## DEFINITION of Unamortized Bond Premium

Unamortized bond premium refers to the amount between the face value and the amount the bond was sold at, minus the interest expense. It is what remains of the bond premium to be written off against expenses over the bond’s life. Unamortized bond premiums do not include any interest that has been amortized or written off.

## BREAKING DOWN Unamortized Bond Premium

A bond premium is a bond that is priced higher than its face value. When prevailing interest rates in the economy decrease, the price of bonds increase. This is because the market interest rate becomes lower than the fixed coupon rate on outstanding bonds. Since bondholders are holding higher interest paying bonds, they require a premium price to sell the bond. For example, let’s assume that when interest rates were 5% a bond issuer sold bonds with a 5% fixed coupon to be paid annually. After a period of time, interest rates declined to 4%. New bond issuers will issue bonds with the lower interest rate. Investors who would rather buy a bond with a higher coupon will have to pay a premium to the higher-coupon bond holders to incentivize them to sell their bonds. In this case, if the bond’s face value is $1,000 and the bond sells for $1,090 after interest rates decline, the difference between the selling price and par value is the unamortized bond premium ($90).

The unamortized bond premium refers to part of the bond premium that will be amortized (written off) against expenses in the future. The amortized amount of this bond is credited as an interest expense. 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 the 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.

## Calculating the Unamortized Bond Premium

To calculate the amount to be amortized for the tax year, the bond price is multiplied by the yield to maturity (YTM), the result of which is subtracted from the coupon rate of the bond. Following our example above, the yield to maturity is 4%. Multiplying the selling price of the bond by the YTM yields $1,090 x 4% = $43.60. This value when subtracted from the coupon amount (5% coupon rate x $1,000 par value = $50) results in $50 - $43.60 = $6.40, which is the amortizable amount. For tax purposes, a bondholder can reduce his or her $50 interest income to $50 - $6.40 = $43.60. The unamortized premium after a year is $90 bond premium – $6.40 amortized amount = $83.60.

For the second tax year, $6.40 of the bond premium has already been amortized, so the bond's cost basis is $1,090 - $6.40 = $1,083.60. Premium amortization for Year 2 = $50 – ($1,083.60 x 4%) = $50 - $43.34 = $6.64. Premium remaining after the second year or the unamortized premium is $83.60 - $6.64 = $76.96.

Assuming the bond matures in five years, you can run the same calculation for the remaining three years. For instance, the bond's cost basis in the third year will be $1,083.60 - $6.64 = $1,076.96.

## Accounting for Unamortized Bond Premium

Unamortized bond premium is a liability to the bond issuer. On the financial statements, this premium is recorded in a liability account called the Unamortized Bond Premium Account. This account recognizes the remaining amount of bond premium that the bond issuer has not yet amortized or charged off to interest expense over the life of the bond.