# Sum of the years' digits | Depreciation Method

## Definition

**Sum of the years' digits** depreciation method involves calculating depreciation based on the sum of the number of years in an asset's useful life.

Topic Contents:

## Explanation

Sum of the years' digits depreciation method, like reducing balance method, is a type of accelerated depreciation technique that allocates higher depreciation expense in the earlier years of an asset's useful life.

Calculation of depreciation under this method can be summarized in the following 4 steps:

### Step 1: Calculate the sum of the years' digits in an asset's useful life

For an asset having a useful life of 4 years, the sum of the years' digits will be calculated as follows:

**Sum of years' digits = 4 + 3 + 2 + 1 = 10**

### Step 2: Calculate the depreciable amount

Depreciable amount, as with all depreciation methods, is equal to:

- Asset's cost of acquisition or construction including any subsequent capital expenditure
*Less:*Estimated residual value or scrap value at the end of the asset's useful life

### Step 3: Calculate the un-depreciated useful life

Un-depreciated useful life is equal to the number of years in the asset's useful life that have **not** yet been subjected to depreciation.

Hence, for an asset that has a useful life of 4 years, the un-depreciated useful life to be used in calculating depreciation shall be 4 years in the first year of depreciation, 3 years in the second year and so on.

### Step 4: Calculate depreciation using the sum of years' digits & un-depreciated useful life

Depreciation using the sum of the years' digits method can be calculated using the following formula:

Depreciation Expense | = | Un-depreciated useful life (Step 3) | x | Depreciable Amount (Step 2) |

Sum of the years' digits (Step 1) |

## Example

Following information relates to a fixed asset:

Cost | $100,000 |

Residual Value | $10,000 |

Useful Life | 3 Years |

Calculate depreciation over the useful life of the asset using the sum of the years' digits method.

Step 1: Calculate the sum of the years digits

Sum of the years' digits = 3 + 2 + 1 = **6**

Step 2: Calculate the depreciable amount

Depreciable amount = $100,000 - $10,000 = **$90,000**

Step 3: Calculate the un-depreciated useful life

Year 1 | Year 2 | Year 3 | |

Un- depreciated useful life (years) | 3 | 2 | 1 |

Step 4: Calculate depreciation expense

Year 1: Depreciation expense = | 3 (Step 3) | x $90,000 (Step 2) = $45,000 |

6 (Step 1) |

Year 2: Depreciation expense = | 2 (Step 3) | x $90,000 (Step 2) = $30,000 |

6 (Step 1) |

Year 3: Depreciation expense = | 1 (Step 3) | x $90,000 (Step 2) = $15,000 |

6 (Step 1) |

**Note:** Over the life of the asset, the total depreciation charge equals to the depreciable amount , i.e. $90,000 (Step 2). Also note that the amount of annual depreciation progressively declines as the asset ages. This method of depreciation is therefore appropriate for assets whose utility and productiveness is greater in the earlier years of their life (e.g. computer equipment).

Where an entity has a policy of calculating depreciation on full years basis, sum of the years' digits depreciation can be calculated as above. If however, depreciation is to be calculated on monthly basis, it will usually be necessary to time apportion the depreciation charge between accounting periods since it is unusual for the date of acquisition of an asset to coincide with the start of an accounting period (unfortunately).

Try to apply your knowledge to calculate depreciation under the sum of digits method for an asset acquired mid-way during an accounting period in the multiple-choice question below.

## MCQ

**Test Your Understanding**

**An asset is purchased on 1st July 2013 for $90,000. The asset has 3 years useful life at the end of which it is not expected to have any salvage value.How much depreciation expense should be charged in the accounting year ended 31st December 2014 if sum of the years’ digits method is used?**

$22,500

3/6 x $90,000 x 6/12 = $22,500

Depreciation must be charged for the whole 12 months

$15,000

2/6 x $90,000 x 6/12 = $15,000

Depreciation must be charged for the whole 12 months.

$37,500

3/6 x $90,000 x 6/12 + 2/6 x $90,000 x 6/12 = $37,500

Depreciation charges for the first two years of the asset are $45,000 and $30,000 respectively (refer the solution of the example above in case of confusion).

The depreciation expense for the accounting period has been arrived at by apportioning the depreciation charges relating to the two years of the asset's life as follows:

1 Jan 2014 to 30 June 2014: Depreciation expense = $45,000 x 6/12 = $22,500

1 July 2014 to 31 Dec 2014: Depreciation expense = $30,000 x 6/12 = __$15,000__**Total expense for the period = $37,500**

$30,000

2/6 x $90,000 = $30,000

Depreciation expense for the year should comprise of the proportionate share of depreciation charges relating to years 1 and 2 respectively.

$45,000

3/6 x $90,000 = $45,000

Depreciation expense for the year should comprise of the proportionate share of depreciation charges relating to years 1 and 2 respectively.

**Related:** Accounting entries for depreciation