Lec 11

[Music] [Music] Hello and welcome to this course in Lecture 11 of Principles of Management Under Maksh Initiative of Government of India. Our focus today will be on the change in value of money over time. Time Value of Money. Let us remind you that the course The modules in which we are discussing are shown here and today we will start discussing a new module i.e. Construction Economics so let us first see how the cash flow happens at different stages of any project. How is the flow of cash? First of all, understand that below this axis we have plotted negative cash flow i.e. expenditure. Positive cash flow has been plotted above that is revenue. Now if we talk about different stages, then the most First there is planning, then there is construction and finally the operation and maintenance phase which is a very long time of 15 years, 20 years, 25 years. Construction usually ends in two to four to five years. Whatever time it takes for planning, it will take if we consider the cost. According to this, while planning i.e. while planning any project, some cost is incurred, some expenditure is incurred, that expenditure is shown here, similarly expenditure will be incurred during the construction work too, whether it is in concrete or not. Be it in purchasing the locomotive, be it in installing the power supply, in whatever way it is an expense, if it is developed, then it becomes an expense. After that, when we go into the operation maintenance phase, our revenue starts, we get something from that project. Returns start coming and these returns may or may not increase with time, but expenses are also incurred during the operation maintenance phase, we call it Operation and Maintenance Cost, keeping this entire picture in mind. We decide whether this project is economically logical, whether it should be done or not, and when we do this decision making from the economic point of view or economics point of view, then the tools and information we need are included in it. We will start discussing them today. We have already said that in this entire course our focus will be mainly on the construction phase but this picture has been put to give you a total picture, so let us move ahead and see that the investment or The value of the project depends on the following. What is the value? What does it depend on? Analysis of the quantity and time of cash flow expected from the project, i.e. the quantity that we have considered that we will get this much return at this time, this much will be our expenditure, what is its quantity and that Analyzing when it will happen on the time axis and also the uncertainty associated with each part of the cash flow, it is also certain that we cannot decide whether we will get this much revenue, if we talk about the highway project, how much of it will be Our revenue there will depend on both the things, whether there is traffic, how much toll there is, whether there is traffic in our bus, there is so much toll in our bus that we can decide whether our toll will be 00 or 50, but there is very little control over the traffic. Literally, if we are talking about what will happen after 10 years or 15 years, then there is an uncertainty in it. Even during the construction work, there is an uncertainty while executing various works. Price of steel, price of cement, salary of labor, all this is done very carefully. Risks can change and to keep them in mind is to keep uncertainty in mind. Risk Management is a subject which is studied but we will not go into risk management in this course for now, we will assume that The value or figure that we take is stable and does not involve uncertainty. Keeping in mind the rising cost of maintenance, investment options should be evaluated on the basis of the entire life cycle cost of the project apart from the initial investment i.e. simply saying that It is not about whether it will cost Rs 4 crore or Rs 50 crore to complete this project, but we should evaluate it on the basis of what will be the life cycle cost of the project in its entire life span i.e. in service life and that is why you should get that complete estimate. The picture was shown once when the investor earns more than the investment cost then value is created i.e. if we completed a project by investing Rs 100 crore but its returns came to the value of Rs 110 crore then it was a profitable deal, it means Value is created by the project and the selection of the project should be such that the project not only creates value but it creates more value than any other project with similar uncertainty. If we have different options then Among those options, we should choose the country in which more value is being created. All these things have become very important in India in the last 2530 years because in all the projects, the government is encouraging this thing. That if various private investors invest in projects, then what is the meaning of investing in projects, they will also incur costs in the construction process, whereas earlier in the big projects, the government used to invest the cost, the government used to invest money and hence there is cost benefit analysis in it. It was done in another