## Repo agreements – the implied rate of interest

##### Published: Jan 2003

A company can get access to short term cash by entering into a ‘repo’ agreement with another party. A ‘repo’ agreement – strictly a sale and repurchase agreement – involves two transactions. First, a company sells a security to another party for cash, settling according to the market convention. The company then repurchases the same security for the same price plus interest on a predetermined date in the future. In the previous two issues, we have shown, using the example below, how to calculate the amount of cash required to pay for the initial transfer of the security and how to determine the interest payable when repurchasing the security, the repurchase part of the transaction.

In October 2002, Company X had a requirement for some short term cash. It decided to enter into a repo agreement using a bond as security. The bond has a face value of €40m. The bond pays an annual coupon of 6%, quoted on an actual/actual basis. The previous coupon was paid on 25th September 2002.

Company X decided to enter into a repo agreement on 28th October 2002. The initial transaction settled on 30th October 2002. The second leg was to be settled on 24th November 2002, i.e. 25 days later. On 28th October, the clean bond price for value two days later was 105.25. The repo rate was 3.5%, quoted on an actual/360 basis.

#### Step Three: Calculating the implied rate of interest

The final calculation that a company needs to make is to identify the real rate of interest it is being charged for the repo agreement. This is so that the company can assess whether the repo agreement is the cheapest way of securing the required short-term cash. This can be done by comparing the interest rates that apply for the repo agreement with any that apply for other types of funding.

To determine the real rate of interest, use the following formula:

$$Interest \: rate = \frac{Future \: value}{present \: value} \: – \: 1 \: \times \: \frac{year}{number \: of \: days \: between \:1^{st}\: and \: 2^{nd} \:legs}$$

In our example, the present value = 42,297,260.27 ; the future value = 42,400,066.11. When comparing interest rates, it is important that you compare on the basis of the same number of days in the year. If the other potential sources of funding our company wants to compare are quoted on a 365 day basis, then we need to calculate the implied rate on a 365 day year. There are 25 days between the first and second legs.

Therefore:

$$Interest \: rate =\frac{42,400,066.11}{42,297,260.27} \: – \: 1\:\times\:\frac{365}{25} = 0.0355\: or\: 3.55\%$$
##### Conventional calculator

Using a conventional calculator, press the following buttons:

• 42400066.11 ÷ 42297260.27 = 1 = x 365 ÷ 25 = this should give the result 0.03548611
##### Scientific calculator

Using the scientific calculator on a Windows computer (Start, Programs, Accessories, Calculator, View, Scientific), you would need to press the following keys:

• 42400066.11 / 42297260.27 1 x 365 / 25 = this should give the result 0.03548611
##### HP12C

Using an HP12C (or a similar calculator using Reverse Polish Notation):

• 42400066.11 ENTER  42297260.27 ÷ 1 365 x 25 ÷ this should give the result 0.03548611

Had the company wanted to compare on a 360 day basis, the implied rate would have been 3.5%, the same as the repo rate. This highlights the importance of comparing interest rates on a standard basis.