UK Ver.

1/TK

Note about depreciation methods

This is a supplementary note for the textbook chapter 7, Harrison et al, ”Financial Accounting”, 11th ed.

Depreciation in the financial statements

Depreciations are based on answers to the following questions:

How big is the depreciation basis?

The depreciation basis is the cost price A minus the scrap value S, i.e. the total expected loss in value of the
asset. The cost price A is the acquisition sum as well as purchase and installation expenses, cf. ÅRL §40 and
IAS 16, and the scrap value or residual value or salvage value S is the expected value of the asset after the
end of its useful life. The cost price A is quite objective, while the residual value S is an expected amount and
thus a subjective estimate. The depreciation basis, i.e. the difference between A and S, thus also becomes
somewhat subjective. In practice, S is often set equal to 0.

How long is the usage period?

When commissioning, the company must determine the period of use, i.e. how long it expects to use the
asset. The useful life often coincides with the economic life of the asset. Estimating a fixed asset’s economic
lifetime is subject to uncertainty. The estimate must e.g. take into account the asset's capacity and expected
production, expected wear and tear and maintenance, technical obsolescence, possible limitations in the
asset's use and lessons learned from similar assets. If the useful life does not coincide with the economic life,
e.g. if the company plans to dispose of the asset sooner than the end of the economic life, the depreciation
period is the shorter useful life. The residual value will then be correspondingly higher.

Which depreciation method should be chosen?

A depreciation method is a calculation procedure that reduces the book value B from A to S during the
economic life, so that you can pre-calculate an arbitrary Bt (t = 1,2, …, n) that indicates the book value at the
end of year t, as well as dt (t = 1,2, … , n), which indicates the depreciation amount to be attributed to year t
(the difference Bt-1 – Bt).

The ideal is that each year's depreciation amount is, as far as possible, proportional to the fraction of the
fixed asset's total income that is consumed in the year in question, i.e. loss of value for the year. This loss in
value is often assumed to be a simple function of time, so this note will concentrate here on time-based
depreciation methods that only allow an asset's annual depreciation and its book value to depend on its age.

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Depreciation methods
Straight line method
The straight-line method is suitable for depreciation on fixed assets that are expected to be used roughly
equally in each of the accounting years during the useful life. A fixed amount is written off per year. It is
assumed that A, S and n are known and then Bt (the book value at the end of year t) and dt (the depreciation
amount for year t) are sought.

The formulas for calculating dt and Bt are given below:

𝐴−𝑆
𝑑𝑡 =
𝑛
𝑡
𝐵𝑡 = 𝐴 − 𝑛 (𝐴 − 𝑆)

Sum-of-Years-Digits (SYD) method

The method is best explained with an example: If the lifetime of an asset is 3 years, 3/6 is depreciated in the
first year, 2/6 in the second year, and 1/6 in the last year. The denominator of 6 is obtained by adding up the
individual years: year 1 + year 2 + year 3 = 6. The numerator indicates the number of years remaining at the
beginning of the depreciation year. If this method is used, the annual depreciation amount is calculated as a
decreasing fraction of the total depreciation amount (A – S). The method results in depreciation with a
decreasing amount year by year.

The formulas for calculating dt and Bt are given below:

𝑛−(𝑡−1)
𝑑𝑡 = 𝑛(𝑛+1)/2 × (𝐴 − 𝑆)
𝑡

𝑛 − (𝑡 − 1)
𝐵𝑡 = 𝐴 − ∑ ( × (𝐴 − 𝑆))
𝑛(𝑛 + 1)
2
𝑡=1

The declining balance method

The basic idea of the declining balance method is that a constant percentage of each year’s beginning book
value is written off. The year's depreciation is therefore obtained as book value at the beginning times the
depreciation percentage. It is again assumed that A, S, and n are known and now seek the value of the
depreciation rate p, which brings B from A to S over n years.

The formula that determines p is given below:

𝑛 𝑆
𝑝 = 1 − √𝐴

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A prerequisite for meaningful use of the declining balance method is that the residual value (S) is positive
and less than A, which is a realistic prerequisite in many cases. If S=0 or negative, the method makes no sense
because p is either not meaningful or cannot be determined at all, cf. the formula for p. Then an approximate
declining balance method is used, or you switch to straight-line depreciation after using the declining balance
method in the first years of life. With the pure balance method, Bt is depreciated with a fixed percentage p
over the entire useful life.
The SYD method and the declining balance method are suitable for depreciation of fixed assets that are
thought to be heavily used at the beginning of the economic life and with decreasing intensity towards the
end of the life.

