# Methods of Bond Discount or Premium Amortization

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The CFA level 1 exam is approaching, so we have to keep up the pace. Today, let’s discuss the methods of amortizing bond discount or premium.

### Effective Interest Rate Method vs Straight-Line Method

If the company uses the amortized cost approach to measure a long-term debt, it can use two methods to amortize the discount and the premium:

- the effective interest rate method, or
- the straight-line method (
__allowed only under U.S. GAAP__).

The general rule for both methods is the same. For discount bonds, in the consecutive years, we will adjust the historical cost up until we reach the bond’s par value and for premium bonds we will adjust the historical cost down until we reach the par value. However, __the straight-line method assumes__ that in each period throughout the bond’s life the value of __the adjustment is the same__.

According to __the effective interest rate method__, the adjustment __reflects the reality better__. In other words, it reflects what the change in the bond price would be if we assumed that the market discount rate doesn’t change.

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We will illustrate the problem by the following example related to a premium bond.

__Example:__

On 1 January 2014, Robots, Inc. issued 4-year bonds with a total par value of USD 100 million and an annual coupon that amounts to 8% of the par value. The effective annual interest rate at issuance was equal to 7%.

What is the interest payment, interest expense, amortization of premium and bond carrying amount in the first year?

We will solve the problem assuming first the effective interest rate method, and then the straight-line method.

### Effective Interest Rate Method

To apply the effective interest rate method, let’s first calculate the bond price at issuance:

Now, we will compute the interest payment. In each year, the interest payment is equal to coupon payment, that is USD 8 million.

Note, however, that the interest expense will be different in each year. The interest expense in a given period is equal to the effective interest rate at the time of issuing bonds multiplied by the carrying amount at the beginning of the period. So, for the first year the interest expense is equal to 7% multiplied by the price of the bond at the time when the bond was issued, that is by USD 103.3872 million. So, for the first year the interest expense equals USD 7.237105 million.

Note that for premium bonds the interest payment is always greater than the interest expense and __the difference__ between them __is the amortization of premium__.

So, the amount of the premium amortized in the first year, __assuming the effective interest rate method__, is equal to USD 0.762895 million.

The carrying amount at the end of a given year is equal to the carrying amount at the beginning of the year less the amortization of premium. So, the carrying amount at the end of the first year is equal to USD 103.3872 million minus USD 0.762895 and amounts to USD 102.6243 million.

### Straight-Line Method

According to the straight-line method, the amount of the premium amortized in each year will be the same. To compute it, we have to divide the bond premium by the number of years. The bond premium is equal to the price of the bond at issuance minus the par value of the bond, that is USD 103.3872 million minus USD 100 million and amounts to USD 3.3872 million.

So, the premium amortized in each year, assuming the straight-line method, is equal to USD 3.3872 million divided by 4 and amounts to USD 0.846803 million.

### Summary

As you can see, according to the straight-line method the amortization of premium is the same for all periods. However, for the effective interest rate method, the amortization of premium is greater as time passes by.