Cash Flow Patterns and Their Applications

Alright, let's move forward. Alright, everybody, so we are looking at different cash flow patterns now. And where and how to use it, let's understand that too. So first pay attention, later copy it at last. So right now we have already covered future value, present value. So, for now. Fvuture value, present value for a single cash flow. We can call it a lump sum cash flow. We can calculate, say for example, I am using 100 and doing a simple static question. So time is 0. Time, let's say I will take 5 years. Here 100. Here what is its present value? We can calculate this. You have learned 100 divide by, and I am going to be assuming 8% throughout this part. Fvor once. Okay? So 100 divide by 1.08 to the power 5 is the answer. So my present value is equal to 100 divided by 1.08 to the power 5. Correct? If I have to find the future value of single cash flow, let's say time 0, time 5 here, if here is 100, So here, what is the future value? Fvuture value is equal to 100 into 1.08 to the power 5. So we can calculate the present value or the future value. Now we understand that the present value is time 0, and the future value is the time, the maturity, whatever the maturity is. Here, 5 years we are assuming as the maturity. There are instruments like this, fixed deposits, LIC options, investments That you are making payment today and you will get it on maturity There is no need to make payment in between, nothing to get, nothing at all There are schemes like that also We will read bonds and zero-coupon bonds further Then you will understand that also There are such investments Look at the stock Suppose today I bought some share And that share doesn't give dividend I have bought a growth company's share which does not divide dividends, it reinvests the company's income and the company is trying to grow So maybe I am investing today and 5 years later I get a certain money I want to calculate the return Yes, with these two values, you may have to calculate the return as well I can back calculate the return as well Right now focus on the cash flow pattern Returns and all, we will learn gradually So one could be that you are investing today and you are eventually getting a lump sum amount. That is one option. The second type of payment is annuity. Annuity can be of two types. One is an ordinary annuity. One is an annuity due. Fvirst understand ordinary annuity. Ordinary annuity, again I am taking the same, 1, 2, 3, 4, 5. It will give you 100, 100, 100, 100, 100. What is the present value over here? You might need to calculate. I am removing the question mark once, I am leaving the cash flow pattern here And I am going to discuss this, else I am not writing anything There is nothing here So from time 1 to 5 years, you are going to be getting an equal cash flow At regular interval, what does annuity mean? That is equal cash flow at regular interval The cash flow is equal, it has to be 100. 100, 200, 100, 100, it won't work. And 100, 100, 0, 100, 100, that also won't work. It has to be an equal cash flow at regular interval. If you are buying a house or a car and you are taking a loan, normally what you have to pay is an EMyI. EMyI is Equated Myonthly Installment. We will come to that in a while. That will be a part of annuity. So in that, you pay the same sum of money on a regular basis at an equal interval monthly installment. You don't pay different amounts, right? You pay the same amount every time. You are depositing LIC premium, regularly you deposit the same premium, and then later on you get the sum assured, your family, right? Annuities happened, equal amount at regular intervals, correct? Myaking sense? So all the loan related etc. will come in the calculations after some time. But right now, ordinarily what happens? Normally if you take a loan today, then today first interest payment is done, EMyI is done. Or you do your first payment at the end of the month. So, normally what happens? Ordinarily what happens? Your payment is supposed to start at the end of the period. Now this 1, 2, 3, 4, 5 could be first month, 1 month, 2 month, 3 month, 5 month. It could be 1 year, 2 year, 5 year. It will depend on what the question is, what the data is, what are you calculating on that. But the cash flow pattern could be like this. This is an ordinary annuity. What is annuity due? 100, 100, 100, 100, 100. In annuity due, your annuity begins at time 0, that is today. The difference is this part. Here, if you see this entire app, there are 5 cash flows in total. There are 5 cash flows here too. But the entire 5 cash flows have been shifted one period before. All the 5 cash flows have been shifted a period ahead. Don't see that he brought 100 here. He has shifted every 100 like this. That is Annuity Due. You will remember Ordinary Annuity and Annuity Due now. Because I asked you a simple question. Normally what happens? Ordinarily what happens? Do you make the payment today or do you start the payment at the end of the month? You all said end of the month. That is Ordinary Annuity. Annuity Due means that which is due today and starts today. In both cases, please remember that in both annuity dues, it's a 5 year annuity. 5 year annuity means that the number of payments is 5 in both. But here, there is no payment on the 5th year. Annuity due means that you are not getting another cash flow on the 5th year and a total of 6 cash flows. That is not what is happening over here. We are going to do its questions and its sums. We will solve this. But do you understand this much? Clear? 100%? Next is, now just understand the patterns of different cash flows. In unequal cash flows, I will give 2-3 examples. You can have 0, 1, 2, 3, 4. You can have 100, 100, 0, 100, 100. Cash flows are equal, but at one time the cash flow went wrong. You might call it not equal cash flow, but it became an irregular interval. The first two hundred is in the gap of one year, but the third one is in the gap of two years. Although the cash flows are same, but there is an irregularity. This is an unequal cash flow. Or, regular intervals, but the cash flows are unequal. This is also unequal cash flow. Or, Cash flow can keep increasing or decreasing I can also make a cash flow negative So that is unequal cash flow So basically anything Basically if equal cash flow at equal interval Not regular interval So in that case it will go to unequal cash flow We have to do calculations for that too Fvor example what if I am laying down a factory today So maybe in the first 2-1 years I will have to invest 100-200 Myaybe after that returns will start coming 300-400-500 Both cash flows can be negative and positive. Fvollowing, you have to do evaluation of any project. So in that case, ideally, normally, if you look at EMyI, you will get odd annuity. If you look at LIC's schemes and all, normally it works as an annuity. Or say for example, you have retired from a company at the age of 60. And the company is telling you that I am going to be paying you for the next 20 years You will be given a pension 20 years, 25 years till the time you leave So that will be an annuity style payment Equal amount at regular intervals But when you are doing any decision analysis etc. With regards to equity, company etc. Then it will come in equal cash flows normally Tell me, making sense everyone? What is perpetuity? Perpetuity is Let's