 Hello everybody, myself, Dr. Sunil Lathayan Kulkarni, Assistant Professor, Department of Mechanical Engineering, Walchen Institute of Technology, Sholapur. Today I am going to deliver a video session on methods of determining depreciation. This we are discussing with respect of economics of power generation in continuation to my previous video session. At the end of this session, students will be able to tell the meaning of depreciation and explain various methods of depreciation. The contents of this video session are what is depreciation, what are the methods of determining depreciation and in that we are going to discuss straight line method, diminishing value method in this video and one more method will be discussed in the next video session. Now, let us see what is depreciation. From the time the power station is installed, its equipment steadily deteriorates due to wear and tear so that there is a gradual reduction in the value of the plant. So, this reduction in the value of the plant every year is known as annual depreciation. Let us think that if the plant or equipment value goes on reducing every year after its useful life, what provision should be made so that we can replace the equipment or plant by new one. Let us think for a while. Therefore, what is usually done is that we keep aside a suitable amount which is usually called as depreciation charge and it must be set aside annually so that by the time the lifespan of the plant is over, the collected amount will be equal to the cost of replacement of the plant. In this regard, following methods are commonly used for determining the annual depreciation charge. So, let us see now the various methods of determining depreciation. The first and most simple method is straight line method and second method is diminishing value method and third method is sinking fund method. Now, in this video session, we are going to study the first two methods that is straight line method and diminishing value method. Now in straight line method, a constant depreciation charge is made or applied every year on the basis of total depreciation and useful life of the equipment or property. Obviously, the annual depreciation charge will be equal to total depreciation divided by useful life of the property. Let us see how to calculate the annual depreciation charge by straight line method. In general, the annual depreciation charge on the straight line method may be expressed as annual depreciation charge is equal to P minus S divided by N where P is initial cost of the equipment. Of course, it is in rupees S is the salvage or scrap value after the useful life of the plant. Remember, whenever the useful life of the plant is over or equipment is over, its value is never zero. It will have certain scrap value which is called as either scrap or salvage value and N is the number of useful life of the equipment in years. That is the number of years of the useful life of the equipment or plant. So in this method, as I have shown you graphically, okay, let us see what does this graph show. So in this graph, you can see we have shown the value of the equipment. So when the equipment is new, that is at the zero years of age, its initial cost is capital P which we have seen and at the end of useful life of N years, its value becomes equal to S that is scrap value or which we call it as salvage value. Therefore, this is curve line, straight line P to A which is showing how the depreciation is uniformly applied throughout the useful life of the year. So that is why this is the most simplest way. The depreciation is uniformly occurring over the entire lifespan of the equipment. And this is the total depreciation means P minus S will give us the total depreciation of the equipment, value of the depreciated value of the equipment. Now, so as we have seen, the straight line method is extremely simple and it is easy to apply as the annual depreciation chart can be readily calculated from the total depreciation and useful life of the equipment. So as we have seen in the figure, the graphical representation, the initial value of the equipment reduces uniformly through the depreciation to the scrap value in the useful life of the equipment and the depreciation curve P to A follows the straight line path indicating the constant annual depreciation chart. However, this particular straight line method has got two defects or two drawbacks. First is that the assumption of constant depreciation chart every year it is not correct. So remember, depreciation never occurs uniformly and therefore we are charging constant depreciation amount every year it is not correct. And secondly, it is because when the equipment is new one, the depreciation may not be too high and therefore the charges which we are taking should be less actually in the initial year but in this method we are applying it uniformly throughout the lifespan. And secondly, in this method the amount which we are collecting that is depreciation chart does not account for any interest which may be drawn during the accumulation. That is the money saved any neglects actually whenever you save the depreciation chart and if you put it in the bank you will be able to earn the interest but that is neglected in the straight line method. Now let us come to the diminishing value method. So in this method the depreciation chart is made every year at a fixed rate on diminished value of the equipment it is also called as reducing balance method. So in other words the depreciation chart is first applied to the initial cost of the equipment and then to its reduced value or diminished value. Now let us see the mathematical treatment of this method. Let P be the capital cost of the equipment, N is the useful life of the equipment in years and S is the salvage or scrap value after useful life. So suppose the annual depreciation annual unit depreciation is small x means what if the annual depreciation is 10% if we consider fixed depreciation per year so it is 10% then we can say that the annual unit depreciation is 0.1 means 10 divided by 100 so it will be equal to 0.1. So similarly we assume that annual unit depreciation is x so it is desired to find the value of x in terms of P, N and S that is initial cost of the equipment, salvage value and useful life. So value of the equipment after one year will be equal to initial cost is P minus the reduced depreciation charge is x so P minus Px will be the reduced value of the equipment after one year so it will be equal to if we take P common P into 1 minus x. Similarly value of the equipment after say two years will be equal to the diminished value minus annual depreciation. Now diminished value is P into P into P minus P into x that is P into 1 minus x minus again if you multiply to this term by the unit depreciation charge that is P minus Px into x then what after simplification we get P minus Px minus Px plus Px square which upon simplification we will get it as taking out P common outside the bracket P into x square minus 2x plus 1 which will be equal to P into bracket 1 minus x square. Therefore on the similar grounds we can write the value of the equipment after N years that is the diminished value or reduced value of the equipment after N years will be equal to P into bracket 1 minus x raise to N where N is the useful life of the this we are writing by analogy because the value of the equipment after two years is P into 1 minus x square whereas value of the equipment after one year is P into 1 minus x raise to 1. So similarly value of the equipment after N years will be equal to P into 1 minus x raise to N but the value of the equipment after N years that is useful life is nothing but equal to scrap value or salivary value. Therefore we can write S is equal to P into 1 minus x raise to N or 1 minus x raise to N is equal to S by P or 1 minus x is equal to S by P raise to 1 by N or x is equal to 1 minus S upon P raise to 1 by N. So by using this equation one we can calculate the annual unit depreciation charge very easily and once we get this annual unit depreciation charge by using this equation then we can calculate the reduced value of the equipment okay. So depreciation for the first year will be x into P and the reduced value of the or this we can write it as P into putting the value of x as 1 minus S by P raise to 1 by N so we can easily calculate the depreciation charge for subsequent years and we can calculate the total amount fund to be collected. So this is known as the diminishing value method. Now this method is more rational than straight line method. Now let us see the graphical representation of this method. So initial value of the equipment is P which reduces through depreciation to the scrap value S over the useful life of the equipment and the depreciation curve follows the path P A not the straight line as we have seen earlier okay. So it is clear from the curve that the depreciation charges are heavy in the earlier but decreases to low value in the latter years. So this is the graphical method. So initial value of the equipment when it is new that is at the beginning is P and at the end of N years it is S. So P minus S is the total depreciation and this curve shows the diminishing value method curve path followed for the depreciation. So during initial years the depreciation charges are okay. So the during initial years okay earlier the depreciation charges are heavy and they are reducing in the later years. Now this particular method has also got two drawbacks. First is it requires heavy instalment in earlier years when maintenance charges are minimum and it goes on decreasing later years when the maintenance charges increase. And secondly again we are neglecting the interest accumulated on the amount which is saved. These are the references. Thank you.