noc18-ce39-Lecture 15- Effect of depreciation and inflation on economic decision making

Good morning, namaskar and welcome back to this course. In the previous lecture if you remember we discussed different ways of computing the post tax cash flow diagram. I gave you an small example and I told you to draw the post tax cash flow diagram. So, there we found that depending on the depreciation our post tax cash flow diagram is slightly different from the pre tax cash flow diagram. There was no change in the initial and the end of life pre tax cash flow and post tax cash flow diagram. The difference was noticed only during the intermediate periods. Now, in this class we are going to learn how to rather find out the effect of depreciation and inflation on the economic decision making. For this we take one small example. We assume that some equipment has been purchased for rupees 3 and a half lakh and its accounting life and service life happens to be 5 years. The predicted salvage value is nil. The gross income for all the 5 years is assumed to be rupees 2 and a half lakh and expenses are assumed to be nil. So, what I am going to do is I am going to give you 3 cases for the same problem. In the first case I am giving you details only on the income. In the second case we will give you some other data and in the third case we will give you some other data altogether and we will see how to take it for our analysis purpose. So, here what is happening is I am able to purchase one equipment for 3 and a half lakh and this equipment is giving me an income of 2 and a half lakh every year. My expenses are nil. This is to start with I am assuming that my expenses are nil, life is 5 years. Now, I am also going to tell you depending on the method of depreciation there are differences that you are going to get in the cash flow diagram. Although the total tax that you will be paying whether you are using straight line method of depreciation or sum of years or double declining balance method they are going to be the same, but their timings are going to be different. In fact, that is why you will always find the taxpayers given a choice will like to go for a different type of depreciation method than a tax collector. So, we will see which one will be adopted by which agency and why that is also we will see in this particular example itself. So, if you calculate the depreciation using straight line method for this. So, 3 and a half lakh minus 0 because there is no salvage value divided by 5 because life is 5. So, you find 0.7 lakh every year is your depreciation using straight line method. Using sum of years it is going to be different we will see what it will be and for your benefit I have drawn this particular table and this table gives me the values of depreciation using all the 3 methods. So, as I told you straight line method I am getting same depreciation 0.7, 0.7, 0.7, 0.7 and 0.7 every year for 5 years. How do I calculate double declining balance method? You can see the depreciation every year is changing unlike yours straight line method of depreciation. Even in sum of years digit method the depreciation every year is changing. Let us do with sum of years, sum of years life is 5 years. So, sum of years is going to be 5 into 6 by 2 which is 15. So, the first year my asset is going to depreciate by 5 by 15, next year it is going to be 4 by 15, 3 by 15, 2 by 15 and 1 by 15. So, first year the depreciation is going to be 5 by 15 of 3.5 lakh minus 0 of course, because we do not have any salvage value. This year it is going to be 4 by 15 of 3.5, 3 by 15 of 3.5, 2 by 15 of 3.5 and 1 by 15 of 3.5. So, I have already calculated it for you it is coming to be 1.17 for the first year, 0.93 for the second year, 0.7 for the third year, 0.47 and 0.23 for the fifth year. When it comes to double declining balance method the rate of depreciation is going to be 2 by n. So, first year it will depreciate by 2 by 5 and multiplied by 3.5. So, we will find first year itself depreciation is going to be 1.4 lakhs. So, for the next year the book value is going to be 3.5 minus 1.4 which is 2.1. So, the next year my depreciation is going to be 2 by 5 of 2.1 and this is coming to be 0.84. Likewise for the third year it is going to be 0.50 and fourth and fifth year if you see very carefully here I have switched it over to a straight line method of depreciation because otherwise the depreciation for fourth year was coming to be lesser than a straight line method. If I would have gone in for double declining balance method even for fourth year my depreciation in that year would have been lesser than a straight line method. So, tax authorities allow me to make a switch. So, I have switched it over at year 4 and you can see that is the reason this value is 0.38 and which is same as 0.38 here. Now if you sum for all the three cases they are going to be the same. So, this is also 3.5 this is also 3.5 and this is also 3.5. Now gross income which is annual value given to us in this particular problem is 2.5 lakh 2.5 lakh 2.5 lakh 2.5 lakh every year for next 5 years. As I told you in this particular example we are dealing only with income. So, expense is given to be nil here. Now we will see how to go about it. So, when I calculate the net taxable income first let me explain you in the context of a straight line depreciation. So, you remember