The amortizable bond premium is a tax term referring to the excess premium paid over and above the face value of a bond. 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.

## Breaking Down 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 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.

For a bond investor, the premium paid for a bond represents part of the cost basis of the bond, 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, which will reduce the amount of taxable income the investor will have to pay with respect to the bond. 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 his or her 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 Using the Constant Yield Method

The constant yield method amortizes a bond premium by multiplying the adjusted basis by the yield at issuance and then subtracting the coupon interest.

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

It is used to determine the bond premium amortization for each accrual period. 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 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.

Since this bond makes semi-annual payments, the first period is the first 6 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:

Accrualperiod1 = (\$10,150 x 1.75%) - \$250

Accrualperiod1 = \$177.63 - \$250

Accrualperiod1 = -\$72.38

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.

Accrualperiod2 = (\$10,077.62 x 1.75%) - \$250

Accrualperiod2 = \$176.36 - \$250

Accrualperiod2 = -\$73.64

Intuitively, a bond purchased at a premium has a negative accrual; in other words, the basis amortizes. For the remaining 8 periods (there are 10 accrual or payment periods for a semi-annual bond with a maturity of 5 years), use the same structure presented above to calculate the amortizable bond premium.