When bonds are issued at par, bond interest payment equals interest expense. But since the market interest rate generally differs from coupon rate, bonds are issued either at a discount or premium. Hence, bond interest payments and expense generally differ.

For a bond issued at a discount, interest expense must be higher than interest payment. It is because the company received less cash initially and hence its effective interest expense would be higher than its periodic interest payment. This is exactly the opposite in case of a bond issued at a premium.

Amortization of bond discount brings a bond’s carrying value up to par and amortization of bond premium brings its carrying value down to the par value.

There are two methods used to amortize bond discount or premium: effective interest rate method and the straight-line method.

IFRS * requires* the effective interest rate method while US GAAP prefers it.

Under the effective interest rate method, interest expense for a period equals the opening carrying amount multiplied by the effective interest rate (the market interest rate in effect at the time of issuance), and interest paid equals face value multiplied by relevant coupon rate.

## Amortization process

The periodic amortization of discount or premium equals the difference between interest expense and payment. Under the straight-line method, bond discount or premium is amortized equally in each period over the tenor of the bond.

\[ Interest\ Expense\ (Bond\ Issued\ at\ Discount) = I + D \] \[ Interest\ Expense\ (Bond\ Issued\ at\ Premium) = I – P \]Where **I** is the interest paid, **D** is the amortization of discount, and **P** is the amortization of premium.

Companies usually create a bond amortization schedule to work out periodic interest paid, interest expense and associated amortization of bond discount or premium. Which involves the following steps:

- Calculate the cash proceeds of the bond issuance by discounting the cash flows at the market interest rate.
- Compare the cash proceeds with the face value. If cash proceeds exceed the face value, the bond is issued premium. But if face value exceeds cash proceeds, the bond is issued at a discount.
- Calculate interest payment for each period as the product of bond face value multiplied by the periodic coupon rate.
- Determine the interest expense each period as the product of opening carrying amount multiplied by the periodic effective interest rate (the market rate at the time of issuance).
- Determine bond discount or premium as the difference between the interest paid and interest expense. When interest paid exceeds the interest expense, the difference is attributable to the amortization of bond premium. But if interest expense exceeds the interest paid, the difference represents the amortization of bond discount for the period.

In the case of a **zero-coupon bond**, there is no interest paid and the whole of interest expense equals the amortization of discount.

## Bond amortization on statement of cash flows

On a statement of cash flows, IFRSs allow classification of interest payment either as an operating or financing activity, but US GAAP requires interest payment to be classified as an operating activity. Amortization of bond discount or premium is a non-cash item that is shown in the reconciliation of net income with net cash flow from operating activities.