# Accretion of Discount - Explained

What is a Accretion of Discount?

# What is Accretion of Discount?

The accretion of discount refers to the increase in the value of a discounted security as its maturity date approaches. In other words, it is a procedure in accounting used to adjust the value of a bond which has been bought at a discounted price. An example of such a bond is a zero-coupon bond. For instance, lets assume that an investor purchases a bond with a face value of \$200 and he pays 189. Since the investor is guaranteed to get \$200 upon the maturity of the bond, its value will go up between the buying time and the maturity date. This increase is what is referred to as accretion of discount.

## How does Accretion of Discount Work?

The accretion of the discount is used to adjust the bonds book value to the bonds par value at maturity. It considers the bonds paid out interest which accrues in the form of non-cash payments. This is usually during the bonds lifetime whose payment is done only when it reaches maturity. Note that a bond can be bought at par rate, at a premium rate or at a discounted rate. Irrespective of the bonds purchasing price, all the bonds reach maturity at par value. The par value, in this case, it refers to the amount of cash a bondholder will be given when the bond reaches maturity. Also, a bond bought at a premium rate its value is usually above par. However, as the bond nears maturity, its value goes down until it is at par at the date of maturity. Generally, the accretion discount may use the following methods during accounting:

• Straight line method

In this method, accretion of discount is a straight-line accumulation of capital gains

• Constant Yield method

This is a method in which the Internal Revenue Service (IRS) uses to calculate the adjusted cost basis. This is usually from the purchasing amount to the anticipated amount of redemption. In this method, the profits earned are spread out in the remaining bonds lifetime, rather than the profits being paid when the bond reaches maturity.

## How Constant Yield Method is Calculated

This method used the following formula to calculate accretion of discount: Accretion Amount= Purchase Basis x (yield to maturity/Accrual periods per year)- Coupon Interest. When calculating accretion of discount using this method, first you need to determine the yield to maturity (YTM). YTM is the profits earned on a bond that is held to maturity. Note that YTM is highly dependent on how often the profit is compounded. Also, it is the Internal Revenue Service that allows the taxpayer the opportunity to determine the accrual period that is best for computing profits.

## Example

Suppose a bond with a \$100 par value and a coupon rate of 2% is given out for \$75 with maturity duration of 10 years. Assuming that is compounded on an annual basis to ensure simplicity. In this case, the yield to maturity will be calculated as follows: \$100 par value = \$75 x (1 + r ) \$100/75 = (1 + r) 1.3333 = (1 + r ) R = 2.92 The coupon interest on bond will be 2% x \$100 par value = \$2. Hence; Year 1 accretion = (\$75 x 2.92%) - Coupon interest Year 1 accretion = \$2.19-\$2 Year 1 accretion =\$0.19 Note that the buying price of \$75 stands for the basis issuance of the bond. Nevertheless, in the periods that follow, the basis includes accrued interest plus the buying price. For instance, after a period of 2 years, the calculation for accrual interest will be as follows: Year 2 accretion = [(\$75 + \$0.19) x 2.92%] - \$2 Year 2 accretion = \$0.20 Year 2 accretion = \$0.20 From the above sample, a discounted bond can be said to have an accrual that is positive. In general, for the other subsequent period 3-10 years, the calculation can be done in the same manner, using the last accrual periods of each year, to work out the basis of the current period. Accretion of discount has one importance, it increases the shareholders bond value.