# Understanding corporate finance: derivative contracts: interest Forward Rate Agreement

## Managing interest rate risk using a forward rate agreement (FRA)

Cludwin Ltd has just bought a small chain of hotels, previously in private ownership. The company is planning a major refurbishment, starting in 6 months’ time. It plans to borrow £12 million from its bank for 2 years to finance this project, at a rate tied to LIBOR. However, it has no way of knowing how market interest rates will move over the next 6 months. If interest rates rise, it will have to pay significantly more in interest over the 2 years and this could make the whole project unviable.

The company therefore asks its broker to obtain quotes for a FRA covering a period starting in 6 months’ time and finishing in 30 months’ time, to cover a borrowing of £12 million. The broker obtains quotes from a number of banks. The best quote is 5.2%, and Cludwin Ltd accepts this quote, buying the FRA from this bank.

What does this quote actually mean?

The settlement date of the contract is in 6 months’ time. On the settlement date, the agreed rate of 5.2% is applied to a notional loan of £12 million, taken out for two years. This notional loan is the asset underlying the forward rate agreement - rather like the notional loan of £1,000 in the simple example at CFM11211.

The bank compares the result of this calculation with the amount of interest which would be payable at current LIBOR. If LIBOR has gone above 5.2%, the bank repays the difference to the company. If LIBOR is below 5.2%, the company must pay the difference to the bank.

At the settlement date, interest rates have risen, and LIBOR is 5.35%. Thus:

Interest which would be payable on the notional loan at LIBOR is

£12,000,000 x 2 years x 5.35% = £1,284,000

Interest which would be payable on the notional loan at 5.2% is

£12,000,000 x 2 years x 5.2% = £1,248, 000

Difference = £36,000

Therefore the bank makes a payment to Cludwin Ltd. The company will not in fact receive as much as £36,000. It is receiving an up-front cash payment, which it can place on deposit, against payments of interest that it will have to make over the next two years. So the £36,000 will be discounted, at the LIBOR market rate, to allow for this.

If LIBOR had been 0.15% below the quoted rate of 5.2%, rather than 0.15% above, Cludwin Ltd would have had to pay £36,000, similarly discounted, to the bank.

In effect, the settlement process consists of reckoning up what the contract is worth to the company on the settlement date. If the contract has a positive value, the company receives that value from the bank. If it has a negative value, the company pays the bank.

Either way, the outcome is that the company effectively borrows at a pre-arranged rate. If, for example, the real loan will be at an interest rate of LIBOR plus 0.2%, the company knows in advance that it will be paying 5.4% (5.2% plus the margin of 0.2%) for the finance.

This assumes that the real loan is at a constant rate of interest throughout. If the interest rate resets at intervals, the FRA will not provide a good hedge. In such circumstances, you may see companies taking out a strip of FRAs. Suppose, in this example, Cludwin Ltd was taking out a loan in 6 months’ time. The interest rate on the loan will be reset every 3 months. The company might enter into one FRA covering the 3-month period beginning in 6 months’ time, a second FRA covering the 3-month period beginning in 9 months’ time, and so on.

The forward rate agreement is entirely separate from the real loan which the company takes out. It may buy the FRA and the loan from different banks.

How does the bank calculate that it should quote 5.2%? The bank imagines that it has borrowed £12 million for 30 months. It then imagines placing that £12 million on deposit for 6 months (because the customer doesn’t need it immediately) before lending it to the customer for 24 months. It knows the interest rates applicable to the imaginary borrowing and deposit, so it can calculate how much it would have to charge the customer for the money in order to cover its costs (and make a profit) - the so-called forward-forward rate.