## Accretion of Discount Details

A discounted instrument’s value increases according to three factors:

• The interest rate tied to the discounted issuance price
• The instrument’s value upon maturity
• The maturity term of maturity

The formula for calculating the accretion amount is:

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

The yield to maturity (YTM) is determined, the yield a bond will earn until maturity, and it is based on how frequently the yield is compounded. The IRS gives taxpayers extra room to define the accrual period to be used for the yield calculation.

While investors may buy bonds at par or a premium or discount, they will all mature at par value, no matter their price. The par value is equivalent to the investor's amount of money on the bonds upon maturity. However, an investor will value a bond bought at a premium greater than par. As the term to maturity shortens, the bond’s value drops until it becomes at par on the date of maturity. This process is called the amortization of premium. If a bond is issued at a discount, its value is lower than par. Its value will rise until it meets the par value upon maturity while coming closer to its redemption date. This process is referred to as an accretion of discount.

## Real-World Example of Accretion of Discount

Issued for \$75 and maturing in 10 years, a bond has a \$100 par value and 2% coupon rate. If compounded annually, here is its yield to maturity YTM computation:

\$100 par value = \$75 x (1 + r)10

\$100/\$75 = (1 + r)10

1.3333 = (1 + r)10

r = 2.92%

With the bond’s coupon interest at \$2 (2% of the \$100 par value), the computation for accretion of discount is as follows:

First Year Accretion = (\$75 x 2.92%) – Coupon interest

= \$2.19 – \$2

= \$0.19

Considering that a bond’s basis following the first period is the sum of the purchase price and accrued interest, here is the accrual computation following year 2:

Second Year Accretion = [(\$75 + \$0.19) x 2.92%] - \$2

Second Year Accretion = \$0.20

Here, a positive accrual is evident. The base rises as time passes, starting at \$0.19 for the first year, and moving to \$0.20 the second year. The computation for the succeeding years uses the same formula.

## Types of Accretion of Discount

To calculate bond accretion discounts, use either of the following methods:

• Straight-line: The rise in the bond’s value is distributed equally over the maturity term. For instance, a bond of 5 years reported quarterly would have 20 financial periods before its term matures. Split across the 20 periods; the \$500 discount will be applied at \$25 each quarter, which means each period will accrete by \$25. As well, the liability balance will increase by \$25 until redemption.
• Constant Yield: This method will have the bond value increasing more and more as the maturity rate draws near. As opposed to the straight-line method, the increment is not consistent, with certain periods recording more gains than the others. The gains, however, are biggest during the final phase of the term. This method begins with obtaining the yield to maturity (YTM), which is the amount earned by the bond when by its date of maturity. You can calculate this calculator or spreadsheet by entering the bond’s par value, price, term, and interest.