There are several methods for calculating depreciation. The selection of a depreciation method generally depends on either the passage of time or the level of activity or use of an asset. A time-based method allocates depreciation according to the useful life of the asset, while an activity-based method calculates depreciation according to the actual use or production of the asset.
The major methods of depreciation include the Straight-Line Method, Diminishing or Declining Balance Method, Activity or Annuity-Based Depreciation, Sum-of-Years-Digits Method, Units-of-Production Method, Group Depreciation Method, and Composite Depreciation Method.
Straight-Line Method of Depreciation
The Straight-Line Method is the simplest and one of the most commonly used methods of depreciation. Under this method, an equal amount of depreciation is charged every year throughout the estimated useful life of the asset.
The annual depreciation expense is calculated by deducting the expected residual or salvage value from the cost of the fixed asset and dividing the resulting amount by the estimated useful life of the asset.
Annual Depreciation Expense = (Cost of Fixed Asset − Residual Value) ÷ Useful Life of Asset in Years
The formula may also be expressed as:
DE = (Cost − Salvage Value) ÷ Useful Life
The salvage value may be zero. In certain situations, the costs required to retire an asset may result in a negative economic amount. However, for depreciation purposes, salvage value is generally not calculated below zero.
Under the Straight-Line Method, the same depreciation amount is charged each year until the carrying or book value of the asset is reduced from its original cost to its residual or scrap value.
Example of Straight-Line Depreciation
Suppose a vehicle is purchased for $17,000. Its expected useful life is 5 years, and its estimated salvage value is $2,000.
Annual depreciation will be calculated as:
($17,000 − $2,000) ÷ 5 = $3,000 per year
Therefore, depreciation expense of $3,000 will be charged every year for five years.
| Year | Depreciation Expense | Accumulated Depreciation | Book Value at Year-End |
|---|---|---|---|
| Original Cost | — | — | $17,000 |
| 1 | $3,000 | $3,000 | $14,000 |
| 2 | $3,000 | $6,000 | $11,000 |
| 3 | $3,000 | $9,000 | $8,000 |
| 4 | $3,000 | $12,000 | $5,000 |
| 5 | $3,000 | $15,000 | $2,000 |
The book value of an asset is equal to its original cost minus accumulated depreciation.
Book Value = Original Cost − Accumulated Depreciation
The book value at the end of one accounting year becomes the opening book value at the beginning of the next year. Depreciation continues until the book value becomes equal to the scrap or residual value of the asset.
Sale of a Depreciated Asset
If an asset is sold for an amount greater than its depreciated value or net book value, the excess may be treated as a gain and may be subject to depreciation recapture.
The gain above the depreciated value may be recognised as ordinary income for tax purposes. If the sale price is lower than the book value, the resulting capital loss may be tax-deductible.
If the asset is sold for more than its original book value, the gain above the original book value is recognised as a capital gain.
A company may use a depreciation rate different from the rate used by the taxation authority. Such a difference creates a timing difference in the Income Statement because the company and the taxation authority may recognise different amounts of profit at a particular point in time.
Diminishing Balance or Declining Balance Method
The Diminishing Balance Method, also known as the Reducing Balance Method, calculates depreciation on the non-depreciated or remaining book value of an asset.
Under this method, a higher amount of depreciation is generally charged during the earlier years of the asset’s useful life. As the book value of the asset decreases, the amount of depreciation also decreases.
The Double-Declining-Balance Method is an accelerated depreciation method. It applies an accelerated depreciation rate to the remaining non-depreciated balance of the asset.
The salvage value is not considered while determining the annual depreciation amount under the Double-Declining-Balance Method. However, the book value of the asset must never be reduced below its salvage value.
Depreciation stops when either the asset reaches its salvage value or the end of its useful life.
Example of Diminishing Balance Method
Suppose an asset has an original cost of $1,000, a depreciation rate of 40%, and a scrap value of $100.
| Year | Depreciation Rate | Depreciation Expense | Accumulated Depreciation | Book Value |
|---|---|---|---|---|
| Original Cost | — | — | — | $1,000 |
| 1 | 40% | $400 | $400 | $600 |
| 2 | 40% | $240 | $640 | $360 |
| 3 | 40% | $144 | $784 | $216 |
| 4 | 40% | $86.40 | $870.40 | $129.60 |
| 5 | — | $29.60 | $900 | $100 |
In the final period, only $29.60 is charged as depreciation so that the asset’s book value does not fall below its scrap value of $100.
