# Sum of the years digits: A depreciation guide

How do you calculate the sum of the years' digits method of depreciation? What are the pros and cons of sum of the years' digits versus straight line depreciation. Find out if sum of the years' digits is right for your business.

by Alicia Tuovila
updated May 11, 2023 ·  3min read

As a small business owner, you are well acquainted with the tax deduction for depreciation. In addition to the tax benefit depreciation provides, it also allows you to track and decrease the value of your assets over their useful life. When you depreciate an asset, you recognize an expense that represents the value of the asset used during the period.

The most common method of depreciation is straight-line. Straight-line depreciation recognizes the same amount of depreciation each period over the useful life of the asset. On the other hand, accelerated depreciation methods recognize a larger percentage of the total depreciation in earlier periods. This has the tax advantage of allowing a larger depreciation deduction faster.

The two most common accelerated depreciation methods are double-declining balance and the sum of the years' digits. Here's a depreciation guide and overview of the sum of the years' digits method. ## How to calculate sum of the years' digits method of depreciation

There are multiple steps involved in calculating the sum of the years' digits. For the calculation, you will need to know the total useful life of the asset. The useful life is how long you expect the asset will be useable before it is fully depreciated. The Internal Revenue Service (IRS) offers a list of useful lives, referred to as recovery periods, by classification of asset.

You will also need to know your cost basis—your purchase price plus any extra costs you incurred such as sales tax or shipping and handling charges—and the salvage value—how much you anticipate you can receive upon selling or scrapping the asset at the end of its useful life.

### Step 1: Denominator

Take each of the years in the asset's useful life and add them together. For example, if an asset has a useful life of 10 years, the total is 55— 10 + 9 + 8 + 7 + 6 + 5+ 4 + 3 + 2 + 1. Hint: the formula N (N+1) / 2 is a quick way to calculate the sum of all numbers from 1 to N. If you have a long useful life, this can save you time. The sum of these numbers becomes the denominator in the percentage calculation for your annual depreciation.

### Step 2: Numerator

Work backward from the largest digit in the asset's useful life. Using the 10-year example, start with the digit 10 in year one. In year two, you'll use nine and so on. This number becomes the numerator in the percentage calculation for your annual depreciation.

### Step 3: Sum of the years' digits depreciation formula and example

The sum of the years' digits depreciation formula is:

(Current year / sum of the years' digits) x (cost basis - salvage value) = depreciation expense

For example, assume you purchased a \$130,000 machine for your business with an estimated useful life of five years. You anticipate it will be resold for \$30,000 at the end of its useful life. The cost basis minus salvage value is \$100,000. Your depreciation expense calculation is as follows

## How to calculate from beginning book value to depreciation expense

• First year: \$130,000—5/15 x \$100,000 = \$33,333.33
• Second year: \$96,666.67—4/15 x \$100,000 = \$26,666.67
• Third year: \$70,000—3/15 x \$100,000 = \$20,000
• Fourth year: \$50,000—2/15 x \$100,000 = \$13,333.33
• Fifth year: \$36,666.67—1/15 x \$100,000 = \$6,666.67

After you take depreciation in the fifth year, your asset will be worth its salvage value—\$30,000. Notice, also, the sum of the fractions in all the years equals 100%.

## Is the sum of the years' digit right for your business?

Because it's an accelerated depreciation method, the sum of the years' digit more accurately reflects the true value of assets that use up a higher percentage of their useful value in the earlier years. It also allows you to take a larger depreciation deduction faster than using straight-line depreciation.

The downside is, of course, how complicated the formula is. In the example above, your straight-line depreciation expense would have been \$20,000 each year—\$100,000 x 1 /5. Additionally, in later years, your depreciation deduction for this asset will be lower under the sum of the years' digit method. 