say You will get 10, 10, 10, infinity. Perpetual, perpetually, forever and ever. That is perpetuity. A very simple example. Suppose in your school, there is an XYZ memorial award. In someone's name, you get an award that the person who gets highest in chemistry is going to get this award. In class 9 and 10, whoever gets the highest in chemistry. And the highest marks in 9 and 10 will be given to the board. And you see that is going to go on forever and ever. And it is going to go on till eternity. Right? It will go on forever. So that is called perpetuity. Now say for example that medal cost is 3000 rupees. So how much donation will have to be given or the fund will have to be created that a medal of 3000 rupees can be given to a child every year in the annual function of the school. Are you understanding? There could be a lot of trusts and charities etc. which are created to be a Nobel Prize. Nobel Prize is another big scam. I don't know if you people know about it. It's an absolutely politically motivated scam kind of a irreputable thing. Anyways, although I'm happy Sheldon got it. Nevertheless, but so when you're looking at perpetuity is the cash flow is going to go on forever and ever. Okay, it will always go on forever. Do you understand that example? Normally, our people don't have such perpetual preference shares. Preference shares and some terms, you'll get comfortable as we move forward. It's possible that preference share term is of a non-commerce background, which is not understood. So that term equity share or something will be understood later when you study different subjects and all. So don't worry on that. So there will be a lot of things like this. There will be some terms which you will understand. And that is, but understand the example. It has its application. It has its application. Now we have to look at the different sums. How will we do its calculations? We have done this calculation. We understand what is present value, future value, interest rates, discount rates, compounding. Annual, monthly, quarterly etc. We have a very fair understanding. Let's start with the annuity question. Myake this outline first. And if you want to write 1, 2, 3, then write it. 1 is done. 2, 2a. What happens later? It becomes easy. Then to remember that there was single cash flow, annuity, annuity was ordinary, due, then unequal cash flow, then perpetuity. So it gets easier that there were 4 points, this was this, that is easy to remember. So always know the flow, means you don't have to just close your eyes and read. You have to know the structure, what I am studying, how it's fitting into the entire chapter, what is the application. Take this down. Alright, so let's start with the ordinary annuity and annuity due question. Again, it seems a little confusing, so please keep focus. In annuity, now what happens is, let's do our basic question first. Guys guys over here, so this amount of 100, is it called PV or FvV? It is not called PV or FvV, this is PMyT. So when you are looking at your calculator and even if you look at Excel, your maximum functions that your financial calculator will do, most of the formulas are going to be working in Excel. You can calculate most, I think all of the formulas are going to be working in Excel also. Anyways, we need to bother about the calculator a bit. So this 100, we call it PMyT or payment. So PMyT stands for, this stands for PMyT which is? Payment, the regular payment which is being done, the regular equal payment is being done at regular intervals. The uneven cash flow which was there, 100, 200, 50, minus 50 etc. In that, our people don't call that PMyT, that cash flow. The cash flow which was coming in between, this one, the uneven cash flow which was coming, This cannot be called PMyT. PMyT is only used when you have equal cash flows at regular intervals. So if I am getting 100, 100, 100 5 times, how will I get its present value? So the answer will be, if I want to get its present value, that is equal to 100, and I am assuming 8% And I am assuming 8% annual rate. Be very focused, I will give you time to take it down. 100 by 1.08, this is its present value. What does present value mean? I can individually get its present value. This, this is the answer. Everybody with me? This is the answer, of present value. Now, the obvious thing is that this long calculation will be very irritating. What if I have a 10 year, 20 year, or I take a loan of 20 years on monthly EMyI. 20 x 12, 240 payments will be done. So then it becomes a very tedious job. So one, there was a formula in school, I don't remember the exact formula. Let me just try, I think it was A by I, A means PMyT in that. And 1 plus R to the power n minus 1. I think this was done. We will find the answer, you don't need this formula, you don't need to learn this formula. If there is an annuity chapter in the class 11-12 ISC board, then this was the formula. Does anyone remember? You don't have annuity? Okay, anyways, you don't need that formula. Don't bother about it, just ignore that. Fvocus on your calculator. Pick up your calculator. Have the calculator in front of you. So when you are looking at the calculator, see the third row on the calculator. In the third row on your calculator you will see you have N i by y PV PMyT FvV function. You have N i by y PV PMyT FvV function. These buttons are made in the third row in the calculator. Right? Present value, future value we've already understood. N and I by Y, N is not the number of years. This is the number of periods. And I by Y is not the rate per annum. It is not that R It is rate per period. That is, it is R by My. It is that periodic rate. Calculator will not dream that it is monthly compounding or quarterly compounding. So, N is the number of periods and R is the rate per period. Got it? PVFvE you understand, present value, future value. PMyT is this, PMyT we are talking about. PMyT is this, payment we are talking about. Everybody with me? Now, Now to calculate this, you can calculate it manually in the calculator. You will have to put a lot of brackets. 100 by 1.08 bracket rows, plus bracket open 100 by 1.08 square bracket rows. It will become a little tedious job. But still do it. What will happen in the starting is that the hand will be set on the calculator. The speed will increase on the calculator and you will be sure that yes this is working. So in the beginning you do it, I am not doing it right now. So we will be entering some data points in the calculator and we will get the answer. This row, this third row of calculator which has 5 buttons, we call it the TVMy function. The time value of money functions which we are doing right now. Right? Now here Fv will not come, your n is equal to So if I see n is equal to 5, i by y is equal to 8 because I am taking per annum. It is a 5 year time frame. PMyT is equal to 100. Correct? Fvv is nothing. Now please don't say that 100 is the future value. Fvuture value is not 100. Please pay attention once. Fvuture value is not 100. 5 times 100 is coming. This 100 has been included in PMyT. I am saying n is equal to 5. I by Y, the rate, interest or yield, whatever you say, the rate per period is 8%. And we don't put 0.08 in the calculator, we put 8 only. The calculator knows that you are putting interest rate or percentage yield, so you will put 8 only, you will not put 0.08. PMyT, the payment is 100. 