Book value at the end of 2^nd year is equal to book value at the beginning of 2^nd year (i.e. book value at the end of 1^st year) less the depreciation in 2^nd year and is expressed as follows;

BV2 = BV1 -Dm

(3.3)

As already stated depreciation amount is same in every year.

Now putting the expression of ‘BV₁' from equation (3.2) in equation (3.3);

BV2 = (P-Dm) − Dm = P - 2Dm

(3.4)

Similarly the book value at the end of 3^rd year is equal to book value at the beginning of 3^rd year (i.e. book value at the end of 2^nd year) less the depreciation in 3^rd year and is given by;

BV3 = BV2 - Dm BV3 = (P - 2Dm) − Dm = P - 3Dm

(3.5) (3.6)

In the same manner the generalized expression for book value at the end of any given year ‘ m ' can be written as follows;

BVm = P - mDm

(3.7)

Declining balance (DB) depreciation method:-

It is an accelerated depreciation method. In this method the annual depreciation is expressed as a fixed percentage of the book value at the beginning of the year and is calculated by multiplying the book value at the beginning of each year with a fixed percentage. Thus this method is also sometimes known as fixed percentage method of depreciation. The ratio of depreciation amount in a given year to the book value at the beginning of that year is constant for all the years of useful life of the asset. When this ratio is twice the straight-line depreciation rate i.e. , the method is known as double-declining balance (DDB) method. In other words the depreciation rate is 200% of the straight-line depreciation rate. Double-declining balance (DDB) method is the most commonly used declining balance method. Another declining balance method that uses depreciation rate equal to 150% of the straight-line depreciation rate i.e. is also used for calculation of depreciation. In declining balance methods the depreciation during the early years is more as compared to that in later years of the asset's useful life.

In case of declining balance method, for calculating annual depreciation amount, the salvage value is not subtracted from the initial cost. It is important to ensure that, the asset is not depreciated below the estimated salvage value. In declining-balance method the calculated book value of the asset at the end of useful life does not match with the salvage value. If the book value of the asset reaches its estimated salvage value before the end of useful life, then the asset is not depreciated further.

Representing constant annual depreciation rate in declining balance method as ‘d_m', the expressions for annual depreciation amount and book value are presented as follows;

The depreciation in 1^st year is calculated by multiplying the initial cost (i.e. book value at beginning) with the depreciation rate and is given by;

(3.8)