So till now, overall, what are we going to do in this subject? Financial management. Broadly, we are going to take some financial decisions. Not pronouncing financial decisions, that can be broadly classified into three: financing decisions, investing decisions, and dividend decisions.

Financing decisions are divisions taken with respect to raising of capital. By capital, I mean all the sources of finance, correct? And investing decisions are with respect to how am I going to deploy the funds that I have in the right investment avenues, correct? And having done everything successfully, how much amount of the rate, how much amount of the entire profit, how much do they pay as a dividend, and how much should I retain it with myself to my reserves? That's called as a dividend decision. Overall, this is what the entire subject talks about. Each chapter will be achieving either of the three objectives only. Clear with this, guys? This is what we have seen till now. And I shared the exam paper pattern, how it will look. And I also shared some insight about what are the overall careers or career opportunities that are available to you in the field of finance, fine. So this is what we have done till now. So now let's continue the journey.

So first of all, first of all, there is a very important concept that is a very important underlying concept in our subject, which is called as time value of money, which you would have studied in your foundation. Anyways, I am starting it from the scratch because I will take it, I will take it to such a level automatically. From there, I will link it to your finance. Automatically from that, I will link it to finance. By finance, I mean financial management. I'll link it to FM. So you know something still undoing it so that from there I can link it from that I can link it to your FM. Clear with this now? So this chapter, time value of money, is not at all there in any of the 10 chapters that you had just told us. Yes, correct or not? Don't think of this as a chapter. Don't think of this as a chapter. This is like the blood. This is like how, how blood is important to our human body. It's like throughout the presence, or maybe a better example is, this is like oxygen. Oxygen cannot be seen, but its presence can be felt, correct? Trust me, once we finish this chapter, once we finish this chapter, more or less throughout in your financial management, every single day, you will be touching upon the concepts that will be, that I'm going to take today. Every single day, we will be touching upon the concepts that we will be seeing today. This is such a very important aspect. Now, some people, they directly skip and they enter into the subject, but I just don't want to take chances because ideally, this is a foundation level area. But there are certain other aspects that you wouldn't have studied in foundation that we will be dealing here. So I don't want to take any chances. So that's why I'm starting things from the scratch. Clear? But please participate. I am humbly requesting you, please participate. Now, we all, uh, use this freedom of speech only in our social media handle. Use it in the classroom. Use it in the classroom. This is the real knowledge that you will get. Use your freedom of speech in the classroom. You want to learn. That's all. That's all for learning. Whatever it takes, you will do it. Yes. Bring the child mode. Don't, don't think about anyone. Just think about learning the concepts. I'm sure you will automatically start learning everything and you will automatically handle the subject, whatever kind of questions come your way. Clear with this?

So the first aspect that we are going to see here, let's say I'll take this as part A, but it will take this as time value of money. Time value of money. I would have given you some handouts, right? That handout, you keep it safely, right? Now, it's not, uh, it's required. Yes, this handout. Okay. So basically, we will be touching upon the time value of money part first. That is basically entirely cross-classroom discussion. I will be walking you through. I'll just ask you to write down certain things. Formal notes and your running notes. Have that. That goes without saying. I will not keep telling you again and again. That goes without saying. That's how our classroom classes will function. Okay. Having done this, we will be doing certain questions that are linked to some securities valuation. I will tell you what that is. I'll tell you what it is. Once we publish part A, automatically I will link it with part B. That's where from whatever time value of money that you have studied in your mathematics, right? That I will link it with FM. Clear with this? Clear with this? This is a structured way of learning. Once we do this, don't think it's a waste of time. Don't think it's a waste of time. This is the basic. This is the basic. From math, the entire subject will be built. So I am introducing you to the subject in a very structured approach. Please follow the same so that you will also get a proper understanding of the subject. That's very important. So I could have easily gone in the study materials order, but I have sequenced it in such a way that it will not hinder with the logical understanding. So that is the reason why we are learning this concept called time value of money right now. A very, very important aspect which might not be asked separately, but this is imbibed in every single question that is there in financial management. Clear with this, guys? Clear with this? Such is the importance. Such is the importance.

Now, let's get started with this. Now, let's get started with this part A, time value of money. Now, first, first, introduction. Introduction. Now, let's say I give you two options, guys. Now, let's say I give you two options. Two options. Let's say option number one. Option number one. First, what is this concept? Context. You have never explained it. It's a straight away or going by examples. By way of examples, I will introduce you to the concept, fine. Now, I am telling you, fine. You forget whatever you know, knowledge that you existingly, you currently have on the subject. I'm just starting from the scratch. Now, I am giving you two options. Option number one. Option number one. I am asking you, I'm telling you, you take 100 rupees today. I'm telling you, take 100 rupees today. Or I'm giving you one more option. Take 102 rupees after one year. I am giving you two alternatives. I'm giving you an option. Today, I will pay you 100. Okay. Let's say you have sold me something or some some commercial transaction has happened. I am giving you two options. Option number one, today, take 100 rupees, go. That's all. Or option number two, today, I will not pay anything. After one year, I will pay you 102 rupees. Okay. Now, which of the two options is better? Okay, fine. Let's start the poll. First, how many of you say option one, today, 100 rupees is better? Oh, so many students. Okay, fine. Right now, how many of you say 102 at the end of year? That is the best option. How many of you say, own, own your opinion. Own your opinion. Don't look back. If you think that is the right answer, you are the best judge for yourself. Up, up, up. Come on, guys. We don't have much time. Up. Let this sir. No. Okay, okay, fine. Okay, fine. Right. Okay, first, who all didn't raise your hands? Now, you raise it. You never raised it. Why? You need not know 100 percent. Just sell what you feel. No, what is the problem, guys? Once again, option one. Who all say option one is correct? Now, right. Okay, okay. Is there anyone who says neither of the options? Thank God. No one. Huh? No, no one. Second, guys, one second. I'll tell you. I'll tell you. First of all, these two options are not at all comparable. So neither of the options are right. These two options are not at all comparable. Example, two monkeys, five plus five donkeys is equal to how much? Two monkeys plus five donkeys is equal to what? Seven what aliens? Or another. Can you add or can you compare dissimilar items? Can you compare dissimilar items? No. No. Now, the question is, sir, why are you saying that these two are dissimilar items? Correct? That arises or not, guys? Yes. Why are you saying these two are dissimilar items? This is also in rupees. This is also in rupees. No, I'll tell you one example. Especially in your houses, if you have grandparents, you tell them, I am going for a movie. Yes. They will ask you, how much you paid for the ticket? You say 200 rupees. You paid. They will say, in our days, that's how they will start. No. In our days, we paid one rupee and we saw MGR movie or whatever. Yes. All those old times. So during those points, that point of time, whatever movie came yesterday, they used to tell like that. Yes or no, guys? First. Now, if you take the same one rupee and if you go to the counter today, what will that guy tell you? Yes. Nothing. Literally. Literally. Fine. Literally, that one rupee doesn't have a value today. Correct? No. Is it fair on her part, your grandparents' part, to compare the one rupee that they paid 20, 30 years ago with the one rupee that you're going to pay today, guys? Yes or no? Yes or no? Absolutely not. Because over time, the value of money changes. Are you clear with this? And hence, and hence, and hence, the same amount of money and any cash flow, any cash flow that is occurring at different period intervals are not comparable as such. Are you clear with this? Are you clear with this? Why that is because over time, money ideally loses its value. So how are you saying loses, sir? Earlier, one ticket, I paid one rupee. One rupee. Today, the same ticket, I'm paying 200 rupees. So money value has appreciated. No, money value is not appreciated. Now, you get the same benefit. What is the benefit? That movie watching experience. You get earlier. You, if you pay one rupee itself, you are able to get that experience. Correct? For you to get the same experience now, if Facebook say one rupee itself, any value, pay 200 rupees only then you will get the same benefit today. Correct? So, can I say, can I say, either the value of the product has increased, or the value of money has decreased? In our case, value of product has increased? No, it is the same movie watching experience. So why is there a difference in the amount you pay? Because the value of money has decreased over time. Correct or not, guys? Are you all understanding? Now, they say, take another, another example. Property rates. Property rates. 