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Sum of the Years' Digits Method of

Depreciation:

Learning Objectives:

1. 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 isalso 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 thedecrease 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 thesenumbers. 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 laboriousfor 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 ourexample, we have:

5(5 + 1)

=

30 =15

2 2

The yearly depreciation is then calculated by multiplying the total depreciableamount 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 calculationwould:

First year depreciation = 5/15 Depreciation costSecond year depreciation = 4/15 Depreciation cost

Third year depreciation = 3/15 Depreciation costFourth 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:

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ABC Ltd. purchased a truck for $65,000 on 1st January 1991. The expected life was5 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 = 16,000Third year depreciation = 3/15 60,000 = 12,000

Fourth year depreciation = 2/15 60,000 = 8,000Fifth 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 andsucceeding year. Using the data in the above example suppose the truck is

purchased on 30thJune 1991, the depreciation is computed as follows:

End of theyear

Depreciablecost Years' fraction

Years'depreciation

Accumulateddepreciation

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 37,0003. 60,000

60,000 ]4/15 (1/2)3/15 (1/2)

8,0006,000 42,000 65,000 23,000

4. 60,00060,000

3/15 (1/2)2/15 (1/2)

6,0004,000 52,000 65,000 13,000

5. 60,00060,000 ]

2/15 (1/2)1/15 (1/2)

4,0002,000 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.