Diminishing Balance Method

(Written Down Value or Reducing Balance Method)

In order to calculate the annual depreciation under this method, a fixed percentage is applied to the book value of the asset. The book value of the asset means the undepreciated balance of the asset cost, i.e., balance of the asset cost not yet depreciated. In other words, the depreciation is calculated on the reducing balance (asset cost minus  depreciation) and not on the original cost. The producer is that depreciation calculated is deducted from the cost of the asset and balance is known as the written down value. The fixed percentage is applied to a declining base, the depreciation expense for each subsequent accounting period will be less under this method. It is impossible to reduce asset cost to zero because there will always be some balance to reduce asset cost further. The written down value at the end of the estimated useful life of the asset should equal the estimated salvage value. The basic formula for calculating the rate of depreciation to be used in the diminishing balance method is:

        r = 1 – n√(S/C)  x 100
                
Where r = the rate of depreciation; n = number of year of asset’s life; s = salvage (or scrap) value and c = cost of the asset. For example, Somesh buys a second hand motor car for Rs. 40,000 and its scrap value is Rs. 10,480 and the useful life of the car is 6 years, the rate of depreciation under diminishing balance method would be:


        r = 1 – 6 √(10480/40,000)      x 100

        r = 1 – 6 √0.262    x 100
         
          = 1 – 0.8 x 100 = 20%

Attention Please
(i) Calculation of n√(S/C)  can be done by use of logarithms or some manual calculators.
(ii) A reducing balance rate of depreciation can only be computed if some scrap value is assumed and unless the assumed scrap value is a significant amount, an absurd rate will be computed. Thus if the scrap value is nil then a nominal figure of Re. 1 may be attributed to S., otherwise the whole equation would be equal to zero.
(iii) Either variable can be determined by transposing the formula. This is proved as below:
                                                    Rs.      
Cost                                   40,000
Depreciation – year 1        8,000        (20% of Rs. 40,000) 
Written down value         32,000
Depreciation – year 2         6,400        (20% of Rs. 32,000)
Written down value         25,600
Depreciation – year 3         5,120        (20% of Rs. 25,600)
Written down value         20,480   
Depreciation – year 4         4,096        (20% of Rs. 20,480)
Written down value         16,384
Depreciation – year 5         3,277        (20% of Rs. 16,384)
Written down value         13,107
Depreciation – year 6         2,621        (20% of Rs. 13,107)
Salvage Value                   10,486


Attention Please
(1)    Slight difference of Rs. 6 is due to rounding of figures.
(2)    The amount of depreciation taken cannot reduces the book value below salvage value, If it does happen in a specific case, the amount of depreciation will be suitably adjusted in the final year of service life of the asset.

Advantages: The following favourable points are claimed:
(i)    The higher depreciation is charged in the earlier years when the machine is most efficient compared to later years. This matches higher cost with larger revenues resulting from the increased production.
(ii)    The obsolescence problem is given due care because the major part of the depreciation is charged in the first year and the management has no difficulty in replacing the asset.
(iii)    The problem of higher maintenance or repair charges is solved since the deprecation expense in later years is considerably lower than the depreciation expenses of early years.

Disadvantages:
(i)    This method requires considerable amount of figure work.
(ii)    Such a method involves the use of root tables where the arithmetic is difficult and often results in a very heavy first year change.
(iii)    It is also pointed out that obsolescence cannot be reflected by a mechanistic computation without considering the impact of technological changes.

Suitability: In general this method is suitable to plant and machinery where repairs are heavy in the later years and additions, extensions and substitution are frequent.

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