Sum of the Years Digits Method

How the Sum of the Years’ Digits Method Works

The sum of the years’ digits method of depreciation, or “SYD”, reduces the book value of a fixed asset (PP&E) at a front-loaded, accelerated depreciation rate.

The implicit assumption of the sum of the years’ digits depreciation method is that the fixed asset (PP&E) is more productive and provides more near-term value in the periods immediately post-purchase.

Under the sum of the years’ digits method, the depreciation rate is higher in the earlier periods of the fixed asset’s economic useful life relative to that in the latter periods.

In effect, the annual depreciation expense recognized on the income statement is greater in earlier periods, causing the reduction in the book value of the fixed asset on the balance sheet to also be higher early on.

The concept of depreciation in cost accounting is rooted in the matching principle of accrual accounting, which is intended to “match” the timing of an expense being recognized on the income statement with the period that coincides with the economic benefit (or revenue).

There are a multitude of depreciation methods – such as the straight-line method, double declining balance (DDB), and units of production method – but the sum of the years’ digits is categorized as a form of accelerated deprecation.

Under accelerated depreciation methods, like the SYD method, the percentage of the total depreciation expense is weighted more toward the start of the fixed asset’s useful life.

Since fixed assets, such as machinery and equipment, are non-current assets anticipated to contribute positive economic utility in excess of one year (>12 months), depreciation expense is recognized over the useful life assumption.

^{Source: Sum-of-the-Years’ Digits Definition (Source: LII)}

How to Calculate Sum of the Years’ Digits Depreciation

The step-by-step process to calculate the annual depreciation expense under the sum of the years’ digits method is as follows.

• Step 1 → Estimate the Useful Life of the Fixed Asset
• Step 2 → Divide the Remaining Useful Life by the Sum of Years’ Digits
• Step 3 → Determine the Salvage Value of the Fixed Asset (“Scrap Value”)
• Step 4 → Subtract the Purchase Cost by the Salvage Value
• Step 5 → Multiply the Remaining Useful Life by the Depreciable Basis (or Depreciable Base)

Sum of the Years’ Digits Depreciation Formula

The formula to calculate the sum of the years’ digits depreciation divides the remaining useful life by the sum of the years’ digits of the fixed asset (PP&E), which is then multiplied by the depreciable basis.

Where:

• Remaining Useful Life → The number of years remaining in the useful life of the fixed asset (PP&E)
• Sum of the Years’ Digits → The sum of each year in the fixed asset’s useful life assumption
• Depreciable Basis → The total value of a fixed asset (PP&E) that can be depreciated, i.e. the total capital expenditure (Capex).

The depreciable basis is calculated by subtracting the salvage value assumption from the purchase cost (Capex), which refers to the residual value of the fixed asset at the end of the fixed asset’s useful life.

Note: The depreciable basis used to compute the annual depreciation expense under the sum of the years’ digits method remains constant across the entire useful life assumption.

Sum of the Years’ Digits Calculation | Quick Tip

The sum of the years’ digits can be calculated using the formula “(N + 1) ÷ 2”, rather than by manually adding each figure.

Sum of the Years’ Digits Depreciation Calculator

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Sum of the Years’ Digits Depreciation Calculation Example

Suppose a manufacturer purchased industrial components for $45 million in 2024 (Year 1).

The economic useful life of the industrial components is merely 4 years because of the rapid “wear-and-tear” attributable to the use-case.

At the end of its useful life, the components are expected to have a residual value of $5 million (i.e. scrap value), which reflects the sale proceeds the manufacturer could hypothetically earn from selling those used components.

• Purchase Cost = $45 million
• Residual Value = $5 million
• Economic Useful Life = 4 Years

Therefore, the depreciable basis amounts to $40 million, i.e. the cost basis of the fixed asset purchase minus the salvage value.

• Depreciable Basis = $45 million – $5 million = $40 million

The sum of the years’ digits for this particular fixed asset (PP&E) comes out to 10 years.

• Sum of the Years’ Digits = 4 + 3 + 2 + 1 = 10 Years

In the PP&E roll-forward schedule, the ending PP&E balance is the purchase cost ($25 million), plus capital expenditures (Capex), less depreciation.

For illustrative purchases, we’ll assume there were no capital expenditures (Capex), the purchase of fixed assets, in each period.

The depreciation factor – the ratio between the remaining useful life and sum of the years’ digits – is 4/10, 3/10, 2/10, and 1/10 from Year 1 to Year 4, respectively.

• Depreciation Factor, Year 1 = 4 ÷ 10 = 4/10 (40% Depreciation Rate)
• Depreciation Factor, Year 2 = 3 ÷ 10 = 3/10 (30% Depreciation Rate)
• Depreciation Factor, Year 3 = 2 ÷ 10 = 2/10 (20% Depreciation Rate)
• Depreciation Factor, Year 4 = 1 ÷ 10 = 1/10 (10% Depreciation Rate)

Note how the depreciation factor works backward, starting with the largest value (Year 4) before incrementally dropping in each period thereafter.

• Earlier Periods → Higher Depreciation Expense
• Latter Periods → Lower Depreciation Expense

Under the sum of the years’ digits method (SYD), the depreciation expense recognized in each period is the depreciation factor multiplied by the depreciable basis.

• SYD Depreciation Expense, Year 1 = 4/10 × $40 million = $16 million
• SYD Depreciation Expense, Year 2 = 3/10 × $40 million = $12 million
• SYD Depreciation Expense, Year 3 = 2/10 × $40 million = $8 million
• SYD Depreciation Expense, Year 4 = 1/10 × $40 million = $4 million

In conclusion, we’ll confirm our fixed asset (PP&E) roll-forward schedule was built properly by checking to ensure the cumulative sum of the fractions equals 1.0 (or 100%) and the ending PP&E value matches the residual value assumption of $5 million.