Example
The production company Brage A/S buys a new machine on 1/1 20X1. The acquisition price and installation
costs amount to DKK 32,000. (A = 32,000), which corresponds to the book value primo (B0). It is estimated
that the machine can be used for 5 years (n = 5), and that the residual value after the five years will be DKK
1,000 (S = 1,000).

Straight line method

If Brage expects to use the machine roughly equally in each of the five years, the straight-line method would
be an appropriate basis for depreciation. The annual depreciation is calculated below:

𝐴 − 𝑆 32,000 𝑘𝑟. −1,000 𝑘𝑟.

𝑑1 = = = 6,200 𝑘𝑟.
𝑛 5

The figures for the income statement and balance sheet appear in Panel A in the table below. Alternatively,
you can show the assets in the balance sheet as the difference between the acquisition price A and the
accumulated depreciation at the balance sheet date, so that the information about the original purchase
price is not lost. It is the one used in the fixed asset note, and is shown in Panel B below:

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 Straight line method
Panel A: Effect in the income statement and balance sheet
Year Book value beginning Depreciation for the year Book value at year-end
year (income statement) (balance sheet)
1 32,000 6,200 25,800
2 25,800 19,600
6,200
3 19,600 13,400
6,200
4 13,400 7,200
6,200
5 7,200 1,000 (=S)
6,200
Panel B: Information for the fixed asset note
Year Acquisition amount Accumulated depreciation Book value at year-end
1 32,000 6,200 25,800
2 32,000 12,400 19,600
3 32,000 18,600 13,400
4 32,000 24.800 7,200
5 32,000 31,000 1,000 (= S)
Panel C: Graphic design

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Sum-of-Years-Digits (SYD) method
If Brage expects a large utilization of the machine at the beginning and then that the utilization decreases by
a constant fraction, Brage can e.g. apply the SYD method:
5 5
𝑑1 = × (32,000 − 1,000)𝑘𝑟. = × 31,000𝑘𝑟. = 10,333𝑘𝑟.
5(5 + 1) 15
2
(5 − (2 − 1)) 4
𝑑2 = × (32,000 − 1,000)𝑘𝑟. = × 31,000𝑘𝑟. = 8,267𝑘𝑟.
5(5 + 1) 15
2

The figures for the profit and loss account and balance sheet appear in Panel A in the table below, and the
information for the fixed asset note appears in Panel B:

Sum-of-Years-Digits (SYD) method

Panel A: Effect in the income statement and balance sheet
Year Book value beginning year Depreciation for the year Book value at year-end
(income statement) (balance sheet)
1 32,000 10,333 21,667
2 21,667 8,267 13,400
3 13,400 6,200 7,200
4 7,200 4,133 3,067
5 3,067 2,067 1,000 (= S)
Panel B: Information for the fixed asset note
Year Acquisition amount Accumulated depreciation Book value at year-end
1 32,000 10,333 21,667
2 32,000 18,600 13,400
3 32,000 24,800 7,200
4 32,000 28,933 3,067
5 32,000 31,000 1,000 (= S)

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 Panel C: Graphic design

The declining balance method

If Brage expects high utilization of the machine while it is new and then a steadily decreasing utilization rate,
the declining balance method may be another suitable method that provides a depreciation course very
similar to that of the SYD method.

The given information leads to a depreciation percentage of:

𝑛 𝑆 5 1,000
𝑝 =1− √ =1− √ = 0.5
𝐴 32,000

The figures for the profit and loss account and balance sheet appear in Panel A in the table below, and the
information for the fixed asset note appears in Panel B:

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 The declining balance method
Panel A: Effect in the income statement and balance sheet
Year Book value beginning year Depreciation for the year Book value at year-end
(income statement) (balance sheet)
1 32,000 16,000 16,000
2 16,000 8,000 8,000
3 8,000 4,000 4,000
4 4,000 2,000 2,000
5 2,000 1,000 1,000 (=S)
Panel B: Information for the fixed asset note
Year Acquisition amount Accumulated depreciation Book value at year-end
1 32,000 16,000 16,000
2 32,000 24,000 8,000
3 32,000 28,000 4,000
4 32,000 30,000 2,000
5 32,000 31,000 1,000 (=S)
Panel C: Graphic design

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