# Sum Of Years’ Digits Method

This results in a reasonably constant expense related to the asset because depreciation expense declines as repair expense increases. To demonstrate how this fraction is worked out, suppose that an asset has a 5-year life. In the first year, the rate is a fraction that has a numerator of 5, the number of years remaining at the beginning of the year. Note that the asset’s residual value is subtracted from its acquisition cost to determine its depreciable base. For example, if an asset has a 5-year economic useful life, the numbers 1, 2, 3, 4 and 5 are added, and the resulting sum becomes the denominator while the numerator is the number of remaining years of the useful economic life of the asset. In the first year, the asset value subject to depreciation would be expensed 5/15 in value (33.33%). In the second year, the asset value subject to depreciation would be expensed 4/15 (26.67%). In the third year, the asset value subject to depreciation would be expensed 3/15 (20%). This would continue until the asset was fully depreciated, having been completely expensed on the income statement and fully depreciated on the balance sheet.

## Sum Of Years’ Digits Depreciation Formulas

The accelerated or decreasing cost allocation for asset depreciation, such as the sum-of-the-years’ digits method, better matches the cost of using an asset to the benefit the asset use provides each year over the economic life of the asset. Mega Coffee believes that at the end of the computers’ 5-year useful life, they will be worth \$200,000. The company decides to depreciate the assets using the SYD method as it faces a fairly harsh tax environment. Also, there is a high probability that the computers will become obsolete before their useful life is up.

• However, the depreciation expense in the sum of the years’ digits goes down in the linear line instead of the curve line like those in the declining balance method.
• The sum of years’ digits method is a form of accelerated depreciation charge that is based on the assumption that the productivity of the asset decreases with the passage of time.
• The sum-of-the-years’ digits method is another variation on accelerated depreciation.
• Calculate the sum of years’ digits depreciation for each year of the fixed asset above.
• Depreciation is the process of the allocation of fixed assets cost over their useful life.
• From a conceptual perspective, these methods are most suited for assets that give up a greater portion of their benefits in their early years.
• Learn accounting fundamentals and how to read financial statements with CFI’s free online accounting classes.

The useful life of this machine is six years, and the salvage value after eight years will be \$900. You want to compute the depreciation expense for the fourth year, using the sum-of-the-years’-digits method. The same asset, using straight-line depreciation and zero salvage value, would be depreciated at \$5,000 per year for five years (\$25,000 ÷ 5) until the asset depreciates to zero value. The same company, with the exact same assets, would appear 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. Using the information from the example above, you would calculate the applicable depreciation percentage for each depreciable year.

However, Mega Coffee needs to pay \$100,000 in shipping costs in order to move this massive order of computers across the country in due time. In addition, Mega Coffee is faced with a \$400,000 installation charge to ensure that its computers are installed correctly and function at full capacity. Companies typically use accelerated depreciation to minimize their taxable income because it allows for greater depreciation expense deductions in the earlier years of the equipment or asset’s life. As with the double-declining-balance method, the sum-of-the-years’ digits method allocates more depreciation in the early years and less in later years.

## The Best Method Of Calculating Depreciation For Tax Reporting Purposes

It is similar to the declining balance depreciation in which the depreciation expense in the sum of the years’ digits method will go down as time passes making the last depreciation expense the smallest. The company can calculate sum of the years’ digits depreciation with the formula of using the remaining useful life of fixed asset to divide by the sum of years’ digits and then multiply the result by the depreciable cost of the fixed asset. To calculate depreciation charges using the sum of the years’ digits method, you’ll need to first get the depreciable base, which is the cost of the asset. Second, you’ll calculate the salvage value of the asset, which works the same for both the SYD and straight-line depreciation methods. For example, if you buy an asset for \$100,000 and it can be sold for an estimated \$10,000 at the end of its useful life, the balance subject to depreciation is \$90,000, and the salvage value is \$10,000. Next, calculate the applicable percentage of depreciation for each year of the asset’s life.

### What does depreciate mean in math?

Depreciation refers to when the value of something goes down over time. The value of a car is usually decreases in value with time. Therefore its value is said to depreciate .

The depreciation schedule using sum-of-the-years’ digits for equipment is shown below. Depreciation is an accounting method of allocating the cost of a tangible asset over its useful life and is used to account for declines in value over time.

## Economic Usefulness Of Assets

As mentioned, using the sum of years digits depreciation of the fixed assets will make the depreciation expense that the company charged to the income statement higher in the early year, and such expense will go down as time passes. In this case, the company should use the sum of years digits depreciation method on the fixed assets that can produce higher productivity in the early year and such productivity will gradually drop down as time passes.

### What is reducing balance?

The reducing balance method of depreciation results in declining depreciation expenses with each accounting period. In other words, it charges depreciation at a higher rate in the earlier years of an asset. The amount of depreciation reduces as the life of the asset progresses.

Under this plan the allowance for depreciation is computed by applying changing fractions to the unrecovered cost or other basis of the account reduced by estimated salvage. Decimal equivalents of such fractions can be obtained by use of Table I under paragraph of this section. The proper application of this method requires that the estimated remaining useful life of the account be determined each year.

