Question

A corporation knows that it will need to borrow 10,000,000 $ in six months' time for a 12-month period. The interest rate at which it can borrow today is 12-month LIBOR plus 25bp. The 12-month LIBOR currently is at 0.90%, but the company wants to cover against the possible rise of the LIBOR in the next 6 months.
The company decides to buy a 6x18 FRA in order to cover the period of 12 months starting 6 months from now. They receive a quote of 1.25% from the bank, and they decide to buy the FRA for a notional of 10,000,000$.
On the settlement date (six months from today), the 12-month LIBOR fixes at 1.10% (so, the interest to be applied to the loan is 1.10% plus 25bp), which is the settlement rate applicable for the company's FRA.

As anticipated by the treasurer, the 12-month LIBOR rose during the 6-month waiting period, hence the company will receive the settlement amount from the FRA seller.

Find the settlement amount.

1. Based on the above case, what will be the cost (the interests paid by that corporation) of that loan?

And how much will have that Company paid in total (because of the loan plus/minus the cost/gain of the FRA)?

2. Based on the previous exercise 3, what if on the settlement date (six months from today), the 12-month LIBOR fixes at 0.75%? what is the value of the settlement amount the company will receive from the FRA seller, if any?

Answer 1

(a) Notional = $ 10000000, FRA Rate (Fixed Rate to be paid) = 1.25 % and Applicable Settlement Rate = 12-M LIBOR + 25 bps

At the end of Month 6, 12-M LIBOR = 1.1% implying a settlement rate of 1.1 + 0.25 = 1.35 %

Therefore, Settlement Amount = [(Settlement Rate - FRA Rate) x Notional] / [1+Settlement Rate] = [(0.0135-0.0125) x 10000000] / [1.0135] = $ 9866.798

If the FRA is bought, then Interest is paid at the FRA rate. Hence, Interest Expense under FRA = 0.0125 x 10000000 = $ 125000

Gain from FRA = 1.35 - 1.25 = 0.1 or 10 basis points, $ Gains Made in FRA = 0.0001 x 10000000 = $ 10000

Actual Interest Expense in case there was no FRA = 125000 + 10000 = $ 135000

(b) If the LIBOR settles at 0.75%, then applicable settlement rate = 0.75 + 0.25 = 1 %

Settlement Amount = [(0.01- 0.0125) x 10000000] / [1.01] = - $ 24752.475

The company will receive - $ 24752.475 from the FRA seller or in other words the company will have to pay the FRA seller $ 24752.475