# SUM-OF-THE-YEARS' DIGITS METHOD

The sum of the years' digits method of depreciation is an accelerated method of depreciation in which the depreciation charges in the first year of an asset is higher than in subsequent years.

In other words, depreciation is higher in the first year than the second, higher in the second year than the third, and so on.

The fundamental characteristic of sum-of-the-years' digit depreciation is that the year before has higher depreciation costs than the year after.

Under sum-of-the-years digit depreciation, the years an asset will be useful are referred to as "digits" and are therefore added together.

The remaining number of useful years of an asset is then divided by the sum of the digits, after which the result is then multiplied by the depreciable value of the asset.

To calculate sum-of-the-years' digit depreciation, the formula is as follows:

$SOYD=\frac{R}{SOY}×DA$

where R is the remaining useful years of the asset

SOY is the sum of the year's digit, computed as $$SOY=\frac{n(n+1)}{2}$$

DA is the depreciable amount, which is the difference between the cost of the asset and its salvage value,

## Example

A corporation paid N970,000 for an asset that has a 5-year estimated useful life and an N70,000 salvage value. Calculate the depreciation charge throughout the useful life of the asset using the sum-of-the-years digits depreciation

Solution:

The asset's depreciable amount is N970,000 minus 70,000, or N900,000.

The asset has a five-year useful life, hence the total of the year's digits is 5+4+3+2+1=15

Alternatively, you can calculate the sum of the year's digit using the formula given above:  $$SOY=\frac{n(n+1)}{2}$$

Since n is 5, it follows that the sum of the year's digit is calculated as follows.

$$SOY=\frac{5(5+1)}{2}=15$$

Now let's determine the depreciation expenses for each year.

We still have five useful years left for the first year.

$SOYD=\frac{5}{15}×900,000=300,000$

Given that we have previously used the item for one year, the useful years of the asset will be four in the second year

$SOYD=\frac{4}{15}×900,000=240,000$

For the three years, the number of useful years will be 3

$SOYD=\frac{3}{15}×900,000=180,000$

For the fourth year, the number of useful years will be 2

$SOYD=\frac{3}{15}×900,000=120,000$

For the fifth year, the number of useful years will be 2

$SOYD=\frac{3}{15}×900,000=60,000$

Year Book value (year start) depreciationAccumulated depreciation Book value (year-end)
Year 1 N970,000N300,000N300,00N670,000
Year 2 N670,000N240,000N540,000N430,000
Year 3 N430,000N180,000N720,000N250,00
Year 4 N250,000N120,000N840,000N130,000
Year 5 N130,000N60,000N900,0000N70,000

## Advantages Of Sum-of-the-years' Digits Method Of Depreciation

1. Suitable for a long-live asset: Sum-of-the-years' digit is highly suitable for long-lived assets whose useful life is known.

2. Has a uniform effect on profit or loss account: In sum-of-the-years digits depreciation, the amount of depreciation is greater in the early years and lower in the later years of an asset.

In the same vein, the repair and maintenance cost of an asset is generally low in the early life of the asset than in the latter life of the assets

Given this, the sum of depreciation and repair and maintenance expenses will more or less be constant every year so that the charge to the profit and loss account will be uniform each year.

3. Aligns asset's cost with its service capacity: Sum-of-the-years digits is an accelerated method of depreciation, which means that the quantum of depreciation is greater in the early years of an asset than in the later years of an asset.

In this way, it aligns an asset cost with the use of the asset because the benefits received from an asset are higher in the early years in comparison with the latter years.

Keep in mind that depreciation is a periodic allocation of the asset cost to the periods it is used or consumed. When higher cost (depreciation) is allocated in the early years of the asset, it is in line with the fact that assets generally perform more effectively in their earlier years than in their later years.

4. Better for an asset that becomes obsolete quickly: If the assets are retired earlier than expected due to unforeseen obsolescence, the loss upon retirement will be lesser than if the straight-line method of depreciation is used.

This is because assets are deducted at a higher rate in the earlier years and a lower rate in the later years so that only a small fraction of the asset cost is left for deduction in the latter years of an asset.

5. Provide a tax shield: Since the quantum of depreciation is high in the early years, the company may report low net profit and pay low tax.

The implication is that the tax payment for the early years is slightly deferred to the latter years of the asset where the company may report a high net profit and pay high taxes.

## Disadvantages Of The Sum-of-the-years' Digit Method Of Depreciation

1. It may result in a high cost of production: Sum-of-the-years digits depreciation charges high depreciation in the earlier years of an asset.

For instance, if an asset has a five-year useful life, up to one-third of the asset cost will be allocated to the asset's first year of usage, thereby increasing the cost of production for the first year.

An increased cost of production may adversely affect a firm selling in a highly competitive market.

2. It could reduce profits: Sum-of-the-years digits depreciation can reduce profit because of the high cost of production, which may be caused by increased depreciation.

3. Cash flows issues: Reduced profit means less money is available to pay dividends in the earlier years of the asset.

Since the dividend is one of the major motivating factors in investing in any company, sum-of-the years digits may create cash flow issues as the company may find it harder to attract new investors.

4. Difficult to calculate: Unlike straight-line depreciation, the sum-of-the-years' digit method of depreciation is difficult to calculate.

Sum-of-the-years depreciation requires that the depreciation charges be calculated in the first year and then continuously calculated for subsequent years in light of the asset's remaining useful life, as opposed to straight-line depreciation, which only requires that the depreciation be calculated in the first year and then used repeatedly throughout the asset's lifespan.

#### Final words

When depreciating assets that quickly become outdated, the sum-of-the-years digit of depreciation is a highly helpful method of depreciation

Unlike straight line depreciation which allocates a fixed percentage of the asset cost as depreciation, the sum-of-the-years digit allocates a variable percentage of the asset cost as depreciation and this variable percentage is highly dependent on the remaining useful life of the asset.

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