Question

3. On 1/1, a manufacturing firm plans to borrow $100M in 4 months to build a factory. The loan will last one year. A different financial institution is offering a Eurodollar FRA at 5% starting in 4 months and lasting for 3 months on a notional principal of $100M. Assume the bank’s actual loan is at LIBOR+0.5% (annual rate) and interest is compounded and paid quarterly. For the day count convention just assume N/360 is .25 for a quarter. Note that the payout of the FRA is based solely on LIBOR and has no connection to the loan actually being taken out by the manufacturing firm. a. What position does the firm take to hedge its interest rate risk for the first 3 months of the loan? b. What is the interest the bank would pay for the first three months if LIBOR could be set today at 5%? c. It turns out that LIBOR at the end of April is 4%. Please calculate the interest on the loan for the first 3 months, the cash flow associated with the FRA, and the effective interest paid for the first 3 months.

Answer 1

a. As we note that the payout of the FRA is based solely on LIBOR and has no connection to the loan actually being taken out by the manufacturing firm, Manufacturing firm is at having a risk of interest rate(LIBOR) increasing in 3 months time. Therefore it means firm is at short position and to hedge the same firm should make an interest rate FRA/swap under the condition of receiving Floating(LIBOR) and pay Fixed interest rate or others options are, take long position in interest rate Futures, forward on interest rate.

b. As per question, if Bank enters in a FRA of receiving fixed and pay LIBOR+0.5%, then bank will have to pay 0.5% for the first 3 months because as per question, LIBOR is set at 5% today.

c. If firm enters in a FRA with bank in which firm will fixed 5% and receiving LIBOR+0.5% as per FRA contract. Then interest for the first three months for bank will be (0.5%/4)of $100 Mn => 12.5 Mn. Cash flow associated with FRA is the excess interest percentage on $100 Mn for all the 3 months. Effective interest paid for the first 3 months is 0.5/4 = 0.125% per quarter by the bank.