## Repo Agreements

##### Published: Nov 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.

There are three calculations that need to be performed:

• ##### The cash paid for the initial sale of the security.

This is the sum that will be borrowed. Note – as with other money market transactions, repo agreements are subject to trader jargon. Make sure that, should you enter into a repo agreement, you are clear which side of the agreement you will be on. Although you will be borrowing cash, you are also lending the security.

• ##### The cash that the will have to be paid to repurchase the security.

This will equal the initial sum borrowed plus interest.

• ##### The implied interest rate,

which will allow the borrower to determine whether the repo agreement is the best method of accessing short term cash.

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 One: determining the cash paid in return for the initial sale of the security

$$Initial \: purchase \: amount = Face \: value \: of \: the \: bond \: \times \: \frac{clean \: price}{100} \: + \: value \: of \: the \: accrued \: coupon$$

We showed how to calculate the value of the accrued coupon in Treasury Today January 2002.

$$Accrued \: coupon = Face \: value\: x \:coupon \: rate \: x \:\frac{number \: of \: days \: since \: last \: coupon}{number \: of \: days\: in \: the \: year}$$

Initial purchase amount:

• $$= 40,000,000 \: x \: \frac{ 105.25}{100} \: + \: 40,000,000 \: x \: 0.06 \: \times\:\frac{ 30}{365}$$
• $$= 42,100,000 \: + \: 197,260.27$$
• 42,297,260.27
##### Conventional calculator

Using a conventional calculator, press the following buttons:

• 40000000 x 105.25 ÷ 100 = M + C
• 40000000 x 0.06 x 30 ÷ 365 = + MR = this should give the result  42,297,260.27
##### Scientific calculator

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

• 40000000 x 105.25 / 100 + 40000000 x 0.06 x 30 /  365 = this should give the result  42,297,260.27
##### HP12C

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

• 40000000  ENTER  105.25 x 100 ÷
• 40000000  ENTER  0.06 x 30 x 360 ÷ + this should give the result  42,297,260.27