your gross income is 2.5 lakh. So, let us call this as gi gross income is 2.5 lakh and depreciation which you remember now is considered as an expense is 0.70. So, my net taxable income is going to be 2.5 minus 0.7 which is 1.8. So, just look at this figure very carefully 1.8 this is my net taxable income if I am using straight line method of depreciation. Now since depreciation is same in the straight line for all 5 years this value is going to be the same. So, this is my net taxable income. Now let us assume that tax is at a rate of 40 percent of your income. So, my tax for this year is going to be 1.8 multiplied by 0.4 which is 0.72. So, if you see here this is the value using a straight line. So, that means, the tax that we will be paying if I am going to go for straight line method of depreciation it is going to be 0.72. So, in the next year also 0.72, third year also 0.72, fourth year also, fifth year also 0.72. So, if you sum it up you will find that we are getting total tax implication of 3.6 lakhs using a straight line method of depreciation and every year I am going to pay 0.72 lakhs. Now let us move to sum of years digit method and see how my tax calculations change. Now as you know in the sum of years digit method my depreciation is changing every year. So, I will have to do this calculation for every year. So, my gross income is 2.5 as before my depreciation if you remember in sum of years for the first year was 1.17. So, depreciation is 1.17. So, you can calculate this is going to be 1.33 net taxable income this is what it is written here. So, if we are going in for sum of years digit method of depreciation calculation the net taxable income is going to be 1.33. So, I multiply this by 0.4 to calculate my tax for that year. So, it is going to be 1.33 multiplied by 0.4 and this is going to be 0.53. Now when I do it for the next year, next year if you remember my tax liability I mean the depreciation is 0.93. So, what I do 2.5 is my income 0.93 is my depreciation expense I deduct it and I apply 40 percent tax on that. So, I find that the tax that I am paying is 0.63. So, when I calculate my net income what will happen first let me go with straight line method of depreciation. So, you already found that you have paid a tax of 0.72. So, the net income that you will have is 2.5 minus 0.72 which is going to be 1.78. So, this is your net income in year 1 using straight line method of depreciation and it is going to be the same all 5 years 1.78, 1.78, 1.78, 1.78 and 1.78. So, if we have to draw a cash flow diagram post tax cash flow using the straight line method of depreciation it is going to be like this 3.5 year and then your post tax income is going to be 1.78, 1.78, 1.78 all 5 years. On the other hand if you do using sum of years digit method you will get 1.97 in first year, 1.87 in second year, 1.78 in third year, 1.69 and 1.59 in fourth and fifth year respectively. Now, in all these things what is of interest to you is to note that irrespective of the method that we have used the total taxes that we are paying the value remains same. So, you can see here 3.6 in straight line in double declining also and in sum of years also. So, what is the difference what is the point of contention then why there is a dispute between tax payer and tax collector it is because of the timing. So, you can see here if you would have gone in for a straight line method of depreciation first year itself you would have earned an income of 1.78, second year 1.78, third year 1.78, fourth year, fifth year this is using a straight line all same in 5 years, but if you would have gone in for double declining balance method in the first year itself your net income is 2.06, second year 1.84. If you would have gone in for sum of years in the first year itself you are getting 1.97, second year 1.87. So, you find that higher income is realized by faster method of depreciation. So, which are the faster methods of depreciation obviously, your double declining balance method is the faster method of depreciation compared to straight line and the sum of years digit method. So, naturally the income that you get in initial years using faster method of depreciation is more. So, that is why all tax payers would like to use a faster method of depreciation if they are allowed whereas, the tax collectors would like you as a tax payer to go with slower method of depreciation right. So, that is the reason there is always a dispute between tax payer and tax collector. Now, in order to avoid this dispute what most of the governments have done is they have classified all assets in different categories. So, you have asset category 1, category 2, category 3, category 4 and so on. Now, for each of these asset categories they have specified by how much there will be depreciation every year. So, asset category 1 they will say first year the depreciation is going to be 25 percent, second year it is going to be 20 percent. So, they have specified the depreciation percentage for each of these asset categories not only this they have also specified you the salvage value. So, that there is no dispute at all. So, that is how in modern days there is no dispute between tax collectors and tax payers as far as the method of selection of depreciation is concerned. Now, we move to the next case for the same example and in this case we are given operating