# The Effective Interest Method

Typically, companies maintain the historical cost (sales proceeds) of bonds after issuance, and any discount or premium is amortized over the life of the bonds. Some companies report the bonds at their current fair values.

Under IFRS, bonds are reported as a liability on the balance sheet at the amount of the sales proceeds net of issuance costs. Under US GAAP, they are reported at the amount of the sales proceeds, ignoring any bond issuance costs.

If a bond is issued at face value, the amount of periodic interest expense will be the same as the amount of periodic interest payments to bondholders. If the bond is issued at a premium or discount, the premium or discount is amortized systematically over the life of the bonds as a component of interest expense.

## The Effective Interest Rate Method

There are two methods for amortizing the premium or discount of bonds that are issued at a price other than par: (i) the effective interest rate method; and (ii) the straight-line method.

The effective interest rate method reflects the economic substance of a transaction better.  As a result, it is the method that is required under IFRS and preferred under US GAAP. It applies the market rate in effect when a bond is issued to the bond’s current amortized cost to obtain interest expense for the period. The difference between the interest expense and the interest payment is the amortization of the discount or premium. As a bond approaches maturity, the amortized cost will approach the face value.

## Calculating Interest Expense, Amortization of Bond Discounts or Premiums, and Interest Payments

These computations are best explained by the use of an example.

### Example: interest payments and carrying amount

A company issues $1,000,000 face value of seven-year bonds when the market interest rate is 5%. The sales proceeds is$942,136 and the bond pays 4% interest annually.

1. What is the interest payment on the bonds each year?

2. What amount of interest expense on the bonds would be reported in the first two years of issuance, using the effective interest rate method, and what would be the carrying amount of the bonds at the end of the first two years?

Solution

1. Interest payment = $1,000,000 × 4% =$40,000 annually.

2. Since the sales proceeds ($942,136) is less than the bonds’ face value, the bonds were issued at a discount of$57,864. This discount is amortized over time, ultimately leading to an increase in the carrying amount to the bond’s face value.

Under the effective interest rate method, Interest expense = Bond carrying amount × Market rate in effect when the bonds are issued.

In year 1, Interest expense = $942,136 × 5% =$47,107. The amount of the discount amortized in year 1 is the difference between the interest expense of $47,107 and the interest payment of$40,000 = $7,107. The bonds’ carrying amount increases by the discount amortization. Therefore, at the end of year 1, the bonds’ carrying amount is$942,136 + $7,107 =$949,243 (i.e., beginning balance of $942,136 plus$7,107 discount amortization).

For year 2, interest expense = $949,243 × 5% =$47,462 (i.e., carrying amount of bonds at beginning of year 2 multiplied by the effective interest rate).

The amount of the discount amortized in year 2 is the difference between the interest expense of $47,462 and the interest payment of$40,000 i.e. $7,462. At the end of year 2, the bonds’ carrying amount is$956,705 (i.e., beginning balance of $949,243 +$7,462 discount amortization).

### Question 1

A company issues $1,000,000 face value of five-year bonds when the market interest rate is 6%. The sale proceeds are$936,815 and the bond pays 4.5% interest annually. Which of the following is correct?

1. The bonds were issued at a discount, interest payment is $45,000 annually and the first year’s interest expense, under the effective interest rate method, is$56,209.
2. The bonds were issued at a premium, interest payment is $45,000 annually and the first year’s interest expense, under the effective interest rate method, is$56,209.
3. The bonds were issued at a discount, interest payment is $60,000 annually and the first year’s interest expense, under the effective interest rate method, is$42,157.

Solution

The correct answer is A.

Since the sales proceeds ($936,815) is less than the bonds’ face value, the bonds were issued at a discount of$63,185.

Interest payments = $1,000,000 × 4.5% =$45,000 annually.

Interest expense = $936,815 × 6% =$56,209.

### Question 2

At the time of issue of 4.50% coupon bonds, the effective interest rate was 5.00%. The bonds were most likely issued at:

1. par
2. a discount

Solution

The correct answer is B.

The bond must have been issued at a discount to compensate the bondholders for getting an interest rate lower than the market interest rate for bonds with similar risk and maturity.

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