Sum of the Years Digits Depreciation, Made Simple

In accounting, one of the important accelerated depreciation methods is the Sum of the Years’ Digits approach. This type of depreciation is used to accurately reflect the decline of a fixed asset’s usefulness over a period of years until its book value is equal to its salvage value. This method is used to calculate amortization for assets that are more productive when first purchased, but rapidly show loss in productivity as time progresses.

The method used to calculate the depreciable amount involves calculating a figure known as sum of the years’ digits; hence, the name. The formula is as follows:

Sum of the Years’ Digits = (n X (n+1)) /2, where n is the number of useful years estimated for the asset in question.

The depreciation itself is calculated using the formula below:

Depreciation = Depreciable Base x (Useful Life Remaining / Sum of Years’ Digits)

The depreciable base in the formula is nothing but the maximum amount by which that asset can be depreciated before it reaches its salvage price, and is calculated as the difference between the purchase price and the salvage value.

Depreciable Base = Original Purchase Price – Salvage Value

Example:

Let us assume the following attributes for an asset:

Original Purchase Price: $45,000

Salvage Value: $5,000

Number of Useful Years: 4

Sum of Years Digits = 4 + 3 + 2 + 1 = 10

which can also be calculated by this formula:

SYD = (4 X (4+1)) / 2 = 10

In this case, the depreciable value will be:

$45,000 – $5,000 = $40,000

This is the figure on which depreciation is calculated for the 4 years in which the asset serves its purpose.

Therefore, for the first year of depreciation:

SYD Depreciation = $40,000 x (4/10) = $16,000

The depreciable amount at the end of this year will be $40,000 – $16,000 = $24,000

For the second year:

SYD Depreciation = $40,000 x (3/10) = $12,000

Depreciable amount at second year: $24,000 – $12,000 = $12,000

For the third year:

SYD Depreciation = $40,000 x (2/10) = $8,000

Depreciable amount at third year: $12,000 – $8,000 = $4,000

For the final (fourth) year:

SYD Depreciation = $40,000 x (1/10) = $4,000

Depreciable amount at final year: $4,000 – $4,000 = $0

At this point, the book value of this asset has reached its salvage value, and no further depreciation is allowable.

Variance between Sale Price and Salvage Value

Should there be any difference between the actual sale price of the asset at the end of its useful life and the salvage value estimated at the time of its purchase, this amount will be considered as capital. A positive amount (sale price higher than salvage value) will reflect under capital gains, while a negative amount will be considered under capital losses.

Theory and Assumptions

The logic behind using the sum of years’ digits method of depreciation arises from the Matching Principle of Generally Accepted Accounting Principles (GAAP), which requires the value of an asset to be matched to the revenue it helps generate during each year of reporting.

The salvage price and the number of useful years are merely estimates, although they are guided by prevalent accounting principles. The sum of the years’ depreciation method relies on the accuracy of the estimates that are used for the purpose of the calculation.

Using this method, the true value of an asset for each year of its useful life can be calculated and recorded more accurately than, for example, using straight line depreciation. Therefore, it is common to use this method to calculate depreciation for assets that lose value rapidly from year to year.

 

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