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Sum of Years' Digits Method Depreciation Calculator

Useful Life (Total Years):
Year to Calculate:
Months in First Year:
Depreciation for Year:

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.

(Microsoft® and Excel® are registered trademarks of Microsoft Corporation)

Reference

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

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