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So, this is an I had already told you about the other case where suppose we said A and B which we talked about the life of 3 years, and 8 years and we could calculate the CRF values, use the CRFvalues and you can find that this is the B by C ratio for B and the net present value for B comes out to be higher, you can cross-check these numbers. Before we do an example let us now talks about sometimes people confuse the discount rate with inflation. So, the point is that there are situations even if your prices remain constant we still discount the future, so even if there was no inflation, we generally prefer money today compared to money in the future. So, this whole concept of discounting is independent of inflation but let us touch upon what we understand by inflation. (Refer Slide Time: 13:02) So, inflation is a change in the general level of prices and the inflation could be inflation means an increase in the general levels of prices and we have a term called deflation which is a decrease in the general level of prices. In the context of India, we have been fortunate to have always prices have always been increasing. So, we have only seen inflation but there are other countries where prices fluctuate and you keep having inflation and deflation and in which case the decision making becomes very difficult. So, typically how we characterize inflation is we look at a basket of goods and services and we see that for that basket of goods and services in a particular year if you were to buy the goods and services, how much would it cost and you take the last if you take 2019 it costs a certain amount, in 2018 it costs another value, the ratio of these two prices will give you the inflation rate. (Refer Slide Time: 14:17) 2019 P1 2018 P2 P1P2 =(1+i) So, basically what will happen is if you say in 2019 the price is P1 and for the same set of goods and prices in 2018 if it was P2 then P1 by P2 will be 1 plus I, where i is the inflation rate between2018, and 2019 and in typically. So, typically what happens is this is called the inflation rate. The inflation rate as you can understand this is the prices fluctuate in different regions, prices fluctuate in different seasons, and the prices and inflation are sensitive issues. They are political issues and you sometimes want to show that it is the inflation is less or more and, so typically what happens is if you look at the Reserve Bank of India, or the International Monetary Fund, goto their web site you will find that these are indexed. They are indexed usually to a base year when the prices are relatively stable. In that base year, that price is kept as that base year price is taken as 100 and compared to that other prices, other years are index in terms of that 100. So, we have two indices one is called wholesale price index, and the second is the consumer price index, the wholesale price index is important for companies who are buying electricity, urea. So, you see what are the things that companies buy and what have the prices, how of those prices change. The consumer price index is a price that is seen by individuals in households and so we are talking of electricity, we are talking of some fuels, you talk of food items in each of these cases the there is a definition of the basket of goods in terms of how many kgs of what and then what are the weights, we then make this calculation and you will see tables like this. (Refer Slide Time: 16:28) If you see these are the components of the consumer price index and you see in all of these there are food products, there are some electricity, there are other things and each of these has some amounts and then you can see in different locations what have been those prices. (Refer Slide Time: 16:47) In the case of the wholesale price index, you can see that the quantities and the commodities are different again their weight ages. So, these are reasonably transparent things, you can go to this website, see how these wholesale price indices are calculated and then we can use this and calculate. (Refer Slide Time: 17:07) So, as I told you in our country we had essentially we had inflation which has been there and constantly prices have increased. There is only one year where prices decrease and this was between 1975 to 1976 and that was the year in which there was an emergency had been declared and that has resulted in this decrease in prices, but in general overall, this is how this is computed. (Refer Slide Time: 17:38) So, let us now look at a simple, so based on this there are weights, which are given and these weights can be used to make this. (Refer Slide Time: 17:43) Let us take a simple example of, in a state, the consumer price index in 1995 was 140 with 1990 as the base year, in 1990 an investment was made in a fixed deposit account which has the interest rate of 10 per cent. So, we want to find out what is the real interest rate obtained on the investment. Because from 1990 to 95 the prices have increased, the value of that money has gone down and because the value has gone down, we want to know what is the actual amount of interest that you are getting. (Refer Slide Time: 8:22) 1401995n 1001990 100 ¿(1+i) 5 i 7 %(0.07) ( 1+0.1)=( 1+0.07) (1+r) r 2.8 %(0.028) So, what we can do in this case is that we can take 140 is in 1995, the base year is 1990 by definition in the base year it will be 100. So, essentially what we do is we take 140 by 100 is the compound inflation rate raise to 5 and then you will find that I approximately 7 per cent or 0.07 if you look at the interest that we are getting, we are getting 10 per cent. So, 1 plus 0.1 will be equal to 1 plus 0.07 that is the inflation and 1 plus the real rate of return and you find the real rate of return is approximately 2.8 per cent, 0.028. So, similarly, when we talk about the discount rate we are, we can think in terms of two discount rates, one is the nominal discount rate which you take based on the actual prices in that particular year and the real discount rate if you have adjusted for inflation. (Refer Slide Time: 19:48) So, we say that 1 plus d nominal, typically what happens is that the when we make a calculation today for a project which is going for 20 years, 25 years, we do everything based on today's prices. So, often it is better to do the calculations in constant money terms, don’t bother about inflation and talk about the real discount rate. So, unless otherwise specified we have whatever we have been discussing have been on the real discount rate. In some situations where you have different commodities within different kinds of inflation and you can have a projection of what will be the inflation and cash flows in the future, we could use the nominal discount rate. But unless otherwise stated what we are talking of is the real discount rate. The nominal discount rate will fluctuate based on how the economy varies and the inflation happens, the real discount rate is more relatively more stable and reflects the scarcity value of capital. sigma ACk 1 plus d raise to n, k is equal to 1 to n, and that gives us the life cycle cost, the cost of owning and operating that equipment over its lifetime and you can then look at the relative magnitudes of different things. (Refer Slide Time: 10:26) If the annual, if the annual cost is constant then this can be simplified to C0 plus AC by CRF, d, n. Now, there is a situation, when you if you are annual cost which is constant and if we are looking at we can instead of taking the life cycle cost, where we took the what we did was we do this and we took all of this annual cost and we replace all of these by an equivalent upfront cost and we added these two, instead of doing that we could do the situation where we took an annual cost which is constantly take the C0 and replace it by an equivalent annual cost. So, then this case we are now doing this as this is called the annualized life cycle cost. So, either we take the annual cost which is there and bring them up front to an upfront life cycle cost, or we take the initial cost annualize it added to the annual cost, and that becomes the annualize life cycle cost. This is a convenient way often in the case of annualized life cycle cost, especially why because it helps you to tackle equipment and projects with different kinds of lives. (Refer Slide Time: 12:02) So, the ALCC typically would then mean that you just take this will be for this you will take C0 and annualize it plus then the annual cost of fuel, the annual cost of O & M and so on. So, this annual lives life cycle cost is the annual cost of owning and operating the equipment. This is very convenient because for instance if you look at a power plant or you will look at let say a solar photovoltaic plant where you have photovoltaic modules which have a certain life and then you have the battery which has a different life you can take all of these, annualize it get the annual cost, get the annual generation and we can then convert it into a per kWh. So, this is ₹ that is one of how we can look at this. So, let us there is this other concept where we talk about the cost of saved energy which is very similar to this concept, the cost of saved energy is a concept where we take the annualized investment to divide it by the annual energy saving. So, many cases what happens is that when we talk of a new generating plant, we talk of per kWh and when we talk about savings we want to ₹ compare it with generation. So, the cost of saved energy can and calculated for an energy efficiency option by making an investment, annualizing it, dividing it by the annual energy saving and this will mean that. (Refer Slide Time: 13:44) This annual cost of saved energy will be C0 into CRF dn divided by the amount of energy saving and the units they will be in terms of rupees per the energy unit, rupees per kWh, rupees per kilojoule, rupees per kg of coal, rupees per litre of oil, you can then compare it with the price at which you are getting the electricity, or the fuel, and if it is low, this price is lower than the price at which you have purchasing then it will make sense for us to go ahead. So, just to give you an example let us take an example where we take another cost of a standard refrigerator is 10000 rupees and the expected electricity consumption per year is a 450-kilowatt hour, cost of an energy-efficient refrigerator of the same capacity is 10,500 rupees for the same load annual electricity consumption is expected to be a 400-kilowatt hour. So, what is the cost of the saved energy? Now, this cost of the saved energy will depend on the discount rate and typically what happens here is that your incremental investment is 500. So, 500 into the capital recovery ₹ factor, this is the annual amount in terms of rupees that we are paying, in terms of the annualized investment, this divided by the saving which is 50-kilowatt hour will give you the rupees per kilowatt-hour. Now, if we took a discount rate of 0.3 and this is all we said CRF 0.3, 10 then this will be 0.323 we had calculated it earlier. So, you get 500 into 0.323 by 50 and then this the cost of saved energy turns out to be rupees 3.23 per kilowatt-hour if your discount rate is lower