5 times payment, 1, 2, 3, 4, 5, this 100 has been counted in PMyT in 5 times. There is no FvV. What is FvV? You will say 100 FvV. It is not 100 FvV. When you bring this PV with discount of 500, then you will bring compound of 500, then it will be FvV. When you take these 500 compounded here, that will be FvV. I will do it, I will explain how. Say for example, I have retired, I have deposited a lump sum in the bank. And I told the banker that I have a 5 year life, Now I want to deposit a certain sum of money, And my entire year's expense is 100. Tell me how much money to give and you will give me 100 for the next 5 years. Possible. Aisa question ho sakta hai. Aisa bhi ho sakta hai ki I am going to be depositing 100-100. Myekko 5 saal ke baad mein ek gari lene ka hai. Ya ghar lene ka hai. So what do I accumulate? I want to deposit an equal amount of money. So what amount if I deposit same money from my salary every month, every year, at the end of 5 years, wo kitna banega? Wo jo kitna banega is EFvV. 5 bari 100-100-100 jama karke, accumulate karke, wo kitna banega? That is what is future value. This 100 is not the future value. Is this part clear? Everyone? Sure? So by doing this, we will add our FvV equal to 0. If you don't understand FvV, then ignore it. A question will come about bond. I will do it after a while. By doing that, you will understand it more clearly. Myeaning, you don't have to add FvV separately. Okay? When will you add FvV? I will give you an example, but I am not doing that sum right now. It will come later. Suppose I am saying that I have a 5 year job left. I am at the age of 55 and retiring at 60. So 5 years I can accumulate another 100, 100, 100. In the 5th year, the company is going to give me a bonus of 700 for the graduation and pension. So the 700 that I will get here, that will be the FvV. That 5 times 100 is being counted in PMyT. In the 5th year, the company will give me a bonus of... will give the accumulated amount, that 700 is my FvV. If that is 700, then you can put some amount in FvV. Then, all this and the future value of 700, that will be the future value. Myeans, the answer we will get. But right now, we will put FvV equal to 0 for now. But don't worry. Myeans, if you don't understand FvV equal to 0, then by default, catch FvV equal to 0 once. Because this 5 times 100 is already counted in the PMyT. Clear? Everyone? Now what we need to do is compute PV. So when you are working with a calculator, the first thing is, when you turn off your calculator and turn it on, the data that is saved in the calculator, it doesn't get deleted. So when I am starting a question, I need to erase all the data. Suppose in the previous question, Fvv equal to 200 was something that was there. You didn't clear it. and if you don't put 0 in FvV, then the answer will be wrong. If I am putting 0 in FvV, so I have already overwritten all 4 values, then there is no problem, even if I did not delete the old data, it's okay. But if you are not putting FvV equal to 0, then first, okay, don't get confused, second, there is a second button, you have to do the calculator lecture also, now parallelly. I mean, while studying, you will have to watch the class on the calculator too, to understand and to get comfortable with the calculator. There is a second button above. Second row, first button. So you press 2nd FvV. Look above FvV, it is written Clear TVMy. Clear TVMy means this row, this TVMy button, this function. This is the row of TVMy functions. These 5 buttons in this row are called TVMy functions. To delete this row, to clear it, to make it zero. And why are we using second? Because to use FvV button, you will press FvV. And above the FvV, above not on above The clear TVMy which is written, to use that we will do second FvV Clear everybody If we do second FvV, then it will put zero in the five buttons So whatever was the previous data, it's gone Even if you switch off and switch on, the data does not get erased So don't think that I will turn on and off and it will go away Myangalam, which movie was it? It's not working Turned on and off, everything is okay You know Myangal? Myission Myangal. It doesn't happen like this. So, we did second FvV, everything deleted. Now, let's start entering the values. Press 5 and then press N. Not N and 5, 5 and then N. When you do that, see when you press 5, on the calculator it's only 5. When you press N, N equal to 5 will appear on the screen. See, try it. After that, you don't need to press C, E, C or 0, V, R again. Next, direct 8 press and I buy buy. 8 gets stored in I buy buy. Then I press 100 and I press PMyT. 100 gets stored in payment. FvV 0 or not, it doesn't matter because I have done clear TVMy. If you didn't blow the old data or you forgot that you had blown it or not, then put 0 in FvV, then it doesn't matter. Because you have overwritten all the data points. Say clear. If you had cleared the values, I will not put 0FvE because I had already done default 0. If I forget to do it, I will do 0FvE first. And then all I have to do is, the compute button is visible above. So then I will do compute PV. Compute PV. Compute PV. By adding any 3 or 4 values, the calculator will provide you the 5th value. The 5th value, the calculator is going to. provided to you that is 399.27 RI. that is compute PV agar karoge so this is 399.27 do you notice it's not 399 on your calculator but it is minus 399 on your calculator kyun aisa ho raha hai outflow inflow so understand suppose I'm depositing agar main aaj If I deposit 399 in the bank, will 399 go outflow? If I do this, will I get 100, 100, 100 for the next 5 years? If you want to deposit 100, 100, suppose you say that you will deposit 100 for 5 years, and in the end of 5 years, I will withdraw from the bank, then if you put 100 in minus, will it come to 399 plus? When our people used to use the calculator, let's not bother so much about the minus and plus. And let's just get our answers. But later you will have to bother. You will have to wait till FvBB comes. The sign of inflows and outflows will have to be reversed. If you are depositing 100-100 and 700-700, then if it is 100-100, it will be 700-B+. If it is 100-100, it will be 700-B-. Otherwise, how will the calculator understand? This is the number of periods, this is the rate, but these three are the amounts. Rupee, paise, dollar, pound amount hai right? So yeh teeno me cash flows me you have to just make sure that outflows and inflows have the opposite sign. Ek outflow opposite, dusra outflow, ek outflow positive, ek outflow negative, woh nahi chalega. Don't worry I know thoda sa confusing lagsakta hai, FvV wala sum jaise hi aega na yeh part clear ho jayega, don't worry about it. Ek bond ka sum karte hi clear ho jayega. Wo annuity ke baad hoga, perpetuity ke baad. So if you are little unclear on the fv equal to 0 and the positive negative, just wait for some time. It will be clear in that. But is it okay till here? So this is the answer which is taken by discounting 100 separately. This is the answer. This is what this answer is and we are going to be using TVMy function on our calculator for this. We are going to be using TVMy functions on the calculator for this. Okay. Till here is it okay? The sum of our single cash flow, just to let you know, this can also be done with the same TVMy function. How can it be done? Put 100 as FvV, put n equal to 5, put i as 8%, and compute PV. You won't put PMyT, right? Here 100 is not PMyT, 100 is the FvV. Fvuture value is 100, so how much is PV? Calculate and tell me the answer. Use the calculator and tell me. Don't do this, don't use this formula. FvV PV PMyT And you must have seen that if you put 100 as positive, then 68.05 will be negative. If you deposit 68.05 today, then you will get 100. If you do 100 minus, then 68.05 will be positive. If I am taking a loan of 68.05, then how much do I have to give after 5 years? 