What is sum of the years digits depreciation?

Sum of the year's digits depreciation is a method of calculating the depreciation of an asset over the years. Sum of the year's digits falls under the category of accelerated depreciation methods, as opposed to straight-line depreciation.

Accelerated depreciation methods are considered to be more conservative calculations of depreciation and also more accurate methods of depreciation calculation. Accelerated depreciation calculation methods assume and rest on the idea that an asset will lose value more quickly at the beginning of its useful life as opposed to losing value at a steady rate throughout its depreciable life. Another method of calculating depreciation that falls under accelerated depreciation is double-declining balance depreciation, or just plain declining balance depreciation.

Here's a simple way to describe how sum of the years digits works.

1. Take the expected life of the asset (make sure that it is in years). Count from the top number back to one. Then add all of the numbers together. So if you purchase a piece of machinery that is expected to last for 12 years, you would do the following:
12 years useful life = 12 + 11 + 10 + 9 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 Sum of the years = 78


2. To calculate the depreciation of an asset for each year of its useful life, you take the year of its useful life and set it as a percentage of the sum of the years.
This means that in the first year of your machine's life, it would end up being depreciated 12/78 in value. This fraction comes out to 15.38%. So the asset loses 15.38% of its value in the first year. The second year, the machine will be depreciated 11/78, or 14.10% of its value. In the third year, your machine will depreciate 10/78 in value, or 12.82% of its value. And so on and so forth.


3. Let's look at an example. Let's simply use the machine from up above. Let's say that this particular machine cost you $17,000. It has a salvage value of $900. Its useful life is 12 years. We have already calculated the sum of the years for the machine, and it comes out to 78.

We have already calculated that in the first year of use, the machine is going to depreciate by 15.38%. This means that in the first year of use, you will see depreciation expenses of $2467.18 (after subtracting the salvage value from the historical cost). In the second year, the machine has depreciation expenses of 14.10%. This means that you will see depreciation expenses of $2270.10. In the third year, the value will depreciate by 12.82%. Your depreciation expenses will end up being $2064.02.

That was the simple way of describing sum of years digits depreciation. Here's the more technical and complicated way of describing its formula.

Sum of years digits can also be described as a historical depreciation method. Its accelerated is in between straight line depreciation and declining balance depreciation. Here is the formula that is used to determine sum of years digits depreciation.
N = depreciable life of an asset
B = cost basis
S = salvage value
D(t) = depreciation charge for year t
Sum = (N(N + 1))/2
Then
D(t) = (N - t + 1) x ((B - S)/Sum)

Sum of the years digits depreciation is a way of calculating depreciation that will allocate the cost of whatever asset you have over its useful life. A simpler way of describing the formula than that above is to simply say that the numerator of the fraction is the number of years left to be depreciation out of the useful life of the asset. The denominator is the sum of the years digits, determined with the formula: ( N (N + 1) ) / 2 where N is the years of the depreciable life

The sum of the years’ digits, often referred to as SYD, is a form of accelerated depreciation. (A more common form of accelerated depreciation is the declining balance method used in tax depreciation.) The sum of the years’ digits method will result in greater depreciation in the earlier years of an asset’s useful life and less in the later years. However, the total amount of depreciation over an asset’s useful life should be the same regardless of the depreciation method used. The difference is in the timing of the total depreciation.

To illustrate the sum of the years’ digits method of depreciation, let’s assume that a plant asset is purchased at a cost of $160,000. The asset is expected to have a useful life of 5 years and then be sold for $10,000. This means that the asset’s depreciable amount will be $150,000 to be expensed over its useful life of 5 years.

Next the digits in the years of the asset’s useful life are summed: 1 + 2 + 3 + 4 + 5 = 15. In the first year of the asset’s life, 5/15 of the depreciable amount (5/15 of $150,000) or $50,000 will be debited to Depreciation Expense and $50,000 will be credited to Accumulated Depreciation. In the second year of the asset’s life, $40,000 (4/15 of $150,000) will be the depreciation amount. In the third year, $30,000 (3/15 of $150,000) will be the depreciation. The fourth year will be $20,000 (2/15 of $150,000) and the fifth year will be $10,000 (1/15 of $150,000). As indicated earlier, the total depreciation during the asset’s useful life needs to sum to the depreciable cost (in this case $150,000) regardless of the depreciation method used.

Instead of adding the individual digits in the years of the asset’s useful life, the following formula can be used: n(n+1) divided by 2. In this formula, n = the useful life in years. Let’s use the formula to check our calculation above. When the useful life is 5 years, the formula will be 5(5+1)/2 = 5(6)/2 = 30/2 = 15. If the useful life is 10 years, the formula will show 10(10+1)/2 = 10(11)/2 = 110/2 = 55. In the first year of the asset having a 10 year useful life, the depreciation will be 10/55 of the asset’s depreciable cost. The second year will be 9/55 of the asset’s depreciable cost. In the tenth year, the depreciation will be 1/55 of the asset’s depreciable cost.
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