Function DepreciationNonLinearLife(PurchaseDate, NextPeriodDate, Cost, Salvage, Life, Period, Basis, Mode)

DepreciationNonLinearLife

The function DepreciationNonLinearLife returns the depreciation of an asset for the specified period, using fixed declining balance depreciation. The accounting periods have a length of one year, but they don’t necessary need to start January 1. The depreciation amounts decline by a fixed rate for every succeeding period.

DepreciationNonLinearLife(
    PurchaseDate,             ! (input) scalar string expression
    NextPeriodDate,           ! (input) scalar string expression
    Cost,                     ! (input) numerical expression
    Salvage,                  ! (input) numerical expression
    Life,                     ! (input) numerical expression
    Period,                   ! (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 \([0, Cost)\).

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.

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.

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 DepreciationNonLinearLife returns the depreciation of an asset for the specified period.

Equation

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

\[\begin{split}\begin{aligned} \tilde{d_1} &= \begin{cases} f_{PN}rv_1 & \mbox{for $\textit{Mode} = 0$}\\ \left(1-(1-r)^{f_{PN}}\right)v_1 & \mbox{for $\textit{Mode} = 1$} \end{cases} \\ \tilde{d_i} &= rv_i \qquad\qquad (i \neq 1) \end{aligned}\end{split}\]

where the depreciation rate \(r\) equals

\[r = 1 - \left(\frac{s}{c}\right)^{1/L}\]

Note

The function DepreciationLinearNonLife is similar to the Excel function DB.

Example

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

_p_life := 10 ;
_s_periods := ElementRange(1,_p_life+1  );
_p_deprec( _i_per ) := DepreciationNonLinearLife(
    PurchaseDate     :  "2024-03-01",
    NextPeriodDate   :  "2025-01-01",
    Cost             :  1e5,
    Salvage          :  1e4,
    Life             :  _p_life,
    Period           :  _i_per,
    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 : 17459.581473,
   2 : 16976.233585,
   3 : 13484.701656,
   4 : 10711.279262,
   5 :  8508.271548,
   6 :  6758.360319,
   7 :  5368.356422,
   8 :  4264.237080,
   9 :  3387.203912,
  10 :  2690.551704,
  11 :   391.223038 } ;

References