In the same manner the generalized expression for depreciation in any given year ‘m ' can be written as follows (referring to equations (3.8), (3.11) and (3.14));

(3.16)

Similarly the generalized expression for book value at the end of any year ‘m' is given as follows (referring to equations (3.9), (3.12) and (3.15));

(3.17)

The book value at the end of useful life i.e. at the end of ‘n ' years is given by;

(3.18)

The book value at the end of useful life is theoretically equal to the salvage value of the asset. Thus equating the salvage value (SV) of the asset to its book value (BV_n) at the end of useful life results in the following;

(3.19)

Thus for calculating the depreciation of an asset using declining balance method, equation (3.19) can be used to find out the constant annual depreciation rate, if it is not stated for the asset. From equation (3.19), the expression for constant annual depreciation rate ‘d_m' from known values of initial cost ‘ P ' and salvage value (SV > 0) is obtained as follows;

(3.20)

In double-declining balance (DDB) method, for calculating annual depreciation amount and book value at the end of different years, the value of constant annual depreciation rate ‘d_m' is replaced by ‘ ' in the above mentioned equations.

Example -1

The initial cost of a piece of construction equipment is Rs.3500000. It has useful life of 10 years. The estimated salvage value of the equipment at the end of useful life is Rs.500000. Calculate the annual depreciation and book value of the construction equipment using straight-line method and double-declining balance method.

Solution:

Initial cost of the construction equipment = P = Rs.3500000

Estimated salvage value = SV = Rs.500000

Useful life = n = 10 years

For straight-line method, the depreciation amount for a given year is calculated using equation (3.1).