# Method of Amortization Based on Effective Interest Rates

Can You Please Explain the Effective Interest Rate Amortization Technique?

The effective interest approach involves basing interest payments on a constant interest rate, which is the market rate at the time of issuance.

Therefore, the interest rate remains the same throughout the bond’s duration, albeit the actual interest expenditure varies with the bond’s carrying value.

At each amortization date, the carrying value of the bonds is equivalent to the present value of the future cash outflow when using the effective interest method.

## Method of Effective Interest: Explanation

The straight-line method is convenient, but it does not result in a correct discount or premium amortization.

Assuming that interest expense remains constant from period to period despite the fluctuating carrying value of the liability is unrealistic.

Using this technique, interest costs would remain constant at a dollar level across all reporting periods. The effective annual percentage rate, however, varies inversely with the change in carrying value of the bond.

## The carrying value of Valenzuela discount bonds was \$92,976 on the date they were issued.

Using a straight-line method of amortization, the interest cost between January 2, 2020 and July 1, 2020 is \$6,702. In dollar terms, this works out to \$92,976 at an effective interest rate of 7.2%.

Since the interest expense for the next quarter will be the same at \$6,702, the interest rate will drop to 7.15%. The bonds’ carrying value, however, has climbed to \$93,678 as illustrated in our article about discounted bond issues.

That makes the annual percentage rate 7.15 (or \$6,702 divided by \$93,678).

This annual percentage rate of interest decreases over the life of the bond, eventually reaching 6.7% (or \$6,702 / \$99,294) on January 2, 2025.

The identical conceptual difficulty arises in the premium example, except that the annual percentage rate keeps rising when the bond’s carrying value falls from \$107,722 to \$100,000.

The interest cost is the same each half year at \$5,228.

The Financial Accounting Standards Board (FASB) mandates the use of the effective interest technique rather than the straight-line approach because of a conceptual problem with the straight-line method, unless there are no substantive differences between the two.

Now we’ll look at the discount and premium scenarios where the effective interest method would be useful.

Method of Effective Interest Amortization

## Amortization with a Discount

Bonds issued with a 12% coupon for 5 years and priced at \$1,007,000 were sold for \$92,976, a savings of \$7,024. You can see the effective interest approach used to amortize this discount throughout the bond’s life in the table below.

Using the semiannual yield rate established at the time of issuance and the carrying value of the bond at the beginning of the period, we can derive the effective periodic bond interest expense shown in the table below.

On July 1, 2020, the interest expenditure listed in Column 2 will be \$6,508. This amount can be calculated by multiplying \$92,976 by 7%.

Column 4’s discount amortization amount of \$508 represents the difference between Column 3’s necessary cash interest payment of \$6,000 (\$100,000 x 6%) and Column 2’s effective interest expense of \$6,508.

The final amount in Column 5 for 1 July 2020, the unamortized discount, is \$6,516. This is calculated by taking the original discount of \$7,024 and subtracting the amortized discount of \$508. Column 6 now reflects a \$508 rise in the bond’s carrying value, from \$92,976 to \$93,484.

Alternatively, the unamortized discount of \$6,516 will be the bond’s carrying value as of July 1, 2020.

The data required for the semiannual interest expenditure journal entry can be taken straight from the amortization schedule. Below is the entry for July 1, 2020.

Under the straight-line method, the interest over the 10 periods is \$67,024, as shown in the table.

Interest expense for the first half of the year under the effective interest method is \$6,508, and it will rise with the bond’s carrying value in subsequent periods.

Total interest expenditure is \$67,024 whether you use the effective interest technique or the straight-line method. It’s crucial to note that during the course of the five years, the overall interest expense does not vary, simply the allocation.

Bonds with a face value of \$100,000 and a maturity of five years and a yield of 10% were issued at a price of \$107,722, or a premium of \$7,722, according to the pro forma balance sheet in our article on bonds issued at a premium.

## The effective interest method of premium amortization is outlined in the table below.

Cash interest expenditure is reduced on a periodic basis thanks to premium amortization, which follows the same format as the discount amortization plan above illustration.

Interest paid in Column 2 is calculated by multiplying the bonds’ carrying value at the start of the period by the semiannual yield rate at the time of issue (in this case, 5%).

Column 4’s premium amortization is the sum deducted from Column 3’s cash interest. Column 6 shows the decrease in carrying value of the bond due to premium amortization during the period.

Similar to the discount scenario, both the straight-line and effective interest techniques result in the same total interest expense throughout the life of the loan. It is spread out in a non-uniform fashion across the time frames.

The effective interest amortization method yields the same discount and premium as the straight-line method. For extremely large bond offerings, however, this variation can become material.

In this scenario, you must utilize effective interest amortization in accordance with generally accepted accounting standards.