When depreciation is applied to the value of an asset for accounting purposes, one of the common methods used is the * declining balance depreciation* method. In this approach, a multiplication factor known as an accelerator is used to show increased depreciation at the end of the first year of purchase, and this depreciation amount declines for every consecutive year that the asset is “on the books.” This decline is seen because each year’s depreciation is calculated as a percentage of the book value, not as a percentage of the original purchase price.

**The Theory behind Declining Balance Depreciation Method**

This method of amortization is typically applied to assets that generate more revenue when they are initially purchased and decline over time (for example a mining equipment that is supposed to process certain minerals but the productivity of the machine lowers with age). As the productivity of the asset lowers with age, the rate of depreciation is calculated in proportion to that reduction. As with the straight line depreciation method, this method is followed because of the Matching Principle under Generally Accepted Accounting Practices (GAAP).

**How is This Calculated?**

In the straight line depreciation method, the depreciation is spread out evenly over the life of the asset. Therefore, if an asset was purchased for $1,000, the depreciation will be calculated at 20%. In contrast, the declining balance depreciation method uses double that depreciation percentage, and that figure is applied to the book value taken from the end of the previous year, rather than the original purchase value.

Depreciation = Rate of Depreciation x Book Value of Asset, where

Rate of Depreciation = Accelerator x Straight Line Depreciation Rate

If the accelerator used is 2, then the rate of depreciation in the above example would be 40%. In such cases, the method is known as **double-declining balance** amortization.

Below is an example of how double-declining balance depreciation is used to calculate the yearly book value of an asset.

**Example:**

If a mining equipment costing $10M has a salvage value of $2M (the amount it is likely to be sold for after its useful life has been depleted) and it has a useful life of 5 years, then the straight line rate of depreciation is 20% (1/5^{th} of the original price); the double-declining balance rate of depreciation, therefore, would be 40%. Using these figures, the following is calculated:

Double-Declining Balance Depreciation = 40% x $10M = $4M

Therefore, at the first year of depreciation (the year after the purchase value was recorded) the book value will be:

$10M – $4M = $6M (Book Value)

In the second year of depreciation, the same 40% is now applied to the previous year’s book value rather than the original purchase value, which means that for that year, depreciation will be calculated as follows:

40% x $6M = $2.4M

In the subsequent year, the depreciation will be:

40% x ($10M –$6.4M) = 40% x $3.6M = $1.44M

The following year:

40% x ($10M – $7.84M) = 40% x $2.16M = $0.864M

And so on.

Since the book value cannot be shown to be less than the salvage value, depreciation can only be applied until the book value reaches the salvage value. If the book value is greater the salvage value at the end of the useful life of the asset, the excess is considered a Capital Gain.

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