Amortization in general is a way of allocating total costs of a subject matter over some equal periods of time. For bond issuers, total bond discount is a form of interest expense in addition to cash payments based on the stated bond coupon rate. A bond discount occurs when an issuer sells a bond and receives proceeds from investors for less than the face value of the bond. By amortizing a bond discount, the amount of amortization for each period can be used to determine periodic interest expense, as well as the changing bond carrying value over time.

## Bond Discount

Bond issuers can sell their bonds at a discount, at face value, or at a premium, depending on the difference between the documented bond coupon rate and the market interest rate at the time of the issuance. Bond issuers often decide on the bond coupon rate according to the prevailing market interest rate. But market interest rates change over time. If prior to a bond issuance, the market interest rate increases, to avoid re-documenting the bond coupon rate to the higher market rate, the bond issuer can go ahead to sell bonds at a discount to compensate investors for the rate difference. A bond discount is the difference between the proceeds received and the face value of the bond.

## Discount Amortization

A bond discount is a hidden cost to the bond issuer, considering that it must later pay back investors more than it receives from them. There are two basic methods of bond discount amortization: the straight-line amortization and the effective-interest-rate amortization. Under the straight-line method, the amount of periodic amortization is equal to the total bond discount divided by the number of interest-payment periods. Under the effective-interest-rate method, the amount of periodic amortization is equal to the difference between the periodic coupon payment and the corresponding effective interest expense calculated as the period's discounted bond carrying value timed by the market interest rate.

## Interest Expense

When a bond is sold at a discount, the total effective interest expense on the bond for the issuer consists of the nominal interest expense that a bond issuer pays in coupon payments over time, and the total amount of bond discount. Bond discount amortization helps to determine the real periodic interest expense. The effective interest expense on the bond for each payment period is then the sum of the periodic coupon payment and the allocated bond discount amortization. The amount of periodic bond discount amortization is dependent on the amortization method used.

## Outstanding Carrying Value

Bond discount amortization also helps adjust the discounted bond carrying value over time. Because bonds sold at a discount will be repaid at their full face value, total bond discount is added back to arrive at the bond face value. The adjustment is done periodically by adding the allocated amount of bond discount amortization to the corresponding bond carrying value at the beginning of each interest-payment period. Bond discount amortization has effects on both total interest expense and outstanding bond carrying value. Bond discount amortization over time increases bond carrying value, which in turn increases the total interest expense.