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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.
(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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