What Is Accretion of Discount?

Accretion of d♔iscount is the increase in the value of a diᩚᩚᩚᩚᩚᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ⁤⁤⁤⁤ᩚ𒀱ᩚᩚᩚscounted instrument as time passes and the maturity date looms closer. The value of the instrument will accrete (grow) at the interest rate implied by the discounted issuance price, the value at maturity, and the term to maturity.

How Accretion of Discount Works

A bond can be purchased at par, at a premium, or at a discount. Regardless of the purchase price of the bond, however, all bonds mature at par value. The par value is the amount of money that a bond investor will be repaid at maturity. A bond that is purchased 澳洲幸运5官方开奖结果体彩网:at a premium has a value above par. As the bond gets closer to maturity, the value of the bond declines until it is at par on the maturity date. The decrease in value over time is referred to as the 澳洲幸运5官方开奖结果体彩网:amortization of premium.

A bond that is issued 澳洲幸运5官方开奖结果体彩网:at a discount has a value that is less than the par value. As the bond approaches its redemption date, it will increase in value until it 澳洲幸运5官方开奖结果体彩网:converges with the par value at maturity. This increase in value over time is referred to as an accretion of discount. For example, a three-year bond with a face value of $1,000 is issued at $975. Between issuance and maturity, the value of the bond will increase until it reaches its ful🎉l par value of $1,000, which is the amount that will be paid to the bondholder at maturity.

Special Considerations

Accretion can be accounted for using a straight-line method, whereby the increase is evenly spread throughout the term. Using this method of portfolio accounting, accretion of discount can be said to be a straight-line accumulation of 澳洲幸运5官方开奖结果体彩网:capital gains on a discount bond in anti🔯cipation of receipt of par at maturity.

Accretion can also be accounted for using a 澳洲幸运5官方开奖结果体彩网:constant yield, whereby the increase is closest to maturity. The constant yield method is the method required by the Internal Revenue Service (IRS) for calculating the 澳洲幸运5官方开奖结果体彩网:adjusted cost basis൲ from the purchase amount to the expected redemption amount. This method spreads out the gain over the remaining life of the bond, instead of recognizing the gain in the year of the bond’s redemption.

Calculating Accretion

To cꦺalculate the amount o𝕴f accretion, use the formula:

Accretion Amount = Purchase Basis x (YTM / Accrual periods per year) - Coupon Interest

The first step in the constant yield method is determining the 澳洲幸运5官方开奖结果体彩网:yield to maturity (YTM) which is the yield that will be earned on a bond held until it matures. The yield to maturity depends on how frequently the yield is 澳洲幸运5官方开奖结果体彩网:compounded. The IRS allows the taxpayer some flexibility in determining which accrual period to use for computing yield. For example, a bond with a $100 par value and a 澳洲幸运5官方开奖结果体彩网:coupon rate of 2% is issued for $75 with a 10-year maturity date. Let’s a𝓰ssume it is compounded annually for the sake of simplicity. The YTM can, 💮therefore, be calculated as:

• $100 par value = $75 x (1 + r)¹⁰
• $100/$75 = (1 + r)¹⁰
• 1.3333 = (1 + r)¹⁰
• r = 2.92%

Coupon interest on the bond is 2% x $100 par value = $2. Therefore,

• Accretion_period1 = ($75 x 2.92%) – Coupon interest
• Accretion _period1 = $2.19 – $2
• Accretion_period1 = $0.19

The purchase price of $75 represents the bond’s basis at issuance. However, in subsequent peri🌃ods, the basis becomes the purchase price plus accrued interest. For example, after year 2, the accrual can be calculated as𝓡:

• Accretion_period2 = [($75 + $0.19) x 2.92%] - $2
• Accretion_period2 = $0.20

Using this example, one can see that a 澳洲幸运5官方开奖结果体彩网:discount bond h🎉as a positive accrual; in other♉ words, the basis accretes, increasing over time from $0.19, $0.20, and so on. Periods 3 to 10 can be calculated in a similar manner, using the former period’s accrual to calculate the current period’s basis.