Function DepreciationSum(PurchaseDate, NextPeriodDate, Cost, Salvage, Life, StartPeriod, EndPeriod, Factor, Basis, Mode, Switch)

DepreciationSum

The function DepreciationSum returns the depreciation of an asset for the specified interval, using factor-declining depreciation. The accounting periods have a length of one year, but they don’t necessary need to start January 1. A parameter Switch is used to indicated that, when straight-line depreciation results in greater depreciation than factor-declining depreciation, the calculation of the depreciation has to be based on that method.

DepreciationSum(
    PurchaseDate,             ! (input) scalar string expression
    NextPeriodDate,           ! (input) scalar string expression
    Cost,                     ! (input) numerical expression
    Salvage,                  ! (input) numerical expression
    Life,                     ! (input) numerical expression
    StartPeriod,              ! (input) numerical expression
    EndPeriod,                ! (input) numerical expression
    Factor,                   ! (input) numerical expression
    [Basis,]                  ! (optional) numerical expression
    [Mode,]                   ! (optional) numerical expression
    [Switch]                  ! (optional) numerical expression
    )

Arguments

PurchaseDate

The date of purchase of the asset. PurchaseDate must be given in a date format. This is the first day that there will be depreciated.

NextPeriodDate

The next date after the balance is drawn up. NextPeriodDate must also be in date format. NextPeriodDate is the first day of a new period and must be further in time than PurchaseDate, but not more than one year after PurchaseDate. When NextPeriodDate is an empty string, it will get the default value of January 1st of the next year after purchase.

Cost

The purchase or initial cost of the asset. Cost must be a positive number.

Salvage

The value of the asset at the end of its useful life. Salvage must be a scalar numerical expression in the range \([0, Cost)\).

Life

The number of periods until the asset will be fully depreciated, also called the useful life of the asset. Life must be a positive integer.

StartPeriod

The starting period of the interval, for which you want to compute the sum of depreciation, this may also indicate a partial period. StartPeriod must be an integer in the range \(\{1, Life\}\). StartPeriod must have the same unit as Life.

EndPeriod

The last period of the interval, for which you want to compute the sum of depreciation. EndPeriod must be an integer in the range \(\{StartPeriod, Life\}\). EndPeriod must have the same unit as Life.

Factor

The rate by which the depreciation declines is \(\frac{Factor}{Life}\). Factor must be a numerical expression in the range \([1, \infty )\). In case \(Factor = 2\) we define this method as double declining depreciation.

Basis

The day-count basis method to be used. The default is 1.

Mode

Specifies how partial periods will be handled. Mode must be binary. \(Mode = 0\): we just take a relatively equal part of the depreciation for a full year. This is mathematically incorrect, but is rather common in the financial world. \(Mode = 1\): the depreciation for the partial periods is calculated so that the asset exactly equals its Salvage after its useful life. The default is 0.

Switch

Indicates whether to switch to straight-line depreciation when the depreciation amounts will be higher applying that method, or not to switch. Switch must be binary. If \(Switch = 0\): do not switch, if \(Switch = 1\): switch. The default is 1.

Return Value

The function DepreciationSum returns the depreciation of an asset for the specified period.

Note

The function DepreciationSum is similar to the Excel function VDB.

Example

Using DepreciationSum for declining depreciation over a period of 10 years:

_p_life := 10 ;
_s_periods := ElementRange(1,_p_life  );
_p_deprec( _i_per ) := DepreciationSum(
    PurchaseDate   :  "2024-03-01",
    NextPeriodDate :  "2025-01-01",
    Cost           :  1e5,
    Salvage        :  1e4,
    Life           :  _p_life,
    StartPeriod    :  _i_per,
    EndPeriod      :  _i_per,
    Factor         :  2,
    Basis          :  1,
    Mode           :  1,
    Switch         :  1);
_p_totDeprec := sum( _i_per, _p_deprec( _i_per ) );
block where single_column_display := 1, listing_number_precision := 6 ;
    display _p_deprec( _i_per ) ;
endblock ;

The actual values computed are:

_p_deprec(_i_per) := data
{  1 : 16968.734756,
   2 : 16606.253049,
   3 : 13285.002439,
   4 : 10628.001951,
   5 :  8502.401561,
   6 :  6801.921249,
   7 :  5441.536999,
   8 :  4353.229599,
   9 :  3706.459199,
  10 :  3706.459199 } ;

References