The depreciation is greatest in the first year and declines each year after that. Finally, the
depreciation in the last year is limited to the amount necessary to reduce book value to residual
value, Br. 2500 = Br.12,500
–
Br.10,000 (i.e. Previous book value minus residual
value).Because, total
depreciation over the life of the asset
is limited to total depreciable
cost/base.
Fractional Period Depreciation
Under this method, fractional years involve a very simple adaptation to the approach presented
above. The first partial year will be a fraction of the annual amount, and all subsequent years
will be the normal calculation (twice the straight-line rate times the beginning year book value).
Assuming from previous example that the plant asset is purchased and put in use on April 1,
year 1.
The depreciation expense of each period would be:
Year
Depreciation expense
*
Accumulated
depreciation
Book value
Year1
37,500
(
100,000 * 50% * 9/12
)
37,500
62,500
Year2
31,250 (
100,000 - $37,500 * 50%)
68,750
31,250
Year3
15,625(
100,000 - $68,750 * 50%)
84,375
15,625

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Chapter 5 / Exercise 40

**Finite Mathematics for the Managerial, Life, and Social Sciences: An Applied Approach**

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Year4
5,625 (
100,000 - $84,375 * 50%)
or
15625
–
10,000 (salvage value)
90,000
10,000
4.
The Sum of Years Digits Method
Like the declining balance method, the sum of the
year‟s digits method
also provides a higher
amount of periodic depreciation expense in the earlier use of the asset and declining
depreciation expense thereafter. This method takes the anticipated life of the asset as the basis
and weights its years most heavily. Under this technique, depreciation expense for a given year
is determined by multiplying the depreciable base by a fraction; the numerator is a digit relating
to the year of use and the denominator is the sum of the year‟s digits.
For example, if there are 5 years in the asset‟s life, the sum of the digits is 15 (5 + 4 + 3 + 2
+1). In the first year 5/15
th
of the depreciable cost of the asset is charged for depreciation. In the
2
nd
year 4/15
th
, and so on until the final year has 1/15
th
charged for depreciation. To save time
in adding up the digits for each asset each year, use the following shortcut to compute the
denominator:
Denominator
=
n (n+1)
2
Where “n” is the
useful life of the asset.
= 5 (5+1)/2 = 30/2 = 15
On the other hand, the numerator of the fraction is the digits representing useful life of the asset
in reverse order or years remaining in the assets life as of the beginning of the year. For
example, if you are depreciating an asset with a 10-year estimated life, the numerator to use at
the end of Year 1 is 10 because that is the number of years remaining in the asset‟s life as of the
beginning of the first year. The numerator to use at the end of Year 2 is 9, because that is the
number of years remaining in the asset‟s life as of the beginning of Year 2. Because the
numerator changes each year, the SYD depreciation rate also changes each year.