20 years ago, 20, 30 years ago, you can buy one flat for one lakh rupees, right? The same flat will now cost at least 50 by 0 to 60 lakhs. Correct or not? Why? Time value of money. Over time, the value of money changes. Can I directly say one lakh I will pay? No. Also, one lakh? No, no. Correct or not? So, to put it short, to put it short, the cash flow arising at multiple point of time, at multiple periods, are not comparable as such. Yes. Yes. Correct or not, guys? Cash flows are arising. Please write down. Are arising at different periods are not comparable. Comparable as such. Yes. Are you clear with this? Are you clear with this? Can I compare 100 rupees today with some other money that I'm going to receive after one year? No. Correct or not? These two are not comparable. Sir, you are saying not comparable, then how can I make it comparable? Only if I make it comparable, you will be able to decide whether to take 100 rupees today or 102 after one year. Correct or not? So, first thing I need to do is, I need to make these two options comparable. Correct. How do I make these two, uh, these two cash flows comparable? Using concepts called as, using time value of money techniques. Using time value of money techniques. That brings us to the second concept. Write down. Time value of money techniques. Time value of money techniques. So, what is the time value of money techniques? There are broadly two techniques. Now, now, let us just understand the same example. I gave you 100 rupees today. Can I say it is the present value? Can I say it is a present value? Value at the date of present, correct? This is 102 is some future value. Correct? It is the value that I will be, that will be arising on a future date, correct or not, guys? Please participate. Yes. No. I have two options. I have two options. Sir, how can I make them comparable? You take this 100 and find out how much this 100 will be worth at the end of year one. Correct? Or in other words, I can find the future value of the current cash flow. Correct? And I will get some figure. I will get some figure. This 100, I work, I have converted into at the end of year one, whatever is the value that can be directly comparable with 102. Yes or no? Or, or, or, another option is, this 102 is at the end of the first year. Correct? I can find out what is the current value of the future cash flow. Yes or no? I can, I can arrive at today's value of tomorrow's money. I will get some figure. Yes. That I can readily compare with 100 rupees that you I'm offering. With this, you can take a meaningful decision. Correct or not? Correct or not? So, in other words, can I say there are two techniques of time value of money? One is future value, and another one is present value. Yes. Future value, present value. Correct? Yes. One, future value is called as compounding technique, and, and present value is called as discounting technique. Please write down. Please write down. Please write down. Two techniques. Uh, okay. One second. Yes. Two techniques. Pull an arrow here. Pull an arrow here. Write down future value. Future value. And present value. Future value. And present value. Future value is called as compounding technique. And present value is called as discounting technique. I will tell you why it is called such in a short span from now. Please wait. Okay. So, future value. Future value means what? I have today's cash flow. I will use some technique and convert it into tomorrow's value. That is future value. Correct? Or I have a future cash flow. With that, I will do something to arrive at today's value of tomorrow's money. Are you clear with this? Are you clear with this? Why are we doing? Only then cash flows are comparable. Are you clear with this, guys? Are you all clear with this? Are you all clear with this? Now, now, let us say I am giving you an example. I am giving an example. I'm giving an example. Let's say you have 100 rupees today. You have 100 rupees today. Let's say the interest rate. Let's say the interest rate is 10 percent. That is, let's say a typical example. If you open an FD, if you open an FD, you know, fixed deposit. Yes. Today, you pay the bank 100 rupees. The bank is saying, we will pay you 10 percentage interest. That is the rate of interest. Okay, fine. Now, you tell me, what will be the value at the end of year one? Huh? What will be the value at the end of year one? 100 plus whatever is the interest that you get. Can I say the value at the end of year one will be 110? Correct or not? Can I say this is the present value? 100. And this is the future value? 110. Correct? Or can I put it in a small formula? Can I put it in a small formula? And say, please write down the third one. I will give you sufficient examples. Please don't worry about it. We have just started. We have just started. Okay. Okay. Write down compounding technique. First, we will talk about the future value. Compounding technique. Compounding technique. So, here the formula is, can I say future value is equal to present value into 1 plus r the whole power n? Please note it down. I will logically derive this. I will logically derive this. Now, you have today's value. You have today's value. In our example, I know today I will be paying him 100 rupees, correct, guys? Correct, guys? Now, he is saying 1 plus r means what? It is the interest rate. What is the interest rate? 10 percentage. 10 percentage can be written as 0.10. Can I say this is plus 0.10? To the power n. We are trying to find out the value at the end of year one. Correct? So, n will be 1. N is the period. Correct? Now, just apply this formula and see how much it is coming. This is 100 into 1.10. How much is this? Rupees 110. Can I say this is the future value at the end of year one? Correct? Correct. What is the future value at the end of year two? Year two. Just apply the same formula. Present value is 100 into 1 plus 0.10 to the power 2. At the end of year 2, how much is it? Sorry, how much is it? It's going to be 121. Now, sir, you are giving me some formula. You are giving me some formula. What is the logic for it? You guys would have already seen this formula in your foundation. Anyways, let me just give you the logic for this. Let me just give you the logic for this. This is not required for exam, but I'm just telling you since it's a conceptual learning. You need to know why this formula. If you mark this up and go, then also you will be able to crack it. But just, I'm telling you the logic for this formula. Let's say, let's say I'm just opening some column here. Now, let's say I am opening an FD. Okay. I am doing, putting it as year 0. Year 0 means today, right? Now, this second. Let's say I am introducing 100 rupees. Okay. Today, you are giving the bank 100 rupees and FD. Correct? Today itself, is the bank pay anything? No. Correct? So, basically, the closing balance as on today is going to be 100. Correct or not? Fine. At the end of year one, at the end of year one, let's say January 1st, you put 100 rupees and on 31st of December, on 31st December, end of the year, end of the year. So, what is the opening balance? Opening balance is the closing previous closing balance. 100 rupees. Correct, guys? Guys, everyone participate. Correct? Now, what will be the interest? He will pay the interest on the opening balance. Correct or not? Throughout the year. Yes. Use your 100 rupees. Correct. On that, he will pay 10. How much is that? 10 rupees. So, closing balance is how much? 110. Correct. Now, you are not withdrawing this. You are not asking him to pay out the interest to you. You are saying, please accumulate it. Please give me, you know, cumulative FD. Yes. A will not pay you the interest. Keep on accumulating. At the end of three years, five years, whatever it is, whatever is the value that you pay me. Clear? Clear? Our entire concept of discounting and compounding arises only in case of reinvestment assumption. Reinvestment assumption means you will not withdraw the money then and there. Clear with this? This is the assumption we take. So, for the year two, can I say the opening balance is 110, guys? Correct. Correct. Now, for the year two, he will pay 10 percent on 110. Correct? Because the entire 110 is available with him for the entire period of second, second year. Correct or not? So, how much will be the interest? 11. So, what would be the closing balance? 110 plus 11 is 121. Correct. Third year. Third year, it's going to be, sorry, this is 121. So, the third year opening balance is 121. On this, you will pay an interest of 10 percentage. How much is that? 12.1. So, what is the closing balance? 133.10. Correct? Now, sir, why are you doing all this? I know. Wait. Let me just come up with the formula and link it to you here. Now, this 110. This 110. Can I say this is nothing but 100 plus what is this? 0.1 into 100. Correct or not? That's how you got this figure. That's how you got this figure. Or, can I say this is nothing but, take 100 common? 100 into 1 plus 0.1. Correct or not? To the power one is one of the same. Correct, guys? Are you understanding this? Yes. No. At the end of year two, you get this third closing balance of how much? 121. How did you get this? It is opening balance of 110 plus 0.1 on what? On 110. Correct or not? Take this 110 common. How much you get? 110 into 1 plus 0.10. Correct or not? Can I say 110 you got here? No. This is nothing but 100 into 1 plus 0.10. Can I substitute this 100, 110 and write it as 100 into 1 plus 0.10? Yes or no? And then multiply this once again with 1 plus 0.10. Correct or not? This is nothing but 100 into 1 plus 0.10 squared. Correct, guys? Correct. This is nothing but your formula. Your future value at the end of year 2 is equal to present value into 1 plus r the whole power n. Are you clear with this? You guys are able to understand this? You guys are able to understand this? So, if someone asks you, what will be the future value at the end of year 2, directly you can just use this formula and arrive at the future value. Correct? Provided you have the present value. Present value means what? Today, whatever is the value. If I invest 100 rupees, at the end of year 3, what is its value? Are you clear with this? Are you all clear with this? So, this is the logic behind this formula. This is the logic behind this formula. Can we take one small example? Please write down an example. Please write and here, if you see here, if you see 100 is the present value. 110 is the future value at the end of year one. 121 is the future value at the end of year two. 133.10 is the future value at the end of year three. Correct, guys? And how can you, without using all this table, can you directly arrive? Yes. How? Using the formula. Please tell me, what is the formula? Future value is equal to present value into 1 plus r the whole power n. Correct, guys? Correct, guys? Yes. So, now, here, please write it down. Write it down. So, here, at the end of one year, it's going to be, substitute, substitute the formula here. 100 into 1 plus 0.10 to the power one. Correct, guys? Yes. Here, it's going to be 100 into 1 plus 0.10 squared. I mean, to the power two. Here, it's going to be 100 into 1 plus 0.10 to the power 3. 