*The Business Professor*, updated September 20, 2019, last accessed August 3, 2020, https://thebusinessprofessor.com/lesson/accretion-of-discount-definition/.

Back to: ECONOMICS, FINANCE, & ACCOUNTING

**Accretion of Discount Definition**

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, let’s 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.

**A Little More on What is Accretion of Discount**

The accretion of the discount is used to adjust the bond’s book value to the bond’s par value at maturity. It considers the bond’s paid out interest which accrues in the form of non-cash payments. This is usually during the bond’s 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 bond’s 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 bond’s 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 )¹⁰

$100/75 = (1 + r)¹⁰

1.3333 = (1 + r )¹⁰

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.

### Reference for “Accretion of Discount”

https://www.investopedia.com/terms/a/accretion-of-discount.asp

www.businessdictionary.com/definition/accretion-discount.html

https://financial-dictionary.thefreedictionary.com/Accretion+of+Discount

www.investorwords.com/6966/accretion_of_discount.html

**Academic Research on “Accretion of Discount”**

An **Accretion **Corporate Income Tax. **Knoll, M. S. (1996). An Accretion Corporate Income Tax. ***Stan. L. Rev.***, ***49***, 1.**

The role of earnings persistence in valuation accuracy and the time horizon, **Pimentel, R. C., & AGUIAR, A. B. D. (2016). The role of earnings persistence in valuation accuracy and the time horizon. ***Revista de Administração de Empresas***, ***56***(1), 71-86. Bas**ed on the assumption that persistence of profits has implications for financial analysis and elaboration of incentive contracts, the purpose of this paper is to investigate its role in considering that more persistent profits are likely to be (i) better information for valuation models and (ii) a measure to capture the firm’s long-term orientation. The analysis uses data from companies that have shares traded on BM & F Bovespa between 1995 and 2013. The results provide evidence supporting the relevance of the persistence of profits in the financial analysis and evaluation; however, do not support the relationship between persistence of profits and long-term orientation. These results are maintained even in the face of different specifications; Besides that, additional analyzes suggest that the firm’s idiosyncratic risk (total risk) is relevant to explain the focus on short-term financial results among observed firms. The main contribution of this article is to provide empirical evidence regarding the relevance of accounting numbers in valuation models and contract theory in an emerging market.

Periodicity and **Accretion **Taxation: Norms and Implementation, **Strnad, J. (1989). Periodicity and Accretion Taxation: Norms and Implementation. ***Yale LJ***, ***99***, 1817.**

Do appearances matter? The **impact **of EPS **accretion **and dilution on stock prices, **Andrade, G. (1999). Do appearances matter? The impact of EPS accretion and dilution on stock prices. ***The Impact of Eps Accretion and Dilution on Stock Prices (June 1999)***. **There is a widespread concern among practitioners and corporate managers that transactions which result in changes in future earnings-per-share (“EPS”) have real effects on stock prices, irrespective of whether these changes reflect differences in future cash flows. As a result, investment decisions are often conditioned on their being accretive to EPS. This paper addresses this notion by testing whether there is any relation between EPS accretion and both announcement and long-term abnormal returns for acquiring firms in mergers and acquisitions. Using a sample of 224 transactions completed between 1975 and 1994, and a measure of EPS accretion designed to exclude the real effects of any potential synergies from the acquisition, I find that EPS accretion has a positive and statistically significant effect on acquirer abnormal performance, both at announcement and for the period up to 18 months following completion of the deal. This effect is robust across different measures of abnormal performance, and after controlling for other factors known to affect the long-term performance of acquiring firms. Also, the magnitude of the effect is higher for firms with a larger percentage of unsophisticated investors. On the other hand, the estimated effect, although reliably positive, is one order of magnitude smaller than implied by practitioners’ views, suggesting that the concerns expressed by managers are largely exaggerated.

The **accretion **concept of income, **Philips, G. E. (1963). The accretion concept of income. ***The Accounting Review***, ***38***(1), 14.**

A note on the **discounted **present value concept, **Peasnell, K. V. (1977). A note on the discounted present value concept. ***Accounting Review***, 186-189. **The discounted present value concept plays an important part in accounting theory, often being viewed as the ideal concept of value. There is, though, a school of thought which, while recognizing the importance of the concept in decision making, argues that the primary function of financial accounting is in the assessment of achievements. It also argues that this indicates a need for ex-post measures which are conceptually distinct from discounted present value. This note complements their work by arguing that accountants do not have a comparative advantage in the determination of discounted present value for investors and that this task should be left to the stock market.