Declining balance method

Declining balance method of depreciation is similar to reducing balance method but there is a slight difference between these two methods of depreciation. In declining balance method, we use a fixed predetermined rate which is not directly applied on the book value of a fixed asset rather than it’s first applied on straight line rate of depreciation and the resultant rate of depreciation is used to calculate depreciation expense

**There are two versions of decline balance method**

150% declining balance method of depreciation which is commonly known as Declining balance method

200% declining balance method of depreciation which is called double declining balance method

Consider the example of double declining blance method to help grasp the concept. XYZ Company purchased a machine for $9000. Machine’s useful life = 5 years and residual value = $1000

**To calculate depreciation expense under double declining balance method, follow these steps**

**Step one**

Calculate the straight line rate of depreciation which in this case is “20%” (1/5=0.2 or 20%)

**Step two**

Double the straight line rate of depreciation or make it 200%. Therefore, the rate should be “40%” (20% X 2=40%)

**Step Three**

Apply the doubled straight line rate of depreciation (40%) on the book value of the fixed asset and you should be done, you would get the depreciation expense for an accounting period.

Book value of the machine in the first year is $9000. Therefore, its depreciation should be: “3600” (9000 X 40% =3600)

Following table shows the depreciation expense for each year

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

Purchase 1st year 2nd year 3rd year 4th year 5th year | $9000 X 40%=3600 $5400 X 40%=2160 $3240 X 40%=1296 $1944 X40%=778 $1166 X 40%= **166 | $3600 2160 $1296 $778 $166 | $3600 5760 $7056 $7834 $8000 | $9000 $5400 $3240 $1944 $1166 $1000 |

*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

**Note that the estimated residual value of the machine was $1000 and the depreciaton expense for the last year in accordance with the declining balance method should be $466 which gives 1000-466=534 residual value (less than the estimated residual value). Therefore, we are not counting 466 and 1166-1000=166 should be regarded as the depreciation expense for the last year of machine useful life in order to justify the estimated residual value ($1000)

Sum of the years digit method of depreciation

Also known as SYD, another method of depreciation which gives higher depreciation expense in the early life of an asset and lower depreciation afterward. In this method, depreciation rate is shown as a fraction. The fraction gets smaller each accounting period and this is the reason why depreciation expense constantly decreases with the passage of time. To calculated depreciation expense for a given accounting period, you just need to apply this fraction on depreciable amount (Depreciable amount = Cost – Residual value) of the fixed asset

**Example:**

XYZ Company purchased a vehicle for $6000. The vehicle will be used for 5 years and $1000 was estimated as its residual value

**To calculate depreciation expenses follow these steps:**

**Step one**

Calculate the depreciable amount of the fixed asset

Depreciable amount = Cost – Residual value

**In the current example,**

Cost = $6000

Residual value = $100

By putting values in the formula

Depreciable amount = 6000 – 1000

Depreciable amount = 5000

Hence, the depreciable amount is equal to $5000. This is the amount that will be depreciated over the useful life of that vehicle

**Step Two**

Calculate the “sum of the digits fraction” (which is a kind of depreciation rate)

At the time of purchase, the vehicle’s useful life is = 5 years

At the beginning of 2nd year, the vehicle’s useful life is = 4 years

At the beginning of 3rd year, the vehicle’s useful life is = 3 years

At the beginning of 4th year, the vehicle’s useful life is = 2 years

At the beginning of 5th year, the vehicle’s useful life is = 1 years

Now sum these digits 5 years+4 years+3 years+2 years+1 year = 15 years (or 15)

Finally, the "sum of the digits fractions" for each year

Sum of the digits fraction for the 1st year = 5/15

Sum of the digits fraction for the 2nd year = 4/15

Sum of the digits fraction for the 3rd year = 3/15

Sum of the digits fraction for the 4th year = 2/15

Sum of the digits fraction for the 5th year = 1/15

These fractions are applied on the depreciable amount to calculated the depreciation expense for each year or accounting period as the following table shows

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

Purchase 1st year 2nd year 3rd year 4th year 5th year | $5000 X 5/15 $5000 X 4/15 $5000 X 3/15 $5000 X 2/15 $5000 X 1/15 | $1667 $1334 $1000 $667 $334 | $1667 $3001 $4001 $4668 Approx. $5000 | $6000 $4333 $2999 $1999 $1332 Approx. $1000 |

*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