Depreciation is the most important item in the fixed costs and it represents the reduction in the value of the equipment and other property of the plant every year due to continuous wear and tear and also due to obsolescence.
The first factor can be reduced by proper maintenance of the equipment and the buildings, but the second factor is quite unpredictable. To account for the depreciation, a certain fixed amount is set aside every year so that by the time the life span of the plant is over, the total amount accumulated equals the replacement cost (original cost of the equipment less the expected salvage value).
The methods commonly used for determination of annual depreciation charges are:
1. Straight Line Method,
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2. Diminishing Value Method, and
3. Sinking Fund Method.
1. Straight Line Method:
This method assumes that certain depreciation occurs according to the straight line law and, therefore, in this method a constant depreciation charge is made every year on the basis of total depreciation (initial cost – scrap or salvage value) and useful life of the equipment/property.
Though this method is very popular because of its simplicity but it does not take into account the amount of interest earned by the amount set aside yearly. The assumption of constant depreciation every year is also not correct.
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Figure 14.1 illustrates this method graphically.
2. Diminishing Value or Declining Balance Method:
In this method provision is made for setting each year a fixed rate, first applied to the original cost and then to the diminishing value; such rate depending upon the useful life of the plant. This method results in distribution of the total expenses on the plant (depreciation plus maintenance cost) over its total useful life because in this method depreciation charges are heavy in early years when maintenance charges are low and depreciation charges are low in the late years when maintenance charges are heavy.
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The serious drawback of this method is that a heavy burden towards depreciation charges is imposed in the early years when the plant is to develop and build up its income. In this method also the amount of interest earned by the reserve accumulation is ignored.
Let the capital cost of the plant be P, salvage value after useful life of equipment of n years be S and annual unit depreciation be x.
Figure 14.2 illustrates this method graphically.
3. Sinking Fund Method:
In this method provision is made for setting aside each year such a sum as, invested at certain interest rate compounded annually, will give the amount equal to replacement cost of the installation at the end of its useful life. As compared to straight line method, it requires smaller annual amounts and also the amounts for annuity are uniform.
Let P be the initial value of the equipment, n be the useful life of equipment in years, S be the scrap or salvage value after useful life of equipment of n years, and r is the rate of interest per annum expressed as a fraction.
If the annual deposit be q, it will earn interest rq in one year, so that it will worth q + rq = q (1 + r) at the end of one year. Thus its value will be multiplied by the ratio (1 + r) every year and it will worth q(1 + r)2 at the end of 2 years, q(1 + r)3 at the end of 3 years and q( 1 + r)n at the end of n years.
This method is illustrated graphically in Fig. 14.3.
Example 1:
A 300 kVA distribution transformer costs Rs. 20,000 and has a salvage value of Rs. 1,000 at the end of 20 years. Determine the depreciated value of the plant at the end of 10 years on the following methods of assessment:
(i) Straight line depreciation.
(ii) Sinking fund depreciation of 8% compounded annually.
Solution:
Example 2:
A plant costs Rs. 7.56 × 105 and it is estimated that after 25 years it will have to be replaced by a new one. At that instant its salvage value will be Rs 1.56 × 105. Calculate- (i) annual deposit to be made in order to replace the plant after 25 years, (ii) the value of plant after 10 years on the following basis:
(i) Reducing balance depreciation method.
(ii) Sinking fund depreciation method at 8% annual compound interest.
Solution:
