An FI has purchased (borrowed)a one-year $10 million Eurodollar deposit at an annual interest rate of 6 percent.It has invested these proceeds in one-year Euro (€)bonds at an annual rate of 6.5 percent after converting them at the current spot rate of €1.75/$.Both interest and principal are paid at the end of the year.

What is the spread earned by the bank if the end-of-year exchange rate is €1.77/$?

Question

An FI has purchased (borrowed)a one-year $10 million Eurodollar deposit at an annual interest rate of 6 percent.It has invested these proceeds in one-year Euro (€)bonds at an annual rate of 6.5 percent after converting them at the current spot rate of €1.75/$.Both interest and principal are paid at the end of the year.

What is the spread earned by the bank if the end-of-year exchange rate is €1.77/$?

Quizplus · Accepted Answer

The FI borrowed $10 million at 6% and then converted it into € at a spot rate of €1.75/$, giving them €17.5 million. They then invested this amount in € bonds at 6.5% for one year. At the end of the year, they received interest and principal totaling €18.5375 million (€17.5m + €1.0375m), assuming annual compounding. If the exchange rate at the end of the year is €1.77/$, then the dollar value of the investment is $32.84775 million (€18.5375m*$1.77/€1).

The FI's cost of funds was $10.6 million ($10m*$1.06), so their net profit is $22.24775 million ($32.84775m-$10.6m). The spread is the difference between the yield on the investment (6.5%) and the cost of funds (6%), which is 0.5%. However, the exchange rate also changed from €1.75/$ to €1.77/$, which represents a 1.14% appreciation in the euro against the dollar. Since the FI is long euros, this also represents a gain for them. The net spread is therefore 0.5%-1.14%=-0.64%, which is closest to answer choice B (-0.70%).

An FI Has Purchased (Borrowed)a One-Year $10 Million Eurodollar Deposit