# Unamortized Bond Premium

A bond's face value and sale price are referred to as an unamortized bond premium. The issuer must still pay back the full face value of the bond, or 100 cents, if it is sold at a discount, such as 90 cents on the dollar. The total interest amount represents a liability for the issuer, as it has not been disbursed to the bondholders yet.

## Understanding Unamortized Bond Premium

The amount above the bond's face value at which it is priced is known as the bond premium. Bond prices rise when the economy's benchmark interest rates decline. The market interest rate declines to a level below the fixed coupon rate on outstanding bonds as a result.

Bondholders need a premium as compensation in the market because they are holding bonds that pay higher interest rates. The portion of the bond premium that the issuer hasn't yet deducted as an interest charge is known as the unamortized bond premium.

For illustration, suppose a bond issuer sold bonds with a 5% fixed coupon that was to be paid annually when interest rates were at 5%. Interest rates dropped to 4% after some time. Bonds with the reduced interest rate will be issued by brand-new bond issuers. To entice bondholders with higher coupons to sell their bonds, investors who would want to purchase bonds with higher coupons will have to pay a premium. If a bond has a $1,000 face value and sells for $1,090 after interest rates drop, the unamortized bond premium ($90) is the difference between the selling price and par value.

## Special Considerations

Investors in taxable premium bonds usually profit from amortizing the premium since the amount amortized can be used to offset interest income from the bond, lowering the amount of taxable income the investor will be required to pay with respect to the bond. The amount of premium amortized each year is deducted from the cost basis of the taxable bond.

The bond investor is required to amortize the bond premium in circumstances where the bond pays tax-exempt interest. The taxpayer must deduct the annual amortization from his or her basis in the bond even if this amortized amount is not deductible when calculating taxable income.

## Example: Unamortized Bond Premium Calculation

The bond price is multiplied by the yield to maturity (YTM), and the result is deducted from the bond's coupon rate to determine the amount that must be amortized for the tax year. The yield to maturity in the aforementioned example is 4%.

- The bond's selling price multiplied by the YTM yields $1,090 x 4%, which equals $43.60.
- This amount, when deducted from the coupon amount ($1,000 par value x 5% coupon rate = $50), gives the amortizable amount ($50 - $43.60 = $6.40).
- A bondholder can lower their $50 interest income for tax purposes to $50 - $6.40 = $43.60.
- After a year, the unamortized premium is equal to $83.60 ($90 bond premium - $6.40 amortized amount).
- The bond's cost basis for the second tax year is $1,090 minus $6.40, or $1,083.60. This is because $6.40 of the bond premium has already been amortized.
- Amount to be amortized for the second year of premiums is $50 - ($1,083.60 x 4%) = $50 - $43.34 = $6.64.
- During the second year, the unamortized premium or the remaining premium is $83.60 – $6.64, which is $76.96.

You can perform the same calculation for the remaining three years if the bond matures in five years. The bond's cost basis, for instance, will be $1,083.60 - $6.64, or $1,076.96, in the third year.

## Conclusion

The net difference in the price that a bond issuer sells securities for less than the bonds' real face value at maturity is known as an unamortized bond premium.

As the issuers have not yet written off this interest expense, which will eventually become due, the unamortized bond premium is a liability for them.

On financial statements, an unamortized bond premium is recorded in a liability account called the Unamortized Bond Premium Account.