What Is an Amortizable Bond Premium?

The amortizable bond premium is a tax term that refers to the excess price paid for a bond over and above its face value. Depending on the type of bond, the premium can be tax-deductible and amortized over the life of the bond on a pro-rata basis.

Understanding an Amortizable Bond Premium

A bond premium occurs when the price of the bond has increased in the secondary market due to a drop in market interest rates. A bond sold at a premium to par has a market price that is above the face value amount.

The difference between the bond’s current price (or carrying value) and the bond’s face value is the premium of the bond. For example, a bond that has a face value of $1,000 but is sold for $1,050 has a $50 premium. Over time, as the bond premium approaches maturity, the value of the bond falls until it is at par on the maturity date. The gradual decrease in the value of the bond is called amortization.

Cost Basis

For a bond investor, the premium paid for a bond represents part of the cost basis of the bond, which is important for tax purposes. If the bond pays taxable interest, the bondholder can choose to amortize the premium—that is, use a part of the premium to reduce the amount of interest income included for taxes.

Those who invest in taxable premium bonds typically benefit from amortizing the premium, because the amount amortized can be used to offset the interest income from the bond. This, in turn, will reduce the amount of taxable income the bond generates, and thus any income tax due on it as well. The cost basis of the taxable bond is reduced by the amount of premium amortized each year.

In a case where the bond pays tax-exempt interest, the bond investor must amortize the bond premium. Although this amortized amount is not deductible in determining taxable income, the taxpayer must reduce their basis in the bond by the amortization for the year. The IRS requires that the constant yield method be used to amortize a bond premium every year.

Amortizing Bond Premium With the Constant Yield Method

The constant yield method is used to determine the bond premium amortization for each accrual period. It amortizes a bond premium by multiplying the adjusted basis by the yield at issuance and then subtracting the coupon interest. Or in formula form:

• Accrual = Purchase Basis x (YTM /Accrual periods per year) – Coupon Interest

The first step in calculating the premium amortization is to determine the yield to maturity (YTM), which is the discount rate that equates the present value of all remaining payments to be made on the bond to the basis in the bond.

For example, consider an investor that purchased a bond for $10,150. The bond has a five-year maturity date and a par value of $10,000. It pays a 5% coupon rate semi-annually and has a yield to maturity of 3.5%. Let’s calculate the amortization for the first period and second period.

The First Period

Since this bond makes semi-annual payments, the first period is the first six months after which the first coupon payment is made; the second period is the next six months, after which the investor receives the second coupon payment, and so on. Since we’re assuming a six-month accrual period, the yield and coupon rate will be divided by 2.

Following our example, the yield used to amortize the bond premium is 3.5%/2 = 1.75%, and the coupon payment per period is 5% / 2 x $10,000 = $250. The amortization for period 1 is as follows:

• Accrual_period1 = ($10,150 x 1.75%) – $250
• Accrual_period1 = $177.63 – $250
• Accrual_period1 = -$72.38

The Second Period

The bond’s basis for the second period is the purchase price plus the accrual in the first period—that is, $10,150 – $72.38 = $10,077.62:

• Accrual_period2 = ($10,077.62 x 1.75%) – $250
• Accrual_period2 = $176.36 – $250
• Accrual_period2 = -$73.64

For the remaining eight periods (there are 10 accrual or payment periods for a semi-annual bond with a maturity of five years), use the same structure presented above to calculate the amortizable bond premium.

Intrinsically, a bond purchased at a premium has a negative accrual; in other words, the basis amortizes.

What Is at Par?

The term “at par” means at face value. A bond, preferred stock, or other debt instrument may trade at par, below par, or above par.

Par value is static, unlike market value, which fluctuates with credit ratings, time to maturity, and interest rate fluctuations. The par value is assigned at the time the security is issued. When securities were issued in paper form, the par value was printed on the face of the security, hence the term “face value.”

Understanding at Par

Due to the constant fluctuations of interest rates, bonds and other financial instruments almost never trade exactly at par. A bond will not trade at par if current interest rates are above or below the bond’s coupon rate, which is the interest rate that it yields.