100 into 1 plus 0.10 to the power 4. And 100 into 1 plus 0.10 to the power 5. So, tell me, how much? How much? How much? How much? And how much figures? Because, hello. Yes. 110. Then 121. Then 133.10. Then 146.41. Then 161.051. Now, you might be wondering, how some students got it so quickly? There is a simple calculator trick for this. That is a very simple calculator trick for this. And that is the reason why I asked you to bring this calculator. And I was very specific about the usage of calculator and all that. Now, now, now, now, guys, if you haven't done till now, it's okay. Just wait patiently. Listen patiently. Listen. Now, the problem here is, all these things are in power. Correct? So, basically, can I say there's nothing but 1 plus 0.10 is nothing but 1.1. Correct? So, 1.1, I need to keep on multiplying 1.1 with itself again and again and again. That is called power. No. Correct? The power 2 means twice. Three means repeated. Clear? Again and again doing it physically. 1.10 into 100. Then 1.10 into 1.10 into 100. It is actually a waste of time doing like this. There is an easier method. Just pick your calculator. Please pick your calculator. And just do what I say, guys. Please. You can do your own calculations a little later. Please follow whatever I'm saying. Please follow whatever I'm saying. Pick your calculator. Now, now, now, type 1.1. Just type 1.1. Right? 1.1 to the power 1 is always 1.1. No problem. 1.1 power 2. This 1.1 into 1.1. Right? 1.1 power 3 is 1.1 into 1.1 into 1.1. Instead of doing this again and again, there is a simple trick. You have clicked. You have, you have typed 1.1. Click the multiply button once. Correct? And click the is equal to button once. How much you get? Huh? How much you get? So, this is equal to 1.21. That is 1 plus. That is 1.1 to the power 2 is nothing but 1.21. Wait, wait. Don't do anything in the calculator. Click is equal to one more time. Click is equal to one more time. How much is it? It gives you 1.331. Which means you have once again multiplied the same number with 1.1. Clear? Click is equal to one more time. How much is it coming? 1.4641. Correct? Click. Click it once again. How much does it come to? 1.61051. Whatever it is. Fine. Are you clear with this? So, when you want to multiply the same number again and again, what you do is, type the number that you wish to multiply. Yes. Into once. Is equal to. You will get the figure. Again, is equal to the next figure. Again, is equal to next topic. Next speaker. Are you clear with this? Simple, guys? Simple, guys? Are you all clear with this? Are you all clear with this? Any doubts here? Anyone has any doubts? Does it not work in your calculator or something like that? Because some brands will have some issues. Which brand? Cassie? Only. Hey, you cannot have that calculator. Exam. Let's know. It's prohibited. Such a scientific calculator. You cannot have that. In fact, in scientific calculator, it's much more easier. Are they layer to the power line? It's not allowed in the exam. Please don't use your calculator. Don't bring it for tomorrow's class or next class. Please don't bring it. It's not scientific calculator. Okay, guys? Anyone has any doubts? Please let's not waste further time here. Let's not waste further time. Does anyone have any doubts? If you want to power a number again, what some students do is they will write 1.1 into is equal to into is equal to into is equal to. Important point. A pound. Don't multiply the, you know, that, uh, enter that multiply button again and again. Multiply button should be typed only once. Is equal to button alone you need to keep clicking it based on the number of periods for which you want to do it. Are you clear with this? Are you clear? So, 1.1, if you do, click into, and if you click is equal to, you will get a second year's factor. Correct? Click again, third year's factor. Click again, fourth year's factor. Are you clear with this? Simple, guys? Simple, guys? Are you all clear with this? Are you all clear with this? Did anyone teach you in foundation level? This was taught. This was already taught. Perfect. Right. Clear with this, guys? Clear with this? And once I find this, once I find all these factors, it is simple. Will, right? I can directly multiply and get the answer. Are you all clear with this? Are you all clear with this, guys? Yes. You're all understanding this? Perfect. Now, now, now, in exam, in exam, what they will do is, these factors, they themselves will give you. These factors. See, if you see this is called as, this is called as future value interest factor. That is the amount by which it compounds. It's called as future value interest factor. Whatever you are putting here, whatever you are putting here, within the to the power, you are doing something, no? This component alone is called as future value interest factor. Okay? And, and, Institute, they have given you a future value interest factor table. All these things will be given directly in the exam. So, then why should we take the efforts in doing this? Not every time will it be given. In case it is not given, then you should know how to handle it by yourself. Are you clear? You cannot say, question, unless something is missing. So, I will not answer. You cannot say this. These are some basic things that you need to know. Are you clear? Can you just take this table that I have given you? That financial tables. I had given you, right? There are multiple tables in that. I'll tell you what is what. Foreign. Just go to this. Now, guys, if you look at this. Yes. If you look at this. If you look at this, guys, guys, guys. I will tell you how to look at how to use this table. They have given here. What is this table? Future value interest factor. When will you use? When the present value is given and your interest rate is given and the number of years is also given. You need to arrive at the future value. How can you find out? That is what is being covered in this table. Now, in our example, in our example, what was the interest rate? 10 percentage. So, you go here. This is the relevant column for us. 10 percentage. Correct? First, you should pick the right table. There are four tables that I've given you here. See here. There is a future value table. Then here, you have a present value table. Then you have two more tables. Some future value annuity table and present value annuity table. You should pick the right table. Don't go to the wrong table and say, sir, answer is not coming. Fine. Clear? That's why I gave it to you. Right on day one. All the time that we are spending here is an investment. Whenever we are doing sums, each sum will have its own concepts by itself. There, we cannot time spend the time on time value of money concepts. So that the entire focus will be on the concepts related to those particular sums. That's why I am just keeping the base ready. Base ready. This is like a runway. Once everything is fine, we can beautifully take off. Clear with this, guys? Now, now, in our example, present value is given. We need to find out future value. That's why I am going and to the future value table. It's called as future value interest factor. Okay? Now, here, they have great something. If you can see it here. Here, they have given within bracket I and N. What is I? What is N? I stands for the respective interest that is covered here. And N stands for the number of years that is the period that is covered here. So, the future value interest factor of 10 percentage at the end of one year is going to be how much? 1.10. At the end of two, is going to be how much? 1.2210. This is what we did it here. This is nothing but 1.10, 1.21, 1.331. All these things are only given here. 1.464. 1.464. And here it's 1.611. 1.611. Instead of doing all this calculation, they themselves have given you by way of a table. If the table is given, pick it directly. Don't take the efforts in doing manual calculation. Are you clear with this? Are you all clear with this? Ideally, all these things should have been covered in your CA Foundation. Anyways, I am just doing it for the benefit of everyone. Clear up with this, guys? Clear with this? Perfect. Now, now, when present value is given, so when, sorry, uh, yeah. So, when your, uh, yes, when your present value is given, present value into 1 plus r the whole power n gives you what? Future value. Correct? Now, when future value is given, can you find out the present value? Yes. So, we know that, we know that, we know that. If you see, future value is equal to present value into 1 plus r the whole power n. Correct? Correct? Suppose, suppose they want to ask, they want you to find out the present value, but they have given the future value, rate, and number of years. You can easily, can I say, present value is equal to future value divided by 1 plus r the whole power n? Correct or not? Yes. So, this, if I multiply, that's called as compounding. And if I divide to arrive at the present value, it is called as discounting. I told you, today's value can be converted into tomorrow's value. Today's money can be converted into tomorrow's value, or alternative, tomorrow's money can also be converted into today's value. Correct? If I am, I'm having the future value, I want to find out the present value, I will discount. Are you clear with this? And throughout our subject, we will be talking about discounting. Compounding, generally, not, not in many areas, it will come. Discounting is what we will be doing left, right, and center. We will be seeing. Clear? So, write down the fourth concept. The fourth concept. Write down discounting technique. Discounting technique. It's also called as present value technique. Present value technique. What is the formula, guys? Come on, tell me. Yes. Present value. That is what I need to find out. They have given me the future value divided by 1 plus r the whole power n. Are you clear? The logical derivation for compounding, I told you. Then, simple cross multiplication, you will arrive at discounting. Clear with this? Clear with this? Clear with this? Fine. Right. Now, now, take another example. Here, they have given you future. I hope you guys are riding along. Future value 2. That is at the end of year 2 is 121. The rate is given as 10 percentage. The period is given as two years. Calculate the present value. Can you calculate this? Can you calculate this? You guys know, present value is nothing but the future value 121 divided by 1 plus 0.10 to the power 2. Correct? Uh, guys? Correct or not? Yes. Now, now, now, you again have this thing that in the denominator, there is something that you need to do to the power of. Correct, guys? There is another trick for this. There is again a trick for this. Now, in the denominator, what you need to do is, take your calculator. 1 divided by 1.1. Correct? How much is it coming? You. One second. Go to year one. Go to year one. Can I say this is nothing but 110 into 1 divided by 1.01 the whole power one? Correct or not? Correct or not? Can I say this is nothing but 121 into 1 divided by 1.01? So, can I say this? Now, this alone, if I'm able to have some calculated trick to find a value that I will just multiply with the respective figure. Correct or not? Now, how can I do this? Very simple. Take your calculator. 