way, but when an investor invests money in it, it becomes necessary to keep all these things in mind. Let us move ahead to the time value of money, which is the main topic of our today's lecture. What is the meaning of focus? The value of money keeps changing with time, that is, what will be the value of Rs. 00 that we have today, tomorrow? If we try to understand in simple language, then when we keep Rs. 00 in the bank and the bank Whatever interest we give on ₹ 5 at ₹ 7, then ₹ 00 becomes ₹ 1078, but after one year, is the value of that ₹ 8 or ₹ 10 more than today's ₹ 1 or not? Its value changes if we say inflation. Inflation means its value is decreasing due to inflation and its quantity is increasing due to interest rate, so keep these things in mind and take decisions keeping these things in mind. This comes in the review of our construction economics, this is what we will discuss. After all, what is interest? We can see interest as the amount given to the owner of the money for not being able to use the money or not to use it. When the bank says that you keep Rs. 00 with us, we will give you Rs. So, the interest is earned but you cannot use the money which is yours in that period, then it is a kind of compensation, that is interest. For any investment, there is present value and future value. Present value and future. What is value? We have seen that when we make a cash flow diagram or picture on time access, it is a picture that lasts for many years. There is a planning phase, a construction phase, an operation maintenance phase, so it includes the changes that occur over time. The change in the value of money cannot be ignored, it has to be kept in mind, so to keep this in mind or keeping this in mind, if we evaluate the expenditure here or the income here. If we want then what we have to do is that we take this quantity as present, whether it is here or it is here, whatever present time we take, we take the present time here, it is necessary to know what is its value and this is the change of value or To find out the change, we should know the interest rate. What is the interest rate value? We consider it at 5, we consider it at 10, whatever but if we know the interest rate then we can decide that here which is 00. What will be its today's value? Now the way I have made it, so here this A and this B, so A is ahead in time, suppose we take this time of two years, then think about whether the current value of A and B. I am leaving this question for you, which of these values ​​will be higher, so let us try to understand this through an example. A cash flow diagram is given here, outflow i.e. expenditure and inflow i.e. revenue. The revenue is shown. It is shown here that there will be an expenditure of Rs 10 lakh and this is our expenses on year 1 doti ch pa 6 sa and this is our revenue. Now what has to be decided is the present value or the future value of this investment. Now decide this. What we have to do is what is the present value or future value of this investment? Is the investment to be made logical if we know that we have to spend Rs 10 lakh, here we will get 2 lakh, here we will get 500, here we will get 3 lakh, here we will get one lakh. We will get Rs. 4 lakhs and this will be our expense, so should we do this project or not, so it is necessary that we either bring all these figures to the point that what is their present value, we also have to bring it to the present value only. Let us look at another example. Suppose there are two projects A and B. Project A has higher initial cost and annual maintenance cost is lower while Project B has lower initial cost but higher annual maintenance cost. As an investor which project should you choose? This is not only for projects, any construction equipment, whether it is a crane or an earth mover, there is a challenge while purchasing it that we have two options, one is a machine, the other is a machine, one is the initial of the machine. Cost: Initial cost of one is less, one is more but maintenance cost of both is different, so how will we model it and how will we take decisions, then we will have to convert this type of text into cash flow diagram. Project A has to be done in which the initial cost is high so the cost is high and the maintenance cost is low. In comparison, we can say that the initial cost of Project B is less but the maintenance cost is less. Now to choose one of these two options it is necessary that we calculate the present cost or present value present value of these two options at any point in time and then take the decision and this In this context, it is important to consider the time value of money. It must be kept in mind. Now when it comes to how interest can be calculated, unless the interest is known, we cannot calculate the present value or future value. If we cannot talk about value then it is necessary to calculate interest. It is necessary to understand about it. We calculate interest on the basis of single payment. Compound amount factor and present worth factor are two terminologies. Based on that we learned in high school. We have read about compound interest and simple interest, what happens in it is that if we pay an amount