than this cost of saved energy would be lower. So, we can see this I have shown you this plot. (Refer Slide Time: 16:17) So, this gives the example which shows you how as the discount rate increases the cost of saved energy would then increase because of the effect that initial investment that we are making is now equivalent in terms of higher annualized investment. This one concept, an additional conceptthat we need to understand which often gets confused in the process whenever we are doing this calculation is about depreciation. So, we must understand the depreciation is an accounting concept, it is a concept to wear if you look at an asset, we adjust the value of the asset and we depreciate it over its lifetime. (Refer Slide Time: 17:26) So, typically what happens is that we considered an annual depreciation and one of how you do that is we take a straight-line depreciation, we say that if you have the C0 and at the end of its life if you have a salvage value S, the book value of this asset is adjusted. So, that every year we reduce this by a straight-line depreciation, which is C0 minus S where S is the salvage value at the end of the life. There are situations where if you take S is equal to 0 then the depreciation is taken as every year C0 by n. Now, in general, since we have already taken this C0 as an upfront cost and we are using that in the calculations it would not make, it does not make sense to again add up the depreciation then will be double counting the cost. (Refer Slide Time: 18:56) However, there is a benefit that we get from the depreciation in the sense that if there is a company which is a profit-making company, then the company after we will have a set of gross profits. And from the gross profits, we are allowed to subtract the depreciation to get the net profits and the company is a tax based on the net profit. So, essentially if you look at a company today the tax rate may be of the order of 30% or 33% the saving each year is T into AD, the tax rate into the AD. Now, in a sense will not make too much of a difference and we can neglect the effect of the tax on the depreciation because the value of the book, the value of the asset gets depreciated. However, there are situations for instance in the case of renewable where the government provides a policy of accelerated depreciation, accelerated depreciation for instance, for instance for till sometime back we had 100 % depreciation for some of the energy, renewable energy equipment like wind farms. So, for instance, if a company has made an investment of 50 crores in a wind farm, in the first year itself it was allowed to depreciate this 50 crores. (Refer Slide Time: 20:44) So, that suppose the company had a profit of letting us say 400 crores and the tax rate says 33%. So, it would have been paying 0.33 into 400 as the tax, which is 13.2 crores would have been the tax that is paid, sorry. So, this is, this would be 132 crores would have been the tax. So, in the case of supposing we have made an investment of 50 crores in a wind farm and there is a 100 % depreciation, it will mean that that company is now going to be taxed only on 350 crores. So, the net saving is 50 into the tax rate of 0.33 is 16.5 crore tax saving at the end of 1 year. So, in terms of the benefits stream that we have after wind farm, where we have C0 and you have these annual cash flow streams we are getting at the end of 1 year an additional tax saving stream which will be 16.5 divided by 1 plus D with the result that all the indicators that we talk of the net present value, benefit by cost ratio, the internal rate of return, all of these would improve with this. In any situation when we do the economic calculations there are when we look at a project there are a large number of parameters which are outside our control, there several variables and assumptions that we make and it will be worthwhile in all these cases to try and show some of these parameters. (Refer Slide Time: 23:17) For instance, this is the cost of generation from a solar thermal power plant and you can see that when you look at it we are talking about the field, the efficiency, technical parameters, the plant output which will depend on the insulation solar field cause, capital cost, storage cost, annualized cost, replacement cost, discount rate. So, all these parameters and we can see in many of these cases if there are ranges of values we can do sensitivity and do the calculation for this. (Refer Slide Time: 24:00) We would like to just, I would like to just talk to you about using the concepts that we have learnt so far to calculate for the marginal abatement cost curve. So, when we talk in terms of we introduce this concept of energy and environment and the issue of climate change and when we look at climate change, we are looking at for different options we see what is the impact in terms of the greenhouse gas emissions, or this CO2 emission. So, one of the curves which has been introduced and this was introduced by McKinsey is called McKinsey cost curve on the X-axis is the amount of annuals CO2 savings from a particular method, annual GHG reduction potential. So, what happens is we start with a base year and we see what is the kind of emissions in that base year. If we take the base year and continue with the same kind of growth in the future we will have a business as usual scenario, till a future year let say 2020 if we wanted to have more investments in renewables that would involve a certain cost that cost is expressed in terms of the rupees, or dollars, or euros per ton of CO2 saved on the Y-axis and on the X-axis