1. Type down 1 divided by 1.1. Is equal to. How much is it coming, guys? How much is it coming? This is the present value factor for the first one. 0.909. Correct? You did not do anything. Click is equal to one more time. How much you get? How much you get? How much you get? 0.826. Correct? That is the factor for year two. Click again, you will get the factor for year three. Click again, you will get the factor for year four and so on. Clear? So, 1 divided by 1.1 is equal to, you get for the first year. Click is equal to, second year. Is equal to, third year and so on. Are you clear with this? Simplest trick to use your calculation. Basic things that you should be knowing while you are entering into this subject. Clear with this, guys? Clear with this? So, tell me, what is the value here? What is the value here? This is nothing but 121 into. We just found out 0.826. How much is it? How much is it? 99.99. And yes, you can round it up to 100. Now, now, another thing that students generally ask, sir, three decimals, four decimals. Your wish. Your wish. I would say, I would say, look at what this is nothing but I have just taken this from the Institute study material. Okay. I have just taken this from the Institute study material. Okay. Now, what has the Institute done? How many decimal points have they kept? How many decimal points have they kept? Really three. You know, everywhere, you know, fine. Only three. Correct or not? Let us follow them. As simple as that. Clear with this? The Institute is having a requirement. Let us acknowledge it. As simple as that. Clear with this, guys? We will also follow three. Simple. Clear. Sir, shouldn't I, should I not follow fourth? There is nothing wrong. Rounding off here and there, you will have some issues. As simple as that. So, don't make a big issue about the rounding off thing. You know, rounding off issue here and that will be that. Depending on the decimals, you take. You are free to take three and above. Not below three and above. You can take. Clear with this, guys? Let's follow three for our classroom discussion. Are you all clear with this? Are you all clear with this? So, similarly, if I give you, if I give you, find out the future, future value for year three is given. Let's say, future value at the end of year three is given as 133.10. The rate is given at the rate of 10 percent. And they have given you a period, a period of three years. Calculate present value. What will you do? What would be the formula? Yes. This is nothing but 133. Point. Guys, participate. I know that you all know. Still, can you just participate? Nice. Yes. Divided by 1 plus 0.10 to the whole power three. Or, I can just say this is 133.10 into 1 divided by 1.10 the whole power three. This part, take the calculator. Do this. 1 divided by 1.1 is equal to. Is equal to. Is equal to. How much you get? How much you get? 0.751. Correct? 0.751. So, this is nothing but 133.10 into 0.751. How much is this? Approximately, this will come to 100. Correct or not, guys? Are you all clear with this? So, compounding and discounting. Are you all able to understand with this? You can move between present value and future value. How can you make the present value and future value comparable? Using time value of techniques. From present value, if you want to go to the future value, it's called as compounding. From future value, if you want to arrive at the present value, it's called as discounting. As simple as that. Now, you can compare things. You can bring everything into today's value. Then it makes sense for you in taking your decisions. Correct? Correct. Now, now, you will be able to understand. Have you seen the concept of time value of money in costing? Have you seen it in costing? No. Why? Because there, the relations you take are generally for less than a year. And within, when it is less than a year, time value will not change. Are you clear? Whereas in finance, financial management, we are talking about long-term decisions. To make the cash flows comparable, I use the cons called as time value of money. Are you all able to relate it now? Are you able to relate it now, guys? Are you all able to understand? This is the basic. This is the very basic understanding that you have. And of course, you had a future value table. Similarly, we'll also have a present value table. Now, in this example, you tell me, what is the present value here? You have for year 1, 0.826. Sorry, this is year two. Year one, it is 0.909. Year 2, 0.826. Year 3, 0.751. Go to this. Go to this table that I have given you. In that, you go to the second table. So, the first two pages are continuation. Go to the second table. What are they given? Present value interest factor of 1 rupee at I percentage for N years. So, here, our percentage is what? What is the rate that we have taken? 10 percentage. At the end of year one, what is the discount factor? 0.909. Year 2, 0.826. Year 3, 0.751. Correct or not? That is exactly what we did using these formula method. Are you all clear? So, if the Institute, in the question, if they give you the table, just pick it up and do it. Just pick it up and do it. So, here, what I will do is, here, what I will do is, if in the Institute, if in the, uh, exam, they have given you the interest factors, what you can do is, very simple. Present value is equal to future value into present value interest factor at the rate of I percentage for N years. Clear? This would, this is nothing but 1 divided by 1 divided by 1 plus r the whole power n. Correct? That is why I am directly multiplying this. It is factor. The denominator also. That's why I am directly multiplying it with it. Are you all clear with this? That's why, if you see, that's why, if you see in your present value table, everything in will be less than 1.06. It will be less than one everywhere. Whereas in future value table, everything will be more than one. Everything will be more than one. Because you are multiplying it here. You are dividing. Correct? When you are dividing, obviously it will be less than one. No? Correct or not? Yes. That is the reason why present value tables. This is another way of knowing whether you are looking at the right table or not. Correct? And predominantly, in our subject, we will be using present value tables. They will give you future cash flows and they will ask you to find out what is the present value of all of that. Are you clear with this, guys? You can either go with this formula method or you can resort to this. Resort to this table if it is given in the question. Guys, are you all able to understand this? Are you all able to understand this? Yes. Clear with this? Is everyone clear with this? Shall we proceed further? Shall we proceed further? Perfect. Now, let's go to the next one. Let's go to the next one. Concept number five. Present value of multiple, multiple unequal cash flows. Present value of multiple unequal cash flows. Multiple unequal cash flows. What is this? What is this? Take down an example and I will explain. Year, end, and future value. This is all is given in the question. We are saying one, two, three, four, and five. At the end of year one, they are saying there is a cash flow of thousand. At the end of year two, it's 1500. Year three, 800. Year four, 1100. Please note this down. Year five, 400. What are these? These are some cash flows that will be arising at the end of the respective years. Are you clear with this? Always remember, when year is given, you should always assume it as arising at the end of the year. Are you

Clear with this. If I assume at the beginning of year one, is the student correct or not correct? Or not correct? So if this word "end" is not given, simply they have given "year" and "future values." In this case, what will you assume? You will assume that these cash flows are arising at the end of the respective years. Are you clear with this? That is one underlying assumption. Now, this assumption can also be broken. How? We will see that later, in a short span from now, we will say it. But if nothing is given, what will you assume? You will assume that these cash flows are arising at the end of the year. Clear with this?

Now, they have given you the rate is equal to 10 percent. Calculate the present value. This is the question. Calculate the present value. So, what have they given in the question? They have given you the cash flows arising at the end of five different years. Yes, guys, correct? Or can I call this as future values? Correct. Correct. What are they asking you? What is the value of all these cash flows that you will be receiving? What is the today's value of all that? What is the today's value of tomorrow's money? That is what they are asking you. Correct? Correct, guys? The correct, guys.

Now, what is it? 1000 plus 1500 plus 800 plus 1100 plus 400. Yes, yes, yes. Can you add monkeys and donkeys? Can you add monkeys and donkeys? This is arising at the end of year one. This is arising at the end of year two. Are they comparable? What will you do? Convert this into present value. Convert this into present value. This into present value. This into present value. This into present value. Sum total of all that will give you the total present value of all the cash flows. Only then it is addable. Correct or not? Correct or not? Can I add these cash flows as such? No, you cannot touch them. Why? Because they are arising at different points of time. Correct. And when cash flows arise at different points of time, I told you, 100 rupees today, option one, option two, 100 rupees tomorrow. Not comparable. Convert it and then add. Convert and then add. Or do, take whatever direction you want, subtract, add, whatever you want, you do. But bring everything into a common comparable term and then you do your operation. Operation, addition, deletion, whatever it is. Clear. So, I can't compare these cash flows as such. I will convert everything into the present value and then I will add it. Clear with this?

Now, take down the solution. Take down the solution. Can I say simply, present value is equal to? Now, 1000 rupees is there. When is it arising? At the end of year one. So, what is the present value of 1000 today? Formula, formula, formula. Just tell me. Can I say this is 1000 divided by 1 plus 0.10 to the power 1? Correct. Correct. Now, I will add 1500 divided by. Come on, tell me. Tell me. 1 plus 0.10 squared. Why? Why are these addable now? Yes, this is also in present value. This also I have converted. This 1500 into today's value. It is addable now. It is addable now. If I convert everything into present value, these terms are addable. I can't add 1000 and 1500 as such. But if I convert everything into today's value, I can add it. Correct or not? Fixed. Yes. Are you all understanding this? Are you all understanding this?

