John Williams, CFA, works in the treasury department of Sam Smith Leisure Inc., a U.S. based manufacturer of gym equipment. Recently he has been considering using derivative instruments to lock in returns on excess cash flows that tend to accumulate in the final quarter of each year as demand for equipment peaks during that time.
He estimates that this year, in 60-days, the company will have $28.5 million in excess funds to invest for 90 days.
Williams is presenting to the board 60 days before the excess funds need to be deposited, which is also 30 days before the year end. He intends to suggest an FRA as a method of locking in a return on the deposit. He intends to make the following two statements in favor of using an FRA.
Statement 1: As we are depositing cash, committing to an FRA will generate a cash inflow on the date we enter into it.
Statement 2: If rates move in our favor, we will receive a cash payment at the end of the notional borrowing period.
Williams will present the hypothetical rates and LIBORs shown in Exhibit 1 to illustrate the result of using an FRA. Current 2x5 FRA price is 3.8%. All rates are annualized.
Exhibit 1 – FRA Price and Theoretical Future LIBOR rates
Using the price and predicted LIBOR rates in exhibit 1, which of the following is closest to the predicted value of the FRA at the year end?
A) -$100,000
B) -$62,000
C) -$85,000
Answer
The year end is 30 days away. At that point the required FRA would be a 1X4 (90 days borrowing in 30 days time).
To value the FRA, first price this FRA to compare to the current FRA price.
30 day LIBOR at year end 3.9% x 30/360 = 0.325%
120 day LIBOR at year end 4.5% x 120/360 = 1.5%
FRA price = 1.015/1.00325 – 1 = 0.01171
Quoted annually = 0.01171 x 360/90 = 0.046848 = 4.685%
Value = (3.8% - 4.685%) x $28.5 million x 90/360 = -$63,056
Discounted to year end = -$63,056/1.015 = -$62,124
My doubt is how can we use 14 FRA? after 30 days, there would only be 2 months left. So we should be using 13 FRA right?
