Sum of the Years' Digits Accelerated Depreciation Method

Investing Lesson 4 - Analyzing an Income Statement

Sum of the Years' Digits Accelerated Depreciation Methdology
The same computer example we used earlier shows that with the sum of the years digits method, depreciation expense is higher in the early years, causing a more rapid drop in the carrying value. It is more realistic than the straight line method. Joshua Kennon

In some cases, a company will decide to employ an accelerated depreciation method, such as the sum of the years' digits method or double declining balance method (either the 150% or 200% method), to calculate depreciation expense, accumulated depreciation, and, ultimately, net income.  Accelerated depreciation methods allow a firm to take greater charges against earnings in the early years following the acquisition of an asset with lower charges later on so earnings are hit more heavily in the near-term.

 By their very nature, accelerated depreciation methods are more conservative and, in many situations, more accurate as they assume that an asset loses a majority of its value in the first several years of use.

To help you understand how they differ from the straight-line depreciation method, I'm going to walk you through a couple of these depreciation methods.  We'll start by going over the sum of the years' digits method.

How to Calculate the Sum of the Years' Digits Depreciation Method

To calculate depreciation charges using the sum of the years' digits method, we need to do several things.

First, we have to calculate the salvage value of an asset the same way we would with the straight-line depreciation method.  For example, if you buy an asset for $100,000 and it will be worth an estimated $10,000 at the end of its useful life, the balance subject to depreciation is $90,000.

Next, we have to calculate the so-called "applicable percentage".

 To do this under the sum of the years' digits method, we need to take the expected life of an asset in years, count backward to one, then add the figures together.  For example, let's assume an asset has ten years of estimated useful life.  This case, we would do the following calculation:

10 years useful life = 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1

Sum of the years' digits = 55

Using this information, we could calculate applicable percentage each year.  In the first year, the asset value subject to depreciation would be expensed 10/55 in value (the fraction 10/55 is equal to 18.18%).  In the second year, the asset value subject to depreciation would be expensed 9/55 (16.36%).  In the third year, the asset value subject to depreciation would be expensed 8/55 (14.54%).  This would continue until the asset was fully depreciated, having been completely expensed on the income statement and, ultimately, written off the balance sheet, too.  

To complete the example we've been using, the sum of the years' digits depreciation expense for the life of this asset would be as follows:

Example Depreciation Calculation Using Sum of the Years' Digits Depreciation Method
YearApplicable Percentage Depreciation RateAnnual Depreciation Expense on Income StatementRemaining Depreciation BaseSalvage ValueNet Carrying Value on Balance SheetRatio of Depreciation in Year
118.18%$16,363.64$73,636.36$10,000$83,636.3610/55
216.36%$14,727.27$58,909.09$10,000$68,909.099/55
314.55%$13,090.91$45,818.18$10,000$55,818.188/55
412.73%$11,454.55$34,363.64$10,000$44,363.647/55
510.91%$9,818.18$24,545.45$10,000$34,545.456/55
69.09%$8,181.82$16,363.64$10,000$26,363.645/55
77.27%$6,545.45$9,818.18$10,000$19,818.184/55
85.45%$4,909.09$4,909.09$10,000$14,909.093/55
93.64%$3,272.73$1,636.36$10,000$11,636.362/55
101.82%$1,636.36$0.00$10,000$10,000.001/55


Going back to our example from our discussion on the straight-line depreciation method, a $5,000 computer with a $200 salvage value and 3 years useful life would be calculated under the sum of the years' digit depreciation method as follows:

3 years useful life = 3 + 2 + 1 Sum of the years = 6

Taking $5,000 - $200 we have a depreciation base of $4,800. In the first year, the computer would be depreciated by 3/6ths (50%), the second year, by 2/6 (33.33%) and the third and final year by the remaining 1/6 (16.67%). This would have translated into depreciation charges of $2,400 the first year, $1,599.84 the second year, and $800.16 the third year. In contrast, the straight-line example would have simply charged $1,600 each year, distributed evenly over the three years useful life.  

The exact same company, with the exact same assets and the exact same transactions, appeared to be earning different amounts of profit, and have assets carried at different values on the balance sheet, depending upon which depreciation method was utilized.

 In both cases, economic reality was identical.

This page is part of Investing Lesson 4 - How to Read an Income Statement. To go back to the beginning, see the Table of Contents.