So, one second. Okay. Then, then, come on. 800 divided by. Everyone, answer, guys. Everyone, answer. Huh? 1 plus 0.10 to the power 3. Correct. Then, plus 1100. 1100. 1100. Plus 1 plus 0.10 to the power of 4. Plus 400 divided by 1 plus 0.10 to the power 5. Are you clear with this? This is called as a cash flow equation. This is called as a cash flow equation. Only if you convert everything into today's value, it is addable. It is addable. Clear with this? Are you all understanding this? Are you all understanding this? These cash flows are not addable as such. Do some operation and convert everything into today's value. That operation is called discounting. Correct. You arrive at today's value and then it is addable. Are you all clear with this? Are you all clear with this?

Now, now, what you need to do is, now just calculate. Now, just calculate. What I will do is, first, this is 1000 into something. Okay. Something. We will use a calculator later. Okay. 1000 into something plus 1500 into something. What is something? 1 divided by 1.1 to the power 2. Correct. So, we will do the calculator as and when it comes. First, let us frame this equation and put it. Plug the figures here. This is 800 into something plus 1100 into something plus 400 into something. Now, please fill all these things. Take your calculator. Take your calculator. Write down 1 divided by 1.1 is equal to how much is it, guys? 0.909. Then click one more is equal to how much is it? 0.826. One more is equal to how much? 0.751. One more is equal to how much? 0.683. One more is equal to how much? 0.621. 6209. You just round it off. Clear. Clear. Five and above, round it up to the next number. Clear with this, guys? Clear with this? Are you all able to understand? Are you all able to understand?

So, tell me the values. Ah, tell me the values. Okay. So, 9.9. I'm relying on your numbers. Tell me. One, two, three. One, two, three. Nine point six. Okay, fine. Six naught one point. See, whatever you've done here. Appendix. I have just told you how to use it. If it is there, it's simple. It's very simple. But let's do it during the classroom. Let's do it in the classroom. That's why I've done it. Okay, fine. So, what is the second? 800 into 0.751. How much is it? 600.8. You took four decimals. Six zero one point zero five. Okay, fine. Then seven one point three. Then two four eight point four. Okay, whatever is this. Sub. This is always an issue. Rounding up here and there. Finally, tell me what's the total value. Three seven four. I'm getting three seven four eight point five zero. Then we got this three seven four eight point seven. Guys, what happened? What is the problem here? Don't round it up here. Don't round it up here. Once you get it finally. Why? You can maintain three decimals. Let's have that habit. We can maintain three decimals. Let's not round off anything here. Let's maintain. Three seven four eight point. You're getting three seven four eight point seven five. Something more or less. It is one and the same. Always. This is a problem. Some people take three decimals. Some people take four decimals. Accordingly, one or two rupees might change. Maximum. That's all. But are you getting the concept, guys? Are you all getting the concept? In exam, if the table is not given, please do it like this. This is your conceptual understanding. Clear. This is where the execution part, the tricks, and all these things. This is where comes into picture. Clear. If you write this, if you write this, it clearly shows your understanding of the subject. What is the understanding? The cash flows cannot be comparable as such, since it is occurring at different points of time. I am converting everything into present value and then only adding it. That is where the concept comes in. Are you all clear with this, guys? Is this understandable to everyone? Yes. We are spending a lot of time. Don't think we sir, we will finish. Don't worry about it. Don't worry about it. I told you on day one. One more quote. I told you Abraham Lincoln's quote. I told you. Yes. Give me six hours to chop down a tree. I will spend the first four hours sharpening the ax. Spend more time on learning the concept. Problem solving is nothing. It will take just little time. You will see how many number of sums you can finish very, very quickly, provided if you are very strong in your concepts. No one can shake you. No one can shake you. That is how it is. You take any example. Take big players like Virat Kohli, Sachin, anyone. You take them. Every day before they come to the match, they practice. And they say, "I know." That's all. No. Every day they practice. Every time they bat, they say that they learn new things. Or they say that, of course, these people, they say that they are experts in that. Still, what I'm telling you is, if you are able to do it, and if you're consistently practicing, and if you're learning the concept, spend more time. What happens in actual? That is when you're taking the time that you take while solving the question will be very, very less. I will prove it right in front of you. I'll prove it right in front of you right now. Let us take this time in learning. One by one, slowly. I will increment for the time being. Have you, have you all understood this? Have you all understood? Is this understandable? Any doubt here? Any doubt here? Yes. Clear with this? Perfect. Shall we move to the next one? Shall we move to the next one? So, so far, we have covered five concepts. Take the sixth one. Don't worry. I will summarize everything at the end. Right now, you just focus on one concept at a time. I will cover. I will revise everything. Or I will show you the overall graph as to how we have proceeded. You will automatically be able to connect the dots. Right now, see, please write down. Present value of multiple, take a reading and write. Equal. Multiple. Equal. Come back to green ink. Cash flows. Multiple. Equal. Cash flows. What happened? You think it's fine? Okay. Shall we proceed? Shall we proceed, guys? Shall we proceed? Yes. Now, now, now. The same. Let me take one more example. Year and this is what future value. Year, future value. One, two, three, four, and five. Future values, 100, through a hundred, hundred, hundred, hundred, and hundred. Rate is given as 10 percentage. Calculate present value. Can you do this, guys? Can you do this? Any difficulties? What is the difference between the previous example and this example? Here, the cash flows were different. Erratic. Thousand, thousand, one hundred, anything. Here, I am saying I will receive the same fixed amount at the end of every year. So, what is the new thing that we are going to learn here? We will see. We will see. I'll let you know. Yes. Are you all able to understand? Simple. First, can I add all these five together at the end of year two? Definitely not. Can I add? See, no. Here also, I need to discount it. Concept is one and the same. So, write down solution, guys. Right on. Present value is equal to. Frame the equation. Cash flow equation. Please tell me what is the equation, guys? Guys, everyone participate. I told you, learn like a child. Yes. 100 divided by 1 plus 0.10 to the power 1. Plus 100 divided by 1 plus 0.10. Please write down. Don't think that I know all this. Please write it. Please write it. Yes. Then 100 divided by. Huh? 1 plus 0.10 to the power 3. Plus 100 divided by 1 plus 0.10 to the power 4. 10. 100 divided by 1 plus 0.10 to the power 5. Clear. Clear, guys? Clear, guys? So, in the previous sum, only we just found out. This is nothing but 100 into something plus again 100 into something else plus 100 into something like that. You need to do five times. Correct. Ah, plus 100 into something. So, tell me, what are the present value interest factors? 1 divided by 1.1 is equal to how much? 0.909. Again, click is equal to how much? 0.826. Once again, click is equal to how much? 0.751. Am I going fast? Sure. Yes. These are all some already basic concepts. So, I'm just, I'm just trying to be a little quick. If you, should I slow down the pace? Can I continue? Okay, fine. Then, fourth year, once again, is equal to. Huh? 0.683. Then, 0.621. Clear, guys? Clear. Clear. No, no, once. One second. Now, one uniqueness about this question is, I have 100 common. Correct. I have 100 in common. Correct. Correct. I know for the next five years, every year I'm going to receive 100 rupees. Receive or pay, whatever it is. Cash flow can be in floor outflow. 100 rupees. Assume I'm going to receive. Correct. So, can I take out 100 in common? If I take out 100 in common, this will be like 100 into 0.909 plus 0.826 plus 0.751 plus 0.683 plus 0.621. Correct. Simple mathematics. Simple mathematics. I have not even entered into FM. I am just still in mathematics. Simple mathematics. Take 100 common. You can write these things. Add. Add it up. Yes or no? So, add up and tell me. 0.909 plus 0.806. How much? 100 into how much is it? What it's going to be? Three point seven nine one. You just add it up. You just add it up. It's going to be three point. What is 3.791? It is some total of all that discount factors for the respective year. Sir, how can these be added? Because they are multiplied with the same amount of cash flow. I'm taking in common. Correct or not? Correct. Are you all understanding this? How much is the value? How much is the present value today? Yes. How much is it? 300 and 79.10. Oh, sorry. This is just 379. You. Okay, so it is 379.0. It's only 379. Decimals. Fine. Forget it. Are you clear with this? Are you clear with this? Now, now, now, guys, guys, guys, please listen. You want me to explain anything? Don't, don't, you know, hesitate. If you don't know something, please ask me. You're stuck somewhere. Sure. You stuck somewhere. You know, guys, please feel free to ask me. That is one basic thing. I am here for your purpose. And if I'm not able to fulfill that, then it's of no use. If you don't understand something, please ask me. Then and there, you're finding some difficulty. Tell me what it is. Okay, fine. This cash flow equation. Are you able to understand this cash flow equation? You are able to understand. I am saying 100 rupees received at the end of multiple years are not addable as such. Opinion. Huh? 100 rupees received at multiple different points of time is not addable as such. Yeah, because this is 100 rupees received at the end of year one, and this is 100 rupees received at the end of year two. Can I add this directly? No. I need to convert everything into present value. That's what I did using this equation. Correct. Present value equation. I just did it. Now, this is nothing but 100 into 1 divided by 1.1 to the power 1. 