Sum of the Years’ Digits Depreciation Method

By Yuriy Smirnov Ph.D.

Definition

The sum of the years’ digits depreciation method refers to an accelerated depreciation method. The assumption is that assets have higher productivity in early years of useful life than in later years. The other assumption is that some of the assets are subject to rapid obsolescence, e.g., computers and other electronics, so accelerated depreciation helps to recover their initial cost more quickly.

Formula

To apply the sum of the years’ digits depreciation method, an accountant should estimate the useful life and salvage value (also referred to as residual value) of an asset. The useful life determines the annual depreciation rate (DR) as follows:

 Depreciation Rate = Remaining Useful Life in Years × = 100% Sum of the Years’ Digits

The sum of the years’ digits can be easily calculated using the following formula:

 Sum of the Years’ Digits = N × (N + 1) 2

Please note that the sum of the years’ digits depreciation method can also be applied quarterly and monthly.

No Salvage Value

If an accountant estimates an asset’s salvage value as zero, the annual depreciation expense can be calculated as follows:

Depreciation Expense = Asset Cost × Depreciation Rate

When the useful life of an asset expires, its book value equals zero.

With Salvage Value

If an asset has a salvage value, the formula above should be transformed as follows:

Depreciation Expense = (Asset Cost - Salvage Value) × Depreciation Rate

When the useful life of an asset expires, its book value equals its salvage value.

Calculation Examples

Example 1

XYZ Logistic bought a new truck for \$200,000 at the beginning of the financial year. The accountant has estimated the useful life of the truck as 5 years and its salvage value as \$50,000.

The sum of the years’ digits equals 15 [5×(5+1)÷2]; thus, the depreciation rate for each year is as follows:

Knowing the depreciation rate, we can calculate the annual depreciation expense (DE).

DE 20X4 = (\$200,000 - \$50,000) × 33.33% = \$50,000

DE 20X5 = (\$200,000 - \$50,000) × 26.67% = \$40,000

DE 20X6 = (\$200,000 - \$50,000) × 20.00% = \$30,000

DE 20X7 = (\$200,000 - \$50,000) × 13.33% = \$20,000

DE 20X8 = (\$200,000 - \$50,000) × 6.67% = \$10,000

The sum of the years’ digits depreciation schedule is shown below.

At the beginning of 20X4, the net book value of the truck equals its cost of \$200,000. At the end of 20X4, depreciation expense amounts to \$50,000, and the net book value of the truck is \$150,000. At the end of 20X5, depreciation expense amounts to \$40,000, accumulated depreciation totals \$90,000, and the net book value amounts to \$140,000. The same calculation should be applied for the remaining years.

Please note that the net book value of the truck at the end of its useful life equals the salvage value of \$50,000.

Example 2

Pixelart Entertainment has acquired a brand-new laptop for \$4,000. The useful life has been estimated as 2 years, and the salvage value is zero.

Assuming that the company prepares financial statements on a quarterly basis, the useful life is 8 quarters (2 years). Thus, the sum of the years’ digits equals 36 [8×(8+1)÷2], and the depreciation rate (DR) for each quarter is as follows:

The quarterly depreciation expense will be as follows:

DE 1Q 20X7 = \$4,000 × 22.22% = \$888.89

DE 2Q 20X7 = \$4,000 × 19.44% = \$777.78

DE 3Q 20X7 = \$4,000 × 16.67% = \$666.67

DE 4Q 20X7 = \$4,000 × 13.89% = \$555.56

DE 1Q 20X8 = \$4,000 × 11.11% = \$444.44

DE 2Q 20X8 = \$4,000 × 8.33% = \$333.33

DE 3Q 20X8 = \$4,000 × 5.56% = \$222.22

DE 4Q 20X8 = \$4,000 × 2.78% = \$111.11

Thus, the depreciation schedule will be as follows:

At the end of the useful life, the net book value equals \$0, and accumulated depreciation amounts to the laptop cost of \$4,000.

Graph

Let’s review the case described in Example 1 to draw a graph of the sum of the years’ digits depreciation method.

As shown in the graph, the biggest proportion of the depreciable amount is assigned to depreciation expense in the first years. In later years, this proportion is gradually reduced, and finally the net book value of an asset reaches its salvage value at the end of its useful life.

Journal Entries for Sum of the Years’ Digits Depreciation

Let’s review Example 1 to make general journal entries, assuming that XYZ Logistic prepares annual financial statements. This means that 5 entries should be made at the end of each year by debiting the Depreciation Expense account and crediting the Accumulated Depreciation account.

As far as Accumulated Depreciation is a contra asset account, its balance is deducted from the balance of the Equipment account in the balance sheet. In other words, the net value of an asset is reported in the balance sheet.

Revision in Estimates

If previously made estimates of the useful life and/or salvage value of an asset are revised, the depreciation schedule should be reconsidered. Let’s review Example 1 and assume that at the end of Year 2 the estimate of useful life was revised to 4 years and the salvage value to \$40,000.

As far as the net book value at the end of Year 2 is \$110,000 and the new salvage value is \$40,000, the depreciable amount is \$70,000 (\$110,000-\$40,000). Assuming that only 2 years remain until the end of useful life, the revised depreciation rates are as follows:

The revised depreciation schedule under the sum of the years’ digits method is as follows:

DE 20X6 = (\$110,000 - \$40,000) × 20.00% = \$46,666.67

DE 20X7 = (\$110,000 - \$40,000) × 13.33% = \$23,333.33