# Sum of years digits method

Sum of years digits method

Sum of years digits method is one of the degressive depreciation methods in the balance sheet law (P. Brown, 2008, pp.17 – 21). Annual depreciation is calculated using this method by multiplying the initial value of the asset (less the recovery value) by the fraction that varies from one year to the next. Fracture counter: This is the number of years for which an asset will still be in use (P. Brown, 2008, pp.17 – 21). In subsequent years, the counter will decrease by 1. Fracture denominator: is the sum of digits of the total useful life of an asset, e.g. 1+2+3+4+5 = 15, when the asset will be used by the company for 5 years. The denominator can be calculated from the formula (P. Brown, 2008, pp.17 – 21)$\text {(n(n+1))/2}$ n – number of years of use of the measure

The name sum of years digits method is not correct for operating periods longer than 9 years (because 10, 11 and more are not digits), therefore the name sum of amortisation periods method is used in such cases (P. Brown, 2008, pp.17 – 21).

## Example

What is the depreciation schedule for a truck using the sum of annual numbers method, if its initial value was 360 000, the recovery value is 80 000 and the depreciation period is 5 years.

The depreciation schedule is presented in the table below (P. Brown, 2008, pp.17 – 21).

year annual write-down amortization existing discontinuance book value of the measure (net)
1 5/15*280 000 ≈ 93 333,33 93 333,33 266 666, 67
2 4/15*280 000 ≈ 74 666,66 167 999,99 192 000,01
3 3/15*280 000 = 56 000 223 999,99 136 000, 01
4 2/15*280 000 ≈ 37 333,33 261 333,32 98 666,01
5 1/15*280 000 + 0,02 ≈ 18 666,68 280 000 80 000

In the last year, 2 cents were added to the depreciation level to compensate for earlier rounding and to give a net value equal to the recovery value (P. Brown, 2008, pp.17 – 21). This method is based on the fact that the years of expected use of the fixed asset are added (e.g. 40 years i.e. 1+2+3+4+5+...+40=820). Their sum is the denominator. The numerator shall be the consecutive years of use in reverse order (P. Brown, 2008, pp.17 – 21). This method is particularly appropriate for those measures that deliver proportionally higher profits in the first years of their life, e.g. high-tech equipment (computers). It is particularly useful for the depreciation of assets, where wear and tear due to technical progress is an important factor (P. Brown, 2008, pp.17 – 21).

## Assets and amortization

In balance sheet and tax law, amortization means the cost associated with the gradual wear and tear of fixed assets and intangible assets. Amortization is a cost that is not related to cash outflow. Amortization is connected with the concept of depreciation (G. Pichop, 2009, pp. 52-54). Amortization is the consumption of a fixed asset (intangible asset) expressed in terms of value from the beginning of its use. Amortization is the otherwise accumulated (cumulative) depreciation (G. Pichop, 2009, pp. 52-54). For example, an item of property, plant and equipment has a cost of €6,000. Amortization in the first year of use was €1,200, and in the second year also €1,200. The depreciation of a fixed asset after two years of use amounts to 2,400 €. Fixed assets are: tangible fixed assets and equalized with them, with the expected period of economic usefulness longer than one year, complete, fit for use and intended for the needs of the entity (to conduct operations). In particular, they include them (G. Pichop, 2009, pp. 52-54):

• real estate - including land, perpetual usufruct of land, buildings and structures, as well as premises being a separate property, cooperative ownership right to a dwelling unit and cooperative right to a usable unit
• machines, equipment, means of transport and other things
• improvements in third-party fixed assets
• livestock

The inclusion or non-inclusion of an asset in fixed assets is not determined by its value. In addition to fixed assets, intangible assets are also depreciated, i.e. non-monetary, not physically present, identifiable fixed assets used in the production process, supplies of goods and services, i.e. for operating activities, which are not investment assets (e.g. computer software, development costs, licences, patents, trademarks, goodwill, etc.) (G. Pichop, 2009, pp. 52-54) . The balance sheet law approaches some issues related to amortization slightly differently than the tax law. Differences include, but are not limited to, the timing of the commencement of amortization exclusions from amortization and amortization rates and methods (G. Pichop,2009, pp. 52-54). Property, plant and equipment and intangible assets are depreciated not earlier than at the moment of putting them into use. Therefore, e.g. fixed assets under construction are not amortizated (G. Pichop, 2009, pp. 52-54). Example: An enterprise has purchased a machine. The machine must be installed. Depreciation of an item of property, plant and equipment should commence only after the installation (commissioning) has been completed (G. Pichop, 2009, pp. 52-54).

## Amortization method

The amortization method shall reflect the pattern in which the benefit of the depreciable asset is derived. Balance sheet law does not prescribe a particular depreciation method. In practice, entities use it for financial reporting purposes(L.C.,de Freitas et al., 2007,pp.8-9):

• straight-line method
• degressive methods (accelerated double digit, sum of annual digits)
• progressive methods
• methods based on inputs and outputs (working hours method, fixed asset productivity method)

The depreciation method used does not affect the total amount of depreciation, which will always be equal to the replacement value of the asset. However, it determines not only the length of the depreciation period, but also the amount of the tax burden, which is a consequence of the amount of income earned(L.C.,de Freitas et al., 2007,pp.8-9).

## Sum of years digits method as degressive method

Degressive methods (accelerated methods) are methods that recognise higher depreciation charges over earlier periods of assets useful lives when they provide more benefits because they are more efficient and require less repair and maintenance (V. D. Giudice, B Manganelli., 2016, pp.214). The benefits of these assets are assumed to diminish over time and depreciation amounts are assumed to decrease. In practice, fast-track methods use the fast-track double method and the sum of annual digits (S.B. Jackson, X. K. Liu, 2009,  pp. 56).

## References

Author: Dawid Misiura

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