## Repo agreements – the reverse leg

##### Published: Dec 2002

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.

Last month, we showed, using the example below, how to calculate the amount of cash required to pay for the initial transfer of the security. This month, we show 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 Two: determining the cash to be paid to repurchase the security

$$Interest \: paid = initial \: purchase \:amount \: \times \: repo \: rate \:\times\: \frac{repo \:days}{days\: in\: repo\: year}$$

$$Interest \: paid = 42,297,260.27 \: \times \: 0.035 \: \times \: \frac{25}{360} = € 102,805.84$$
##### Conventional calculator

Using a conventional calculator, press the following buttons:

• 0.035 x 25 / 360 x 42297260.27 = this should give the result  102,805.84
##### Scientific calculator

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

• 42297260.27 x 0.035 x 25 / 360 = this should give the result  102,805.84
##### HP12C

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

• 42297260.27  ENTER  0.035 x 25 x 360 ÷ this should give the result  102,805.84

This is then added to the initial purchase price to give the amount paid when repurchasing the security.

Amount paid when repurchasing the security = initial purchase amount + interest paid

• = 42,297,260.27 + 102,805.84
• = € 42,400,066.11

Next month, we will examine how to calculate the implied interest rate.