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Sum-of-Years Digits

An asset often loses more of its value early in its lifetime. A method that exhibits this dynamic is desirable.

Assume an asset depreciates from price to salvage value in years. First compute the sum-of-years as . The depreciation for the years after the asset’s purchase is:

Table 59.1: Sum-of-Years General Example

Year Number

Annual Depreciation

first

second

third

final

For the ith year of the asset’s use, the annual depreciation is:

For our example, and the sum of years is . The depreciation during the first year is

Table 59.2 describes how Declining Balance would depreciate the asset.

Table 59.2: Sum-of-Years Example

Year

Depreciation

Year-End Value

1

2

3

4

5

As expected, the value after years is .