Sum of the years' digits (SYD) depreciation method is one of the accelerated depreciation accounting methods which takes more of assets’ depreciation in its first years of useful life of the property. Accelerated depreciation means declining amounts of depreciation expense from year to year of the depreciable asset’s service life compare to the straight line depreciation method where each period of the asset’s usage there is the same amount of depreciation expense.

For example,

An entity has the initial cost of a purchased depreciable asset (equipment) $20,000, salvage value $4,000 (the expected asset’s value at the end of the property’s service life), and estimated that they are going to use it for 4 years. To compute the depreciation expense of the equipment for the period by using the sum years’ digits depreciation method the company needs to apply the following formula

**Depreciation expense = (Initial cost - Salvage value) x Fraction**

First of all, before even starting to apply the above formula the firm needs to determine the proper fraction. The numerator of the fraction will be the remaining life of the depreciable asset at the beginning of the current year. So, if according to the assumption the firm expected to use the equipment for 4 years then the first numerator would be 4, next one - 3, then - 2, and 1.

There is two ways the company can use to compute the denominator:

- The digits in the years of the property service life can be summed to find the fraction denominator. In the example the asset has 4 years of useful life and since the series of fractions should go from highest to lowest the company will add 4 + 3 + 2 +1 = 10.

- Use formula: **(n x (n+1)) / 2**

If the asset had many years of expected service life then it would be better and faster to use the above formula to find the denominator of the fraction where n stands for years of useful life of the property. After applying the numbers from the assumption to the formula the result will be still 10.

(4 x (4+1))/2 = 10. Therefore, it doesn’t really matter which method to use in our case, the result will be the same anyway. Note that the denominator will stay the same for all fractions.

Calculation of depreciation for a period by using the sum years’ digits depreciation method

Years |
**Initial cost** |
**Depreciation base** |
**Depreciation expense** |
**Accumulated depreciation** |
**Carrying value** |

A |
B |
C* |
D |
E |
F = B - E |

1 |
$20,000 |
$16,000 x 4/10 |
$6,400 |
$6,400 |
(D1) |
$13,600 |

2 |
$20,000 |
$16,000 x 3/10 |
$4,800 |
$11,200 |
(D1 + D2) |
$8,800 |

3 |
$20,000 |
$16,000 x 2/10 |
$3,200 |
$14,400 |
(D1 + D2 + D3) |
$5,600 |

4 |
$20,000 |
$16,000 x 1/10 |
$1,600 |
$16,000 |
(D1 + D2 + D3 +D4) |
$4,000 |

**Advantages of the sum years’ digits depreciation method**

- the sum years’ digits depreciation method as one of accelarated depreciation methods better matches costs to revenues because it takes more depreciation in the early years of an assets’ useful life compare to the straight line depreciation method

- this method reflects more accurately the difference in usage of different assets from one period to the other compare to the straight line depreciation method

**Disadvantages of the sum years’ digits depreciation method**

- SYD depreciation method might be more confusing and harder to compute compare to the straight line one

- It has declining amounts of depreciation expense. Declining amounts of depreciation expense usually offsets by increasing the maintenance expense which might smooth the income over the years

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