What Is Sum-of-the-Years' Digits Depreciation? Formula and Example

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Sum-of-the-years’ digits (SYD) depreciation is an accelerated depreciation method that charges more of an asset’s cost to expense in its early years and less in later years. Each year’s charge equals the asset’s depreciable base (cost minus salvage value) multiplied by a fraction. The numerator is the number of years of useful life remaining at the start of that year. The denominator is the sum of the digits of every year in the asset’s useful life.

How Sum-of-the-Years’ Digits Depreciation Works

Depreciation allocates the cost of a long-lived asset to the periods that benefit from using it. Straight-line depreciation spreads that cost evenly. Accelerated methods such as SYD and declining balance front-load it.

SYD does this with a set of shrinking fractions. For a five-year asset the fractions are 5/15, 4/15, 3/15, 2/15 and 1/15, or roughly 33%, 27%, 20%, 13% and 7%. They always add up to 100%, which is why the method lands precisely on salvage value at the end of the asset’s life.

The SYD formula

The sum of the years’ digits for a useful life of n years is:

SYD = n × (n + 1) / 2

For five years, 5 × 6 / 2 = 15. For six years, 6 × 7 / 2 = 21. The shortcut matches adding the digits by hand and is faster for long lives (a 20-year asset has a sum of 210).

Depreciation for any year t is:

Depreciation = (Cost − Salvage value) × (n − t + 1) / SYD

The term (n − t + 1) is the remaining life at the start of year t. In year 1 it equals n, and in the final year it equals 1. For a six-year asset, the first-year rate is 6/21 (about 28.6%) and the second-year rate is 5/21 (about 23.8%).

Example of Sum-of-the-Years’ Digits Depreciation

Hypothetical example. A company buys a machine for $50,000. It expects a five-year useful life and a $5,000 salvage value. The depreciable base is $45,000, and the SYD is 15.

• Year 1: $45,000 × 5/15 = $15,000. Ending book value: $35,000
• Year 2: $45,000 × 4/15 = $12,000. Ending book value: $23,000
• Year 3: $45,000 × 3/15 = $9,000. Ending book value: $14,000
• Year 4: $45,000 × 2/15 = $6,000. Ending book value: $8,000
• Year 5: $45,000 × 1/15 = $3,000. Ending book value: $5,000

Total depreciation is $45,000, and the machine ends at its $5,000 salvage value. The charge drops by $3,000 every year, which is one-fifteenth of the base.

Straight-line depreciation would book $9,000 a year, so SYD records $6,000 more expense in year 1 and $6,000 less in year 5. That lowers reported profit on the income statement early on and reduces the asset’s carrying value on the balance sheet faster. Because depreciation is a non-cash charge, the method changes reported earnings, not the cash spent on the machine, and metrics that add depreciation back, such as EBITDA, are unaffected.

Using SYD with year fractions

Assets are rarely bought on the first day of a fiscal year. When an asset is placed in service mid-year, each asset year straddles two fiscal years, and each fiscal year’s charge blends the two. Suppose the same machine is placed in service with nine months left in the fiscal year:

• Fiscal year 1: 9/12 × $15,000 = $11,250
• Fiscal year 2: 3/12 × $15,000 + 9/12 × $12,000 = $3,750 + $9,000 = $12,750

The pattern continues until a final three-month stub in fiscal year 6 uses up the last part of the $3,000 asset-year-5 charge.

Sum-of-the-Years’ Digits in Excel

Excel’s function is =SYD(cost, salvage, life, per), where per is the period being calculated and uses the same units as life. For the example, =SYD(50000, 5000, 5, 2) returns $12,000. The function assumes full periods. For a partial first year, calculate each asset-year amount with SYD and blend them by month as shown above.

Why Companies Use It

The main argument for SYD is matching. Many assets deliver more service when new, so a larger early charge aligns expense with the benefit the asset produces. Vehicles are the classic case, because they lose much of their value early.

Repair and maintenance costs point the same way, because they tend to rise as equipment ages. When depreciation falls while upkeep climbs, the combined annual cost of owning the asset stays steadier.

Limitations

• Estimates drive everything. Useful life and salvage value are judgments, and a different life changes both the denominator and every fraction.
• More work than straight-line. Straight-line remains the simplest method and the default for many businesses.
• Tax rules differ from book rules. For U.S. federal income tax, most tangible property placed in service after 1986 falls under MACRS, which uses prescribed declining-balance and straight-line schedules rather than SYD. SYD is therefore mainly a financial reporting choice.
• Consistency is expected. Once a method is chosen for an asset, a company is expected to keep using it. Under U.S. GAAP, a change in depreciation method is applied prospectively as a change in estimate and must be justified. For tax purposes, changing an accounting method generally requires IRS consent.

How SYD Differs From Other Methods

SYD vs. declining (reducing) balance. Declining balance applies a constant rate, such as double the straight-line rate, to the asset’s shrinking book value. Salvage value is ignored in that calculation and acts only as a floor. SYD applies a shrinking fraction to a fixed base of cost minus salvage. As a result, SYD’s charge falls by a constant dollar amount each year, while declining balance falls by a constant percentage.

SYD vs. straight-line. Both depreciate the same total (cost minus salvage). They differ only in timing.

SYD vs. units of production. Units of production ties depreciation to actual output or usage rather than the passage of time, so the charge rises and falls with activity instead of following a fixed schedule.

The Bottom Line

SYD suits companies whose assets, such as vehicles, deliver the most service when new and cost more to maintain as they age. It lowers reported profit early without changing cash spent, and it lands exactly on salvage value. Because U.S. tax rules generally require MACRS and method changes need justification, companies should choose SYD for financial reporting deliberately and apply it consistently.