Sum-of-the-years'-digits (SYD) is an accelerated method for calculating an asset's depreciation. This method takes the asset's expected life and adds together the digits for each year; so if the asset was expected to last for five years, the sum of the years' digits would be obtained by adding: 5 + 4 + 3 + 2 + 1 to get a total of 15. Each digit is then divided by this sum to determine the percentage by which the asset should be depreciated each year, starting with the highest number in year 1.

## Breaking Down Sum-Of-The-Years' Digits

Depreciation is a method of asset cost allocation that apportions an asset's cost to expenses for each period expected to benefit from using the asset. Depending on the chosen cost apportionment or depreciation rate, depreciation charges can be variable, straight-lined, or accelerated over the useful life of an asset.

Accelerated depreciation uses decreasing charge methods, including the sum-of-the-years' digits (SYD), providing higher depreciation costs in earlier years and lower depreciation charges in later periods. Under the SYD method, the depreciation rate percentage for each year is calculated as the number of years in remaining asset life for the same year divided by the sum of remaining asset life every year through the asset's life. As the depreciation rate decreases over time, so does the depreciation charge.

It makes sense to use an accelerated depreciation method such as the SYD method when an asset will lose most of its value toward the beginning of its useful life — as is the case with automobiles, for example. In the five-year example above, the SYD method would yield the following depreciation schedule:

• Year 1: 5/15 = 33%
• Year 2: 4/15 = 27%
• Year 3: 3/15 = 20%
• Year 4: 2/15 = 13%
• Year 5: 1/15 = 7%

The percentages for all these years should add up to 100%.

## Economic Usefulness of Assets

The accelerated or decreasing cost allocation for asset depreciation, such as the sum-of-the-years'-digits method, better matches the cost of using an asset to the benefit the asset use provides each year over the economic life of the asset. The benefit of using an asset declines as the asset gets older, meaning an asset provides greater service value in earlier years. Therefore, charging higher depreciation cost early on and decreasing depreciation charge in later years reflects the reality of an asset's changing economic usefulness over time.

## Repair and Maintenance Costs

As an asset gets older, repair and maintenance costs are to rise. A decreasing depreciation charge over time helps provide a constant overall cost between depreciation charges and repair and maintenance costs, the latter of which are lower in the earlier years and can offset higher depreciation charges early on. Without accelerated depreciation and decreasing depreciation charges, earnings, as reported, may be distorted — too high early on and too low later on — when depreciation cost allocation does not accommodate actual changes in repair and maintenance costs over an asset's useful life.