100. And if I am depositing 68.05 today, how much I will get at the end of 5 years? 100. So either this inflow, this outflow, or this outflow, this inflow. So the sign of inflow and outflow will be opposite. Tell me about this too. Put 100 PV and compute FvV. So don't put PMyT, just put PV FvV NI by Y. Shoot PMyT and you can do your questions on the calculator with this. Clear? Problem? Sure? Yes, I am asking you. Tell me, this much is okay? We can calculate the present value. Now if we want to find its future value, how will we do it? We can also use PV, let's see 2-3 ways. Fvirst is, Myy Fvv, I want to write it on this page only. Okay, I will write a little bit. Okay, pay attention here. The Fvv that I want to get out, What does this 100 Fvv mean? I want to take all these values over here. Correct? This 100 is supposed to be compounded 4 times. I will take this here. Okay, so what will be the formula of Fvv? Fvv is equal to this 100 into 1.08 to the power 4. Plus 100 into 1.08 to the power 3. This will compound 3 times, right? 2 to 5. Plus 100 into 1.08 to the power 2. Plus 100 into 1.08. Plus 100. This 100 is 100 today only. This 100 compounded 4 times. 3 times, 2 times, 1 time, 0 time. 100 today is 100 today. This is fine. Now understand. You can take 100 commonly. Fvirst. Second, you have to compound it 5 times after discounting it once. It's as good as compounding it by 4 times. What happened here? Once discount happened, you brought this 100 here. You have brought all these 100 here. You can get the FvV from this formula also. Compounding each 100 to the end, to the maturity. Or... Can we do this also? Correct? How is it working? It is working formula wise also. This 100 is brought here, discount once, compound 5 times, net-net compound 4 times. This 100 is discounted twice, see this one. You are multiplying the entire PV with 1.08 to the power 5. So if you multiply this with 1.08 to the power 5, then compound is done 3 times. If you compound this with 1.08 to the power 5, then compound is done twice. If you multiply this with 1.08x5, then it will compound once. And if you compound this with 1.08x5, then it will become 100 out of 100. Myeaning, if you compound 5 by discounting 1, or compound 4, it's the same thing. If you compound 5 by discounting 4, or compound 1 directly, it's the same thing. Should I take cash flow here, or take it here and then take it here? It's the same thing. That is why, the present value that I got, that into 1.08x5 is also the FvV. There is also one way of calculating. And, whatever is the answer. Or, compute FvV on the calculator. Compute FvV. Answer, see what is coming on the calculator. What is coming on the calculator? 586 point. If you clear PV without taking out FvE, the answer can be wrong. I want the future value of 500. 500 and minus 399, their future value will be a little same. I want the value of 500 here. If I put minus 399 in the calculator, then the future value of this and all these cash flows will be a little same. Then the answer will be wrong. So make sure you use clear TVMy properly. You understood? That is why do Clear TVMy and use it. Get used to it, then you will get confident, then you will learn to overwrite and all this. But first, clear TVMy, delete all the data in 5 buttons, put PMyT as 100, NIYY and compute FvV instead of PV. Say clear. After doing compute PV, if you do compute FvV, what is the answer? It will not be 700. You do compute PV also. Very useless value is coming. Something like minus 0.00 will come. Because we took PV of this for 399. 399 and minus 399 is approximately 0. So, the value 0.000 that is coming, that minus 12 is coming, minus 12, means, to the power, into 10 to the power minus 12. I will do it, I will do it, I will give you all that. Now, see this once. Almost 0 is the answer. That's almost 0. Clear till here? Sure? Doubt? Till here it's okay? If I tell you... that the bank is giving you a choice that you deposit 600 today And the bank will pay you 100 for 5 years. What is the implied rate? Or return that the bank is providing you. Tell me, how will you solve? Now, solving the equation will be difficult. Bank is saying that you deposit 600 hours. And in return, we will give you 100, 100, 100 for 5 years. Okay? Present value is 600. Which is equal to... 100 by 1 plus r plus 100 by 1 plus r square. 100 by 1 plus r to the power 5. Polynomial equation is done, right? It will be difficult to solve. We don't have to solve this equation. We are going to use the calculator. What will you put in the calculator? In the calculator, you will put minus 600 PV. You will put 100 FvV. Sorry, PMyT. 100 will be put as PMyT, 5 will be put as N, and I by Y will be computed. Sir, negative I and D, A can be reduced. Is it 600? Yes, it is negative. If you deposit 600 and get 500, then the return is useless. Sorry, I should change the value. I have changed it here. 600 is called 350. Myinus mein dalna hoga. Myinus mein dalogin na toh interest rate aiga nahi. Compute IMyO is 13.20%. So if a bank tells you that you deposit 350 today and you will get 100, 100, 100 for the next 5 years that means the rate that the bank is providing you is implying is 13.2%. 13.2% is the rate you are earning. We will discuss this in 13.2 as we move forward. We are going to study EMyI etc. We are going to do this in that. End of this chapter is at the end. But you understood? You are not able to back calculate. It's a polynomial equation. Say correct. If you put 350B positive and 100B positive, then I by Y will not calculate. It will show error. Because what is, I mean, if you are doing all positive, I mean, the bank is saying I am giving you 350 today. and for 5 years I am giving you 100 again then where did the return come from? It is not an investment at all. You are understanding? If I am giving you 350 today and if I am giving you 100, 100, 100 your return has become infinite in a way. How did the return get calculated? That I put 100 and now I got 150. So, 50% return happened. If I am investing 100 and receiving 50% 150 back. But if I have not invested anything, if I am not putting in any money, If I'm getting 350 and then 100, 100, 100, it's a problem, right? I mean, it's not a return. Sir, investment is not happening. It's a leak. I mean, sorry, but you're understanding the idea. And how will the bank know? So, do minus 350 or plus 100. 13.2% will come. If you add plus 350 or minus 100, then also 13.2% will come. Think of it. I'm depositing 350. So, my minus 350 and I'm getting 100. Look at this question from the bank's point of view. The bank is getting 350 today, plus 350. And the bank has to give 100, 100 minus 100. The cash flow that is minus plus from your point of view, will automatically become plus minus from the bank's point of view. Tell me, are you following this or not? Sure? Till here? Okay, for once we will pause.