100 into 1 divided by 1.1 to the power 2. 100 into 1 divided by 1.1 to the power 3. And so on. This one divided by 1.1 to the power 1. 1 divided by 1.1 to the power 2. I have just calculated using my calculator, arrived at it separately, and I have just reframed the entire equation, which was in fraction. Right now, I put it as decimals. And right now, I can see that 100 is a common multiple here. I took 100 outside, and automatically I am just adding all other present value factors. Guys, any issue here? Any issue here? Are you able to understand further? If you are not able to understand after the class, you can ask me. Clear. Okay, fine. Guys, you're all able to understand this? Yes. Really? Yes. Now, why am I able to add all these things? Because it is getting multiplied with the same number. Correct. And this concept is called as present value interest factor of annually. Present value interest factor of annuity. Present value interest factor of annuity. When will you use this? Now, there is a separate table. There is a separate table. You saw the financial tables, right? Financial table, two different tables we saw. One was the present value interest factor. The other one was future, first piece of future value interest factor. Then we saw present value interest factor. Now, we are seeing one more thing called as present value interest factor of annuity. What is this? This is nothing but sum total of my. Sum total of my present value table. That present value table. For example, for example, now, guys, for example, let us say, let us prepare this table. Let us prepare this table. Year, one, two, three, four, five. Present value interest factor, 10 percentage. Now, guys, simple, simple. Let us just take this example. Now, you tell me, what is the present value interest factor here? You got right. Here, you got right. 0.909. That is 1 divided by 1 plus r the whole power n. So, when the interest rate is 10 percentage, what is the first year interest factor? How much is it? 0.909. What is what is it for second year? Not annuity, just simply for second year. How much is it? 0.826. Third year, 0.751. For fourth year, 0.683. For the fourth year, 0.621. Correct. Now, when the cash flows is equal, I can take the cash flow outside and I can accumulate only this interest factor. Correct. That is called as annuity table. So, present value interest factor of annuity for 10 percent. Can I say for year one, it is going to be 0.909? For year two, it will be 0.909 plus 0.826. How much is it? Add it up. 1.735. For year three, it is going to be how much? 0.909 plus 0.806 plus 0.751. How much? 2.486. For year three, it is going to be. Add this also. For year four, 3.169. For year four. Year five, 3.79 and something. Yes. Are you clear with this? Right now, we did it for six years. Huh? Wait. For five years. So, this is what we have got here. Did you see how we've got this? We have just added the present value interest factor for the five years put together. Are you clear with this? This is present in a table called as present value interest factor of annuity table. Now, let me just show this to you. Let me just show this to you. Open that. This table. Financial table that I've given you. There you can see percent value interest factor. A7. Are okay? Look at this. Present value interest factor of annuity of 1 rupee. That is, every rupee becomes how much? If you look at this, it is 0.909. 1.736. This is nothing but interest factor of year 1 plus year 2. This is nothing but interest factor of year 1 plus year 2 plus year 3. This is nothing but year 1 plus 2 plus 3 plus 4. This is nothing but 1 plus 2 plus 3 plus 4 plus 5. Are you clear with this? This is the same figure that we got here. This is the same figure that we got here. This is the same figure that we got here. This can also be referred to directly from the table. And when will you refer the annuity table? When you have equal cash flows arising in your futures. Are you clear with this? Are you cleared with this? Nothing simple. The present value. If you just aggregate it. If you aggregate it. If you aggregate the present value table, you get your present value annuity table. Are you clear with this? And this can be used only if the cash flows are same. Only if the cash flows are equal. Are you all able to understand this, guys? Are you all able to understand this? Yes. Is everyone able to follow? Is everyone able to follow this? Clear. Shall we proceed to the next one? Shall we proceed to the next one, guys? Yes. Okay, fine. Now, so till now, what we have seen? We have seen the simple. Your present value, future value, how to toggle between that. The formula we have seen. Your present value is equal to future value divided by 1 plus r the whole power n. Then, what, what will happen if there are unequal cash flows? We saw. And what will happen if there are equal cash flows? Technically, concept-wise, both are one and the same. But if you have equal cash flows, you can take the cash flow in common and aggregate the discount factors separately. That aggregating the discount factor separately is called as annuity. That annuity table you can find out. Are you clear with this? Are you clear with this? Fine. Let's move to the next one. Let's move to the next one. Please write down the seventh one. The seventh concept that we're learning today. Present value of equal cash flows up to perplexity. What do you mean by perpetuity? Whatever. Correct. Whatever. Yes, guys. Here, now, let's say, let's say I want to invest in a company. That is, I want to buy shares of a company. Correct. When I'm buying shares of a company, now, why am I going to, why am I investing in this company? I know that this company is going to perform well. Correct or not? Now, companies go with the companies go on a, what assumption? Going concern assumption. Correct or not? They will be forever. Correct. That is the assumption. Where this time of starting the company itself, will they think about winding it up? Will they know that, okay, exactly for five years only this company will be open? Is there anything like that? That sort? No. So, in a real-life situation, you know that if I invest some money in a company for a lifetime, I will be receiving some dividends. Correct. I will be receiving, receiving some dividends. Now, let's say, every year I receive some money. Let's say, five rupees. Every year I receive. Till how many years? I don't know. Correct. Till now, we knew the number of years. Five years. Now, every year, you could discount easily. But if it is going to be forever, can you also keep extending that equation? Cash flow equation? It will only keep going. There is a, there is no, there is no tangible end to it. Correct or not? Correct or not? In this case, what do you do? So, let's take an example. Let's take an example. Let's take an example. Let's say, year and cash flows are given. Cash flows are future value. You can take anything. One, two. At the end of year one, let's say the cash flow is 100. Year two, let's say the cash flow is 100. Year three, cash flow is 100. It goes on like that till infinity. You don't know. It doesn't have any end at all. Here, it goes on. So, basically, the scenario that I've taken is, I will be receiving 100 rupees at the end of every year for how many years? I don't know. It will just, I will keep on receiving it. I will keep on receiving this money. That's that's all. I don't know. There is no tangible end to it. This is an indefinite period. Correct. In this case, I should find out the present value. I should find the present value. How will you find out the present value? You know the present value equation. What is the equation, guys? Tell me. 100 divided by. And of course, of course, let us take the rate to be 10. Example. Sir, why do you take the rate 10 percent? How would I arrive at the rate? That is one separate chapter by itself. We will see it later. For the time being, I will just tell you what the rate is. You just accept it. Later on, we will see how to arrive at the rate and all of that. Clear. This is called as a discount rate. Basically, this called as a discount rate. If you are using it for discounting, it's called discount rate. If you're using it for compounding, it's called as compounding rate. Thank you. Fine. It was much needed. I'm really sweating. Okay, fine. So, let's calculate the present value. Let's calculate the present value. Okay. Right now, you tell me, ideally, how will your cash flow equation look like? 100 divided by. Come on. 1 plus 0.10 to the power 1. Plus 100 divided by 1 plus 0.10 to the power 2. It goes on. Is there an end to it? Is there an end to it? Can you actually keep doing it like this? There should be some tangible end. Correct or not? Can this be added manually? Can this be added? So, then, what is the formula? So, how will I do it? Sum total of all this. All this. That is the present value today. Correct. Please take down. Take a reading. Take a reading. And write down. In this case, the present value is equal to. Please write down. Annual cash flow divided by discount rate. Annual cash flow divided by discount rate. Very simple. The formula is very simple. So, what is your annual cash flow? Every year, how much will you receive? 100 rupees. Correct. Sorry, this is not thousand. This is 100 by mistake I wrote it. Okay. So, this is 100 rupees divided by discount rate. What is your discount rate? 0.10. How much is this? How much is this? 100 divided by 0.10. How much is it, guys? Use your calculator. What are you looking? Use your calculator. How much is it? This is going to be 1000 rupees. So, this is the answer. So, the present value of 100 rupees that I will be receiving forever is 1000 rupees. Correct. Using the formula, annual cash flow divided by discount rate. No, sir. I already arrived at this. This formula. How did it come? This formula. How did it come? Now, in exam, it's enough if you write this. But you should know why this formula has come. Correct. I will just take little more time. I will do it on a blue wing because it's not required from an exam point of view. Now, I will do it. I will tell you why they have arrived at this formula. For this, I need your cooperation. Whatever I ask, answers, you need to keep telling me. Have your calculator. Just keep telling me the answers. Clear. Clear with this? Yes. First, first. Now, do you guys know GP? Not GP. Moto GP? Yes. Geometric Progression. Ross Profit. Wow. Okay. Right. GP is gross profit. Accounting perspective. Okay. Great. I just now I told you, no, mathematics. You know. Okay. Right. Okay, fine. So, mathematics. In your mathematics, I should start like this. GP. You have read? Yes, yes. What is it? What does it stand for? Geometric Progression. Example for GP. Can I say 2, 4, 8, 16, 32, so on? First, when will I call a series as dormitory progression? When there is a common ratio. Common ratio. You take any two adjacent. And I need to adjacent uh numbers and divide it. Here, if I do 4 by 2, how much I get? 2. 