we have the annual CO2 savings. So, with this, this is a marginal abatement curve and with this kind of curve, we can then compare all these options. So, we go for the cheaper ones. Now, you will find that there are some which are negative, some options which are negative in terms of cost and that is because even if you do not consider the CO2 savings they cost-effective. So, these are energy efficiency options mostly and so the idea is that in overall if we want to have a fixed amount of CO2 saving that we target, we should go in this order and look at all these options. So, we can take and we will do an example where we will see how to calculate. (Refer Slide Time: 26:16) So, essentially what happens is if we look at a, we can look at the ALCC for the option that we have minus the ALCC for the base case, or the business as usual case and then we can have the CO2, annual CO2 emissions, annual CO2 emissions with the option that we have. So, you get CO2 savings, annual CO2 savings, we have the annualized and then we can get this income of rupees per ton of CO2 saved. You can find these curves in terms of you will see dollars per ton of CO2 and then they can be compared and then we can see which of these options does a wind firm, is a wind firm cheaper than energy efficiency option, is it cheaper than a biomass option, is it cheaper than doing carbon capture and storage, and we can do some of this calculation. So, will do an example where we can take this, so, we have seen how to do the annualized life cycle cost, we have also seen in a previous lecture how we can calculate what are the CO2 emissions from first principles and then we can take this and get the marginal abatement curve. (Refer Slide Time: 27:59) So, similar fashion this is showing you the McKinsey curve for the world and you can see that there are many these options mostly the energy efficiency options, and then depending on where we want to stabilize we are already today at more than 400 parts per million in terms of this CO2 emissions. If you want to stabilize at 450 PPM or 500 PPM the more the stabilization then will go for all the costlier option (Refer Slide Time: 28:33) So, today we have looked at the economic criteria which are used as a basis for decisions, we looked at the simple payback period and we said the simple payback period is a good index to use for projects which are relatively low cost but we are not taking in that the effect of the time value of money with the time value of money, we looked at net present value, benefit by cost ratio, and internal rate of return, all three come from the same equation but there is a slight difference in how it can be calculated. We then look at also what is the concept of inflation and how it affects the decisions in terms of we said we can always look at we do not need to adjust for inflation though everything in terms of constant money terms and look at the real discount rate, or if you have inflation and the nominal values, we can take the nominal discount rate, the discount rate is the critical concept that we need to understand which reflects the scarcity of capital and typically if companies are more capitals scares they would rather prefer options which have lower investments initially. We then talked about the concept of life cycle costing and annualized life cycle costing and briefly introduced the marginal cost of carbon save all of this we saw the effect of taxes and depreciation, and the taxes government policies all of this can affect the viability of techno(Refer Slide Time: 28:33) So, today we have looked at the economic criteria which are used as a basis for decisions, we looked at the simple payback period and we said the simple payback period is a good index to use for projects which are relatively low cost but we are not taking in that the effect of the time value of money with the time value of money, we looked at net present value, benefit by cost ratio, and internal rate of return, all three come from the same equation but there is a slight difference in how it can be calculated. We then look at also what is the concept of inflation and how it affects the decisions in terms of we said we can always look at we do not need to adjust for inflation though everything in terms of constant money terms and look at the real discount rate, or if you have inflation and the nominal values, we can take the nominal discount rate, the discount rate is the critical concept that we need to understand which reflects the scarcity of capital and typically if companies are more capitals scares they would rather prefer options which have lower investments initially. We then talked about the concept of life cycle costing and annualized life cycle costing and briefly introduced the marginal cost of carbon save all of this we saw the effect of taxes and depreciation, and the taxes government policies all of this can affect the viability of the technology, or a system when we are doing a calculation and we have multiple sets of parameters, we can also look at the sensitivity and look at the impact of variables on this. With this, we will conclude this session on energy economics. We will take up one or two examples in detail, where we can illustrate some of these concepts in a later class. logy, or a system when we are doing a calculation and we have multiple sets of parameters, we can also look at the sensitivity and look at the impact of variables on this. With this, we will conclude this session on energy economics. We will take up one or two examples in detail, where we can illustrate some of these concepts in a later class.