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Classic

Amortization

Amortization

  • Recognition of a decline in the value of an assets
  • NON-CASH expense in the income statement
  • calculated expense

Depreciable asset

  • tangible assets (except land, work of art, and historical artifacts)
  • intangible assets (patents, licenses, softwares)

Financial assets = not depreciable

Authorization period

Period of use of the asset

  • Equipment: between 6 and 10 years
  • Transport equipment: between 4 and 5 years
  • Software & Hardware: 3 years

Amortization Schedule

  • Original Value (cost of the asset excluding VAT)
  • Amortization annuity (amount of the amortization expense each year)
  • Normal duration of use (number of years of use of the asset fixed by the fiscal authorities)
  • Amortization rate: 100% / Normal duration of use
  • Net Book Value: Original Value - Cumulative amortization annuities = annual depreciation

Methods of amortization

Linear method

Linear method Image Linear method Image

Degressive method

  • Decreasing annual amortization
  • Higher tax savings

Degressive method Image Degressive method Image

Example

Purchase of a machine $25000, duration of use 5 years

  • Case 1: date = 1 January N
  • Case 2: date = 12 August N

Linear method

Case 1

Annuity rate = 100%Duration of use\frac{100\%}{\text{Duration of use}}
Amortization annuity = Annuity rate×Original Value\text{Annuity rate} \times \text{Original Value}
Net Book Value = Original ValueCumulated annuities\text{Original Value} - \text{Cumulated annuities}
or
Net Book Value = Depreciable BaseCumulated annuities\text{Depreciable Base} - \text{Cumulated annuities}

Amortization rate=100%5=20% = \frac{100\%}{5}=20\%
Amortization annuity=20%×$25000=$5000 = 20\%\times\$25000 = \$5000

YearDepreciable baseAnnuityCumulated annuitiesNet Book Value
N250005000500020000
N+12500050001000015000
N+22500050001500010000
N+3250005000200005000
N+4250005000250000

Case 2

Annuity rate = 100%Duration of use\frac{100\%}{\text{Duration of use}}
Amortization annuity = Annuity rate×Original Value\text{Annuity rate} \times \text{Original Value}
Net Book Value = Original ValueCumulated annuities\text{Original Value} - \text{Cumulated annuities}
or
Net Book Value = Depreciable BaseCumulated annuities\text{Depreciable Base} - \text{Cumulated annuities}
Annuity for the first year = Annuity rate×Original Value×Number of used days360\text{Annuity rate} \times \text{Original Value} \times \frac{\text{Number of used days}}{360}

Amortization rate=100%5=20% = \frac{100\%}{5}=20\%
Amortization annuity=20%×$25000=$5000 = 20\%\times\$25000 = \$5000
Annuity for the first year=20%×$25000×4×30+(3012)360=$1916,66 = 20\%\times\$25000 \times \frac{4\times30+(30-12)}{360} = \$1916,66

Used days explanation Image Used days explanation Image

YearDepreciable baseAnnuityCumulated annuitiesNet Book Value
N250001916,661916,6623083,34
N+12500050006916,6618083,34
N+225000500011916,6613083,34
N+325000500016916,668083,34
N+425000500021916,663083,34
N+5
Complementary annuity
250003083,34250000

Degressive method

Case 1

DurationOriginal Coefficient
Between 3 and 4 years1.25
Between 5 and 6 years1.75
More than 6 years2.25

Linear Annuity rate = 100%Duration of use=RL\frac{100\%}{\text{Duration of use}} = R_L

Compared Linear Annuity rate = 100%Remaining years=100%N - Current year=RCL\frac{100\%}{\text{Remaining years}} = \frac{100\%}{\text{N - \text{Current year}}} = R_{CL}

Degressive Annuity rate = RL×Original Coefficient=100%Duration of use×Original CoefficientR_L \times \text{Original Coefficient} = \frac{100\%}{\text{Duration of use}} \times \text{Original Coefficient}

Amortization annuity = Annuity rate×Original Value\text{Annuity rate} \times \text{Original Value}

Net Book Value = Original ValueCumulated annuities\text{Original Value} - \text{Cumulated annuities}

or

Net Book Value = Depreciable BaseAnnuity\text{Depreciable Base} - \text{Annuity}

Linear Amortization rate=100%5=20% = \frac{100\%}{5}=20\%

Degressive Annuity rate=20%×1.75=35% = 20\%\times1.75 = 35\%

RCLvsRDR_\text{CL} \text{vs} R_D YearDepreciable baseAnnuityCumulated annuitiesNet Book Value
20%<<35%N250008759875016250
25%<<35%N162505687.514437.510562.5
33%<<35%N10562.53696.8718134.376865.62
50%<<35%N6865.623432.8121567.183432.81
100%>>35%N3432.813432.81250000

Case 2

DurationOriginal Coefficient
Between 3 and 4 years1.25
Between 5 and 6 years1.75
More than 6 years2.25

Linear Annuity rate = 100%Duration of use=RL\frac{100\%}{\text{Duration of use}} = R_L

Compared Linear Annuity rate = 100%Remaining years=100%N - Current year=RCL\frac{100\%}{\text{Remaining years}} = \frac{100\%}{\text{N - \text{Current year}}} = R_{CL}

Degressive Annuity rate = RL×Original Coefficient=100%Duration of use×Original CoefficientR_L \times \text{Original Coefficient} = \frac{100\%}{\text{Duration of use}} \times \text{Original Coefficient}

Amortization annuity = Annuity rate×Original Value\text{Annuity rate} \times \text{Original Value}

Net Book Value = Original ValueCumulated annuities\text{Original Value} - \text{Cumulated annuities}

or

Net Book Value = Depreciable BaseAnnuity\text{Depreciable Base} - \text{Annuity}

Annuity for the first year = Annuity rate×Original Value×Number of used months360\text{Annuity rate} \times \text{Original Value} \times \frac{\text{Number of used months}}{360}

Linear Amortization rate=100%5=20% = \frac{100\%}{5}=20\%

Degressive Annuity rate=20%×1.75=35% = 20\%\times1.75 = 35\%

Annuity for the first year=35%×$25000×4×30+(3012)360=$3354,16 = 35\%\times\$25000 \times \frac{4\times30+(30-12)}{360} = \$3354,16

RCLvsRDR_\text{CL} \text{vs} R_D YearDepreciable baseAnnuityCumulated annuitiesNet Book Value
20%<<35%N250003354.163354.1621645.84
25%<<35%N21645.847576.0410930,2014069.79
33%<<35%N14069.794924.4215854.639145.36
50%<<35%N9145.364572.6820427.314572.68
100%>>35%N4572.684572.68250000

Accounting Documents

Recording Book

Recording book Image Recording Book Image

Income Statement

Income Statement Image Income Statement Image

Balance Sheet

Balance Sheet Image Balance Sheet Image

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