18.5.3. Sum of Years’ Digits Method

Accelerated method of depreciation. Formula:

Remaining life of asset Depreciation= × (Cost−Residual Value) Sum of years’ digits

The Sum of Years’ Digits Method is an accelerated depreciation technique. This means that a higher amount of depreciation expense is recognized in the earlier years of an asset's useful life compared to later years. The calculation involves taking the remaining life of the asset and multiplying it by the difference between the cost of the asset and its residual value. This value is then divided by the sum of the years' digits, which helps determine how much depreciation to charge during a specific year.

To clarify, the formula includes understanding the total number of years the asset is expected to be used. For example, if an asset has a useful life of five years, you will calculate the sum of the digits from 1 to 5, which totals 15. Each year, the asset will receive a depreciation amount that reflects how much useful life remains, with more depreciation taken in the early years.

Imagine you purchase a new car for $20,000, expecting to keep it for five years. In the first year, you value the car highly because it’s new and fully functional, so you use the Sum of Years’ Digits Method to account for depreciation. Here, the car's value drops more significantly during the first two years as newer models are released and your car becomes relatively older. This method resembles how a smartphone depreciates faster in terms of value right after it’s released because most people want the latest model.

Remaining life of asset Depreciation= × (Cost−Residual Value) Sum of years’ digits

In this method, 'remaining life' refers to how many years the asset is expected to still provide useful service. The 'cost' of the asset is the purchase price plus any additional costs incurred to get the asset ready for use. The 'residual value' is what you expect the asset to be worth at the end of its useful life. By subtracting the residual value from the cost, you determine the total value that will be depreciated over the asset's life.

Consequently, the depreciation expense for each year reflects how much of the asset's value you are recognizing that year based on its usage and age. This approach shows that newer assets lose value faster due to higher utility in their early years.

Consider a company that buys industrial machinery for $100,000, with an expected residual value of$10,000 after 5 years. The sum of the digit years would be 1+2+3+4+5 = 15. In the first year, the remaining life is 5 years, so the depreciation would be calculated on 5/15 of the total depreciable amount ($100,000 -$10,000), which allows the company to reflect the higher utility costs of the machine immediately, benefitting from its efficiencies.

Depreciation= × (Cost−Residual Value) Sum of years’ digits

To apply the Sum of Years’ Digits Method, you first determine the total depreciation amount, which is the cost of the asset minus its expected residual value. Then, you identify the total number of years in the asset's useful life and sum these years together to get a composite number, as indicated in the formula. Each year, you will calculate the fraction of the total depreciation to apply, which is based on how many years of life remain compared to this total sum of the years.

Imagine a company has a truck that costs $50,000 and has a residual value of$5,000 after a useful life of 5 years. The sum of the years is 1 + 2 + 3 + 4 + 5 = 15. In Year 1, the company will apply 5/15 of the depreciable amount ($50,000 -$5,000), receiving a larger deduction sooner. It reflects the truck being more productive and thus, more valuable in its first year of usage.

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