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

Degressive method

Decreasing annual amortization
Higher tax savings

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

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

Year	Depreciable base	Annuity	Cumulated annuities	Net Book Value
N	25000	5000	5000	20000
N+1	25000	5000	10000	15000
N+2	25000	5000	15000	10000
N+3	25000	5000	20000	5000
N+4	25000	5000	25000	0

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

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

Used days explanation Image

Year	Depreciable base	Annuity	Cumulated annuities	Net Book Value
N	25000	1916,66	1916,66	23083,34
N+1	25000	5000	6916,66	18083,34
N+2	25000	5000	11916,66	13083,34
N+3	25000	5000	16916,66	8083,34
N+4	25000	5000	21916,66	3083,34
N+5 Complementary annuity	25000	3083,34	25000	0

Degressive method

Case 1

Duration	Original Coefficient
Between 3 and 4 years	1.25
Between 5 and 6 years	1.75
More than 6 years	2.25

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

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

Degressive Annuity rate = $R_L \times \text{Original Coefficient} = \frac{100\%}{\text{Duration of use}} \times \text{Original Coefficient}$

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

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

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

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

Degressive Annuity rate $= 20\%\times1.75 = 35\%$

$R_\text{CL} \text{vs} R_D$	Year	Depreciable base	Annuity	Cumulated annuities	Net Book Value
20% $<$ 35%	N	25000	8759	8750	16250
25% $<$ 35%	N	16250	5687.5	14437.5	10562.5
33% $<$ 35%	N	10562.5	3696.87	18134.37	6865.62
50% $<$ 35%	N	6865.62	3432.81	21567.18	3432.81
100% $>$ 35%	N	3432.81	3432.81	25000	0

Case 2

Duration	Original Coefficient
Between 3 and 4 years	1.25
Between 5 and 6 years	1.75
More than 6 years	2.25