## Definition of the Sum-of-the-Years'-Digits Depreciation

The sum-of-the-years'-digits depreciation (SYD depreciation) is one method for calculating accelerated depreciation. (A more common method for calculating accelerated depreciation is the declining-balance method often used for U.S. income tax depreciation.) Compared to the straight-line depreciation method, the sum-of-the-years'-digits method results in greater depreciation in the earlier years of an asset's useful life and less in the later years. However, the *total amount of depreciation over an asset's useful life should be the same* regardless of which depreciation method is used. In other words, the difference is in the *timing* of when the same total amount of depreciation will be reported.

## Example of the Sum-of-the-Years'-Digits Depreciation

To illustrate SYD depreciation, assume that a service business purchases equipment at a cost of $160,000. This asset is expected to have a useful life of 5 years at which time it will be sold for $10,000. This means that the total amount of depreciation will be $150,000 spread over the equipment's useful life of 5 years.

The next step is to sum (or add up) the digits in the five years of this asset's useful life: 1 + 2 + 3 + 4 + 5 = 15. The "15" will be the denominator for the fractions 5/15, 4/15, 3/15, etc. In the first full year of the asset's life, 5/15 of the $150,000 = $50,000 will be debited to Depreciation Expense and $50,000 will be credited to Accumulated Depreciation.

In the second full year of the asset's life, the amount of depreciation will be $40,000 (4/15 of $150,000). In the third full year of the asset's life, the depreciation will be $30,000 (3/15 of $150,000). The fourth year depreciation will be $20,000 (2/15 of $150,000), and the fifth year will be $10,000 (1/15 of $150,000). Remember that the total amount of depreciation during this asset's useful life should be $150,000.

Instead of adding the individual digits in the years of the asset's useful life, the following formula can be used to compute the sum of the digits: n(n+1) divided by 2, where n = the useful life in years. Using this formula in our example of an asset with a useful life of 5 years, we have: 5(5+1)/2 = 5(6)/2 = 30/2 = 15.

If the above formula is used for an asset having a useful life of 10 years, the sum of the digits will be: 10(10+1)/2 = 10(11)/2 = 110/2 = 55. In the first year of an asset with a 10-year useful life, the depreciation will be 10/55 of the amount to be depreciated. The second year will use 9/55 and the tenth year will use 1/55.