What Is Accretion of Discount?
Let me explain what accretion of discount means. It's the increase in the value of a discounted instrument as time passes and the maturity date gets closer. You see, the value of the instrument will accrete, or grow, at the interest rate implied by the discounted issuance price, the value at maturity, and the term to maturity.
Key Takeaways
- The accretion of discount is a reference to the increase in the value of a discounted security as its date of maturity closes in.
- It's an accounting process used to adjust the value of a financial instrument that has been bought at a discounted rate.
- While a bond can be bought at par, at a premium, or at a discount, its value is at par at the time of maturity.
- A bond purchased at a discount will slowly increase in value until it reaches par value at maturity; this process is the accretion of discount.
How Accretion of Discount Works
You can purchase a bond at par, at a premium, or at a discount. But no matter the purchase price, all bonds mature at par value. That's the amount of money you'll get repaid as a bond investor at maturity. If you buy a bond at a premium, it has a value above par. As the bond nears maturity, its value declines until it's at par on the maturity date. We call this decrease in value over time the amortization of premium.
Now, if a bond is issued at a discount, its value is less than the par value. As it approaches its redemption date, the value increases until it meets the par value at maturity. This increase is what we refer to as accretion of discount. For instance, take a three-year bond with a face value of $1,000 issued at $975. Between issuance and maturity, the bond's value will rise until it hits the full par value of $1,000, which is what gets paid to the bondholder at maturity.
Special Considerations
You can account for accretion using a straight-line method, where the increase is evenly spread throughout the term. In this portfolio accounting approach, accretion of discount is essentially a straight-line accumulation of capital gains on a discount bond, building up to receipt of par at maturity.
Alternatively, you can use a constant yield method, where the increase is greatest closest to maturity. This is the method the Internal Revenue Service (IRS) requires for calculating the adjusted cost basis from the purchase amount to the expected redemption amount. It spreads out the gain over the bond's remaining life, rather than recognizing it all in the year of redemption.
Calculating Accretion
To calculate the amount of accretion, use this formula: Accretion Amount = Purchase Basis x (YTM / Accrual periods per year) - Coupon Interest.
The first step in the constant yield method is determining the yield to maturity (YTM), which is the yield you'll earn on a bond held until maturity. YTM depends on how frequently the yield is compounded. The IRS gives you some flexibility in choosing the accrual period for computing yield. For example, consider a bond with a $100 par value and a 2% coupon rate, issued for $75 with a 10-year maturity. Assume it's compounded annually for simplicity. You calculate YTM as: $100 par value = $75 x (1 + r)^10, so $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%) – $2 = $2.19 – $2 = $0.19.
The purchase price of $75 is the bond’s basis at issuance. But in later periods, the basis becomes the purchase price plus accrued interest. For example, after year 2, the accrual is: Accretion_period2 = [($75 + $0.19) x 2.92%] - $2 = $0.20.
In this example, you see that a discount bond has a positive accrual; the basis accretes, increasing over time from $0.19, $0.20, and so on. You can calculate periods 3 to 10 similarly, using the previous period’s accrual to find the current period’s basis.
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