What Are the Difference Between Annual Straight Line Amortization vs. Effective Interest Amortization?

The coupon rate a company pays on a bond is the most obvious cost of debt financing, but it isn't the only cost of financing. The price at which a company sells its bonds -- and the resulting premium or discount -- is an important factor, and it must be accounted for.

For example, consider a company that issues 10% bonds with a face value of $100,000 for $95,000. It will pay $10,000 in interest to its bondholders each year. However, the difference between how much it has to ultimately repay in principal ($100,000) and the amount it received from selling the bonds ($95,000) represents an additional cost of financing.

The premiums or discounts from bonds can be accounted for in two ways. Here's how to account for bonds under the straight line and effective interest methods.

Accounting with straight line amortization
Straight line amortization is always the easiest way to account for discounts or premiums on bonds. Under the straight line method, the premium or discount on the bond is amortized in equal amounts over the life of the bond.

This is best explained by example.

Suppose a company issues $100,000 of 10-year bonds that pay an 8% annual coupon. The bonds are sold at a discount, and thus the company only receives $90,000 in proceeds from investors. The $10,000 difference between the face value and the carrying value of the bonds must be amortized over 10 years.

Each year, the company will have to pay $8,000 in cash interest (coupon rate of 8% X $100,000 in face value). In addition, it will also record a charge for the amortization of the discount. This annual amortization amount is the discount on the bonds ($10,000) divided by the 10-year life of the bond, or $1,000 per year. Thus, the company will record $9,000 of interest expense, of which $8,000 is cash and $1,000 is the amortization of the discount.

Premiums are amortized similarly. Suppose the company issued $100,000 of 10-year bonds that pay an 8% annual coupon. The bonds are sold at a premium, or $110,000 in total. The $10,000 difference between the sales price and the face value of the bond must be amortized over 10 years.

Thus, the company would record $8,000 in cash interest annually (coupon rate of 8% X $100,000 in face value). In addition, it would record premium amortization of $1,000 per year ($10,000 in premium divided by the 10-year life of the bond). Interest expense is $7,000 each year (cash interest of $8,000 minus $1,000 of premium amortization).

Effective interest amortization of discounts
More frequently, businesses account for bond premiums or discounts under the effective interest method. This method is more mathematically complex, but can be done fairly quickly with the help of a finance calculator or Excel.

Let's start first with a scenario in which a company issues bonds at a discount.

Suppose a company sells $100,000 in 10-year bonds with an annual coupon of 9% at a discount to face value. Investors demand a 10% annual return to buy the bond, and thus will only pay $93,855.43 for the bonds.

I calculated this with a finance calculator with the following inputs:

• Future value: $100,000
• Number of periods: 10
• Payment: $9,000
• Rate: 10%

Solve for present value to get $93,855.43, or the amount investors will pay for these bonds if they want a 10% annual return, also known as a yield to maturity.

Accounting for this bond in the first year takes a few more steps.

In the first period, we record $93,855.43 as the carrying amount of the bond. To calculate total interest expense for the first year, we take the carrying amount of the bond and multiply it by investors' required return of 10%.

$93,582.34 X 10% = $9,385.54.

This figure is the interest expense for year one.

The cash interest is calculated by taking the coupon rate of the bond (9%) and multiplying it by the bond's face value ($100,000), resulting in $9,000 of cash interest.

You can find the amount of discount amortization by taking the interest expense we calculated ($9,385.54) and subtracting the cash interest ($9,000), resulting in $385.54 of discount amortization in year one.

Each year, we add the amortization to the carrying value and repeat these steps to find the next year's interest expense and discount amortization. Under the effective interest method, a company's interest expense and amortization amount will change every single year.

The table below shows how the bond would amortize over the full 10-year period. 

Effective interest amortization of premiums
Premiums are amortized in similar fashion to discounts under the effective interest method. Suppose a company issues $100,000 in 10-year, 9% coupon bonds at a premium to face value. Investors only demand an 8% return for owning the bond, and thus pay the company $106,710.08 for the bonds.

I calculated this with the help of a finance calculator, using the following inputs:

• Future value: $100,000
• Number of periods: 10
• Payment: $9,000
• Rate: 8%

Solve for present value to get $106,710.08, or the amount investors will pay for these bonds assuming they want an annual return of 8%, also known as a yield to maturity.

To calculate interest expense for the first period, we multiply the carrying value of the bonds ($106,710.08) by investors' required return (8%) to get interest expense of $8,536.81.

To calculate cash interest, we multiply the face value of the bonds ($100,000) by the coupon rate (9%) to get $9,000.

To calculate premium amortization, we take the amount of cash interest ($9,000) and subtract the interest expense ($8,536.81) to get premium amortization of $463.19.

Each year the amortization is subtracted from the carrying amount, and the new carrying amount is used to calculate interest expense and amortization for the next year.

The table below shows how this example bond would be accounted for over the full 10-year period. Note that the only static figure is the amount of cash interest -- interest expense and amortization are different in every single year. Over time, the carrying amount of the bonds is slowly reduced to $100,000 due to the amortization of the premium each year.

Straight line vs. effective interest method
The critical observation to make is that the straight line method is a much more simple calculation. Straight line amortization of premiums or discounts results in the same amount of interest expense, amortization, and cash interest in every single year until the bond is repaid.

The effective interest method results in a different amount of interest expense and amortization each year. The only thing that doesn't change from year to year is the amount of cash interest paid on the bond.

Knowing this, you'll notice that the straight line method will result in more discount or premium amortization during earlier years than the effective interest method. Conversely, the effective interest method results in more amortization in later years than the straight line method. When the bond matures, however, there should be no difference at all in the total amount of cash interest, interest expense, or amortization between the two methods for the same bond. 

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