Sum of the Years' Digits Method of Depreciation:
Learning Objectives:
-
Explain the sum of the years'
digits method of depreciation.
Definition and Explanation:
Sum of the Years' Digits Method an accelerated method
of depreciation which is also based on the assumption that the loss in the
value of the fixed asset will be greater during the earlier years and will
go on decreasing gradually with the decrease in the life of such asset. The
SYD is found by estimating an asset's useful life in years, then assessing
consecutive numbers to each year, and totaling these numbers. For n years:
SYD = 1 + 2 + 3 + 4 + ......
+ n
For example if the useful life of an asset
is 5 years, the SYD would be 1 + 2 + 3 + 4 + 5 = 15. Determining the SYD
factor by simple addition can be somewhat laborious for long-lived assets.
For these assets the formula n (n + 1) / 2 where n = the number of periods
in the asset's useful life can be applied to derive the SYD. In our example,
we have:
The yearly depreciation is
then calculated by multiplying the total depreciable amount for the life of
the asset by a fraction whose numerator is the remaining useful life and
whose denominator is the SYD. Thus in our example the calculation would:
| First year
depreciation |
= |
5/15 |
× |
Depreciation cost |
| Second year
depreciation |
= |
4/15 |
× |
Depreciation cost |
| Third year
depreciation |
= |
3/15 |
× |
Depreciation cost |
| Fourth year
depreciation |
= |
2/15 |
× |
Depreciation cost |
| Fifth year
depreciation |
= |
1/15 |
× |
Depreciation cost |
The formula for
depreciation for this method is:
|
Depreciation = Depreciation cost × (Remaining useful life/SYD)
|
Example:
ABC Ltd. purchased a truck for
$65,000 on 1st January 1991. The expected life was 5 years and salvage value
$5,000. Calculate the annual depreciation expense by applying
sum-of-the-years' digits (SYD) method.
Solution:
Amount to be written of =
$65,000 - 5,000 = 60,000
SYD = 1 + 2 + 3 + 4 + 5 = 15
The annual depreciation is:
| First year
depreciation |
= |
5/15 |
× |
60,000 |
= |
20,000 |
| Second year
depreciation |
= |
4/15 |
× |
60,000 |
= |
16,000 |
| Third year
depreciation |
= |
3/15 |
× |
60,000 |
= |
12,000 |
| Fourth year
depreciation |
= |
2/15 |
× |
60,000 |
= |
8,000 |
| Fifth year
depreciation |
= |
1/15 |
× |
60,000 |
= |
4,000 |
| |
|
|
|
|
|
|
| Total |
60,000 |
| |
|
|
|
|
|
|
When the asset is acquired
during the year, the depreciation expense may be determined by dividing the
fractional multipliers between the current and succeeding year. Using the
data in the above example suppose the truck is purchased on 30thJune 1991,
the depreciation is computed as follows:
|
| End
of the year |
Depreciable cost |
|
Years' fraction |
Years' depreciation |
Accumulated depreciation |
Cost |
Book
value |
|
|
1. |
60,000 |
|
5/15 (1/2) |
10,000 |
1,000 |
65,000 |
55,000 |
|
2. |
60,000
60,000 |
] |
5/15 (1/2)
4/15 (1/2) |
10,000
8,000 |
28,000 |
65,000 |
37,000 |
|
3. |
60,000
60,000 |
] |
4/15 (1/2)
3/15 (1/2) |
8,000
6,000 |
42,000 |
65,000 |
23,000 |
|
4. |
60,000
60,000 |
3/15 (1/2)
2/15 (1/2) |
6,000
4,000 |
52,000 |
65,000 |
13,000 |
|
5. |
60,000
60,000 |
] |
2/15 (1/2)
1/15 (1/2) |
4,000
2,000 |
58,000 |
65,000 |
7,000 |
|
6. |
60,000 |
|
1/15 (1/2) |
2,000 |
60,000 |
65,000 |
5,000 |
|
Scope of the Sum of Years' Digits Method (SYD):
As an accelerated depreciation
method, the SYD approach is most appropriate for those situations in which
the asset is judged to render greater utility during its earlier life and
less in its later life.
|
