The Sum of the Years’ Digits (SYD) Method is an accelerated method of depreciation. Under this method, a higher amount of depreciation is charged during the earlier years of an asset’s useful life and the amount of depreciation gradually decreases as the asset becomes older.
The Sum of the Years’ Digits Method generally results in a faster write-off of the depreciable cost than the Straight Line Method. It may also result in a more accelerated depreciation charge than the Declining Balance Method.
Under this method, annual depreciation is calculated by multiplying the depreciable cost or depreciable base of the asset by a schedule of fractions. The fraction used for each year is based on the remaining useful life of the asset and the sum of the digits representing the total useful life.
Basic Principle of Sum of the Years’ Digits Method
The Sum of the Years’ Digits Method is based on the assumption that assets are generally more productive when they are new and their productivity decreases as they become older.
Since a new asset may provide greater economic benefits during the earlier years of its useful life, a higher amount of depreciation is charged during those years.
As the remaining useful life and productivity of the asset decrease, the depreciation charge also decreases.
Therefore, the SYD Method provides an accelerated allocation of the depreciable cost of an asset, with higher depreciation in earlier years and lower depreciation in later years.
Formula for Sum of the Years’ Digits Method
Depreciation under the SYD Method is calculated using the following formula:
SYD Depreciation = Depreciable Base × (Remaining Useful Life ÷ Sum of the Years’ Digits)
The depreciable base is calculated as:
Depreciable Base = Cost of Asset − Salvage Value
The depreciable base remains the same throughout the useful life of the asset. However, the depreciation fraction changes every year according to the remaining useful life of the asset.
Calculation of Sum of the Years’ Digits
The first step under the SYD Method is to determine the sum of the digits representing the useful life of the asset.
For example, if an asset has a useful life of five years, the years’ digits are:
5, 4, 3, 2 and 1
The sum of the years’ digits is:
5 + 4 + 3 + 2 + 1 = 15
Therefore, 15 becomes the denominator of the depreciation fraction for each year.
The sum of the years’ digits may also be calculated using the formula:
Sum of Years’ Digits = (n² + n) ÷ 2
or
Sum of Years’ Digits = n(n + 1) ÷ 2
Here, n represents the useful life of the asset in years.
For an asset having a useful life of five years:
(5² + 5) ÷ 2 = (25 + 5) ÷ 2 = 15
Therefore, the sum of the years’ digits is 15.
Depreciation Fractions under SYD Method
After determining the sum of the years’ digits, a depreciation fraction is calculated for each accounting year.
For an asset having a useful life of five years, the depreciation fractions will be:
First Year = 5/15
Second Year = 4/15
Third Year = 3/15
Fourth Year = 2/15
Fifth Year = 1/15
The numerator represents the remaining useful life of the asset, while the denominator represents the sum of the years’ digits.
The numerator decreases every year. Therefore, the depreciation expense also decreases every year.
Example of Sum of the Years’ Digits Method
Suppose an asset has an original cost of $1,000, an estimated useful life of 5 years, and an estimated salvage value of $100.
The depreciable base is calculated as:
Depreciable Base = Cost − Salvage Value
$1,000 − $100 = $900
Therefore, $900 is the amount to be allocated as depreciation over the five-year useful life of the asset.
The sum of the years’ digits is:
5 + 4 + 3 + 2 + 1 = 15
The annual depreciation is calculated by multiplying the depreciable base of $900 by the applicable depreciation fraction.
First Year Depreciation
In the first year, the remaining useful life is five years. Therefore, the depreciation fraction is 5/15.
Depreciation = $900 × 5/15 = $300
The accumulated depreciation at the end of the first year is $300.
The book value of the asset becomes:
$1,000 − $300 = $700
Second Year Depreciation
In the second year, the remaining useful life is four years. Therefore, the depreciation fraction is 4/15.