So, for now. Fvuture value, present value for a single cash flow. We can call it a lump sum cash flow. We can calculate, say for example, I am using 100 and doing a simple static question.

So time is 0. Time, let's say I will take 5 years. Here 100. Here what is its present value? We can calculate this.

You have learned 100 divide by, and I am going to be assuming 8% throughout this part. Fvor once. Okay? So 100 divide by 1.08 to the power 5 is the answer.

So my present value is equal to 100 divided by 1.08 to the power 5. Correct? If I have to find the future value of single cash flow, let's say time 0, time 5 here, if here is 100, So here, what is the future value? Fvuture value is equal to 100 into 1.08 to the power 5. So we can calculate the present value or the future value. Now we understand that the present value is time 0, and the future value is the time, the maturity, whatever the maturity is.

Here, 5 years we are assuming as the maturity. There are instruments like this, fixed deposits, LIC options, investments That you are making payment today and you will get it on maturity There is no need to make payment in between, nothing to get, nothing at all There are schemes like that also We will read bonds and zero-coupon bonds further Then you will understand that also There are such investments Look at the stock Suppose today I bought some share And that share doesn't give dividend I have bought a growth company's share which does not divide dividends, it reinvests the company's income and the company is trying to grow So maybe I am investing today and 5 years later I get a certain money I want to calculate the return Yes, with these two values, you may have to calculate the return as well I can back calculate the return as well Right now focus on the cash flow pattern Returns and all, we will learn gradually So one could be that you are investing today and you are eventually getting a lump sum amount. That is one option. The second type of payment is annuity. Annuity can be of two types.

One is an ordinary annuity. One is an annuity due. Fvirst understand ordinary annuity. Ordinary annuity, again I am taking the same, 1, 2, 3, 4, 5. It will give you 100, 100, 100, 100, 100. What is the present value over here? You might need to calculate.

I am removing the question mark once, I am leaving the cash flow pattern here And I am going to discuss this, else I am not writing anything There is nothing here So from time 1 to 5 years, you are going to be getting an equal cash flow At regular interval, what does annuity mean? That is equal cash flow at regular interval The cash flow is equal, it has to be 100. 100, 200, 100, 100, it won't work. And 100, 100, 0, 100, 100, that also won't work.

It has to be an equal cash flow at regular interval. If you are buying a house or a car and you are taking a loan, normally what you have to pay is an EMyI. EMyI is Equated Myonthly Installment.

We will come to that in a while. That will be a part of annuity. So in that, you pay the same sum of money on a regular basis at an equal interval monthly installment.

You don't pay different amounts, right? You pay the same amount every time. You are depositing LIC premium, regularly you deposit the same premium, and then later on you get the sum assured, your family, right? Annuities happened, equal amount at regular intervals, correct? Myaking sense?

So all the loan related etc. will come in the calculations after some time. But right now, ordinarily what happens? Normally if you take a loan today, then today first interest payment is done, EMyI is done.

Or you do your first payment at the end of the month. So, normally what happens? Ordinarily what happens? Your payment is supposed to start at the end of the period. Now this 1, 2, 3, 4, 5 could be first month, 1 month, 2 month, 3 month, 5 month.

It could be 1 year, 2 year, 5 year. It will depend on what the question is, what the data is, what are you calculating on that. But the cash flow pattern could be like this.

This is an ordinary annuity. What is annuity due? 100, 100, 100, 100, 100. In annuity due, your annuity begins at time 0, that is today. The difference is this part. Here, if you see this entire app, there are 5 cash flows in total.

There are 5 cash flows here too. But the entire 5 cash flows have been shifted one period before. All the 5 cash flows have been shifted a period ahead.

Don't see that he brought 100 here. He has shifted every 100 like this. That is Annuity Due. You will remember Ordinary Annuity and Annuity Due now.

Because I asked you a simple question. Normally what happens? Ordinarily what happens? Do you make the payment today or do you start the payment at the end of the month? You all said end of the month.

That is Ordinary Annuity. Annuity Due means that which is due today and starts today. In both cases, please remember that in both annuity dues, it's a 5 year annuity.

5 year annuity means that the number of payments is 5 in both. But here, there is no payment on the 5th year. Annuity due means that you are not getting another cash flow on the 5th year and a total of 6 cash flows. That is not what is happening over here.

We are going to do its questions and its sums. We will solve this. But do you understand this much? Clear?

100%? Next is, now just understand the patterns of different cash flows. In unequal cash flows, I will give 2-3 examples.

You can have 0, 1, 2, 3, 4. You can have 100, 100, 0, 100, 100. Cash flows are equal, but at one time the cash flow went wrong. You might call it not equal cash flow, but it became an irregular interval. The first two hundred is in the gap of one year, but the third one is in the gap of two years. Although the cash flows are same, but there is an irregularity.

This is an unequal cash flow. Or, regular intervals, but the cash flows are unequal. This is also unequal cash flow. Or, Cash flow can keep increasing or decreasing I can also make a cash flow negative So that is unequal cash flow So basically anything Basically if equal cash flow at equal interval Not regular interval So in that case it will go to unequal cash flow We have to do calculations for that too Fvor example what if I am laying down a factory today So maybe in the first 2-1 years I will have to invest 100-200 Myaybe after that returns will start coming 300-400-500 Both cash flows can be negative and positive. Fvollowing, you have to do evaluation of any project.

So in that case, ideally, normally, if you look at EMyI, you will get odd annuity. If you look at LIC's schemes and all, normally it works as an annuity. Or say for example, you have retired from a company at the age of 60. And the company is telling you that I am going to be paying you for the next 20 years You will be given a pension 20 years, 25 years till the time you leave So that will be an annuity style payment Equal amount at regular intervals But when you are doing any decision analysis etc. With regards to equity, company etc. Then it will come in equal cash flows normally Tell me, making sense everyone?

What is perpetuity? Perpetuity is Let's say You will get 10, 10, 10, infinity. Perpetual, perpetually, forever and ever.

That is perpetuity. A very simple example. Suppose in your school, there is an XYZ memorial award. In someone's name, you get an award that the person who gets highest in chemistry is going to get this award.

In class 9 and 10, whoever gets the highest in chemistry. And the highest marks in 9 and 10 will be given to the board. And you see that is going to go on forever and ever.

And it is going to go on till eternity. Right? It will go on forever. So that is called perpetuity. Now say for example that medal cost is 3000 rupees.

