12/08/2008 23:24

# 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 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:

 5(5 + 1) = 30 = 15 2 2

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.