Depreciation = $900 × 4/15 = $240
Accumulated depreciation becomes:
$300 + $240 = $540
The book value of the asset becomes:
$1,000 − $540 = $460
Third Year Depreciation
In the third year, the depreciation fraction is 3/15.
Depreciation = $900 × 3/15 = $180
Accumulated depreciation becomes:
$540 + $180 = $720
The book value of the asset becomes:
$1,000 − $720 = $280
Fourth Year Depreciation
In the fourth year, the depreciation fraction is 2/15.
Depreciation = $900 × 2/15 = $120
Accumulated depreciation becomes:
$720 + $120 = $840
The book value of the asset becomes:
$1,000 − $840 = $160
Fifth Year Depreciation
In the fifth and final year, the depreciation fraction is 1/15.
Depreciation = $900 × 1/15 = $60
Accumulated depreciation becomes:
$840 + $60 = $900
The final book value of the asset is:
$1,000 − $900 = $100
The remaining $100 represents the scrap or salvage value of the asset.
Depreciation Schedule under SYD Method
| Year | Depreciable Base | Depreciation Rate | Depreciation Expense | Accumulated Depreciation | Book Value at Year-End |
|---|---|---|---|---|---|
| Original Cost | — | — | — | — | $1,000 |
| 1 | $900 | 5/15 | $300 | $300 | $700 |
| 2 | $900 | 4/15 | $240 | $540 | $460 |
| 3 | $900 | 3/15 | $180 | $720 | $280 |
| 4 | $900 | 2/15 | $120 | $840 | $160 |
| 5 | $900 | 1/15 | $60 | $900 | $100 |
The depreciation schedule clearly shows the accelerated nature of the SYD Method. Depreciation is highest in the first year and gradually decreases during each subsequent year.
The depreciable base remains constant at $900, but the depreciation fraction decreases from 5/15 to 1/15.
At the end of the fifth year, accumulated depreciation is $900 and the remaining book value is $100, which is equal to the estimated salvage value.
Accounting Treatment under SYD Method
The depreciation expense calculated under the Sum of the Years’ Digits Method is recorded as an expense of the accounting period.
The accounting entry is:
Depreciation Expense A/c Dr.
To Accumulated Depreciation A/c
For example, the depreciation expense for the first year is $300. The accounting entry will be:
Depreciation Expense A/c Dr. $300
To Accumulated Depreciation A/c $300
In the second year, depreciation expense is $240. Therefore, the entry will be:
Depreciation Expense A/c Dr. $240
To Accumulated Depreciation A/c $240
Depreciation expense is charged to the Income Statement, while accumulated depreciation increases and reduces the carrying value of the asset in the Balance Sheet.
Difference between SYD and Straight Line Method
Under the Straight Line Method, an equal amount of depreciation is charged every year throughout the useful life of the asset.
Under the Sum of the Years’ Digits Method, depreciation is higher in the earlier years and lower in the later years.
The Straight Line Method assumes equal allocation of depreciable cost over the useful life. The SYD Method is based on the assumption that an asset is generally more productive when it is new and its productivity decreases with age.
Therefore, the SYD Method provides an accelerated depreciation charge compared with the Straight Line Method.
Exam Focus
The Sum of the Years’ Digits Method is an accelerated depreciation method that charges higher depreciation in the earlier years and lower depreciation in the later years of an asset’s useful life.
The method is based on the assumption that assets are generally more productive when new and their productivity decreases as they become older.
The main formula is:
SYD Depreciation = Depreciable Base × (Remaining Useful Life ÷ Sum of the Years’ Digits)
The depreciable base is:
Cost − Salvage Value
The sum of the years’ digits is calculated as:
n(n + 1) ÷ 2
For a five-year asset, the sum of the digits is 15, and the depreciation fractions are 5/15, 4/15, 3/15, 2/15, and 1/15.
Under the SYD Method, the depreciable base remains constant but the depreciation fraction decreases every year. The final book value of the asset is reduced to its estimated salvage or scrap value.