3.5.14 Interest Method for Computing Coupon Interest

Apart from the above-mentioned method for calculating the interest, you can also use the ACT/ACT–ISMA Interest Method and ACT/ACT–FRF Interest Method.

ACT/ACT–ISMA Interest Method

The ACT/ACT–FRF Interest Method is applied for periodic coupons using the following coupon:Coupon Interest = Nominal x (Coupon Rate/Number of Coupons) x (Number of elapsed Days/ Number of days in coupon period)

For ACT/ACT–ISMA, you need to maintain the following parameters:

• Numerator Method – Any of the option in the list
• Denominator Method – Actual
• Denominator Basis – Per Annum
• Rate Denomination Basis – Per Coupon Period

Let us understand the above with the following example:

Consider the following facts:

Security purchased for 10 million at a rate of 5% p.a with the coupon date of 15th Jan.

In case the frequency of the coupon is Yearly:

The ACT/ACT–ISMA method for a non leap year is

Amount x 5/100 x 365/365 x 1

And for a leap year the ACT/ACT–ISMA method is

Amount x 5/100 x 366/366 x 1

In case the frequency of the coupon is Half yearly:

Then, for a coupon on 15/01 the formula used in ACT/ACT–ISMA method is

Amount x 5/100 x 184/184 x 2

And for coupon on 15/07, the formula used in this method is

For a non leap year:

Amount x 5/100 x 181/181 x 2

For a leap year the formula is:

Amount x 5/100 x 182/182 x 2

In case the frequency of the coupon is Quarterly:

Then, for coupon on 15/01 the formula used in ACT/ACT–ISMA method is

Amount x 5/100 x 92/92 x 4

For coupon on 15/07, the formula used in this method is

For a non leap year:

Amount x 5/100 x 90/90 x 4

For a leap year the formula is:

• Amount x 5/100 x 91/91 x 4
• For coupon on 15/10, the formula used in this method is Amount x 5/100 x 92/92 x 4

366 Basis

specify whether the system should use a leap year or leap date for calculating the interest

• Leap Year (Y) – Indicates that the system will compute the interest based on the number of calendar days in the year.
• Leap Date (D) – Indicates that the system will use the ACT/ACT–FRF Interest Method to compute the interest. Specify whether the system should use a leap year or leap date for calculating the interest

Note:

This field is enabled only if the Denominator Basis value is Per Annum, and the Denominator Method is ACTUAL.

ACT/ACT–FRF Interest Method

In ACT/ACT–FRF Interest Method, the Numerator will be the actual number of days between two coupon dates and the denominator will be 366 under the following cases:

• If 29th February falls between the duration of two coupon dates (i.e. previous coupon date and next coupon date)
• If the previous coupon date and the next coupon date fall in different years (annual frequency, next coupon dates in the immediately subsequent year of previous coupon date)
• If the coupon schedule is not periodic and spreads across multiple years. The system will apply 366 as the denominator for all the years for computing the day count, even if one instance of 29th February falls in between the coupon dates.

Let us understand the formula applied for calculating the interest in ACT/ACT–FRF methodwith an example:

Consider the following facts:

A security purchased for 10 million at a rate of 5% p.a with the coupon date of 15th January.

Case 1:

Assume the following parameters are maintained for a yearly coupon:

• Nominal - 10,000,000
• Interest Rate – 5% per Annum
• Coupon Frequency – Annual
• Previous Coupon Date – 15/01/1999
• Next Coupon Date – 15/01/2000
• Numerator Method – ACTUAL
• Denominator Method – ACTUAL
• Denominator Basis – Per Annum

In case 366 basis is Leap Year:

The interest is calculated based on the day count derived for each of the two years in which the coupon date fall and the formula applied is:

10,000,000 x 5/100 x 350/365 + 10,000,000 x 5/100 x 15/366

In case 366 basis is Leap Date:

Here the system will apply the ACT/ACT–FRF interest method to compute the coupon interest. Since this period does not include 29th February, the denominator for interest calculation will be 365 and the formula will be:

10,000,000 x 5/100 x 365/365

Assume the following parameters are maintained for a half yearly coupon:

• Nominal - 10,000,000
• Interest Rate – 5% per Annum
• Coupon Frequency – Half yearly
• ƒn Previous Coupon Date ¡V 15/01/2000 (PCD 15/07/1999)
• Next Coupon Date – 15/07/2000 (PCD 15/01/2000)
• Numerator Method – ACTUAL
• Denominator Method – ACTUAL
• Denominator Basis – Per Annum

In case 366 basis is Leap Year:

The interest is calculated based on the day count, derived for each of the two years in which the coupon dates fall (if the previous and the next coupon dates fall in different years). If both coupon dates fall in the same year, the denominator will be 365 or 366 respectively, depending on whether the current year is a leap year or a non-leap year.

For coupon on 15/01/2000, the formula used is

10,000,000 x 5/100 x 169/ 365 + 10,000,000 x 5/100 x 15/366

And for coupon on 15/07/2000, the formula used in this method is

10,000,000 x 5/100 x 182/366

In case 366 basis is Leap Date:

For coupon on 15/01/2000, the formula used in ACT/ACT– FRF method is

10,000,000 x 5/100 x 184/ 365

This period does not include 29th February.

And for coupon on 15/07/2000, the formula used in ACT/ACT– FRF method is

10,000,000 x 5/100 x 182/366

29th February falls in this period.

Case 2:

Assume the following parameters are maintained for a Quarterly coupon:

• Nominal - 10,000,000
• Interest Rate ¡V 5% per Annum
• Coupon Frequency ¡V Quarterly
• Coupon Date 1¡V 15/01/2000 (PCD 15/10/1999)
• Coupon Date 2¡V 15/04/2000 (PCD 15/01/2000)
• Coupon Date 3¡V 15/07/2000 (PCD 15/04/2000)
• Coupon Date 4¡V 15/10/2000 (PCD 15/07/2000)
• Numerator Method ¡V ACTUAL
• Denominator Method ¡V ACTUAL
• Denominator Basis ¡V Per Annum

In case 366 basis is Leap Year:

The interest is calculated based on the day count derived for each of the two years in which the coupon dates fall (if the previous and next coupon dates fall in different years). If both coupon dates fall in the same year, the denominator will be 365 or 366 respectively depending on whether the current year is a leap year or non-leap year.

For coupon on 15/01/2000 the formula used in is

10,000,000 x 5/100 x 77/ 365 + 10,000,000 x 5/100 x 15/366

For coupon on 15/04/2000, the formula applied is

10,000,000 x 5/100 x 91/366

For coupon on 15/07/2000, the formula applied is

10,000,000 x 5/100 x 91/366

For coupon on 15/10/2000, the formula applied is

10,000,000 x 5/100 x 92/366

In case 366 basis is Leap Date:

For coupon on 15/01/2000, the formula used in ACT/ACT– FRF method is

10,000,000 x 5/100 x 92/ 365

This period does not include 29th February.

For coupon on 15/04/2000, the formula used in this method is

10,000,000 x 5/100 x 91/365

29th February falls in this period.

For coupon on 15/07/2000, the formula used in this method is

10,000,000 x 5/100 x 91/365

This period does not include 29th February.

For coupon on 15/10/2000, the formula used in this method is

10,000,000 x 5/100 x 92/365

This period does not include 29th February.