There is a reduction in the value of the equipment and other property of the plant every year due to depreciation. Therefore, a suitable amount (known as depreciation charge) must be set aside annually so that by the time the life span of the plant is over, the collected amount equals the cost of replacement of the plant. The following are the commonly used methods for determining the annual depreciation charge:
(i) Straight line method
(ii) Diminishing value method
(iii) Sinking fund method
Straight Line Method:
In this method, a constant depreciation charge is made every year on the basis of total depreciation and the useful life of the property.Obviously, annual depreciation charge will be equal to the total depreciation divided by the useful life of the property.
Annual depreciation charge = total depreciation ÷ useful life
= (P—S) ÷ n
Where,
P = Initial cost of equipment
n = Useful life of equipment in years
S = Scrap or salvage value after the useful life of the plant.
The straight line method is extremely simple and is easy to apply as the annual depreciation charge can be readily calculated from the total depreciation and useful life of the equipment. The figure below shows the graphical representation of the method. It is clear that initial value P of the equipment reduces uniformly, through depreciation, to the scrap value S in the useful life of the equipment.
The depreciation curve (PA) follows a straight line path, indicating constant annual depreciation charge. However, this method suffers from two defects. Firstly, the assumption of constant depreciation charge every year is not correct. Secondly, it does not account for the interest which may be drawn during accumulation.
Diminishing Value Method:
In this method, depreciation charge is made every year at a fixed rate on the diminished value of the equipment. In other words, depreciation charge is first applied to the initial cost of equipment and then to its diminished value.
Let say,
P = Capital cost of equipment
n = Useful life of equipment in years
S = Scrap value after useful life
Suppose the annual unit depreciation is x. It is desired to find the value of x in terms of P, n and S.
Value of equipment after one year = P − Px = P (1 − x)
Value of equipment after 2 years = Diminished value − Annual depreciation
= [P − Px] − [(P − Px)x]
= P − Px − Px + Px^2
= P(x 2 − 2x + 1)
= P(1 − x)^2
∴ Value of equipment after n years = P(1 − x)^n
But the value of equipment after n years (i.e., useful life) is equal to the scrap value S.
∴ S = P(1 − x)^n
Or (1 − x)^n = S/P
Or 1 − x = (S/P)^1/n
Or x = 1 − (S/P)^1/n ...(i)
From exp. (i), the annual depreciation can be easily found. Thus depreciation to be made for the first year is given by:
Depreciation for the first year = xP
= P[1 − (S/P)^1/n ]
Similarly, annual depreciation charge for the subsequent years can be calculated. This method is more rational than the straight line method.The figure below shows the graphical representation of diminishing value method. The initial value P of the equipment reduces,through depreciation, to the scrap value S over the useful life of the equipment. The depreciation curve follows the path PA. It is clear from the curve that depreciation charges are heavy in the early years but decrease to a low value in the later years.This method has two drawbacks. Firstly, low depreciation charges are made in the late years when the maintenance and repair charges are quite heavy. Secondly, the depreciation charge is independent of the rate of interest which it may draw during accumulation. Such interest money, if earned, are to be treated as income.Sinking Fund Method:
In this method, a fixed depreciation charge is made every year and interest compounded on it annually. The constant depreciation charge is such that total of annual installments plus the interest accumulations equal to the cost of replacement of equipment after its useful life.
Let
P = Initial value of equipment
n = Useful life of equipment in years
S = Scrap value after useful life
r = Annual rate of interest expressed as a decimal
Cost of replacement = P − S
Let us suppose that an amount of q is set aside as depreciation charge every year and interest compounded on it so that an amount of P− S is available after n years. An amount q at annual interest rate of r will become q(1 + r)^n at the end of n years.
Now, the amount q deposited at the end of first year will earn compound interest for n − 1 years and shall become q(1 + r)^n − 1 i.e.,
Amount q deposited at the end of first year becomes = q (1 + r)^n − 1
Amount q deposited at the end of 2nd year becomes = q (1 + r)^n − 2
Amount q deposited at the end of 3rd year becomes = q (1 + r)^n − 3
Similarly amount q deposited at the end of (n − 1) year becomes = q (1 + r)^n − (n − 1)
= q (1 + r)
∴ Total fund after n years = q (1 + r)^n − 1 + q (1 + r)^ n − 2 + .... + q (1 + r)
= q [(1 + r)^n − 1 + (1 + r)^n − 2 + .... + (1 + r)]
This is a G.P. series and its sum is given by :
Total fund = [q(1 + r)^n −1]÷ r
This total fund must be equal to the cost of replacement of equipment i.e., P − S.
∴ P − S = [q(1 + r)^n −1]÷ r
Or Sinking fund, q = (P—S)[r ÷ (1 + r)^n −1]...(i)
The value of q gives the uniform annual depreciation charge. The parenthetical term in eq. (i) is frequently referred to as the “sinking fund factor”.
∴ Sinking fund factor = r ÷ (1 + r)^n −1
Though this method does not find very frequent application in practical depreciation accounting, it is the fundamental method in making economy studies.
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