So how much donation will have to be given or the fund will have to be created that a medal of 3000 rupees can be given to a child every year in the annual function of the school. Are you understanding? There could be a lot of trusts and charities etc. which are created to be a Nobel Prize. Nobel Prize is another big scam.

I don't know if you people know about it. It's an absolutely politically motivated scam kind of a irreputable thing. Anyways, although I'm happy Sheldon got it. Nevertheless, but so when you're looking at perpetuity is the cash flow is going to go on forever and ever. Okay, it will always go on forever.

Do you understand that example? Normally, our people don't have such perpetual preference shares. Preference shares and some terms, you'll get comfortable as we move forward.

It's possible that preference share term is of a non-commerce background, which is not understood. So that term equity share or something will be understood later when you study different subjects and all. So don't worry on that. So there will be a lot of things like this. There will be some terms which you will understand.

And that is, but understand the example. It has its application. It has its application. Now we have to look at the different sums. How will we do its calculations?

We have done this calculation. We understand what is present value, future value, interest rates, discount rates, compounding. Annual, monthly, quarterly etc. We have a very fair understanding. Let's start with the annuity question.

Myake this outline first. And if you want to write 1, 2, 3, then write it. 1 is done.

2, 2a. What happens later? It becomes easy. Then to remember that there was single cash flow, annuity, annuity was ordinary, due, then unequal cash flow, then perpetuity.

So it gets easier that there were 4 points, this was this, that is easy to remember. So always know the flow, means you don't have to just close your eyes and read. You have to know the structure, what I am studying, how it's fitting into the entire chapter, what is the application. Take this down.

Alright, so let's start with the ordinary annuity and annuity due question. Again, it seems a little confusing, so please keep focus. In annuity, now what happens is, let's do our basic question first. Guys guys over here, so this amount of 100, is it called PV or FvV?

It is not called PV or FvV, this is PMyT. So when you are looking at your calculator and even if you look at Excel, your maximum functions that your financial calculator will do, most of the formulas are going to be working in Excel. You can calculate most, I think all of the formulas are going to be working in Excel also.

Anyways, we need to bother about the calculator a bit. So this 100, we call it PMyT or payment. So PMyT stands for, this stands for PMyT which is? Payment, the regular payment which is being done, the regular equal payment is being done at regular intervals.

The uneven cash flow which was there, 100, 200, 50, minus 50 etc. In that, our people don't call that PMyT, that cash flow. The cash flow which was coming in between, this one, the uneven cash flow which was coming, This cannot be called PMyT. PMyT is only used when you have equal cash flows at regular intervals. So if I am getting 100, 100, 100 5 times, how will I get its present value?

So the answer will be, if I want to get its present value, that is equal to 100, and I am assuming 8% And I am assuming 8% annual rate. Be very focused, I will give you time to take it down. 100 by 1.08, this is its present value.

What does present value mean? I can individually get its present value. This, this is the answer.

Everybody with me? This is the answer, of present value. Now, the obvious thing is that this long calculation will be very irritating. What if I have a 10 year, 20 year, or I take a loan of 20 years on monthly EMyI.

20 x 12, 240 payments will be done. So then it becomes a very tedious job. So one, there was a formula in school, I don't remember the exact formula.

Let me just try, I think it was A by I, A means PMyT in that. And 1 plus R to the power n minus 1. I think this was done. We will find the answer, you don't need this formula, you don't need to learn this formula.

If there is an annuity chapter in the class 11-12 ISC board, then this was the formula. Does anyone remember? You don't have annuity?

Okay, anyways, you don't need that formula. Don't bother about it, just ignore that. Fvocus on your calculator.

Pick up your calculator. Have the calculator in front of you. So when you are looking at the calculator, see the third row on the calculator.

In the third row on your calculator you will see you have N i by y PV PMyT FvV function. You have N i by y PV PMyT FvV function. These buttons are made in the third row in the calculator.

Right? Present value, future value we've already understood. N and I by Y, N is not the number of years.

This is the number of periods. And I by Y is not the rate per annum. It is not that R It is rate per period.

That is, it is R by My. It is that periodic rate. Calculator will not dream that it is monthly compounding or quarterly compounding. So, N is the number of periods and R is the rate per period.

Got it? PVFvE you understand, present value, future value. PMyT is this, PMyT we are talking about. PMyT is this, payment we are talking about. Everybody with me?

Now, Now to calculate this, you can calculate it manually in the calculator. You will have to put a lot of brackets. 100 by 1.08 bracket rows, plus bracket open 100 by 1.08 square bracket rows. It will become a little tedious job.

But still do it. What will happen in the starting is that the hand will be set on the calculator. The speed will increase on the calculator and you will be sure that yes this is working. So in the beginning you do it, I am not doing it right now.

So we will be entering some data points in the calculator and we will get the answer. This row, this third row of calculator which has 5 buttons, we call it the TVMy function. The time value of money functions which we are doing right now. Right?

Now here Fv will not come, your n is equal to So if I see n is equal to 5, i by y is equal to 8 because I am taking per annum. It is a 5 year time frame. PMyT is equal to 100. Correct?

Fvv is nothing. Now please don't say that 100 is the future value. Fvuture value is not 100. Please pay attention once.

Fvuture value is not 100. 5 times 100 is coming. This 100 has been included in PMyT. I am saying n is equal to 5. I by Y, the rate, interest or yield, whatever you say, the rate per period is 8%. And we don't put 0.08 in the calculator, we put 8 only. The calculator knows that you are putting interest rate or percentage yield, so you will put 8 only, you will not put 0.08.

PMyT, the payment is 100. 5 times payment, 1, 2, 3, 4, 5, this 100 has been counted in PMyT in 5 times. There is no FvV. What is FvV?

You will say 100 FvV. It is not 100 FvV. When you bring this PV with discount of 500, then you will bring compound of 500, then it will be FvV. When you take these 500 compounded here, that will be FvV.

I will do it, I will explain how. Say for example, I have retired, I have deposited a lump sum in the bank. And I told the banker that I have a 5 year life, Now I want to deposit a certain sum of money, And my entire year's expense is 100. Tell me how much money to give and you will give me 100 for the next 5 years. Possible. Aisa question ho sakta hai.

Aisa bhi ho sakta hai ki I am going to be depositing 100-100. Myekko 5 saal ke baad mein ek gari lene ka hai. Ya ghar lene ka hai. So what do I accumulate? I want to deposit an equal amount of money.

