HomeDefinitionsInvesting DictionarySum of the Years Digits Depreciation

# Sum of the Years Digits Depreciation

## Definition

The financial accounting term sum of the years’ digits depreciation refers to one of several methods of allocating the cost of an asset over its expected lifetime. The sum of the years’ digits approach is an accelerated method of depreciation and is based on the assumption an asset’s value declines at a greater rate in the early years of its serviceable life.

### Calculation

Sum of the Years’ Digits = (Life of Asset^2 + Life of Asset) /2

Depreciation Rate (%) = Remaining Life / Sum of the Years’ Digits

Note: Unlike the double declining balance approach, the sum of the years’ digits method takes into account the asset’s salvage value when determining annual depreciation expense.

### Explanation

The sum of the years’ digits approach to depreciation is an accelerated technique since it results in higher depreciation values in the early years of the asset’s life relative to the straight line method. This technique is based on the assumption an asset provides greater value when it is newer.

The sum of the years’ digits approach takes into consideration the salvage value of the asset when calculating the annual depreciation expense. With this method, the depreciation rate is always a fraction. In any given accounting period, the numerator would contain the remaining life of the asset while the denominator would contain the sum of the years’ digits.

Depreciation is an accounting method of cost allocation. It is used to allocate the cost of an asset over its useful life. It’s also referred to as a non-cash expense because the cash used to buy the asset left the company when it was purchased. Depreciation allows the cost of a balance sheet item (an asset) to flow smoothly to the income statement (an expense) over its serviceable life.

### Example

Company A purchases a backup generator for \$200,000. The estimated service life is projected to be 10 years. The generator is predicted to have a scrap value of \$50,000 at the end of its serviceable life. The first step with this method involves the calculation of the sum of the years’ digits:

= (10^2 + 10) / 2 = (100 + 10) / 2 = 110 / 2, or 55

The depreciation rate in the first year of operation can now be calculated as:

= 10 / 55, or 0.1818

This rate is then applied to the asset’s depreciable balance:

= 0.1818 x (\$200,000 – \$50,000) = 0.1818 x \$150,000, or \$27,273

In Year 2, the depreciation rate would be:

= 9 / 55, or 0.1636

Once again, this rate is then applied to the asset’s depreciable balance:

= 0.1636 x (\$200,000 – \$50,000) = 0.1636 x \$150,000, or \$24,545

A complete sum of the years’ digits depreciation schedule for this asset is shown below:

 Depreciation Expense Accumulated Depreciation Book Value Year 0 \$200,000 Year 1 \$27,273 \$27,273 \$172,727 Year 2 \$24,545 \$51,818 \$148,182 Year 3 \$21,818 \$73,636 \$126,364 Year 4 \$19,091 \$92,727 \$107,273 Year 5 \$16,364 \$109,091 \$90,909 Year 6 \$13,636 \$122,727 \$77,273 Year 7 \$10,909 \$133,636 \$66,364 Year 8 \$8,182 \$141,818 \$58,182 Year 9 \$5,455 \$147,273 \$52,727 Year 10 \$2,727 \$150,000 \$50,000