Question

PIB wants to offer a $40 million, 6-months Eurodollar deposit to one of its major clients at 6-months LIBOR less 2.5%. 6-month LIBOR is 5.3%. The bank intends to use the proceeds of this deposit to buy a 5.0% 3-months grade AAA commercial paper and to rollover the investment for another three months at the end of the first three months cycle. To protect itself from interest rate exposure, the bank also buys a “3 against 6” $40 million, FRA for a three month period beginning three months from the day of receipt of the deposit and ending six months from the day of receipt of the deposit. The agreement rate with the seller is 5.0%. There are 94 days in the first three months and 92 days in the remaining three months period.

a. Calculate the banks interest expense on the 6-month Eurodollar deposit.

b. Calculate the bank interest income on the first three month commercial paper loan.

c. Calculate the value of the FRA from the last three months of the investment period if 3-months LIBOR (SR) for that period is 5.3%.

PIB Global is a global investment bank operating in the US and has $100 Billion in

assets. The bank has open interest in a wide range of domestic and foreign securities and

continues to seek profitable opportunities in foreign and domestic markets.

Answer 1

Eurodollar deposit offered by PIB to client                           = $40 million

Tenor of the deposit                                                              = 6 months

Rate on the deposit                                                               = LIBOR – 2.5%

LIBOR at the time of the deposit                                           = 5.3% pa

Thus rate on the deposit                                                       = 5.3% - 2.5%     = 2.8% pa

                                                                                              = 2.8%/2              =1.4% for 6 months

1. Bank’s interest expense for 6 months     = Rate * Deposit amount

= 1.4% * $40mn

= $0.56 mn

Thus, the bank pays an interest of $0.56 mn to the client for the 6 month Eurodollar deposit

2. Proceeds of the deposit                                                                       = $40 mn

Investment rate of 3 month AAA Commercial Paper                                = 5%pa

Investment return for the 3 month period = 5%/4 =1.25%pa

Interest income for the first 3 month CP = Rate * Amount

                                                                                        =1.25% * $40mn

                                                                                        =$ 0.5 mn

Thus, the banks received as interest income of $0.5 mn for the first 3 months from the AAA commercial paper investment

3. Agreement rate of 3X6 FRA, $40 mn amount                                               = 5% pa

Actual 3 month LIBOR rate after 3 months of the FRA agreement = 5.3%pa

Thus, the value of FRA is the net savings in interest payments at the end of 3 months discounted to the present day

ie Value of the FRA         =[ (Actual LIBOR rate – FRA agreement rate)/((1+LIBOR rate)^N)] * Value of the agreement

where N      = the number of days of the period / 365

                        = 92/365               =0.25

Thus, value of the FRA = [(5.3%*90/360 - 5%*90/360) / ((1 + 5.3%*90/360)^0.25)]*$40mn

                                                        = [(1.325% - 1.25%) / ((1+1.1325%)^0.25)]*$40mn

                                                        = (0.075%/1.0735)*$40mn

                                                                = $27,945.8