Conversion to Straight-Line Method
The Double-Declining-Balance Method may not always fully depreciate an asset by the end of its useful life.
Therefore, some methods calculate both declining balance depreciation and straight-line depreciation every year and apply the higher amount.
This approach results in a change from the Declining Balance Method to the Straight-Line Method at an appropriate point during the asset’s useful life.
The Double-Declining-Balance Method may provide a better representation of the depreciation pattern of certain assets, such as vehicles, because such assets may lose more value during their earlier years of use.
Depreciation Rate under Declining Balance Method
The depreciation rate required to fully depreciate an asset to its residual value by the end of its estimated life may be calculated as:
Depreciation Rate = 1 − (Residual Value ÷ Cost of Fixed Asset)^(1/N)
Here, N represents the estimated useful life of the asset, generally expressed in years.
Activity or Annuity-Based Depreciation
Activity-based depreciation is not based mainly on the passage of time. Instead, depreciation is calculated according to the level of activity or use of the asset.
The level of activity may be measured in terms of miles driven by a vehicle or the number of operating cycles completed by a machine.
When the asset is acquired, its expected life is estimated in terms of the total level of activity.
For example, suppose a vehicle costing $17,000 has a salvage value of $2,000 and is expected to travel 50,000 miles during its useful life.
The depreciation rate per mile is:
($17,000 − $2,000) ÷ 50,000 miles = $0.30 per mile
The depreciation expense for each year is calculated by multiplying the actual number of miles driven during the year by $0.30 per mile.
Therefore, a year in which the vehicle is used more will have a higher depreciation expense.
Sum-of-Years-Digits Method
The Sum-of-Years-Digits (SYD) Method is an accelerated depreciation method. It results in a faster write-off of an asset’s cost than the Straight-Line Method.
The method is based on the assumption that assets are generally more productive when they are new and their productivity decreases as they become older.
Under this method, annual depreciation is calculated by multiplying the depreciable cost of the asset by a specified fraction.
The formula is:
SYD Depreciation = Depreciable Base × (Remaining Useful Life ÷ Sum of Years’ Digits)
The depreciable base is calculated as:
Depreciable Base = Cost − Salvage Value
Example of Sum-of-Years-Digits Method
Suppose an asset has an original cost of $1,000, an estimated useful life of 5 years, and a salvage value of $100.
The depreciable base is:
$1,000 − $100 = $900
The years’ digits are:
5, 4, 3, 2 and 1
The sum of the years’ digits is:
5 + 4 + 3 + 2 + 1 = 15
The sum may also be calculated using the formula:
(n² + n) ÷ 2
Where n is the useful life of the asset in years.
For five years:
(5² + 5) ÷ 2 = 15
The depreciation rates will therefore be 5/15 in the first year, 4/15 in the second year, 3/15 in the third year, 2/15 in the fourth year, and 1/15 in the fifth year.
| Year | Depreciable Base | Rate | Depreciation Expense | Accumulated Depreciation | Book Value |
|---|---|---|---|---|---|
| Original Cost | — | — | — | — | $1,000 |
| 1 | $900 | 5/15 | $300 | $300 | $700 |
| 2 | $900 | 4/15 | $240 | $540 | $460 |
| 3 | $900 | 3/15 | $180 | $720 | $280 |
| 4 | $900 | 2/15 | $120 | $840 | $160 |
| 5 | $900 | 1/15 | $60 | $900 | $100 |
Thus, a higher amount of depreciation is charged in the earlier years and a lower amount in the later years.
Units-of-Production Method
The Units-of-Production Method calculates depreciation according to the actual production or use of an asset.
Under this method, higher depreciation is charged during years in which the asset is heavily used and lower depreciation is charged during years of lower production.
The formula is:
Annual Depreciation Expense = [(Cost of Fixed Asset − Residual Value) ÷ Estimated Total Production] × Actual Production
It may also be written as:
DE = [(Original Value − Salvage Value) ÷ Estimated Production Capacity] × Units Produced during the Year
Example of Units-of-Production Method
Suppose an asset has an original cost of $70,000, a salvage value of $10,000, and an estimated total production capacity of 6,000 units.