expense alone. So, if you remember similar type of problem we did it in the previous lecture where we discussed about the expense part alone. So, if you remember you had two options of equipment A and equipment B and for both of them you are given the only operating expenses. Now, in this case let us assume that the equipment is purchased for 3 and a half lakh, life is 5 years, salvage value is nil. So, this is as before. Now, we assume that there is no data on gross income given to me and it is given that we are incurring 1 lakh rupees annually as part of its operating expense and it is also given that this whole of 1 lakh is admissible for tax rebate. So, what is happening? I am purchasing the equipment for 3 and a half lakh, life is 5 years, salvage value is nil, no information on income, but I am told that I am incurring an expense of 1 lakh every year and this 1 lakh is all admissible for giving me tax benefit. So, I go with the similar calculation once again. So, you are already familiar with the depreciation now. So, I calculated the depreciation of 3.5 lakh using the three methods. In the first case it is going to be 0.7, 0.7 every year for next 5 years. This is using a straight line method of depreciation. If you go for double declining first year it is very large depreciation 1.4, second year 0.84, third year 0.5 and fourth and fifth I switched it to straight line and I am getting 0.38, 0.38. Likewise sum of years I am getting very high depreciation in initial years 1.17 year, 0.93 year, 0.7 year, 0.47 and 0.23 year. Gross income as I told you this is nil in this particular example, expense every year it is 1 lakh and as I told you these are all admissible for tax rebates. So, now how I perform the calculation would be like this. Let us take the case for a straight line because this calculation will remain same for all 5 years. So, income is 0 here, depreciation expense is 0.7, other expense is 1.0. So, my total expense becomes 1.7. So, if you subtract this from 0 you can as well say that my net taxable income is net taxable income is minus 1.7 lakhs. Now, just look at this minus sign that means you have not earned any money. So, if you have not earned no question of paying taxes. So, what is happening here is in another way if you look when you are charged tax at 50 percent or let us say 40 percent in our case in this example. So, 1.7 multiplied by 4 I am getting a tax implication of 0.68 in minus. What does this mean? That means I am getting a benefit of 0.68 lakh. In earlier case when my income was given I was getting positive tax implications. So, I had to pay taxes. Now, here in this case since government is giving me tax rebate and when I am getting a tax of minus 0.68 it is as good as I am getting a rebate of 68000. So, this is what it is written. So, straight line method all 5 years you are getting a tax rebate of 0.68. So, what will be your post tax net expense? So, you were spending 1 lakh and now you are getting a rebate of 0.68 lakh. So, net expense after taxes is 1 minus 0.68 which is 0.32. So, this is what you find here 0.32 in the case of a straight line in year 1, 0.32 in year 2, year 3, year 4 and year 5. Now, if you look at the total tax liability it is 3.40 in a straight line double declining also same and sum of years digit method also same. So, what you find here is that the total tax liability remains same it is only the timing that matters. Now, similar analysis you can do it using double declining balance method as you can see here the depreciation in year 1 using double declining was 1.4 lakh. So, the net taxable income becomes 2.4. So, when you are paying tax you are getting a tax rebate of 96000 and so your post tax net expense becomes very less 0.04 in double declining 0.26 in next year, 0.4 in next year and when you have switched it to a straight line you are getting a net expense of 0.45 in year 4 and 0.45 in year 5 also. Likewise if you go for sum of years you are going to get 0.13 as post tax net expense 0.23 here, 0.32 here, 0.41 and 0.51 respectively. So, you have seen here how you are getting a tax rebate even though you did not have any income because of your expenses you are getting some tax benefit and that is getting reflected in reducing your net expense. Now, we will see the last case here in which we are assuming that income and expense both are given and this is what is most practical because in most of the cases you will be knowing what is the income that you are getting and what is the expense you are getting. So, let us assume as before we are purchasing a equipment for 3 and a half lakh salvage value is nil life is 5 years. Let us further assume that the gross income is 2 and a half lakh and expense is 1 lakh and let us further assume that this whole of 1 lakh is admissible for taxes. That means you are going to get benefit on this particular expense. So, let us do the calculation again we calculate the depreciation. So, there is nothing new here 0.7 every year for next 5 years using a straight line double declining 1.4, 0.84, 0.5 and in year 4 I am switching over to a straight line. So, I am getting 0.38 and 0.38 sum of years you have already seen nothing new here. Now, in this column you can see I am having 2 and a half lakh. So, I am getting 2 and a half lakh income every year for next 5 years expense 1 lakh for every 5 years. Now, let