Reducing/diminishing balance method

The second most popular method of depreciation. This method is generally applied on certain fixed assets that are more productive or useful initially and with the passage of time or with constant use their usefulness decrease

The calculating of depreciation expenses in this method is not that difficult. Under this method, a certain percentage of a fixed asset’s book value is considered as depreciation expense for an accounting period. For example if a car has a book value = $5000 and depreciation is to be charged at 20%, the depreciation expenses should be 5000 X 20% = 1000. Therefore, depreciation expenses is $1000 for the current accounting period

Consider the following formula for Reducing/diminishing balance method

For example cost of a car is = $12000, Residual value = $4901 and its useful life is 5 years

**Here is the calculating of depreciation**

First of all, we have to calculated the rate of depreciation or percentage of the car’s book value that should be considered as depreciation expense

Formula

**Values**

n = Number of years = 5 years

S = Scrape value/Salvage value/Residual value = $4901

C= Cos the fixed asset/car = $12000

R = Rate of depreciation expense = ?

**By putting values in the formula**

r = 1- (4901/12000)^1/5

r = 1- (0.41)^1/5

r = 1- 0.836

r = 0.164 or we can say 16.4%

Therefore,

**rate of depreciation is 16.4%**or 16.4% of the car’s book value should be regarded as depreciation expense in every accounting period

Following table shows the depreciation expenses over entire useful of the car

Years | Calculation of Depreciation | DepreciationExpenses | AccumulatedDepreciation | Book value of the Asset |

Purchase 1st year 2nd year 3rd year 4th year 5th year | $12000 X 16.4%=$1968 $10032 X 16.4%=$1645 $8387 X 16.4%=$1375 $7012 X 16.4%= $1150 $5862 X 16.4%=$961 | $1968 $1645 $1375 $1150 $961 | $1968 $3613 $4988 $6138 $7099 | $12000 $10032 $8387 $7012 $5862 $4901 |

*Accumulated depreciation = The total or accumulated amount of depreciation expenses at a point in time

*Book value = Cost the asset - Accumulated depreciation expenses

*Depreciable amount = Cost the asset - Residual value the asset

**EXAMPLE**

XYZ Company purchased a truck costing $5000 on January 2012. The truck’s useful life was estimated to be 5 years with residual value of $1000.

Required: Calculated the amount of truck's depreciation expense using reducing balance method of depreciation for the first 3 years

**Solution**

First of all, we need the rate of depreciation for the computation of depreciation expense.

Formula for depreciation rate:

Where,

n = Useful life = 5 years

S = residual value = $1000

C = Cost = $5000

r = Rate of depreciation =?

**By putting these values in the formula**

r = 1- (1000/5000)^1/5

r = 1- 0.2^1/5

r = 1- 0.725

r = 0.275 or 27.5% approximately

**Depreciation for the first year**

Book value = Cost – Accumulated depreciation

By putting values

Book value = $5000 – 0

Book value = $5000

Depreciation expense = Book value X Rate of depreciation

By putting values

Depreciation expense = $5000 X 27.5%

Depreciation expense = 1375

**Depreciation for the 2nd year**

Book value = Cost – Accumulated depreciation

By putting values

Book value = $5000 – 1375

Book value = $3625

Depreciation expense = Book value X Rate of depreciation

By putting values

Depreciation expense = $3625 X 27.5%

Depreciation expense = $997

**Depreciation for the 3rd year**

Book value = Cost – Accumulated depreciation

By putting values

Book value = $5000 – 2372

Book value = $2628

Depreciation expense = Book value X Rate of depreciation

By putting values

Depreciation expense = $2628 X 27.5%

Depreciation expense = 723