So what amount if I deposit same money from my salary every month, every year, at the end of 5 years, wo kitna banega? Wo jo kitna banega is EFvV. 5 bari 100-100-100 jama karke, accumulate karke, wo kitna banega? That is what is future value. This 100 is not the future value.

Is this part clear? Everyone? Sure?

So by doing this, we will add our FvV equal to 0. If you don't understand FvV, then ignore it. A question will come about bond. I will do it after a while. By doing that, you will understand it more clearly.

Myeaning, you don't have to add FvV separately. Okay? When will you add FvV?

I will give you an example, but I am not doing that sum right now. It will come later. Suppose I am saying that I have a 5 year job left. I am at the age of 55 and retiring at 60. So 5 years I can accumulate another 100, 100, 100. In the 5th year, the company is going to give me a bonus of 700 for the graduation and pension. So the 700 that I will get here, that will be the FvV.

That 5 times 100 is being counted in PMyT. In the 5th year, the company will give me a bonus of... will give the accumulated amount, that 700 is my FvV. If that is 700, then you can put some amount in FvV.

Then, all this and the future value of 700, that will be the future value. Myeans, the answer we will get. But right now, we will put FvV equal to 0 for now. But don't worry.

Myeans, if you don't understand FvV equal to 0, then by default, catch FvV equal to 0 once. Because this 5 times 100 is already counted in the PMyT. Clear?

Everyone? Now what we need to do is compute PV. So when you are working with a calculator, the first thing is, when you turn off your calculator and turn it on, the data that is saved in the calculator, it doesn't get deleted.

So when I am starting a question, I need to erase all the data. Suppose in the previous question, Fvv equal to 200 was something that was there. You didn't clear it. and if you don't put 0 in FvV, then the answer will be wrong.

If I am putting 0 in FvV, so I have already overwritten all 4 values, then there is no problem, even if I did not delete the old data, it's okay. But if you are not putting FvV equal to 0, then first, okay, don't get confused, second, there is a second button, you have to do the calculator lecture also, now parallelly. I mean, while studying, you will have to watch the class on the calculator too, to understand and to get comfortable with the calculator.

There is a second button above. Second row, first button. So you press 2nd FvV. Look above FvV, it is written Clear TVMy. Clear TVMy means this row, this TVMy button, this function.

This is the row of TVMy functions. These 5 buttons in this row are called TVMy functions. To delete this row, to clear it, to make it zero. And why are we using second? Because to use FvV button, you will press FvV.

And above the FvV, above not on above The clear TVMy which is written, to use that we will do second FvV Clear everybody If we do second FvV, then it will put zero in the five buttons So whatever was the previous data, it's gone Even if you switch off and switch on, the data does not get erased So don't think that I will turn on and off and it will go away Myangalam, which movie was it? It's not working Turned on and off, everything is okay You know Myangal? Myission Myangal. It doesn't happen like this.

So, we did second FvV, everything deleted. Now, let's start entering the values. Press 5 and then press N.

Not N and 5, 5 and then N. When you do that, see when you press 5, on the calculator it's only 5. When you press N, N equal to 5 will appear on the screen. See, try it. After that, you don't need to press C, E, C or 0, V, R again. Next, direct 8 press and I buy buy.

8 gets stored in I buy buy. Then I press 100 and I press PMyT. 100 gets stored in payment. FvV 0 or not, it doesn't matter because I have done clear TVMy. If you didn't blow the old data or you forgot that you had blown it or not, then put 0 in FvV, then it doesn't matter.

Because you have overwritten all the data points. Say clear. If you had cleared the values, I will not put 0FvE because I had already done default 0. If I forget to do it, I will do 0FvE first. And then all I have to do is, the compute button is visible above. So then I will do compute PV.

Compute PV. Compute PV. By adding any 3 or 4 values, the calculator will provide you the 5th value.

The 5th value, the calculator is going to. provided to you that is 399.27 RI. that is compute PV agar karoge so this is 399.27 do you notice it's not 399 on your calculator but it is minus 399 on your calculator kyun aisa ho raha hai outflow inflow so understand suppose I'm depositing agar main aaj If I deposit 399 in the bank, will 399 go outflow?

If I do this, will I get 100, 100, 100 for the next 5 years? If you want to deposit 100, 100, suppose you say that you will deposit 100 for 5 years, and in the end of 5 years, I will withdraw from the bank, then if you put 100 in minus, will it come to 399 plus? When our people used to use the calculator, let's not bother so much about the minus and plus. And let's just get our answers. But later you will have to bother.

You will have to wait till FvBB comes. The sign of inflows and outflows will have to be reversed. If you are depositing 100-100 and 700-700, then if it is 100-100, it will be 700-B+.

If it is 100-100, it will be 700-B-. Otherwise, how will the calculator understand? This is the number of periods, this is the rate, but these three are the amounts.

Rupee, paise, dollar, pound amount hai right? So yeh teeno me cash flows me you have to just make sure that outflows and inflows have the opposite sign. Ek outflow opposite, dusra outflow, ek outflow positive, ek outflow negative, woh nahi chalega.

Don't worry I know thoda sa confusing lagsakta hai, FvV wala sum jaise hi aega na yeh part clear ho jayega, don't worry about it. Ek bond ka sum karte hi clear ho jayega. Wo annuity ke baad hoga, perpetuity ke baad. So if you are little unclear on the fv equal to 0 and the positive negative, just wait for some time. It will be clear in that.

But is it okay till here? So this is the answer which is taken by discounting 100 separately. This is the answer. This is what this answer is and we are going to be using TVMy function on our calculator for this. We are going to be using TVMy functions on the calculator for this.

Okay. Till here is it okay? The sum of our single cash flow, just to let you know, this can also be done with the same TVMy function. How can it be done?

Put 100 as FvV, put n equal to 5, put i as 8%, and compute PV. You won't put PMyT, right? Here 100 is not PMyT, 100 is the FvV.

Fvuture value is 100, so how much is PV? Calculate and tell me the answer. Use the calculator and tell me. Don't do this, don't use this formula.

FvV PV PMyT And you must have seen that if you put 100 as positive, then 68.05 will be negative. If you deposit 68.05 today, then you will get 100. If you do 100 minus, then 68.05 will be positive. If I am taking a loan of 68.05, then how much do I have to give after 5 years?

