What it means
Depreciation spreads the cost of a long-lived asset across the years that use it. Straight line splits that cost evenly, which is simple but assumes the asset gives the same value in year five as in year one.
Sum-of-the-years' digits assumes the opposite, that newer assets are more productive and cheaper to run, so it front-loads the expense. The mechanics are easy once you see them.
Add the digits of the useful life together, so a five-year asset gives 1 + 2 + 3 + 4 + 5 = 15, and that total becomes the denominator of every year's fraction. The numerator is the number of years of life remaining at the start of each year, counting down from five to one.
The base being depreciated is the depreciable amount, which is the cost of the asset less its expected residual value at the end of its life. That distinction matters, because reducing balance methods apply their rate to the full carrying amount instead, which is why the two accelerated methods give different yearly numbers.
In practice the method suits assets that genuinely lose usefulness quickly, such as delivery vehicles, computing hardware, moulds and production tooling. It is less appropriate for buildings or fixtures whose service potential is steady across their lives, where straight line reflects reality better.
The commercial consequence is that reported profit is lower in the early years and higher later, even though cash flow is unchanged, so comparing two companies using different depreciation methods requires care. Note also that many tax authorities set their own capital allowance rules, so the depreciation in the accounts and the deduction in the tax computation are frequently different numbers.
In practice
Real-world examples.
Example
A courier firm depreciates its vans over four years using sum-of-the-years' digits, because maintenance costs rise steeply after year two and the method matches the higher early expense with the years of heaviest use. Its finance director notes the resulting dip in first-year operating profit when setting depot budgets.
Example
An architecture practice buys $90,000 of workstations and rendering hardware with a three-year life and no residual value. The digits sum to 6, so it charges $45,000, $30,000 and $15,000 across the three years rather than $30,000 each year.
Example
A plastics manufacturer applies the method to injection moulds that lose precision with use. When a client contract ends early in year three, the mould's carrying amount is already low, so the write-off on disposal is small compared with what straight line would have left on the books.
Formula
Calculation
Sum of the years' digits = n x (n + 1) / 2, where n is the useful life in years
Annual depreciation = (Remaining life at start of year / Sum of the years' digits) x (Cost - Residual value)
A printing company buys a digital press for $60,000, expects to use it for five years and estimates it will be worth $6,000 as a trade-in at the end.
Depreciable amount = $60,000 - $6,000 = $54,000
Sum of the years' digits = 5 x 6 / 2 = 15
Year 1: 5/15 x $54,000 = $18,000
Year 2: 4/15 x $54,000 = $14,400
Year 3: 3/15 x $54,000 = $10,800
Year 4: 2/15 x $54,000 = $7,200
Year 5: 1/15 x $54,000 = $3,600
Total charged = $18,000 + $14,400 + $10,800 + $7,200 + $3,600 = $54,000, leaving a carrying amount of exactly $6,000, the residual value. Straight line would have charged $54,000 / 5 = $10,800 every year, so the method moves $7,200 of expense from year five into year one.Case study
Seen in the real world.
Mercer Tooling is an illustrative, clearly fictional engineering firm used to show why the choice of depreciation method changes the story a set of accounts tells. It invested $60,000 in a digital press and, expecting the press to do most of its heavy work in the first two years of a customer contract, chose sum-of-the-years' digits over straight line.
In year one the press carried $18,000 of depreciation rather than $10,800, which cut reported operating profit by $7,200 and prompted an awkward question from a minority shareholder about declining margins. The finance director's answer was that cash was unaffected, the total charge over five years was identical at $54,000, and the profile simply matched expense to the years the machine actually earned its keep.
By year five the position reversed, with the press costing just $3,600 in depreciation against $10,800 under straight line, and margins looked correspondingly better. The illustrative point is that accelerated depreciation borrows profit from the early years and repays it later, so any year-on-year margin comparison has to account for where each major asset sits in its depreciation schedule.
Watch out
Common mistakes.
- Applying the fraction to the full cost of the asset instead of to cost less residual value, which depreciates the asset below its expected trade-in value.
- Keeping the numerator fixed instead of counting down the remaining life each year, so the annual charges never decline and the schedule does not add up to the depreciable amount.
- Assuming the method reduces the total cost charged over the asset's life, when it only changes the timing and the five-year total is identical to straight line.
Questions
People also ask.
How do you calculate the sum of the years' digits quickly?
Use n x (n + 1) / 2, so an eight-year asset gives 8 x 9 / 2 = 36 without adding the digits one at a time.
Is this method allowed under international accounting standards?
Yes, since the standards require a method that reflects the pattern in which the asset's benefits are consumed, and accelerated methods are acceptable where that pattern is front-loaded.
How does it differ from reducing balance?
Sum-of-the-years' digits applies a shrinking fraction to a fixed depreciable amount, whereas reducing balance applies a fixed percentage to a shrinking carrying amount, which never quite reaches zero on its own.
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