The sum of the years digits depreciation method (SYD depreciation) is used to calculate the annual depreciation expense of a fixed asset.

The purpose of using the sum of the years digits depreciation method is to produce a depreciation expense which is higher in the earlier years than in the later years of the assets useful life, as such it can be classified as an accelerated depreciation method.

The method takes the total depreciation over the useful life of the asset and allocates this to each year in proportion to the remaining life of the asset at the beginning of the year.

## Sum of the Years Digits Depreciation Formula

The depreciation charge for a particular year is given by the sum of the years digits depreciation formula as follows:

Where:

**Total depreciation** is the cost of the asset less the salvage value.

**Remaining life** is the useful life remaining at the **beginning** of the year.

**SYD useful life** is the sum of the years digits for the useful life

Since the remaining life is declining each year, the depreciation charge will decline each year.

## Calculation of SYD

The sum of years digits (SYD) is simply the sum of the year numbers. So for example, if there are 3 years then the sum of years digits is equal to 1+2+3 = 6, if there are 8 years then the SYD is equal to 1+2+3+4+5+6+7+8 = 36. This process can be summarized in the sum of years digits formula as follows:

Where:

**n** is the number of years.

For example if there are 8 years as above,

Useful life = 8 years SYD = n x (n + 1) / 2 SYD = 8 x (8 + 1) / 2 SYD = 36

## Sum of the Years Digits Depreciation Example

Suppose a business purchases an asset costing 9,000 with an estimated salvage value of 1,000 after a useful life of 4 years.

### Step 1: Calculate SYD

The first step is to calculate the sum of the years digits (SYD) for the useful life of the asset using the sum of years digits formula.

Useful life = 4 years SYD useful life = n x (n + 1) / 2 SYD useful life = 4 x (4 + 1) / 2 SYD useful life = 10

### Step 2: Calculate Total Depreciation

The next step is to calculate the total depreciation required over the lifetime of the asset, which is simply the cost of the asset less its salvage value.

Cost = 9,000 Salvage value = 1,000 Total depreciation = Cost - Salvage value Total depreciation = 9,000 - 1,000 Total depreciation = 8,000

### Step 3: Allocate Depreciation to Years

The final step is to allocate this total depreciation to each of the years of its useful life in proportion to the remaining life of the asset at the beginning of the year using the sum of the years digits depreciation formula.

Total depreciation = 8,000 SYD useful life = 10Year 1Remaining life at start of the year = 4 Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life Sum of the years digits depreciation = 8,000 x 4 / 10 Sum of the years digits depreciation = 3,200Year 2Remaining life at start of the year = 3 Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life Sum of the years digits depreciation = 8,000 x 3 / 10 Sum of the years digits depreciation = 2,400Year 3Remaining life at start of the year = 2 Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life Sum of the years digits depreciation = 8,000 x 2 / 10 Sum of the years digits depreciation = 1,600Year 4Remaining life at start of the year = 1 Sum of the years digits depreciation = Total depreciation x Remaining life / SYD useful life Sum of the years digits depreciation = 8,000 x 1 / 10 Sum of the years digits depreciation = 800

The table below summarizes the breakdown of the depreciation expenses for each year.

Notice that the depreciation is highest in the first year and is declining each year which means that the sum of the years digits depreciation is an accelerated depreciation method. In addition the total depreciation is 8,000 which is the same as the cost less the salvage value of the asset.

Our sum of years digits depreciation calculator is available and can be used to calculate the depreciation expense by entering details relating to the cost of the asset, the asset salvage value at the end of its useful life, and the number of periods in the useful lifetime.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.