8 by 4, how much I get? 16 by 8, how much I get? 2. Correct. Correct. Which means the common ratio between two adjacent numbers is a common number. Correct. The ratio between two adjacent numbers is a common number. Yes. Only if a series indicates a common ratio, it can be called as a geometric progression. Correct. Correct. Now, now, in your geometric progression, in your geometric progression, there is a formula that you guys would have studied. Sum of infinite geometric progression is equal to A divided by 1 minus R. Correct. Character. Where A stands for the first term. The first term. That is the first number. And R stands for what? The common ratio. The common ratio. What do you mean by the common ratio? In this case, the common ratio is 2. Correct. Correct. Sum of infinite geometric progression is what? A divided by 1 minus R. That is A divided by 1 minus R. Sir, how this formula came? As your mathematics faculty. Yes. How this is not required. That is not required. You, you guys are aware of this sum of geometric infinite geometric progressions. Yes or no? Write down. Write down. What is the equation that we have got? This is the equation that we have got. Correct. We need to sum total of all this. For this, first, we should find out whether this series is a geometric progression. Correct or not? Correct or not? Do I start or not? So, now, this series. This series. What is the series? This is 100 divided by 1.10 to the power 1. Plus 100 divided by 1.10 to the power 2. Plus 100 divided by 1.10 to the power 3. Plus so on. Correct, guys? Correct. Now, I will be able to use this formula only if this series is a geometric progression. Correct. So, first, I need to prove whether this series is geometric progression or not. Correct or not? What can you do? What can I do? Divide this by this and see. Then, divide this by this and see. Correct. Correct. Any two other sent you take. If the answer is same, it means it is a geometric progression because it has a common ratio. Correct. Can we just do that and see? Take the second number. Take the second number. What happened? Take the second number. 100 divided by 1.10 Square divided by 100 divided by 1.10 to the power one. Correct. You know how this happens? This is 100 divided by 1.10 Square into 1.10 to the power 1 divided by 100. Correct. This gets knocked off. Correct. This gets knocked off to the extent of one. This is nothing but 1 divided by 1.10. Correct. Of. Correct. So, what I did? The second term divided by first term. I did. Correct. Now, what I'm going to do? The third term divided by second term. If that also indicates 1 divided by 1.1, I can say that this is a geometric progression. Are you all able to follow this? This is foundation mathematics. Foundation mathematics. Correct. Correct. So, let's do this. The third term is going to be. Participate. 100 divided by 1.10 to the power 3. The whole divided by 100 divided by 1.10 to the power 2. This is nothing but 100 divided by 1.10 to the power 3 into 1.10 to the power of 2 divided by 100. This gets knocked off. Twice. This becomes one. This is also 1 divided by 1.10. So, now, do you agree that this is a geometric progression? Yes, guys. And sum of infinite geometric progression series is equal to A divided by 1 minus R. Correct. A divided by 1 minus R. Where R is what? The common ratio. Common ratio. Shall we substitute? What is the first number? What is the first term? We have 100 divided by 1.10 to the power 1. Correct. Divided by 1 minus. What is the common ratio? Just now we found out. 1 divided by 1.1. Correct. Divided by 1 divided by 1.10. Correct. Now, what we will, what will you do here? 100 divided by 1.10 to the power 1 is same. Minus. So, you take an LCM here. This is nothing but 1.10 minus 1 divided by 1.10. Correct, guys? Correct. So, you just remove the two. This can, this is divisible. This becomes 100 divided by 1.1 minus 1. Correct. How much is that? 100 divided by 100 divided by 0.10. This is nothing but. This is nothing but annual cash flow divided by discount rate. Correct or not, guys? Direct or not, guys? Are you getting this? This is nothing but your annual cash flow divided by your discount rate. Are you all able to follow this? Don't worry. You want me to share this with you? This, whatever I have scribbled? Yes. So, this I will convert it into a PDF and put it on the group. You guys can have access to it. But just because I'm doing this, please don't take running notes. My running notes might not be, you know, as comprehensive as you take. So, please have the habit of taking running notes. Keep this as an external reference. In case you feel you have missed out something, you look at this, you will understand. Clear. Clear. I will share this with you. Don't worry. But anyways, I just want you to take running notes. Please don't leave the habit of taking running notes. It's a very good habit. Clear with this, guys? This is a derivation. Sir, the derivation. Forget it. It's okay. Take it as annual cash flow divided by discount rate. Clear. Fine. But it is my duty to explain why things have come here. That is the reason I'm giving you. Don't accept something just because it is given. Clear with this, guys? Are you all able to understand? Is anyone having any doubts? They're even having any doubts? Sure. Shall we proceed forward? So, tell me one last thing. What is the present value of present value of equal cash flows up to perpetuity? What is it? Annual cash flow divided by divided by 1 minus 1 minus R divided by this country. Annual cash flow divided by discount rate. Logic. Geometric progression. Sum of infinite series. I have derived it and shown it to you. Clear with this, guys? Clear with this? Now, let's go to the next one. Let's move to the next one. The next concept. Concept number eight. Write down. Present value of Perpetual growing cash flow. Perpetual growing cash flow. Present value of Perpetual growing cash flow. Perpetual growing cash flow. What is this? Now, I told you, I invest in a company. I will be receiving 100 rupees dividend every year. You tell me, logically, the company will they be paying 100 rupees exactly every year? Or exactly will they be paying the same amount forever? The company will also grow, no? As they grow, they will also pay me more, right? Correct or not? Correct or not? So, when there is a growth, when there is a growth, and that growth is up to perpetuity. Let's say, every year the cash flow also grows at the rate of five percent. Okay. It grows up to perpetuity. In this case, how do I add the sum? How do I add all the cash flows? That is the example I'll give you an example. Please write down. Please write down. Mr. A. Yes, I'll just tell you that. I'll just tell you. Then let's finish this and then I'll come to that. Okay? Please write down. Mr. A. Mr. A wants to receive wants to receive rupees 100 at the end of year one. After that, he wishes to receive a cash flow that grows by percentage every year. Every year up to perpetuity. Rate is equal to 10 percentage. Calculate the present value. This is the question. Now, now, what are they saying? Basically, to put it in rough, can I say one, two, three, four, so on? The cash flow will be at the end of year one, he wants to receive 100 rupees. At the end of year two, how much? He says he wants to receive this has to grow by five percent. Correct. So, he says, he says 100 into 1.05. Correct. How much is this? 105. Third year, five percentage further growth as compared to 105. So, can I say the third year cash flow will be 105 into 1.05? Not 110. It is not a simple interest. It is not simply five, five percent every year. Five percent on the previous year. This five percent will calculate on the previous year. This five percent will be calculated on the previous year. Here. Are you clear with this? Are you clear with this? How much is this? How much is this? 110.25. And it grows on like this. Clear. Clear. That is your cash flows are showing some trend. They are showing some trend. It is moving in a particular direction. Correct or not? Or can I say this at the end of third year? This is nothing but. See, this 105. What is it? 100 into 1.05. Correct. Further, this gets multiplied by another 1.05. Or can I say this is nothing but 100 into 1.05 to the power 2. Correct or not? Correct or not? Yes. For the next year, it will be what? It will be what? 100 into 1.05 to the power 3. Correct, guys? And it keeps on growing. It keeps on growing. It keeps on growing. So, let me just put it here. One, two, three, four. So, the cash flows will be 100. Year. The cash flows will be at the end of year one, it will be 100. At the end of year two, it will be 100 into 1.05 to the power 1. Here, it will be 100 into 1.05 to the power 2. This will be 100 into 1.05 to the power 3. And it goes on like this till infinite. Correct or not? Why? Because they are saying, sir, are we doing any discounting here? No, no, no. They are saying the cash flow, the manner of computing the cash flow, they have given in the question. They are saying the cash flow grows at the rate of 5 percentage every year. When I say 5 percentage growth, it means growth as compared to the immediately preceding year. This 5 percentage should be compared on this year. This 5 percentage should be applied on this. Are you clear with this? Keep on adding another 5 percent. And that's how you arrive at it. Guys, are you all clear with this? Are you all clear with this? Yes. So, now, tell me, how will your cash flow equation look like? How will your cash flow equation look like? How will your cash flow equation look like? Present value. Can I say this is 100 divided by 1.10 to the power 1? 