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. Assume that instead of investing in Euro bonds at a fixed rate of 6.5 percent, the FI invests them in variable rates of LIBOR + 1.5 percent, reset every six months.The current LIBOR rate is 5 percent.LIBOR at the end of six months is 5.5 percent.Assume both interest and principal will be reinvested in six months.Assume the spot exchange rate is €1.75/$.What should be the one-year forward rate in order for the bank to earn a spread of 1 percent?

Question

Quizplus · Accepted Answer

Initially, the FI borrows $10 million at an annual interest rate of 6%, thus the interest expense for a year will be $600,000.
Then, the FI converts the borrowed amount into Euros at an exchange rate of €1.75/$, which gives €17,500,000.
The FI invests this amount in Euro bonds at an annual rate of 6.5%. Hence, the interest income for a year will be €1,137,500. 
Therefore, the net interest income for a year will be €537,500.
Now, assume that the FI invests the proceeds in variable LIBOR + 1.5% rate bonds, which gives an annual rate of 6%. At the end of six months, LIBOR increases to 5.5%. Therefore, for the first six months, the interest income will be (5%+1.5%)/2 x €17,500,000 = €656,250.
At the end of six months, the FI reinvests both the principal and interest at the new LIBOR + 1.5% rate. Thus, for the next six months, the interest income will be (5.5%+1.5%)/2 x €17,656,250 = €712,031.25.
Therefore, the total interest income for the year will be €1,368,281.25.
Next, the FI converts the Euro proceeds into dollars at the spot rate of €1.75/$, which gives $19,047,619.05.
At the end of the year, the FI needs to pay back the borrowed principal of $10 million plus the interest expense of $600,000.
Therefore, the total dollar outflow will be $10,600,000.
Hence, the net dollar profit will be $8,447,619.05.
Now, to earn a spread of 1%, the FI needs to have a total income of $10,100,000.
Thus, the one-year forward rate should be calculated as follows:

€1.75/$ x (1+0.065)/(1+(0.5x0.05)) x (1+(0.5x0.055))/(1+FR) = 1.0100

where FR is the forward rate. Solving for FR gives FR = 0.035, or €1.7478/$.

Therefore, the best choice is C.

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