How do I calculate depreciation using the sum of the years' digits?
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 totaldepreciation 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.