a simple interest whose rate is t, if we keep it for t time then what will be the simple interest. We can calculate this, we have been taught this in high school. In comparison, when it comes to compound interest, we calculate that whatever interest will be earned on the same amount at the same rate in the first year or first time span. That amount will come and will be added to this amount and then this amount plus interest will again be interest on it and when our next interest will come then this is the matter of compound interest. To calculate this also we did different types of exercises in high school. We will discuss the same things in a slightly different perspective. After single payment, comes the issue of equal payment. It is not necessary that we are talking about one lump sum payment, often we discuss about equal payment. It is based on that i.e. we may get some revenue continuously and sometimes we may have some expenditure continuously, so to understand the model, this thing has been equalized. It is not necessary that it should be equal. Mathematics becomes easy. This calculation is very easy but it requires computer or excel sheet. There are many factors. There are many tables available from which we can do these calculations but today we will try to do these calculations ourselves so that If you understand what we want to do and how the factors are calculated then in Equal Payments we will talk about these four namely Compound Amount Factor, Present Worth Factor, Sinking Fund Deposit and Capital Recovery Factor. So let us first talk about The simple thing about Single Payment Compound Amount Factor is that we have one amount at one place in time and another amount at another place. There is a time in between which is given in t years and there is a rate of interest. There is a relationship among the four parameters, that relationship itself is being analyzed. Single Payment Compound Amount Factor, which is called SPCF, what is that given p i and then we know p, we know a, we know n, our The principal that we have taken in the beginning is Aa, which is the rate of interest that we will take and n is the measure of our time. If we are talking about n years, then there we know that SPC F1 is equal to the power of n. Where the percentage has been taken, as an example, if we see how much the deposit amount of Rs 10 lakh will increase in five years at the interest rate of 8%, then it has been done in our high school that we will apply compound interest. And we'll do pi times pi multiplied by pi to the power a and we'll see that it becomes 14 69 328 so if we remove this thing, our factor comes out to be 1.46 so if we know pi and a then we can factor this. You can find out F and if you know the factor then you know your principal amount, you will have no problem in finding F. If we turn this thing around and say that we know F, we want to know how much P should we keep. Then what we have to do is reverse the previous process then it will become N upon 1 ps i to power A. Example of this if we see that if it is assumed that the value of a property after 10 years will be Rs 20 lakh then what is the present value of the property ? Let us assume that the interest rate is Rs 10 per annum, then if we assume this then its value will be Rs 7716. If we look at this from the perspective of construction, then if we see that we have to buy a machine here, the cost of which will be Rs 10 lakh. If we assume, then how much money do we need today which we can set aside at an interest rate so that after n years we get that F amount. We call this as Single Payment Present Worth Factor. So what is the present value of this amount? What is the present value of this Present value of lakh is Rs 7 lakh. Moving ahead, we talk about equal payment compound factor. EP CF. What does it mean that Ai and A means that if we keep this a continuously every year, then what will be A and Aa and A. We know. I and A means rate of interest and number of years so if we know this thing then we can calculate EPC F with this formula if we try to understand it and say a1 a2 a3 a4 or here A If it is -1 then we write n-1, then we pay these installments, then who is contributing how much in this F. The one who is a1 is contributing for so much time, the one who is a2 is contributing for one year less i.e. A3 is doing it for this much time and for one more year less and this is the last installment and this is the last installment, he is doing it only for one year, so a1, a2, a3 etc. till A-1. Looking at the contributions or if we add up everyone's contributions, then the value that will come will be A. So this is the value which is a1 a2 a3 a4. If we keep a rate of interest for n years then what will be its F. So we can call it Let us see through an example what will be the value at the end of 10 years for a simple annuity of Rs. 00 operating on compound interest at the annual compound rate of 8%. If we use this formula, then the value we get is 2897 32 We invested. 