Function DepreciationNonLinearRate(PurchaseDate, NextPeriodDate, Cost, Salvage, Period, DepreciationRate, Basis, Mode)

DepreciationNonLinearRate

The function DepreciationNonLinearRate returns the depreciation of an asset for the specified period, using factor-declining depreciation. The DepreciationRate determines the factor. The accounting periods have a length of one year, but they don’t necessary need to start January 1.

DepreciationNonLinearRate(
    PurchaseDate,             ! (input) scalar string expression
    NextPeriodDate,           ! (input) scalar string expression
    Cost,                     ! (input) numerical expression
    Salvage,                  ! (input) numerical expression
    Period,                   ! (input) numerical expression
    DepreciationRate,         ! (input) numerical expression
    [Basis,]                  ! (optional) numerical expression
    [Mode]                    ! (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 \([0, Cost)\).

Period

The period for which you want to compute the depreciation. Period an integer in the range \(\{1, Life + 1\}\). Period 1 is the (partial) period from PurchaseDate until NextPeriodDate.

DepreciationRate

The value of the asset declines every period by an amount equal to the depreciation rate times the Cost. DepreciationRate must be a numerical expression in the range \([0, \frac{1}{2})\).

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.

Return Value

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

Equation

The method-dependent depreciation \(\tilde{d_i}\) is expressed by the equations

\[\begin{split}\begin{aligned} \tilde{d_1} &= \begin{cases} f_{PN}rfc & \mbox{for $\textit{Mode} = 0$}\\ \left(1-(1-rf)^{f_{PN}}\right)c & \mbox{for $\textit{Mode} = 1$} \end{cases} \\ \tilde{d_i} &= \begin{cases} rfv_i & ( 1 < i < \tilde{L} - 1) \\ \frac{1}{2}v_i & (i = \tilde{L} - 1) \\ v_i - s & ( i = \tilde{L} ) \end{cases} \end{aligned}\end{split}\]

where \(r\) is the DepreciationRate, \(\tilde{L} = \lceil 1/r\rceil\) the useful life of the asset, and the depreciation coefficient \(f\) is determined by

\[\begin{split}f = \begin{cases} 1.5 & \mbox{for $\frac{1}{4} \leq r < \frac{1}{2}$}\\ 2.0 & \mbox{for $\frac{1}{6} \leq r < \frac{1}{4}$}\\ 2.5 & \mbox{for $r < \frac{1}{6}$}\\ \end{cases}\end{split}\]

Note

The function DepreciationLinearNonRate is similar to the Excel function AMORDEGRC.

Example

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

_p_life := 10 ;
_s_periods := ElementRange(1,_p_life  );
_p_deprec( _i_per ) := DepreciationNonLinearRate(
        PurchaseDate     :  "2024-03-01",
        NextPeriodDate   :  "2025-01-01",
        Cost             :  1e5,
        Salvage          :  1e4,
        Period           :  _i_per,
        DepreciationRate :  0.1,
        Basis            :  1,
        Mode             :  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 : 21316.370243,
  2 : 19670.907439,
  3 : 14753.180579,
  4 : 11064.885435,
  5 :  8298.664076,
  6 :  6223.998057,
  7 :  4667.998543,
  8 :  3500.998907,
  9 :   502.996721 } ;

References