Accounting for Long-term Assets
8.2.4 Sum-of-the-years-digits method of depreciation
This method is similar to the double-declining method because it also assumes that an asset is used more extensively during the first years of operation. Under this method, an important consideration is given to the number of years in the asset's useful life.
Sum-of-the-years-digits method applies a decreasing rate to the asset depreciable value and produces a decreasing depreciation expense over the useful life of the asset. The decreasing rate equals the fraction of a current year's digit to the total of all year digits in the asset useful life.
The following steps are to be taken to determine the amounts of depreciation expense:
- Sum up the year digits, beginning with the number of years the asset will be in use and going down to 1. For example, if an asset will be used for 5 years, the resulting total will be 15 = 5 + 4 + 3 + 2 + 1.
- Determine the depreciation for each year by multiplying the depreciable cost (historical cost - salvage value) by the fraction of each year digit to the total of all year digits (from step one). For instance, the depreciation expense for the first year will be Depreciable Cost x 5 / 15, for the second the expense will be Depreciable Cost x 4 / 15, and so on till Depreciable Cost x 1 / 15 in the last year.
The table below shows the depreciation expense computations for our example. Note that the total of all year digits is 10. The number of years the computer will be in use is 4, then 10 = 4 + 3 + 2 + 1:
Illustration 8-13: Schedule of sum-of-the-year-digits depreciation for Mr. Serfy's computer
| Year |
Depreciable |
x |
Factor |
= |
Depreciation |
| 20X7 |
(23,000 - 3,000) |
x |
4/10 |
= |
$8,000 |
| 20X8 |
(23,000 - 3,000) |
x |
3/10 |
= |
$6,000 |
| 20X9 |
(23,000 - 3,000) |
x |
2/10 |
= |
$4,000 |
| 20X0 |
(23,000 - 3,000) |
x |
1/10 |
= |
$2,000 |
|
|
|
|
|
|
$20,000 |
The entire depreciable cost is depreciated over the four years without a remainder or surplus. This is achieved because the factor for each year (i.e., 4, 3, 2, and 1) represents a part of a whole (i.e., 10). The four digits together equal the total (i.e., 4 + 3 + 2 + 1 = 10), and respectively, the entire depreciable cost is allocated to expense.
Suppose that the following numbers represents the revenue steam: $12,000 for 20X7, $10,000 for 20X8, $8,000 for 20X9, and $6,000 for 20X0. Financial statements are shown below:
Illustration 8-14: Financial statements under the sum-of-the-years-digits depreciation method
| Financial Statements under Sum-of-the-years-digits Depreciation Method |
||||
| Income Statement |
||||
|
|
20X7 |
20X8 |
20X9 |
20X0 |
| Revenue |
$12,000 |
$10,000 |
$8,000 |
$6,000 |
| Depreciation Expense |
(8,000) |
(6,000) |
(4,000) |
(2,000) |
| Operating Income |
$4,000 |
$4,000 |
$4,000 |
$4,000 |
| Gain |
0 |
0 |
0 |
1,000 |
| Net Income |
$4,000 |
$4,000 |
$4,000 |
$5,000 |
| Balance Sheet |
||||
| Assets |
|
|
|
|
| Cash |
$14,000 |
$24,000 |
$32,000 |
$42,000 |
| Computer |
$23,000 |
$23,000 |
$23,000 |
0 |
| Accumulated Depreciation |
(8,000) |
(14,000) |
(18,000) |
0 |
| Total Assets |
$29,000 |
$33,000 |
$37,000 |
$42,000 |
| Equity |
|
|
|
|
| Contributed Capital |
$25,000 |
$25,000 |
$25,000 |
$25,000 |
|
Retained Earnings |
4,000 |
8,000 |
12,000 |
17,000 |
| Total Equity |
$29,000 |
$33,000 |
$37,000 |
$42,000 |
| Statement of Cash Flows |
||||
| Operating Activities |
|
|
|
|
| Inflow from Clients |
$12,000 |
$10,000 |
$8,000 |
$6,000 |
| Investing Activities |
|
|
|
|
| Outflow to Purchase Computer |
(23,000) |
$ 0 |
$ 0 |
$ 0 |
| Inflow from Sale of Computer |
0 |
0 |
0 |
4,000 |
| Financing Activities |
|
|
|
|
| Inflow from Capital Acquisition |
$25,000 |
0 |
0 |
0 |
| Net Change in Cash |
$10,000 |
$10,000 |
$8,000 |
$10,000 |
| Beginning Cash Balance |
$ 0 |
$14,000 |
$24,000 |
$32,000 |
| Ending Balance |
$14,000 |
$24,000 |
$32,000 |
$42,000 |
Page 7 of 9
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