20000 10 years ₹ lakh and we got 2 lakh 8972 i.e. the value we got is our interest, here we made equal payment, so the example we had taken earlier is that if our construction equipment is worth 20 lakh and we want to buy it after 10 years. or want to buy it after 4 years, then one way is that we can keep this money somewhere in lump sum and after so many years we will get this money, another option can be that we will not be able to keep this much amount here but we can keep a little amount here. Let's keep it so that we can buy this equipment after so many years. Let's move ahead. Equal Payment Sinking Fund Deposit Factor. FI&A given here. How much should our A be? This is a little different from the previous example. What was the last time? A given here. Here we have been given f and we have to find a, so the example I explained to you is more relevant from this point that we know f that we need to buy 20 lakh equipment, what amount should we calculate for it? Which amount will have to be removed or which amount should we put in a sinking fund and forget about it? Just like we talk about a coin with children, we keep the money aside and do not touch it, then we will put that coin in a sinking fund. What amount should we put in the form every year so that after A years we get F, this is our formula, for that let us see the example of how much should be invested in the bank every year to make an amount of Rs 20 lakh at the end of 20 years. It should be assumed that the rate of compound interest is at 8. In this entire discussion, you must be seeing that the rate of interest is that we have to continuously believe that without the rate of interest, nothing will happen but this is also certain, is it uncertainty? We should also keep in mind what the rate of interest will be at what time and follow a conservative value. This is a principle that every project manager should keep in mind while making decisions. Keep in mind that we are on a conservative side. We are moving on the side of a risk, let's move ahead. The answer is that if we want 20 lakh rupees at the end of 20 years, then we will have to separate 3705 rupees every year and the factor of yours comes out of this here. We call the value coming from EP SADF That is Equal Payment Sinking Fund Deposit Factor. All these factors are available in the form of a table for different rates of interest so we do not need to do this calculation every time. So let's move on to the next factor. Let's talk about Equal Payment Present Worth Factor. Now we are talking about Present Worth. Till now we have talked about Future Worth that what is A. Now we will talk about Present Worth i.e. if we do this for n consecutive years at different rates of interest. If we do this then we can use this formula to find out what is the present value of this investment. For example, we see that what is the present value of ₹ Haj Ordinary Annuity invested for a period of 10 years? Present value means present. So, what is its value at this time? If we use this formula, then our present worth comes out to be 1.3426, so the present value of this entire investment is 3260. Keep in mind that if we are investing 00 in 10 years, then our total The investment is of Rs 2 lakh, but the present value of this Rs 2 lakh is only Rs 1,3260. This means that if we call these values ​​a1, a2, a3 etc., then what is their value here? What is the value of this 00 here? How much is it? If we calculate the present worth, then we will calculate it by adding all these values. So let's move ahead and this last factor is the equal payment capital recovery factor in which p, a and n are given and if a is to be calculated, then as I told you earlier, this is the game. The value here is of only four quantities i and the value here. The second thing is that whether we take this value in perpendicular or we give it to the distributor, when we give it to the distributor, then they make equal amounts. It is not necessary that there should be equal amounts. If these amounts are unequal then we can convert all these values ​​into present worth factor as I told you but for that you will have to do a little mathematics and we will give you an exercise in homework so let's go back. Let us see an example on equal payment capital recovery factor i.e. the number of years is n which is 6 years and the rate of interest is 4. To decide the recovery of Rs 2 lakh i.e. our p is given. 2 lakhs, to neutralize it we have to decide the annual installment i.e. we have to decide A, for this if we use this formula then we come to know that 38000 is 50 then 8150 if we pay for 6 years then we get 2 Now you can see that there is a loan of Rs. lakh, we will give him Rs. 8150 for 6 years, when our loan will end, then how much interest component we have given, you can calculate the interest rate is given. But you can find out from here how much is the component of total interest, so we would like to end today's discussion here where we have discussed about interest and interest rate, present worth, future worth and equal installments. Further we will discuss about these things. How do we take financial decisions, on what criteria do we take them, how do we interpret those criteria, we will continue the discussion on this in the next lecture. This is a list of useful published books. I suggest you to check them out. Thanks Jai [Music] [music] hind [music] b