# Sum of the Years’ Digits Depreciation: Definition, Formula, Method, Example, Calculation

Companies use various depreciation methods to determine the depreciation expense for an asset. One of these methods is the sum of the years’ digits depreciation.

## What is the Sum of the Years’ Digits Depreciation?

Sum of the Years’ Digits Depreciation (SYD) is an accelerated method used to depreciate an asset, which allocates a higher depreciation in the earlier years of the asset’s useful life and a lower expense in the later years. This method is suitable for assets that rapidly lose value initially. SYD aims to match the depreciation expense with the asset’s usage and productivity, which diminishes over time.

The SYD method calculates depreciation based on the sum of the years’ digits of the asset’s useful life. This sum helps create fractions that determine the annual depreciation expense. The result is a more significant depreciation expense in the first years, decreasing yearly. This approach is useful for tax and financial reporting, where reflecting higher early expenses can be advantageous.

## How to calculate the Sum of the Years’ Digits Depreciation?

As mentioned above, companies can calculate the sum of the years’ digit depreciation by determining the useful life of an asset (n). Then, companies must add all digits from 1 to n to get the sum of the years’ digits. The formula for it is below.

Sum of the years’ digits=n(n+1) / 2

As with other depreciation methods, companies must still determine the depreciation base for the asset, calculated as below.

Depreciable base=Initial cost – Residual value

Next, companies must calculate the depreciation fraction for the year. This fraction will determine the proportion of the asset’s cost to be depreciated during a year (x). The calculation is as follows.

Depreciation fraction for year x = (n – x + 1) / Sum of the years’ digits

Finally, companies can calculate the depreciation expense for year x by multiplying the depreciable base with the depreciation fraction for the year, as follows.

Depreciation expense for year x = Depreciable base × Depreciation fraction for year x

## Example

Red Co. owns an asset with an initial value of \$10,000 and a residual value of \$2,000. When the company acquired the asset, it determined its useful life to be five years. Red Co. wants to calculate the sum of the years’ digits depreciation for the third year. Based on this information, the company will use the following steps.

1. Calculate the sum of the years’ digits as follows.

Sum of the years’ digits = n (n+1) / 2

Sum of the years’ digits = 5 (5 + 1) / 2

Sum of the years’ digits = 15

1. Determine the depreciable base as follows.

Depreciable base = \$10,000 – \$2,000

Depreciable base = \$8,000

1. Calculate the depreciation fraction for year 3, as below.

Depreciation fraction = (n – x + 1) / Sum of the years’ digits

Depreciation fraction = (5 – 3 + 1) / 15

Depreciation fraction = 3 / 15 or 20%

1. Calculate the depreciation expense.

Depreciation expense for year 3 = \$8,000 × 20%

Depreciation expense = \$1,600

## Conclusion

The sum of the years’ digit depreciation is a depreciation method that depreciates assets more in the earlier years of their useful life. The calculation for this method involves various steps. However, it can be more accurate when a company uses an asset more during its initial years. It can also have other benefits, such as tax savings.

## Further questions

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