Depreciation per unit will be:
($70,000 − $10,000) ÷ 6,000 = $10 per unit
The depreciation expense for each year is calculated by multiplying $10 by the actual number of units produced during the year.
| Units Produced | Depreciation per Unit | Depreciation Expense | Accumulated Depreciation | Book Value |
|---|---|---|---|---|
| Original Cost | — | — | — | $70,000 |
| 1,000 | $10 | $10,000 | $10,000 | $60,000 |
| 1,100 | $10 | $11,000 | $21,000 | $49,000 |
| 1,200 | $10 | $12,000 | $33,000 | $37,000 |
| 1,300 | $10 | $13,000 | $46,000 | $24,000 |
| 1,400 | $10 | $14,000 | $60,000 | $10,000 |
Depreciation stops when the book value becomes equal to the scrap value of the asset.
At the end of the depreciation period:
Accumulated Depreciation + Scrap Value = Original Cost
Group Depreciation Method
The Group Depreciation Method is used to depreciate multiple assets that are similar in nature and have approximately the same useful lives.
Under this method, similar assets are grouped together and depreciated using a common depreciation method.
The assets included in the group should have similar characteristics and approximately similar periods of useful life.
Composite Depreciation Method
The Composite Depreciation Method is applied to a collection of assets that are not similar in nature and have different useful or service lives.
For example, computers and printers are different assets and may have different useful lives. However, both may be classified as part of office equipment.
Under the Composite Method, depreciation on the assets is determined using the Straight-Line Method.
Suppose the following assets are held:
| Asset | Historical Cost | Salvage Value | Depreciable Cost | Useful Life | Annual Depreciation |
|---|---|---|---|---|---|
| Computers | $5,500 | $500 | $5,000 | 5 years | $1,000 |
| Printers | $1,000 | $100 | $900 | 3 years | $300 |
| Total | $6,500 | $600 | $5,900 | — | $1,300 |
Composite Life
The Composite Life is calculated by dividing the total depreciable cost by total annual depreciation.
Composite Life = Total Depreciable Cost ÷ Total Depreciation per Year
Therefore:
$5,900 ÷ $1,300 = 4.5 years
The composite life of the assets is approximately 4.5 years.
Composite Depreciation Rate
The Composite Depreciation Rate is calculated by dividing annual depreciation by the total historical cost of the assets.
Composite Depreciation Rate = Annual Depreciation ÷ Total Historical Cost
Therefore:
$1,300 ÷ $6,500 = 0.20 or 20%
Depreciation expense is calculated by multiplying the composite depreciation rate by the balance of the asset account at historical cost.
Depreciation Expense = Composite Depreciation Rate × Historical Cost
Therefore:
20% × $6,500 = $1,300
The accounting entry involves debiting Depreciation Expense and crediting Accumulated Depreciation.
Sale of an Asset under Composite Method
When an asset is sold under the Composite Method, the cash account is debited with the amount received and the asset account is credited with the original cost of the asset.
The difference between the amount received and the original cost is debited to Accumulated Depreciation.
Under the Composite Method, no gain or loss is recognised on the sale of an individual asset. The theoretical basis is that gains and losses from assets sold before and after the composite life are expected to average each other out.
Exam Focus
Depreciation methods may be based on the passage of time or the level of activity or use of an asset.
Under the Straight-Line Method, an equal amount of depreciation is charged every year. The formula is (Cost − Residual Value) ÷ Useful Life.
The Diminishing or Declining Balance Method charges higher depreciation in earlier years on the remaining book value of the asset. The asset’s book value should not be reduced below its salvage value.
The Sum-of-Years-Digits Method is an accelerated depreciation method based on the assumption that assets are more productive when new.
The Units-of-Production Method calculates depreciation according to actual production or asset use. Greater use results in higher depreciation expense.
The Group Depreciation Method applies to similar assets having approximately the same useful lives, whereas the Composite Depreciation Method applies to dissimilar assets having different service lives.
Under the Composite Method, no gain or loss is recognised on the sale of an individual asset.