## Calculating the value of the accrued coupon

##### Published: Jan 2002

The buyers of a bond will pay the sellers a price equal to the NPV (net present value) of all the future cash flows. When a bond is sold on the market, it is often sold “between coupons”, i.e. part way through the interest period. The sellers will want to be compensated for the fact that, whilst they have held the bond since the last coupon date, they will not receive the next coupon or interest payment. In other words, they will want to be compensated for that portion of the period between coupon dates when they held the bond. This is known as accrued coupon or accrued interest.

#### To calculate the accrued coupon

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

A bond with a face value of £10,000,000 pays a coupon rate of 8% on a semi-annual basis (i.e. twice a year). We will calculate the accrued coupon, assuming that this bond was sold sixty-one days after the last coupon was paid.

$$Accrued \:coupon = \frac{10,000,000 \: \times \: 0.08 \: \times \:61 }{365} = £133,698.63$$
##### Using a conventional calculator

Press the following buttons:

• 10000000 x 0.08 x 61 ÷ 365 = this should give the result  133698.63
##### Using the scientific calculator

On a Windows computer (Start, Programs, Accessories, Calculator, View, Scientific), you would need to enter the following:

• 10000000 *  0.08 * 61 / 365 = this should give the result  133698.63
##### Using an HP12C

(or a similar calculator using Reverse Polish Notation):

• 10000000 ENTER  0.08 x 61 x 365 ÷ this should give the result 133698.63

In circumstances where the bond is sold very close to, but before, the coupon date, the coupon can be paid to the former owner (because the issuer may not have had time to update their records). In such circumstances, the bond is said to be ‘ex-dividend’ or ‘ex-coupon’ and the seller will have to pay the amount of the coupon due to the buyer. In these circumstances, the accrued coupon is calculated according to the following formula (and is negative):

$$Accrued \:coupon = \frac{Face \:value\: \times \: coupon \:rate\: \times \: number \: of \: days \: to \: next \: coupon}{Number\: of \: days \: in \: the \: year}$$

– Thus the accrued coupon reduces Number of days in the year the amount paid to the seller.