What is the difference between annual straight-line depreciation and effective interest depreciation?

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The coupon rate a business pays on a bond is the most obvious cost of debt financing, but it is not 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 taken into account.

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 every year. However, the difference between the amount she ultimately has to repay in principal ($ 100,000) and the amount she received from the sale of the bonds ($ 95,000) represents an additional financing cost.

Bond premiums or discounts can be accounted for in two ways. Here’s how to account for bonds using the straight line and effective interest rate methods.

Accounting with straight-line depreciation
Straight-line depreciation is still the easiest way to record discounts or premiums on bonds. According to 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 in 10-year bonds that pay an annual coupon of 8%. The bonds are sold at a discount, so the company only receives $ 90,000 in proceeds from investors. The difference of $ 10,000 between the face value and the book value of the bonds must be amortized over 10 years.

Each year, the business will be required to pay $ 8,000 in cash interest (8% coupon rate X $ 100,000 face value). In addition, it will also record a charge for the amortization of the discount. This annual amortization amount is the bond discount ($ 10,000) divided by the 10-year life of the bond, or $ 1,000 per year. As a result, the company will record $ 9,000 in interest costs, including $ 8,000 in cash and $ 1,000 in amortization of the discount.

Premiums are amortized in the same way. Suppose the company issues $ 100,000 in 10-year bonds that pay an annual coupon of 8%. The bonds are sold at a premium, for a total of $ 110,000. The difference of $ 10,000 between the sale 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 (8% coupon rate x $ 100,000 face value). In addition, it would record amortization of premiums of $ 1,000 per year ($ 10,000 of premium divided by the 10-year life of the bond). Interest expense is $ 7,000 annually (cash interest of $ 8,000 less $ 1,000 of amortization of premiums).

Amortization of effective interest on discounts
More frequently, companies recognize premiums or discounts on bonds using the effective interest rate method. This method is mathematically more complex, but can be done quite quickly using a financial calculator or Excel.

First, let’s start with a scenario where a company issues bonds at a discount.

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

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

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

Solve the 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.

Recognizing this obligation in the first year requires a few additional steps.

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

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

This figure corresponds to the interest expense for the first year.

Cash interest is calculated by taking the bond’s coupon rate (9%) and multiplying it by the face value of the bond ($ 100,000), which gives $ 9,000 of cash interest. .

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

Each year, we add the amortization to the book value and repeat these steps to find the interest expense and amortization of the discount for the following year. Under the effective interest rate method, a business’s interest expense and depreciation amount will change each year.

The table below shows how the bond would be amortized over the entire 10-year period.

Effective amortization of interest on premiums
Premiums are amortized in the same way as discounts using the effective interest rate method. Suppose a company issues $ 100,000 in 10-year 9% coupon bonds with a premium over face value. Investors require only an 8% return for owning the bond and thus pay the company $ 106,710.08 for the bonds.

I calculated this using a financial calculator, using the following inputs:

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

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

To calculate interest expense for the first period, we multiply the book value of the bonds ($ 106,710.08) by the yield required by investors (8%) to obtain interest expense of $ 8,536.81.

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

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

Each year, depreciation is subtracted from the book value and the new book value is used to calculate interest expense and depreciation for the following year.

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

Straight-line method vs effective interest rate method
The critical observation to make is that the straight line method is a much simpler calculation. Straight-line amortization of premiums or discounts results in the same amount of interest, amortization and cash interest charges each year until the bond is repaid.

The effective interest rate method results in a different amount of interest and amortization expense 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 will notice that the straight-line method will result in more amortization of discounts or premiums in the first few years than the effective interest rate method. Conversely, the effective interest rate method results in greater depreciation in subsequent years than the straight-line method. When the bond matures, however, there should be no difference in the total amount of cash interest, interest charge, or amortization between the two methods for the same bond.

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