What Is an Amortized Bond?

An amortized bond is one in which the principal (face value) on the debt is paid down regularly, along with its interest expense over the life of the bond. A fixed-rate residential mortgage is one common example because the monthly payment remains constant over its life of, say, 30 years. However, each payment represents a slightly different percentage mix of interest versus principal. An amortized bond is different from a balloon or bullet loan, where there is a large portion of the principal that must be repaid only at its maturity.

Understanding Amortized Bonds

The principal paid off over the life of an amortized loan or bond is divvied up according to an amortization schedule, typically through calculating equal payments all along the way. This means that in the early years of a loan, the interest portion of the debt service will be larger than the principal portion. As the loan matures, however, the portion of each payment that goes towards interest will become lesser and the payment to principal will be larger. The calculations for an amortizing loan are similar to that of an annuity using the time value of money, and can be carried out quickly using an amortization calculator.

Amortization of debt affects two fundamental risks of bond investing. First, it greatly reduces the credit risk of the loan or bond because the principal of the loan is repaid over time, rather than all at once upon maturity, when the risk of default is the greatest. Second, amortization reduces the duration of the bond, lowering the debt’s sensitivity to interest rate risk, as compared with other non-amortized debt with the same maturity and coupon rate. This is because as time passes, there are smaller interest payments, so the weighted-average maturity (WAM) of the cash flows associated with the bond is lower.

Example of Amortizing a Bond

30-year fixed-rate mortgages are amortized so that each monthly payment goes towards interest and principal. Say you purchase a home with a $400,000 30-year fixed-rate mortgage with a 5% interest rate. The monthly payment is $2,147.29, or $25,767.48 per year.

At the end of year one, you have made 12 payments, most of the payments have been towards interest, and only $3,406 of the principal is paid off, leaving a loan balance of $396,593. The next year, the monthly payment amount remains the same, but the principal paid grows to $6,075. Now fast forward to year 29 when $24,566 (almost all of the $25,767.48 annual payments) will go towards principal. Free mortgage calculators or amortization calculators are easily found online to help with these calculations quickly.

Straight-Line vs. Effective-Interest Method of Amortization

Treating a bond as an amortized asset is an accounting method used by companies that issue bonds. It allows issuers to treat the bond discount as an asset over the life of the bond until its maturity date. A bond is sold at a discount when a company sells it for less than its face value and sold at a premium when the price received is greater than face value.

If a bond is issued at a discount—that is, offered for sale below its par or face value—the discount must be treated either as an expense or it can be amortized as an asset. In this way, an amortized bond is used specifically for tax purposes because the amortized bond discount is treated as part of a company’s interest expense on its income statement. The interest expense, a non-operating cost, reduces a company’s earnings before tax (EBT) and, therefore, the amount of its tax burden.

Effective-interest and straight-line amortization are the two options for amortizing bond premiums or discounts. The easiest way to account for an amortized bond is to use the straight-line method of amortization. Under this method of accounting, the bond discount that is amortized each year is equal over the life of the bond.

Companies may also issue amortized bonds and use the effective-interest method. Rather than assigning an equal amount of amortization for each period, effective-interest computes different amounts to be applied to interest expense during each period. Under this second type of accounting, the bond discount amortized is based on the difference between the bond’s interest income and its interest payable. Effective-interest method requires a financial calculator or spreadsheet software to derive.

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.