## Definition of 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 of accelerated depreciation is the declining balance method used in tax depreciation.) Compared to the straight line depreciation method, the sum of the years' digits method will result 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. The difference is in the *timing* of when the depreciation will be reported.

## Example of Sum of the Years' Digits Depreciation

To illustrate the SYD method of depreciation, let's assume that equipment is purchased at a cost of $160,000. This asset is expected to have a useful life of 5 years and then be sold for $10,000. This means that the total amount of depreciation will be $150,000 spread over its useful life of 5 years.

The next step is to sum (add) up the digits in the five years of the 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 year of the asset's life, 5/15 of the $150,000 or $50,000 will be debited to Depreciation Expense and $50,000 will be credited to Accumulated Depreciation.

In the second year of the asset's life, the depreciation amount will be $40,000 (4/15 of $150,000). The third year the depreciation will be $30,000 (3/15 of $150,000). The fourth year depreciation will be $20,000 (2/15 of $150,000). In the fifth year of the asset's life, the depreciation will be $10,000 (1/15 of $150,000). Remember that in this example, the total amount of depreciation during the asset's useful life needs to add up to $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 for our example, we have: 5(5+1)/2 = 5(6)/2 = 30/2 = 15. [If the formula is used for an asset having a useful life of 10 years, the digits will sum to the following: 10(10+1)/2 = 10(11)/2 = 110/2 = 55. In the first year of this asset's 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.]