A bond that was trading at par would be quoted at 100, meaning that it traded at 100% of its par value. A quote of 99 would mean that it is trading at 99% of its face value.

Par value for common stock exists in an anachronistic form. In its charter, the company promises not to sell its stock at lower than par value. The shares are then issued with a par value of one penny. This has no effect on the stock’s actual value in the markets.

A New Bond

If, when a company issues a new bond, it receives the face value of the security, the bond is said to have been issued at par. If the issuer receives less than the face value for the security, it is issued at a discount. If the issuer receives more than the face value for the security, it is issued at a premium.

The yield for bonds and the dividend rate for preferred stocks have a material effect on whether new issues of these securities are issued at par, at a discount, or at a premium.

A bond that trades at par has a yield equal to its coupon. Investors expect a return equal to the coupon for the risk of lending to the bond issuer.

Example of at Par

If a company issues a bond with a 5% coupon, but prevailing yields for similar bonds are 10%, investors will pay less than par for the bond to compensate for the difference in rates. The bond’s value at its maturity plus its yield up to that time must be at least 10% to attract a buyer.

If prevailing yields are lower, say 3%, an investor is willing to pay more than par for that 5% bond. The investor will receive the coupon but have to pay more for it due to the lower prevailing yields.

What Is Average Life?

The average life is the length of time the principal of a debt issue is expected to be outstanding. Average life does not take into account interest payments, but only principal payments made on the loan or security. In loans, mortgages, and bonds, the average life is the average period of time before the debt is repaid through amortization or sinking fund payments.

Investors and analysts use the average life calculation to measure the risk associated with amortizing bonds, loans, and mortgage-backed securities. The calculation gives investors an idea of how quickly they can expect returns and provides a useful metric for comparing investment options. In general, most investors will choose to receive their financial returns earlier and will, therefore, choose the investment with the shorter average life.

Understanding Average Life

Also called the weighted average maturity and weighted average life, the average life is calculated to determine how long it will take to pay the outstanding principal of a debt issue, such as a Treasury Bill (T-Bill) or bond. While some bonds repay the principal in a lump sum at maturity, others repay the principal in installments over the term of the bond. In cases where the bond’s principal is amortized, the average life allows investors to determine how quickly the principal will be repaid.

The payments received are based on the repayment schedule of the loans backing the particular security, such as with mortgage-backed securities (MBS) and asset-backed securities (ABS). As borrowers make payments on the associated debt obligations, investors are issued payments reflecting a portion of these cumulative interest and principal payments.

Calculating the Average Life on a Bond

To calculate the average life, multiply the date of each payment (expressed as a fraction of years or months) by the percentage of total principal that has been paid by that date, add the results, and divide by the total issue size.

For example, assume an annual-paying four-year bond has a face value of $200 and principal payments of $80 during the first year, $60 for the second year, $40 during the third year, and $20 for the fourth (and final) year. The average life for this bond would be calculated with the following formula:

($80 x 1) + ($60 x 2) + ($40 x 3) + ($20 x 4) = 400

Then divide the weighted total by the bond face value to get the average life. In this example, the average life equals 2 years (400 divided by 200 = 2).

This bond would have an average life of two years against its maturity of four years.

Mortgage-Backed and Asset-Backed Securities

In the case of an MBS or ABS, the average life represents the average length of time required for the associated borrowers to repay the loan debt. An investment in an MBS or ABS involves purchasing a small portion of the associated debt that is packaged within the security.

The risk associated with an MBS or ABS centers on whether the borrower associated with the loan will default. If the borrower fails to make a payment, the investors associated with the security will experience losses. In the financial crisis of 2008, a large number of defaults on home loans, particularly in the subprime market, led to significant losses in the MBS arena.

Special Considerations

While certainly not as dire as default risk, another risk bond investors face is prepayment risk. This occurs when the bond issuer (or the borrower in the case of mortgage-backed securities) pays back the principal earlier than scheduled. These prepayments will reduce the average life of the investment. Because the principal is paid back early, the investor will not receive future interest payments on that part of the principal.

This interest reduction can represent an unexpected challenge for investors of fixed-income securities dependent on a reliable stream of income. For this reason, some bonds with payment risk include prepayment penalties.