## Articles

## Sum-of-the-years-digits method

The sum-of-years' digits is an accelerated method that charges more depreciation in the earlier years of an asset’s life and less in the later years. Unlike other methods, the depreciation expense decreases by the same amount each year by applying a declining rate to a fixed amount, for example the depreciable cost of the asset.

To calculate the depreciation expense under the sum-of-years' digits method, fractions are used to multiply the asset’s cost less its estimated salvage value. The numerator of the fraction is the productive year numbers in reverse order. For example, if an asset has a useful life of 5 years, the numerator of the fraction for the first year would be 5 (years in reverse). The denominator is the sum of the individual productive year numbers used in calculating depreciation for each year. For example, the denominator of the fraction would be 15, the sum of the year’s digits (5+4+3+2+1=15). To calculate depreciation for the first year, multiply $30,000 (depreciable cost) of the asset by 5/15 = $10,000.

The following table shows how the yearly deprecation expense is calculated with these data: the original cost of an asset is $65,000. It has a useful life of 5 years and the salvage value is estimated at $5,000.

Since the asset has a useful life of 5 years, 5 digits of the years are used: 5, 4, 3, 2, 1. Each of these five numbers is used as the numerator of the fraction. The total of the five digits is: 5+4+3+2+1=15. This 15 is the constant denominator of the fraction. Thus, the rate of depreciation for the first year is 5/15, second year 4/15, third year 3/15, fourth year 2/15 and fifth year 1/15.

Year |
Depreciable cost |
Depreciation rate |
Depreciation expense |
Accumulated depreciation |
Net book value |

$ | $ | $ | $ | ||

1 | 60,000 | 5/15 |
20,000 | 20,000 | 45,000 |

2 | 60,000 | 4/15 |
16,000 | 36,000 | 29,000 |

3 | 60,000 | 3/15 |
12,000 | 48,000 | 17,000 |

4 | 60,000 | 2/15 | 8,000 | 56,000 | 9,000 |

5 | 60,000 | 1/15 |
4,000 | 60,000 | 5,000* |

*** Salvage value**

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Last Updated (Friday, 03 September 2010 18:47)