Sum of Years Digits

The SYD Formula: How the Digit Sum Works

The sum-of-years-digits method assigns a fraction to each year of the asset's useful life, where the numerator is the remaining years of life and the denominator is the sum of all digits from 1 to n. For a five-year asset, the digit sum is 1+2+3+4+5 = 15, and the annual fractions are: Year 1 = 5/15 (33.3%), Year 2 = 4/15 (26.7%), Year 3 = 3/15 (20.0%), Year 4 = 2/15 (13.3%), Year 5 = 1/15 (6.7%). These fractions are applied to the depreciable base (Cost − Salvage Value). The formula for the digit sum is n(n+1)/2, so a 10-year asset has a digit sum of 55 and Year 1 claims 10/55 = 18.2% of the depreciable base. Unlike the double declining balance method, SYD always depreciates the full depreciable amount by the end of the asset's useful life — there is no residual book value above salvage and no mid-life method switch required.

SYD vs. Double Declining Balance: A Practical Comparison

For a $100,000 machine with a $10,000 salvage value and five-year life, SYD Year 1 deduction is ($100,000 − $10,000) × 5/15 = $30,000; DDB Year 1 is $100,000 × 40% = $40,000. DDB front-loads depreciation more aggressively in years one and two, while SYD produces a smoother decline. DDB requires a mid-life switch to straight-line when the SL equivalent exceeds DDB (typically in years 3–4 for a five-year asset). SYD avoids this complexity because its fractions naturally converge to zero at exactly year n. Over the full life, both methods recover the same depreciable amount — the choice affects only the timing of deductions, not the total. For long-lived assets such as 20-year equipment, the present-value difference between DDB and SYD can be significant: DDB deductions in years 1–5 may be 15–25% higher in present value than SYD for the same asset.

When SYD Outperforms Other Accelerated Methods

SYD is most advantageous for assets whose economic value truly declines more rapidly in early years: consumer electronics, fashion-industry equipment, technology servers, and vehicles. A software company replacing laptops every four years ($2,000 cost, $200 salvage) claims SYD Year 1 depreciation of ($2,000 − $200) × 4/10 = $720 versus straight-line's $450. The SYD pattern also closely mirrors actual resale value curves for vehicles: a three-year-old vehicle typically sells for 40–50% of its original price, consistent with SYD's cumulative depreciation of approximately 60% by that point. IAS 16 paragraph 60 requires the depreciation method to reflect the pattern in which the asset's future economic benefits are consumed — for assets with front-loaded utility, SYD satisfies this requirement more precisely than straight-line and without the mathematical discontinuity of a DDB switch-over. This makes SYD a defensible and auditor-friendly choice for IFRS financial statements when accelerated depreciation is appropriate.