Economic life of most assets is limited. After being used for a number of years, it will come to the end of their lives. As the time of retirement, assets may have a small trade-in or scrap value, or even may be worthless.

Computation of depreciation may involve compound interest and ordinary annuity. The computation of the periodic depreciation include allocating the cost of the property as an expense/ a cost of goods manufactured to the proper business operating periods. The amount of accumulated depreciation is known as accumulated depreciation or allowance for depreciation.

The difference between the original cost of an asset and its total amount in the accumulated depreciation is known as book value. Among reasons for depreciation include time factor, decay, worn out, etc.

In this chapter, we will use the following notation:

C          =   original cost of an asset

T          =   estimated trade-in value or scrap value

C – T   =  total depreciation charges or expenses

n     =  useful life of the asset estimated in years, service-hours, or product-units.

r    =  rate of depreciation expense per year, per service-hour, or per product-units.

6.1.1 Method of Averages

6.1.1.1 The Straight-Line Method

The simplest and most popular method of accounting for depreciation is the straight-line method. The depreciation charges are equal for each year. If R is the depreciation expense per year and n is the number of years, then R is the total depreciation charges divide by n, the number of years or can be written as:

R =

6.1.1.2 Service Hours Method

The service hours method relates depreciation to the estimated productive capacity of the asset in terms of its hours of useful service. The depreciation rate per service hour r is:

r =

Where n is the number of service hours.

The depreciation charges for a given year is equal to r multiplies the number of service hours of that year.

6.1.1.3 Product Units Method

The product units method defined depreciation to the estimated number of units produced by each asset during its useful life. The depreciation rate per unit product r is:

r =

Where n is the number of product units. The depreciation charges for a given period equal to r multiplies the number of units produced in that period.

6.1.2 Reducing Charge Method

6.1.2.1 Sum of the years-digit method

The total depreciation is fixed. It is the difference between the original cost and the trade-in or scrap value (C-T). The rate of depreciation is expressed in a changing fraction which becomes smaller each year. The numerator of the fraction is the number of remaining years of life of the asset. Whereas the denominator is the sum of digits that represent the years of life.

6.1.2.2 Constant/ Fixed rate method on diminishing book value

The depreciation expense for earlier year is higher than the later years. The depreciation expense is equal to fixed/ constant annual rate multiply the diminishing book value of an asset. There are two ways of computation: i) the declining balance method, ii) the fixed rate method.

For the declining balance method, first we need to find the annual depreciation rate by dividing 100% by the number of years of useful life of the asset. Then, find the maximum annual depreciation rate by multiplying the annual depreciation rate obtained by 2.

For the fixed rate method, the book value at the end of the life of the asset is equal to the scrap or trade-in value. The rate of annual depreciation charges (r) can be written as:

r =

6.1.3 Compound Interest Method

6.1.3.1 Annuity method

The annuity method resembles the method of amortizing a debt. The depreciation charges are equal and include not only a part of the cost of the asset but also the interest on the book value for each operating period. The step by step calculation are as follows:

Step 1: Find  the present value of the total depreciation charges. The present value is, P=T(1+i)^-n

Step 2: The annual depreciation charges are required to be equal. Thus, we can assume that the present value of an annuity (A_n) with payments consisting of equal depreciation charges as:

C-P = C- T(1+i)^-n = A_n = R

Step 3: R represents the annual depreciation charges, and can be obtained as follows:

R =

6.1.3.2 Sinking fund method

It is assumed that a sinking fund is established for the purpose of replacing an asset at the end of its useful life. The periodic depreciation charges are exactly the same as the periodic increases including the periodic deposit and interest) in the sinking fund. Hence, the depreciation charges are not equal. But the total of the depreciation charges is equal to the amount in the sinking fund (S_n) at the end of the useful life of the asset. The size of each deposit (R) made in the sinking fund is given by the annuity formula:

= R or R  =  

6.1.4 Composite Rate Method

The composite rate method is used for computing  the depreciation charges of a group of assets. The composite rate is obtained by dividing the total annual depreciation charges by the total cost  of  the  group  of assets. The annual depreciation charges of each asset are obtained by the straight line method. The composite rate may be used to compute depreciation charges  during  the  later  years  if  there  is  no  significant changes in the values and useful lives of assets. The work of computing the depreciation expense of each item can be avoided.  The composite rate of an asset can be calculated as:

The composite rate =

The composite life of a group of assets is the average life of the group. In computing the composite life, the annual depreciation charges of the group of assets may be obtained by using: i) the composite rate, ii) the depreciation charges are assumed to be equal for each year.

The composite life =

6.1.4.1 The sinking fund method

If the depreciation charges are not equal for each year, it is not categorised as a fixed composite rate. The annual deposits in the fund for each asset are equal during the life of the asset. The composite life is the time necessary for the total annual deposits at the given interest rate to accumulate to the total depreciation charges of the group of assets.