# How do I calculate depreciation using the sum of the years' digits?

Author:
Harold Averkamp, CPA, MBA

## 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.

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For the past 52 years, Harold Averkamp (CPA, MBA) has
worked as an accounting supervisor, manager, consultant, university instructor, and innovator in teaching accounting online. He is the sole author of all the materials on AccountingCoach.com.

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