maturity) / (€ amount paid at maturity) 
Implied exchange rate = ($1,040 x exchange rate) / €1,000

Setting this equal to the exchange rate of the dual-currency bond: 
$1,500 / €1,000 = ($1,040 x exchange rate) / €1,000

Simplifying: 
Exchange rate = $1,500 / €1,040

Converting to the requested format: 
Exchange rate = $1.4423/€1.00

Therefore, the best answer is B.

A 1-Year, 4 Percent Euro Denominated Bond Sells at Par