Documentation/Calc Functions/SYD

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    Function name:

    SYD

    Category:

    Financial Analysis

    Summary:

    Calculates the depreciation of an asset for a given period using the sum of the years' digits method. This method is one of the accelerated deprecation methods that leads to the depreciation expense being greater in earlier periods and less in later periods. The function applies a variable rate (that reduces from period to period) to a constant depreciable cost (which is the asset's original cost minus its estimated salvage value at the end of its useful life).

    Syntax:

    SYD(Cost; Salvage; Life; Period)

    Returns:

    Returns a non-negative real number which is the depreciation of the asset for a specified period using the sum of the years' digits method. The number returned is in the same currency unit as the specified cost and salvage values, and by default is formatted in a locale-dependent currency format.

    Arguments:

    Cost is a real number, or a reference to a cell containing that number, which is the cost or value of the asset before depreciation.

    Salvage is a real number, or a reference to a cell containing that number, which is the residual value of the asset at the end of its depreciated life. Salvage must be in the same currency units as Cost.

    Life is a real number, or a reference to a cell containing that number, which defines the number of periods over which the asset is depreciated.

    Period is a real number, or a reference to a cell containing that number, which specifies the period for which the depreciation value is returned.

    • If any argument is non-numeric then SYD reports a #VALUE! error.
    • If Life is equal to 0.0 or -1.0, then SYD returns an invalid numeric value (#NUM!) error.
    • SYD intentionally leaves the user to ensure that numeric argument values are as intended. Argument values are not specifically checked for validity and this means, for example, that the user could enter negative values without any error being reported.

    Additional details:

    • SYD takes the useful life of the asset and adds together the digits for each period in that value. For example, if the Life argument is set to 5, then the sum of the years' digits is [math]\displaystyle{ 5+4+3+2+1=15 }[/math].
    • To calculate the depreciation for each period, the period numbers are taken backward and divided by the sum of the years' digits to give the proportion of the total loss of value to assign to depreciation that period. For example, with the Life argument set to 5, the depreciation in the first period is [math]\displaystyle{ \frac{5}{15} }[/math] times the deprecation amount (which is CostSalvage); similarly the depreciation amount in the second period is [math]\displaystyle{ \frac{4}{15} }[/math] times the deprecation amount; and so on.
    • The formula for SYD is:
    [math]\displaystyle{ \text{SYD}(Cost;~Salvage;~Life;~Period)~=~\frac{(Cost - Salvage)*(Life+1-Period)*2}{(Life+1)*Life} }[/math]
    • For more background information about depreciation, visit Wikipedia’s Depreciation page.

    Examples:

    Note that the formatting of the return values given in the following examples assume the English (USA) locale.

    Simple example with multiple calls to SYD

    The following table illustrates the behavior of the SYD function.


    A B C D E
    1 Cost 1200 Period Depreciation
    2 Salvage 200 1 $400.00
    3 Life 4 2 $300.00
    4 3 $200.00
    5 4 $100.00
    6 5 $0.00
    7
    8 Total $1000.00

    The data in cells B1:B3 contain the values for three of the arguments passed in SYD function calls. The function is called five times, once for each value of the Period argument given in cells D2 to D6. Cell E2 contains the formula =SYD($B$1; $B$2; $B$3; $D2); cell E3 contains the formula =SYD($B$1; $B$2; $B$3; $D3); and so on.

    The values returned from the SYD calls are shown in cells E2:E6 and cell E8 contains the sum of all the values in cells E2:E6. The following features can be seen in these results:

    • For a life of 4, the sum of the years' digits is [math]\displaystyle{ 4+3+2+1=10 }[/math].
    • With a cost value of 1200 and a salvage value of 200, the depreciation amount is [math]\displaystyle{ 1200-200=1000 }[/math].
    • Period 1. The depreciation expense for the first period is [math]\displaystyle{ \frac{4}{10} }[/math] multiplied by the depreciation amount, that is [math]\displaystyle{ 0.4 \times 1000 = 400 }[/math]. Note that by default, the results from SYD are formatted as a currency.
    • Period 2. The depreciation expense for the second period is [math]\displaystyle{ \frac{3}{10} }[/math] multiplied by the depreciation amount, that is [math]\displaystyle{ 0.3 \times 1000 = 300 }[/math].
    • Period 3. The depreciation expense for the third period is [math]\displaystyle{ \frac{2}{10} }[/math] multiplied by the depreciation amount, that is [math]\displaystyle{ 0.2 \times 1000 = 200 }[/math].
    • Period 4. The depreciation expense for the fourth period is [math]\displaystyle{ \frac{1}{10} }[/math] multiplied by the depreciation amount, that is [math]\displaystyle{ 0.1 \times 1000 = 100 }[/math].
    • Period 5. This period is after the useful lifetime of the asset (4 periods) and so SYD returns a value of 0.
    • Note that the total depreciation of 1000.00 is exactly equal to the difference between the cost and salvage values.

    Additional examples

    Formula Description Returns
    =SYD(50000; 10000; 5; 1) A video system initially costing 50,000 currency units is to be depreciated annually for the next 5 years. The salvage value is 10,000 currency units. The depreciation for the first year is 13,333.33 currency units. $13,333.33
    =SYD(50000; 10000; 5; 2) For the same video system as in the above example, the depreciation for the second year is 10,666.67. $10,666.67
    =SYD(28000; 10000; 7.5; 5) A car initially costing 28,000 currency units is to be depreciated over 7.5 years. The salvage value is 10,000 currency units. The depreciation for the fifth year is 1,976.47 currency units. $1,976.47

    Related LibreOffice functions:

    AMORDEGRC

    AMORLINC

    DB

    DDB

    SLN

    VDB

    ODF standard:

    Section 6.12.46, part 2

    Related (or similar) Excel functions:

    SYD