## What is the sum of years’ digits method of depreciation

The **sum of years’ digits method** uses an arbitrary arithmetic system to derive the annual charges. This method is a kind of **Accelerated depreciation methods**. It involves multiplying the depreciable basis amount by an annual fraction. The denominator is the sum of the digits from one to n, where n is the number of years in the asset’s service life.

## Explanation

The depreciation under sum of the years’ digits method is computed by adding up the number of years of the useful economic life (i.e. if the asset has 5 years economic useful life the numbers 1, 2, 3, 4 and 5 are added up and the resulting sum 15, becomes denominator while the numerator is the number of remaining years of the useful economic life of the asset). Accordingly, the depreciation to be provided would be:

5/15 in the first year

4/15 in the second year

3/15 in the third year

2/15 in the fourth year

1/15 in the last year.

The depreciation so determined constitutes the annual depreciation expense and is applied to the cost of acquisition or construction of the asset to be depreciated rather than the WDV of the asset.

### Advantage and Disadvantage of Sum of the years’ digits method of depreciation

The advantage and disadvantage of this method are more or less the same as the declining balance method excepting that perhaps the process of computation under the sum of the years’ digits method is a little more complicated.

## Formula

The Formula for computing depreciation expense through sum of years’ digits method.

The sum-of-the-years-digits method is another variation of accelerated depreciation. Under this method, the asset’s depreciable base is multiplied by a declining rate. Note that the asset’s residual value is subtracted from its acquisition cost to determine its depreciable base. This rate is a fraction, in which the numerator is the number of years remaining in the asset’s life at the beginning of the year and the denominator is the sum of the digits of the asset’s useful life.

To demonstrate how this fraction is computed, assume that an asset has a five-year life. In the first year, the rate is a fraction that has a numerator of 5, the number of years remaining at the beginning of the year. The denominator 1s 15 or 1 + 2 + 3 + 4 + 5. In the second year, the fraction is 4/15 and so forth.

The denominator of the fraction can easily be computed from the following formula:

where N equals the asset’s life. In the above illustration thc denominator is calculated follows:

If the asset’s life is 10 years the denominator is 55, calculated as follows:

The depreciation schedule using the sum-of-the-years-digits method for the equipment is:

As with the double-declining-balance method, the sum-of-the-years-digits method allocates more depreciation in early years and less in later years. However, unlike the double-declining-balance method, the sum-of-the-years-digits method is calculated by applying a declining rate to a constant base, the asset’s depreciable cost.

Partial-year depreciation also can be calculated under the sum-of-the-years-digits method. For example, now assume that the equipment is purchased on October 1 of the current year. In this case, the equipment is in use for only 3 months during the year, and the sum-of-the-years-digits depreciation is $3,000, calculated as follows:

$3,000 = 3/12 x $12,000, or 3/12 x ($36,000 x 5/15)

In the second year, the depreciation expense of $11,400 must be calculated in two steps, as follows:

9/12 x ($36,000 x 5 / 15) = $9,000

3/12 x ($36,000 x 4/15) = $2,400

$9,000 + $2,400 = $11,400

Depreciation expense for the remaining three years is calculated in a similar manner. Both declining-balance and sum-of-the-years-digits are examples of accelerated depreciation. From a conceptual perspective, these methods are most appropriate for assets that give up a greater portion of their benefits in their early years. As such, most of the cost of these assets should be allocated to these same early years. High-tech products are examples of assets in which the decline of benefits is likely to follow such a pattern. Accelerated depreciation is also appropriate for assets that have a greater amount of repair expense in later years.

This results in a reasonably constant expense related to the asset because depreciation expense declines as repair expense increases. Regardless of these conceptual arguments, the management of a firm can choose either accelerated depreciation method for any depreciable asset. The only guideline is that the depreciation method should be systematic and rational, and as we noted, all of the depreciation methods discussed so far meet this requirement. Furthermore, management can choose straight-line depreciation for financial reporting purposes and a special form of accelerated depreciation for tax purposes, This allows a firm to report higher income for financial statement purposes and lower Income for tax return purposes:

## Example

For example, if there are five years in the service life, the denominator is the sum of 1, 2, 3, 4, and 5, which is 15 **( The formula for the denominator is n(n+1) / 2 )**. The numerator gets smaller each year; it begins with the value n in the first year and decreases by one each year until it equals one in the final year of the asset’s estimated service life. Thus, the annual fractions for an asset with a five-year life are: 5/15, 4/15, 3/15, 2/15 and 1/15. They would be used in that order. The following example shows the application of the sum of years’ digits approach to this asset: