How to Calculate Accretion of a Discount?

To calculate the accretion of a discount on a bond, determine the difference between the purchase price and face value, count the days to maturity, divide the difference by the number of days, and multiply the resulting rate by the number of days in each interest period to accrue interest, updating the carrying value accordingly.

Oct 18, 2024 at 07:24 am

How to Calculate Accretion of a Discount

Accretion of a discount on a bond or other fixed-income asset refers to the gradual increase in its carrying value as the bond approaches its maturity date. This is due to the difference between the bond's purchase price (typically lower than its face value due to the discount) and its face value.

Steps to Calculate Accretion of a Discount:

1. Determine the Difference Between the Purchase Price and Face Value:

   • Calculate the difference between the purchase price and the bond's face value.

2. Identify the Number of Days to Maturity:

   • Count the number of days from the purchase date to the maturity date.

3. Calculate the Daily Accrual Rate:

   • Divide the calculated difference (Step 1) by the number of days to maturity (Step 2). This gives you the daily accrual rate.

4. Accrue Interest Daily:

   • Multiply the daily accrual rate by the number of days in each interest period (typically 6 months or a year).

5. Add the Accrued Interest to the Carrying Value:

   • Add the accrued interest (Step 4) to the purchase price to get the updated carrying value at the end of the interest period.

6. Repeat for Subsequent Interest Periods:

   • Repeat Steps 4 and 5 for each subsequent interest period until the maturity date.

Example:

Consider a bond with the following details:

• Purchase price: $950
• Face value: $1,000
• Maturity date: 5 years from purchase date
• Interest payment frequency: Semi-annually

Step 1: Calculate the Difference:

$1,000 - $950 = $50

Step 2: Determine the Days to Maturity:

Assuming there are 365 days in a year and the maturity date is exactly 5 years from the purchase date:

5 years x 365 days = 1,825 days

Step 3: Calculate the Daily Accrual Rate:

$50 / 1,825 days = $0.0274

Step 4: Accrue Interest for 6 Months:

$0.0274 x 180 days (6 months) = $4.93

Step 5: Update Carrying Value:

$950 + $4.93 = $954.93

Note: The carrying value will continue to increase by $4.93 every six months until the bond reaches maturity and the final payment of $1,000 is paid.