Syntax

SYD(cost, salvage, number of periods, period, [month])

This function is a decreasing balance depreciation method like the DB function, however it exists for historic reasons in accounting. Prior to the advent of cheap computing power and easy to use spreadsheet software, calculation of the Decreasing Balance Depreciation fraction was difficult, so an easier to use approximation was developed. The SYD function implements this easier alternative – the Sum of Digits (Sum of Year Digits).

Example

If an item was purchased for $20,000 to be depreciated over 3 years with an expected residual or salvage value of $10,000 then the function would be (for the first period):

    =SYD(20000,10000,3,1)

The function would return $5,000 being 10,000 * (3 / 6)

Discussion

This function determines the period in reverse order divided by the sum of the periods as the fraction to depreciate for this period. So for the above example the depreciation fractions would be:

    Period                Fraction
       1      3 / (1 + 2 + 3) = 3 / 6 = 0.500
       2      2 / (1 + 2 + 3) = 2 / 6 = 0.333
       3      1 / (1 + 2 + 3) = 1 / 6 = 0.167

So the resulting values for our example would be:

    Period      Depreciation (SYD Function)        Value
       0                                      20,000.00
       1               5,000.00               15,000.00
       2               3,333.33               11,666.67
       3               1,666.67               10,000.00

The bigest advantage of this depreciation method is that it is easy enough to calculate with a pen and paper alone. A simple calculator is more than adequate.

Manual Calculation

Note: that the formula given in help (XL2003) for this function is incorrect, as you can verify if you try to reproduce the functions results using the formula in help.

Manual calculation of this value offers no real advantage over using the function, but FYI to calculate this value manually use the following simple formula:

    = (cost – salvage) * (number of periods – period + 1) / (sum of period counter)

Use in Accounting

Under the Australian Equivalent to the International Financial Reporting Standards:

• Depreciation should be started when the item is available for use and concludes when either the item is classified as held for sale or the item is derecognised as an asset (written off). Depreciation does not cease just because an item becomes idle or is retired from active use unless it has already been fully depreciated. (AASB116-55)
• Reducing balance depreciation is appropriate if the pattern of usage of the asset fits the reducing balance model (AASB116-62).
• The depreciation method chosen should be reviewed at least at the end of each annual reporting period (AASB116-61).
• If the pattern of usage changes then the depreciation method should be changed to reflect the current pattern of use (AASB116-61).
• Be aware that the depreciation method chosen for financial reporting (governed by accounting standards) may be different from the depreciation for taxation purposes (governed by taxation legislation). Accounting standards specify that the depreciation method should match the usage of the asset, while taxation legislation may allow for accelerated depreciation under a wider range of circumstances.

Alternative Uses

Geometry – consider a triangle of (cph) units

      O 
     O O 
    O O O 
   O O O O 
  O O O O O 

Using 5 for the cost (the height of the triangle) and 0 for the salvage value we can use the SYD function to tell us the fraction that each row represents of the whole as follows:

    = SYD(height, 0, height, row) / height
    = SYD(5, 0, 5, 1) / 5
    = 1.6667 / 5
    = 33.33% (formatted as a percentage)

If you are into number theory and /or geometry, hey - have a blast!

Disclaimer

The author is not a qualified accountant and makes no claim, warranty or other assurances that the accounting information given above is accurate or that it applies in your jurisdiction.