Forward rate agreements (FRAs) are contracts that allow parties to lock in an interest rate for a future date, protecting them against interest rate fluctuations. FRA valuation is an important consideration for parties entering into these contracts. In this article, we’ll provide an example of FRA valuation.

Let’s say that a company wants to enter into an FRA with a bank. The company wants to protect itself against the risk of interest rates rising in the future. The company agrees to pay the bank a fixed interest rate of 3% on a notional amount of $1 million for a period of three months. The FRA specifies that the settlement date will be three months from the start date of the contract.

Now, let’s also assume that the prevailing LIBOR rate (the benchmark interest rate for many financial instruments) is currently 2.5%. The FRA specifies that the settlement rate will be set at the prevailing LIBOR rate on the settlement date. This means that if the LIBOR rate is higher than 3% on the settlement date, the bank will pay the company the difference. If the LIBOR rate is lower than 3%, the company will pay the bank the difference.

To value this FRA, we need to calculate the present value of the cash flow that will occur on the settlement date. This is the difference between the settlement rate and the fixed rate specified in the FRA, multiplied by the notional amount. The present value is the value of this cash flow at the current time, discounted for the time value of money.

In our example, we can calculate the present value of the cash flow using the following formula:

Present value = (Notional amount * (Settlement rate – Fixed rate) * (Days to settlement / 360)) / (1 + (LIBOR rate * (Days to settlement / 360)))

Let’s assume that the settlement date is exactly three months from the start date of the contract, which is 90 days. Plugging in the numbers, we get:

Present value = ($1,000,000 * (2.5% – 3%) * (90/360)) / (1 + (2.5% * (90/360)))

Present value = -$1,232.56

A negative present value means that the FRA is not worth entering into for the company. In this case, the bank is offering a fixed rate that is higher than the prevailing LIBOR rate, which means that the company could obtain a better rate by waiting and taking its chances with market interest rates.

In summary, FRA valuation is an important consideration for parties entering into these contracts. By calculating the present value of the cash flow that will occur on the settlement date, parties can determine whether an FRA is worth entering into. In our example, the FRA was not worth entering into for the company because the present value was negative.