Question

Citibank need to borrow $1 million for 6 months starting in 3 years.  Citibank is concerned about the interest rate would like to lock in the interest rate it pays by going long an FRA with Bank of America.  The FRA specifies that Citibank will borrow at a fixed rate of 0.03 for 6 months on $1 million in 3 years. If the 6 months LIBOR rate proves to be 0.01. Then to settle the FRA, what is the cash flow to Citibank at the end of 3 years? Please be careful with the sign (positive/negative) of your answer and keep your answer to 2 decimal points.

Answer 1

Borrowing = $ 1million, FRA Rate = 0.03 or 3 %, Actual 6-month LIBOR = 0.01 or 1 %

Tenure of Borrowing = 6-months

Citibank enters into the FRA to guarantee for itself a borrowing rate of 0.03 irrespective of the actual interest rate at the end of Year 3 (when the borrowing takes place). If the actual interest rate at the time of borrowing is higher the FRA counterparty will pay the difference in the interest amount to the FRA buyer which is Citibank in this case. However, if the actual interest rate is lower, then the FRA counterparty will receive the difference in the interest amount from the FRA buyer. This essentially ensures that the FRA buyer has its borrowing rate locked in which is equal to the FRA rate. In the context of this question, Citibank has a fixed borrowing rate of 0.03 and since the actual rate of 0.01 is lower, Citibank (the FRA buyer) will pay the difference to the FRA counterparty (FRA counterparty will receive the difference in the interest amount).

Citibank Payment under FRA = 0.03 x 1000000 x 0.5 (time period is 6-months or 0.5 years) = $ 15000

Actual Payment at LIBOR = 0.01 x 1000000 x 0.5 = $ 5000

Net Payment made by Citibank = 15000 - 5000 = $ 10000