To calculate Sum of Year Digits depreciation

In the sum of Years Digits depreciation method, a fraction of an asset's depreciable cost is written off each year. The fraction is formed by a numerator equal to the remaining life of the asset, and a denominator equal to the sum of the number of the years of the asset's life.

LN considers whether the asset has a life that ends evenly on a year-end boundary when it calculates the sum of years in the life. If the life ends in the middle of a year, LN uses a decimal amount in the sum of years calculation. For example, if you have an asset with a life of five years, LN calculates a denominator of fifteen, computed as follows:

(5 + 4 + 3 + 2 + 1) = 15

For an asset with a life of five years and three months, the sum of the years digits is 16.50, computed as follows:

(5.25 + 4.25 + 3.25 + 2.25 + 1.25 + 0.25) = 16.50

LN uses the resulting fraction to determine the annual depreciation amount. After calculating the annual depreciation expense, LN then proportionally divides each year's expense across the number of periods for that year.

Example

Years of depreciation = 5

cost = $ 10,000

Depreciation:

year 1:   $ 10,000 * 5 / 15 = $ 3,333.33
year 2:   $ 10,000 * 4 / 15 = $ 2,666.67
year 3:   $ 10,000 * 3 / 15 = $ 2,000.00
year 4:   $ 10,000 * 2 / 15 = $ 1,333.33
year 5:   $ 10,000 * 1 / 15 = $   666.67
Sum:                          $10,000.00

Note

If the asset for which you are calculating depreciation contains an averaging convention, LN adjusts the depreciation expense for the first half-year, quarter, or month calculation. For more information, refer to Calculations and Averaging Conventions.

Sum of Years Digits (SYD) has two variations based on the calculation mode in use for the asset in its related books:

  • SYD daily
  • SYD periodic

SYD daily

In the Sum of Years Digits Daily formula, LN considers the exact number of days in each period when calculating the depreciation expense for each period. LN performs three steps each time it calculates depreciation:

  1. Determines the annual depreciation expense for the current year and the next year.
  2. Calculates the change per period.
  3. Calculates the exact depreciation amount for the current period, based on the annual expense and the change value.

The following formulas are used:

  • U.S. tax books:
Depreciation = (cost - salvage - Sec179) * (business percentage/100) *
(remaining years in life / sum of years)
  • Other books:
Depreciation = (cost - salvage) * (remaining years in life / sum of years)

For MACRS and ACRS the salvage value is not applied to depreciation of U.S. tax and commercial books.

To calculate the current period's depreciation:

[(current year's depreciation / 365) * days in period] + 
[change per period * (x - y - days in the period)]

The following applies to the above formula:

change per period = (current year's depreciation - next year's depreciation) / 365 / 365

x = [ ( 184 - days from the start of the year to the start of the current  period) * 
( 185 - days from the start of the year to the start of the current period) ] / 2

y = [ ( 184 - days from the start of the year to the start of the current period
days in the current period) * ( 185 - days from the start of the year to the
start of the current period - days in the current period) ] / 2

SYD periodic

In the Sum of Years Digits Periodic formula, LN considers the exact number of days in each period when calculating the depreciation expense for each period. LN performs three steps:

  1. Determines the annual depreciation expense for the current year and the next year.
  2. Calculates the change per period.
  3. Uses this value to calculate the exact depreciation amount for the current period.

The following formulas are used:

  • U.S. tax books:
Depreciation = (cost - salvage - Sec179) * (business percentage / 100) *
(remaining years in life / sum of years)
  • Other books:
Depreciation = (cost - salvage) * (remaining years in life / sum of years)

For MACRS and ACRS the salvage value is not applied to depreciation of U.S. tax and commercial books.

  • To calculate the current period's depreciation:
( current year's depreciation / 12) + (change per period * [ (number of
periods + 1) / 2 ] - current period number)

The following applies to the above formula:

change per period = (current year's depreciation - next year's depreciation) / 12 / 12

current period number = The position of the current period in the current year of the asset's life. For example, in a fiscal year beginning in January, February is 2.