us see how do we perform further calculation. So, your gross income is 2.5 lakh your depreciation which is expense for accounting purpose is coming to be 0.7 using a straight line your other expenses and remember these expenses are admissible for taxes. So, 1.0. So, my net taxable income is how much 2.5 here you subtract this and this. So, total expense is 1.7. So, 2.5 minus 1.7 is 0.8. Now, we are paying taxes at a rate of 40 percent. So, 0.8 40 percent of that is 0.32. So, my gross income is going to be rather net income is going to be 2.5 minus the taxes and minus remember 1 lakh is your expense. So, this is going to be my net income if you forget about this portion expense if you want to keep this separate. So, your net income is coming to be 2.18 this is what it is shown here you can see here net income is coming to be 2.18 every year for all 5 years. If you do similar calculation for double declining balance method you will find in the first year itself you are getting a net income of 2.46, second year 2.24, third year 2.1, 2.05, 2.05 and if you are going in with net income you are getting 2.37 here 2.27 and these 3 values. So, we have discussed all 3 methods and now you are in a position to find how to take care of different scenarios. So, this is as far as our discussion on impact of method of depreciation on economic evaluation was concerned. Now, we will quickly see the impact of inflation if you remember in one of the assumptions earlier we made that we said that the cash flows do not have any impact on inflation or rather in our market we do not have any inflation, but that is again not the case depending on the market conditions you will find there are certain amount of inflation. Now, as you know any construction project for that matter take a large number of months the time period could be very large 25 months, 30 months even 5 years, 6 years is quite common for construction projects and during this project it is not unlikely that the cost of labor and material and for that matter plant and machinery remain static they are not you will find that every now and then there is increase in the prices of these materials. When it comes to inflation it is generally defined as the increase in the price level resulting in decrease in purchasing power of money. Now, when we see general inflation you will find that the price rise is more or less uniform. So, the difference when you see the relative prices remain constant. So, sometimes it is quite logical to disregard scalation however if you look at the Indian practices especially the one which is recommended in IRC SP 61 2004 they say that when there is a large difference between the rate of inflation and the rate of interest you should calculate the modified discount rate. In fact, they have also suggested one formula we will see this formula, but as long as the inflation is small we need not even worry about this, but let us say for example, if your rate of inflation is high we should go in for modifying our discount rate. So, for a small example I have assumed that the difference between the rate of interest and rate of inflation is not large they are comparable and so, I can calculate this modified discount rate using this formula. It is given in this particular code it says 1 plus interest rate percentage divided by 1 plus inflation rate percentage minus 1 multiplied by 100 percent. So, this is how you calculate the modified discount rate. Now, in general for evaluation of alternatives we take 12 percent as discount rate. Now, suppose for our illustration we assume that rate of inflation is 8 percent. So, we can very well calculate what is the modified discount rate. So, this would be 1 plus 12 percent divided by 1 plus 8 percent minus 1 multiplied by 100. So, you will find this coming to be 3.70 percent. So, what you have to do is you have to find out the modified discount rate and then using this modified discount rate you carry out the same analysis which you have been carrying out so far using any one of the methods which you have learned so far either it could be present worth method, future worth method or rate of return method. So, just to summarize in case you find that inflation rate is negligible may be of the order of 1 to 2 percent 3 percent no need to worry about that, but if you find that there is a large difference between rate of inflation and interest rate then you can use this formula to calculate the modified discount rate and thereafter you can perform similar analysis. So, just to give you the list of references again you can have a look at these textbooks one by me itself and then there are others for example, this by this book on finance for engineers evaluation and funding of capital projects, then there is a book on project management by Kirchner and there are many such books this title engineering economic analysis by Newman and Etchenbach they are quite good books and you will find plenty of examples for your practice. So, just to summarize in this lecture I told you the impact of depreciation on our post tax cash flow analysis and the impact of inflation. As I told you as long as inflation is under check you can neglect that if they are substantial you can change the modified discount rate and carry out the analysis in a similar manner. So, we stop at this point. Thank you very much and see you next time.