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 25^th September 2002.

Company X decided to enter into a repo agreement on 28^th October 2002. The initial transaction settled on 30^th October 2002. The second leg was to be settled on 24^th November 2002, i.e. 25 days later. On 28^th 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