A 2-year, 4 percent euro denominated bond sells at par. A comparable risk 2-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

To compare the returns of the two bonds, we need to convert the cash flows of the dual-currency bond into euros using the implied exchange rate at maturity. Let X be the implied exchange rate at maturity. Then, €1,000 of face value will be worth $1,500X at maturity.

The cash flow from the dual-currency bond in euros is then:
€1,000 + €1,500X

To find the implied exchange rate, we can set this cash flow equal to the cash flow from the euro denominated bond, which is:
€1,000 + €40 (4% of €1,000)

Setting these two equal, we get:

€1,000 + €1,500X = €1,040

Solving for X, we get:

X = $1.2099/€1.00

Therefore, the implied exchange rate at maturity is $1.2099/€1.00.

A 2-Year, 4 Percent Euro Denominated Bond Sells at Par