## Accountingtools

In this depreciation scenario, an asset, such as a piece of equipment, has its book value reduced on the balance sheet at a faster rate than a traditional straight-line depreciation method. Companies use a few different methods for achieving this, such as the Sum of Years’ Digits method. Calculate the sum of years’ digits depreciation for each year of the fixed asset above. On the other hand, the sum of years’ digits can be determined by totaling the digits in every year of the fixed asset’s useful life. Depreciation is the process of the allocation of fixed assets cost over their useful life. However, the company needs to properly allocate the cost so that the depreciation expense charged to the income statement matches the benefits that the company receives from the fixed assets. This is so that the recognition of the depreciation expense in the company’s account is properly in compliance with the matching principle of accounting. The double declining balance depreciation method is an accelerated depreciation method that multiplies an asset’s value by a depreciation rate. Both the declining-balance and sum-of-the-years’ digits methods are examples of accelerated depreciation. Accelerated depreciation uses decreasing charge methods, including the sum-of-the-years’ digits , providing higher depreciation costs in earlier years and lower depreciation charges in later periods. Under the SYD method, the depreciation rate percentage for each year is calculated as the number of years in remaining asset life for the same year divided by the sum of remaining asset life every year through the asset’s life.

## Sample Full Depreciation Schedule

The advantages and disadvantages of this method are more or less the same as the declining balance method. The exception is that the calculations needed in sum-of-the-years’ digits are slightly more complex.

• Once a company decides on a depreciation method it typically has to stick with that depreciation method going forward for that particular asset.
• To illustrate SYD depreciation, assume that a service business purchases equipment at a cost of \$160,000.
• The company decides to depreciate the assets using the SYD method as it faces a fairly harsh tax environment.
• Accelerated depreciation uses decreasing charge methods, including the sum-of-the-years’ digits , providing higher depreciation costs in earlier years and lower depreciation charges in later periods.
• However, the company needs to properly allocate the cost so that the depreciation expense charged to the income statement matches the benefits that the company receives from the fixed assets.

Under the sum of the years-digits method, annual allowances for depreciation may also be computed by applying changing fractions to the unrecovered cost or other basis of the asset reduced by estimated salvage. For decimal equivalents of such fractions, see Table I of subdivision of this subparagraph. For example, a new asset with an estimated useful life of 10 years is purchased January 1, 1954, for \$6,000. Assuming a salvage value of \$500, the depreciation allowance for 1954 is \$1,000 (\$5,500 × 0.1818, the applicable rate from Table I). The depreciation allowance for 1955 would then be \$900 (\$4,500 × 0.2000, the applicable rate from Table I). Sum of the years’ digits depreciation is the type of depreciation method that allocates the higher cost of the fixed assets in the early year and reduces the depreciation expense in later years as time passes.

For example, on January 1, the company ABC buys a machine that cost \$52,000 in order to use for the day-to-day operation. The machine is expected to have 8 years of useful life with a salvage value of \$2,000. Due to the nature of the machine, the company ABC decides to use the sum of years’ digits depreciation method to allocate the cost of the machine over its useful life.

• In the third full year of the asset’s life, the depreciation will be \$30,000 (3/15 of \$150,000).
• The method is more appropriate than the more commonly-used straight-line depreciation if an asset depreciates more quickly or has greater production ca­pacity in its earlier years than it does as it ages.
• It starts with the value n in the first year and decreases by 1 each year until it equals 1 in the final year of the asset’s estimated service life.
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• Companies typically use accelerated depreciation to minimize their taxable income because it allows for greater depreciation expense deductions in the earlier years of the equipment or asset’s life.

Consider coffee company Mega Coffee, which is ready to expand into its new office headquarters. The company is considering investing in the latest available computers in order to make sure that its business runs smoothly. In later years, when the depreciation amount is smaller, the net income will be overstated.

Depreciation is calculated under sum-of-the-years’ digits by adding up the number of years in an asset’s useful economic life. The denominator is the sum of the digits from 1 to n, where n is the number of years in the asset’s service life. Use this calculator to calculate an accelerated depreciation using the sum of years digits method.

It is also more complex to calculate than straight-line depreciation, which can lead to errors in the calculation. Partial-year depreciation also can be calculated using the sum-of-the-years’ digits method. The formula to calculate depreciation expense using sum-of-the-years’ digits is shown below. The sum of years depreciation method works by depreciating the asset’s depreciable amount by a depreciation factor unique to each year. The depreciable amount is equal to the asset’s total acquisition cost less the asset’s salvage value.

## How Does Proration Affect Asset Depreciation?

However, the depreciation expense in the sum of the years’ digits goes down in the linear line instead of the curve line like those in the declining balance method. After all, the calculation formula of the sum of the years’ digits depreciation is different from that of the declining balance depreciation. The sum-of-the-years’-digits depreciation is one method for calculating accelerated depreciation. However, the total amount of depreciation over an asset’s useful life should be the same regardless of which depreciation method is used. In other words, the difference is in the timing of when the same total amount of depreciation will be reported.

Sum-of-the-years’ digits is an accelerated method for determining an asset’s expected depreciation over time. If the taxpayer desires to carry his calculations of decimal equivalents to a greater number of decimal places than is provided in the table, he may use the formula. It starts with the value n in the first year and decreases by 1 each year until it equals 1 in the final year of the asset’s estimated service life. The only guideline is that the depreciation method should be systematic and rational, and as we noted, all of the depreciation methods discussed so far meet this requirement. High-tech products are examples of assets in which the decline of benefits is likely to follow such a pattern. Accelerated depreciation is also appropriate for assets that have higher repair expenses in later years.