The Double-Declining Balance Method
As one of several "accelerated depreciation" methods, double-declining balance (DDB) results in relatively large amounts of depreciation in early years of asset life and smaller amounts in later years. This method can be justified if the quality of service produced by an asset declines over time, or if repair and maintenance costs will rise over time to offset the declining depreciation amount. With this method, a fixed percentage of the straight-line rate (i.e., 200% or "double") is multiplied times the remaining book value of an asset (as of the beginning of a particular year) to determine depreciation for a particular year. As time passes, book value and annual depreciation decrease.
To illustrate, let's again utilize our example of the $100,000 asset, with a four-year life, and $10,000 salvage value. Depreciation for each of the four years would appear as follows:
Depreciation Expense |
Accumulated Depreciation at End of Year |
Annual Expense Calculation |
|||
Year 1 |
$50,000 |
$50,000 |
$100,000 X 50% |
||
Year 2 |
$25,000 |
$75,000 |
($100,000 - $50,000) X 50% |
||
Year 3 |
$12,500 |
$87,500 |
($100,000 - $75,000) X 50% |
||
Year 4 |
$ 2,500 |
$90,000 |
see discussion below |
The amounts in the above table deserve additional commentary. Year one is hopefully clear -expense equals the cost times twice the straight line rate (4 year life = 25% straight-line rate; 25% X 2 = 50% rate). Year two is the 50% rate applied to the remaining balance of the asset as of the beginning of the year; the remaining balance would be the cost minus the accumulated depreciation ($100,000 - $50,000). Year three is just like year two - 50% times the beginning book value
Spreadsheet Software
DDB is also calculable from built-in depreciation functions. Below is the routine that returns the $12,500 annual depreciation value for Year 3.
Fractional Period Depreciation
Under DDB, fractional years involve a very simple adaptation to the approach presented above. The first partial year will be a fraction of the annual amount, and all subsequent years will be the normal calculation (twice the straight-line rate times the beginning of year book value). If our example asset were purchased on April 1, 20X1, the following calculations result:
Depreciation Expense |
Accumulated Depreciation at End of Year |
Annual Expense Calculation |
|||
Year 1 |
$37,500 |
$37,500 |
$100,000 X 50% X 9/12 |
||
Year 2 |
$31,250 |
$68,750 |
($100,000 - $37,500) X 50% |
||
Year 3 |
$15,625 |
$84,375 |
($100,000 - $68,750) X 50% |
||
Year 4 |
$ 5,625 |
$90,000 |
($100,000 $84,375) X 50% Limited to depreciable base |
||
Year 5 |
$ 0 |
Not applicable -assumed disposed on March 31 |
$0 |
Alternatives to DDB
150% and 125% declining balance methods are quite similar to DDB, but the rate is 150% or 125% of the straight-line rate (instead of 200% as with DDB).
The Sum-of-the-Years'-Digits Method
This approach was used in the graphic example at the beginning of this chapter, but without any calculation details. The calculations will undoubtedly be seen as a bit peculiar; I have no idea who first originated this approach or why.
Under the technique, depreciation for any given year is determined by multiplying the depreciable base by a fraction; the numerator is a digit relating to the year of use (e.g., the digit for an asset with a ten-year life would be 10 for the first year of use, 9 for the second, and so on), and the denominator is the sum-of-the-years' digits (e.g., 10 + 9 + 8 + . . . + 2 + 1 = 55). In our continuing illustration, the four-year lived asset would be depreciated as follows (bear in mind that 4 + 3 + 2 + 1 = 10):
Depreciation Expense |
Accumulated Depreciation at End of Year |
Annual Expense Calculation |
|||
Year 1 |
$36,000 |
$36,000 |
($100,000 - $10,000) X 4/10 |
||
Year 2 |
$27,000 |
$63,000 |
($100,000 - $10,000) X 3/10 |
||
Year 3 |
$18,000 |
$81,000 |
($100,000 - $10,000) X 2/10 |
||
Year 4 |
$ 9,000 |
$90,000 |
($100,000 - $10,000) X 1/10 |