100. And if I am depositing 68.05 today, how much I will get at the end of 5 years? 100. So either this inflow, this outflow, or this outflow, this inflow. So the sign of inflow and outflow will be opposite. Tell me about this too. Put 100 PV and compute FvV.

So don't put PMyT, just put PV FvV NI by Y. Shoot PMyT and you can do your questions on the calculator with this. Clear?

Problem? Sure? Yes, I am asking you. Tell me, this much is okay?

We can calculate the present value. Now if we want to find its future value, how will we do it? We can also use PV, let's see 2-3 ways.

Fvirst is, Myy Fvv, I want to write it on this page only. Okay, I will write a little bit. Okay, pay attention here. The Fvv that I want to get out, What does this 100 Fvv mean?

I want to take all these values over here. Correct? This 100 is supposed to be compounded 4 times. I will take this here.

Okay, so what will be the formula of Fvv? Fvv is equal to this 100 into 1.08 to the power 4. Plus 100 into 1.08 to the power 3. This will compound 3 times, right? 2 to 5. Plus 100 into 1.08 to the power 2. Plus 100 into 1.08. Plus 100. This 100 is 100 today only. This 100 compounded 4 times.

3 times, 2 times, 1 time, 0 time. 100 today is 100 today. This is fine. Now understand.

You can take 100 commonly. Fvirst. Second, you have to compound it 5 times after discounting it once. It's as good as compounding it by 4 times.

What happened here? Once discount happened, you brought this 100 here. You have brought all these 100 here.

You can get the FvV from this formula also. Compounding each 100 to the end, to the maturity. Or... Can we do this also? Correct?

How is it working? It is working formula wise also. This 100 is brought here, discount once, compound 5 times, net-net compound 4 times.

This 100 is discounted twice, see this one. You are multiplying the entire PV with 1.08 to the power 5. So if you multiply this with 1.08 to the power 5, then compound is done 3 times. If you compound this with 1.08 to the power 5, then compound is done twice. If you multiply this with 1.08x5, then it will compound once. And if you compound this with 1.08x5, then it will become 100 out of 100. Myeaning, if you compound 5 by discounting 1, or compound 4, it's the same thing.

If you compound 5 by discounting 4, or compound 1 directly, it's the same thing. Should I take cash flow here, or take it here and then take it here? It's the same thing. That is why, the present value that I got, that into 1.08x5 is also the FvV. There is also one way of calculating.

And, whatever is the answer. Or, compute FvV on the calculator. Compute FvV. Answer, see what is coming on the calculator. What is coming on the calculator?

586 point. If you clear PV without taking out FvE, the answer can be wrong. I want the future value of 500. 500 and minus 399, their future value will be a little same.

I want the value of 500 here. If I put minus 399 in the calculator, then the future value of this and all these cash flows will be a little same. Then the answer will be wrong.

So make sure you use clear TVMy properly. You understood? That is why do Clear TVMy and use it. Get used to it, then you will get confident, then you will learn to overwrite and all this.

But first, clear TVMy, delete all the data in 5 buttons, put PMyT as 100, NIYY and compute FvV instead of PV. Say clear. After doing compute PV, if you do compute FvV, what is the answer? It will not be 700. You do compute PV also.

Very useless value is coming. Something like minus 0.00 will come. Because we took PV of this for 399. 399 and minus 399 is approximately 0. So, the value 0.000 that is coming, that minus 12 is coming, minus 12, means, to the power, into 10 to the power minus 12. I will do it, I will do it, I will give you all that. Now, see this once. Almost 0 is the answer.

That's almost 0. Clear till here? Sure? Doubt?

Till here it's okay? If I tell you... that the bank is giving you a choice that you deposit 600 today And the bank will pay you 100 for 5 years. What is the implied rate? Or return that the bank is providing you.

Tell me, how will you solve? Now, solving the equation will be difficult. Bank is saying that you deposit 600 hours. And in return, we will give you 100, 100, 100 for 5 years.

Okay? Present value is 600. Which is equal to... 100 by 1 plus r plus 100 by 1 plus r square. 100 by 1 plus r to the power 5. Polynomial equation is done, right? It will be difficult to solve.

We don't have to solve this equation. We are going to use the calculator. What will you put in the calculator?

In the calculator, you will put minus 600 PV. You will put 100 FvV. Sorry, PMyT.

100 will be put as PMyT, 5 will be put as N, and I by Y will be computed. Sir, negative I and D, A can be reduced. Is it 600?

Yes, it is negative. If you deposit 600 and get 500, then the return is useless. Sorry, I should change the value. I have changed it here. 600 is called 350. Myinus mein dalna hoga.

Myinus mein dalogin na toh interest rate aiga nahi. Compute IMyO is 13.20%. So if a bank tells you that you deposit 350 today and you will get 100, 100, 100 for the next 5 years that means the rate that the bank is providing you is implying is 13.2%. 13.2% is the rate you are earning.

We will discuss this in 13.2 as we move forward. We are going to study EMyI etc. We are going to do this in that. End of this chapter is at the end. But you understood?

You are not able to back calculate. It's a polynomial equation. Say correct.

If you put 350B positive and 100B positive, then I by Y will not calculate. It will show error. Because what is, I mean, if you are doing all positive, I mean, the bank is saying I am giving you 350 today. and for 5 years I am giving you 100 again then where did the return come from?

It is not an investment at all. You are understanding? If I am giving you 350 today and if I am giving you 100, 100, 100 your return has become infinite in a way.

How did the return get calculated? That I put 100 and now I got 150. So, 50% return happened. If I am investing 100 and receiving 50% 150 back. But if I have not invested anything, if I am not putting in any money, If I'm getting 350 and then 100, 100, 100, it's a problem, right?

I mean, it's not a return. Sir, investment is not happening. It's a leak.

I mean, sorry, but you're understanding the idea. And how will the bank know? So, do minus 350 or plus 100. 13.2% will come.

If you add plus 350 or minus 100, then also 13.2% will come. Think of it. I'm depositing 350. So, my minus 350 and I'm getting 100. Look at this question from the bank's point of view.

The bank is getting 350 today, plus 350. And the bank has to give 100, 100 minus 100. The cash flow that is minus plus from your point of view, will automatically become plus minus from the bank's point of view. Tell me, are you following this or not? Sure? Till here? Okay, for once we will pause.

Transcript for:Cash Flow Patterns and Their Applications

Transcript for:
Cash Flow Patterns and Their Applications