# Sum of the years' digits | Depreciation Method

## Definition

Sum of the years' digits depreciation method involves calculating depreciation based on the sum of the number of years in an asset's useful life.

## Explanation

Sum of the years' digits depreciation method, like reducing balance method, is a type of accelerated depreciation technique that allocates higher depreciation expense in the earlier years of an asset's useful life.

Calculation of depreciation under this method can be summarized in the following 4 steps:

### Step 1: Calculate the sum of the years' digits in an asset's useful life

For an asset having a useful life of 4 years, the sum of the years' digits will be calculated as follows:

Sum of years' digits = 4 + 3 + 2 + 1 = 10

### Step 2: Calculate the depreciable amount

Depreciable amount, as with all depreciation methods, is equal to:

• Asset's cost of acquisition or construction including any subsequent capital expenditure
• Less: Estimated residual value or scrap value at the end of the asset's useful life

### Step 3: Calculate the un-depreciated useful life

Un-depreciated useful life is equal to the number of years in the asset's useful life that have not yet been subjected to depreciation.

Hence, for an asset that has a useful life of 4 years, the un-depreciated useful life to be used in calculating depreciation shall be 4 years in the first year of depreciation, 3 years in the second year and so on.

### Step 4: Calculate depreciation using the sum of years' digits & un-depreciated useful life

Depreciation using the sum of the years' digits method can be calculated using the following formula:

 Depreciation Expense = Un-depreciated useful life (Step 3) x Depreciable Amount (Step 2) Sum of the years' digits (Step 1)

## Example

Following information relates to a fixed asset:

 Cost \$100,000 Residual Value \$10,000 Useful Life 3 Years

Calculate depreciation over the useful life of the asset using the sum of the years' digits method.

Step 1: Calculate the sum of the years digits

Sum of the years' digits = 3 + 2 + 1 = 6

Step 2: Calculate the depreciable amount

Depreciable amount = \$100,000 - \$10,000 = \$90,000

Step 3: Calculate the un-depreciated useful life

 Year 1 Year 2 Year 3 Un- depreciated useful life (years) 3 2 1

Step 4: Calculate depreciation expense

Year 1: Depreciation expense:

 = 3 (Step 3) x \$90,000 (Step 2) 6 (Step 1)

=    \$45,000

Year 2: Depreciation expense:

 = 2 (Step 3) x \$90,000 (Step 2) 6 (Step 1)

=    \$30,000

Year 3: Depreciation expense:

 = 1 (Step 3) x \$90,000 (Step 2) 6 (Step 1)

=    \$15,000

Note: Over the life of the asset, the total depreciation charge equals to the depreciable amount , i.e. \$90,000 (Step 2). Also note that the amount of annual depreciation progressively declines as the asset ages. This method of depreciation is therefore appropriate for assets whose utility and productiveness is greater in the earlier years of their life (e.g. computer equipment).

Where an entity has a policy of calculating depreciation on full years basis, sum of the years' digits depreciation can be calculated as above. If however, depreciation is to be calculated on monthly basis, it will usually be necessary to time apportion the depreciation charge between accounting periods since it is unusual for the date of acquisition of an asset to coincide with the start of an accounting period (unfortunately).

Try to apply your knowledge to calculate depreciation under the sum of digits method for an asset acquired mid-way during an accounting period in the multiple-choice question below. 