Sum of Years' Digits Method Depreciation Calculator

Depreciation Schedule

Example - Cost: $125,000.00, Salvage: $15,000.00, Life: 7 years , First Year: 12 months

Year	Book Value Year Start	Total Cost Depreciable	Depreciation Percent	Depreciation Expense	Accumulated Depreciation	Book Value Year End
1	$125,000	$110,000	25.00% (7/28)	$27,500	$27,500	$97,500
2	$97,500	$110,000	21.43% (6/28)	$23,571	$51,071	$73,929
3	$73,929	$110,000	17.86% (5/28)	$19,643	$70,714	$54,286
4	$54,286	$110,000	14.29% (4/28)	$15,714	$86,429	$38,571
5	$38,571	$110,000	10.71% (3/28)	$11,786	$98,214	$26,786
6	$26,786	$110,000	7.14% (2/28)	$7,857	$106,071	$18,929
7	$18,929	$110,000	3.57% (1/28)	$3,929	$110,000	$15,000

Sum of Years' Digits Depreciation Formulas

The sum of years digits method is accelerated depreciation. Depreciation is taken as a fractional part of a sum of all the years.  For example, if an asset has a life of 5 years the sum of years is 1+2+3+4+5 = 15.  Fractional parts are built with the year as the numerator and the sum of years as the denominator but, in reverse order. Year 1 is 5/15 * depreciable cost, Year 2 is 4/15 * depreciable cost, Year 3 is 3/15 * depreciable cost, etc. Since the sum of all fractions will equal 15/15, the total depreciation over the life of an asset will be 1 * depreciable cost = depreciable cost.

Calculating the sum of years can be simplified with the formula (Life * (Life + 1)) / 2 so you do not need to actually add up all the years.

• Depreciable Cost = Original Cost - Salvage Value = (Cost - Salvage)
• Fraction for a Given Period = (Life - Period + 1) / ((Life * (Life + 1)) / 2)
• Depreciation in Any Period:
  • = Fraction for Given Period * Depreciable Cost
  • = [(Life - Period + 1) / ((Life * (Life + 1)) / 2) ] * (Cost - Salvage)
  • = ((Cost - Salvage) * (Life - Period + 1) * 2 / (Life) / (Life +1))
• Partial year depreciation, when the first year has M months requires a bit of manipulation since the period fraction used and the years in which the depreciation are taken will overlap.  If we have an asset with a life of 5 years and the service for the first year is only 4 months:
  • First year depreciation fraction = (4/12) x (5/15)
  • Second year depreciation fraction = [(8/12) x (5/15)] + [(4/12) x (4/15)]
  • Etc .....
  • And, a life, for example, of 5 years will be depreciated across 6 years.

Microsoft® Excel® Functions Equivalent: SYD

The Excel equivalent function for Sum of Years' Digits Method is SYD(cost,salvage,life,per) will calculate the depreciation expense for any period.  For a more accelerated depreciation method see, for example, our Double Declining Balance Method Depreciation Calculator.

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Reference

principlesofaccounting.com, chapter 10 - THE SUM-OF-THE-YEARS'-DIGITS METHOD