1.10. How I got? 1 plus 0.10. Correct. Second year, can I say 100 into 1.05? This is growth. Correct. Divided by 1.10 to the power 2. Correct. Correct, guys? Are you all able to understand? You want me to repeat anything? You guys want me to repeat anything? Yes. What you want me to repeat? Now, here, I'm telling you, this is the cash flow computation. Correct. This cash flow, I put it here. Correct. And I'm discounting. Normal discounting. I'm doing. So, what is the discount? How will I discount it? What is the formula? Your future, future value divided by 1 plus r the whole power n. That remains the same. 1 plus r the whole power n. First year. Here, it is second year. So, 1 plus r the whole power 2. Third year, the denominator will have 1.1 the whole power 3. And so on. That is the discount factor. But cash flow, how it will grow? At the end of year, 100. At the end of year two, 100 plus an additional 1.5. 1.05 percent. At the end of year three, it will be on this. I will apply another five percentage. So, can I say 100 into 1.05? That is this year's value into once again 1.05. This is nothing but 100 into 1.05 to the power 2. That is the cash flow at the end of year three. Correct. This is divided by normal discounting. 1.10 to the power 3. Guys, are you all able to understand the way in which I have framed this equation? Fourier. Do you want me to repeat anything? You're able to understand this. You guys are able to follow. Is everyone able to follow? Is everyone able to follow? Yes, guys. Please participate. You're all able to understand, right? If I'm going fast, please stop me there and there. Please stop me there. That you guys are able to understand. Fine. And this goes on like this till perpetuity. Clear. It's clear. And you all know. You all know when this goes on to perpetuity. What is the logic that we take? Geometric progression. Geometric progression. Correct. Geometric progression. So, geometric progression. What does it say? In case of infinite. Infinite cash flows. Sum of infinite geometric progression is going to be A divided by 1 minus R. But before that, first, we should understand. We should see whether this is a geometric progression or not. This is a geometric progression or not. Okay. But before that, first, write down the formula. In this case, in this case, take a red ink and write. Take a red ink and write. The present value is equal to. The present value is equal to. Cash flow at the end of year one. That is cash flow at the end of year one. Divided by discount rate minus growth rate. Discount rate minus growth rate. In our example, guys, just substitute and tell me. In our example, what is the cash flow at the end of year one? Actual amount. What is the cash flow at the end of year one? Please everyone tell me. What is the capability of your own? 100. Correct. 100 divided by. What is the discount rate? What is the discount rate? 0.10. Minus. What is the growth rate? 0.05. 0.05. I told you, no, it grows at five percent. 0.05. So, how much is this? 100 divided by 0.05. How much is this? How much is this? This is going to be 2000 rupees. So, when your cash flows increases based on some growth rate, the sum total of all that, if it is given for an infinite period, the formula is cash flow at the end of year one divided by discount rate minus growth rate. Are you clear with this? Now, again, again, the logic for this is sum total of all your geometric progression. In case of a geometric progression, sum total of infinite geometric progression series. Shall we just prove it? Shall we just prove it, guys? I'm just taking a blue wing. It's not required for example. I'm just giving you the logic, sir. This formula, how did you arrive? Mathematically, simple. It's simple max. Now, you tell me, is this a, no, this cash flow series that I have given you? Is this a geometric progression or not? How will you know? Divide any two adjacent. Divide any two adjacent items. If it gives you the same number, which means it has a common ratio. And hence, it is a geometric progression. Correct, guys? Can just write a second, second factor divided by the first factor. Can we just try this? What is the second factor? 100 into 1.05 divided by 1.10 Square. The whole divided by 100 divided by 1.10 Square. Correct. So, this is nothing but 100 into 1.05 divided by 1.10 to the power 2. Multiplied by 1.10 to the power of 1 divided by 100. Simple division. It becomes Ulta when you're multiplying. Correct. So, this gets knocked off. This gets knocked off. Correct, guys? These two gets knocked off. Yes or no? Yes or no? And here, it gets knocked off once. Correct. So, basically, you will get 1.05 divided by what? 1.10. Correct. 1.05 divided by 1.10. This is what you get if you divide the second number by the first number. Can you do and tell me? If you divide the third number by second number, do you get the same? 1.1. 1.05 divided by 1.1. Guys, are you able to follow what I'm trying to say? What I did was, what I did was, this second cash flow divided by first cash flow. I saw. I got one answer. What was that answer? 1.05 divided by 1.1. Now, what I'm trying to do? The third cash flow divided by second for cash flow. I'm doing it. And I'm trying to find out whether it is giving me the same answer. If it gives me the same answer, what is it called as? The series is called as a geometric progression. If the series is dormitory progression, then sum of infinite geometric progression series, I can use the formula A by 1 minus R. Yes. Can you just do 3 divided? The third number divided by second number? If you do, I am sure you will get the same 1.05 divided by 1.1. Correct. So, trust me, it is a geometric progression. Clear, guys? Clear, guys? Now, when it is a geometric progression, and you want to sum the entire series, what is the formula? You can use A divided by 1 minus R. Where A is the first term. That is the first number. And R is the common ratio. In our case, the common ratio is. The common ratio is this. Correct. 1.05 divided by 1.10. See, all these things are not required from an examination perspective. But just I'm just giving you the logic behind these formulas. So, tell me, what is the first term? The first number? What is it? So, this is going to be 100. One second. Okay. Fine. Now, now, now. What?

Is the first number, guys? What is the first number? No, no, first number of this particular series. 100 divided by 1.1. No, correct. So, 100 divided by 1.10 to the power one divided by 1 minus r. What is r here? 1.05 divided by 1.10. Can anyone just solve this? 100 divided by 1.1 divided by 1.10 minus 1.05 divided by 1.10. All this is mathematics. You can just cancel these two. This gets 100 divided by how much? 0.05. This is nothing but cash, cash flow at the end of year one divided by your discount rate minus growth rate. Are you clear with this? 0.05 is your 0.10 minus 0.05. Are you clear with this? Basically, we are using geometric progression that formula. We are just substituting it here and we have arrived at it. Clear with this, guys? So, equal cash flows, somewhat equal cash flows received to infinity. What is the formula? Cash flow because every year it is going to be the same cash flow divided by the discount rate. Clear? If it is going to be on a growing model, what will you do? The first year cash flow divided by discount rate minus growth rate. The logic for the two formulas are nothing but sum of infinite geometric progression series. Are you clear with this? Is everyone clear with this? Is everyone here with this? If they give you to infinity, can you do it? So, if there is, if they are giving some series of cash flow to infinity, there can only be two models. One is same amount received every year to infinity, or number two, here is some incremental growth, incremental growth every year till infinity. There cannot be unequal cash flows. There cannot be unequal cash flows. Why? If they are giving unequal cash flows, they should tell in which year you receive what. Correct? If they are able to tell which year you're receiving what, it will, it becomes a finite cash flow. No, it is not infinite. Correct? So, if it is infinite, it can either be equal to infinity or it can be growing to infinity. You cannot have some unequal to infinity and all. Are you clear with this? Are you all clear with this? So, equal amount to infinity, sum total of that is simple cash flow divided by discount rate. Now, if it is on a growing model, cash flow at the end of year one divided by discount rate minus growth rate. Logic, geometric progression. Clear with this? Are you all clear with this? As simple as that. Fine, guys. Clear with this? Now, let's quickly move to the next one. Let's quickly move to the next one. Yes, correct. Cash flow. Okay, you're saying cash flow plus divided by discount rate plus the growth rate. I need to work out. Maybe after the class, I will be able to solve that. Okay? But for that, till now, whatever concept has been done, is that is anyone having any kind of doubt? You are, you guys clear with this? Are you guys clear with this? Yes, let's move to the next one. I think we've covered nine concepts, eight concepts. So, yes. So, let's go to the ninth concept. Let's go to the nine concept. Let's go to the nine concept. Let's go to the ninth concept. Write down annuity. Don't worry, guys. Listen one more, and then today's class, I will close. Don't worry. Little early itself, I will close. Happy? Yes, I know. I don't want to overburden you, throw too much of figures as well. So, obviously, my intention is not to trust you with everything. At the end of the day, even little, whatever you were learning, that also will go off. So, we will learn a bit. Whatever I said, but please revise and come. I know right now, I have told so many areas. You're like, okay, okay, he said something, he said something. Unless and until you go home and revise, it is not going to come. And we will be referring to this throughout our subject, throughout our subject. So, please go through it. I know you might be having a few other doubts. You might be having a few other doubts. Please ask me whenever you get it. Then and there, when you get it, you can just ask me anytime. Clear? But ensure that you're strong with the concepts. You're strong with the concepts. The logic, framing the equations, and all, you should know what to do, when to do, how to do. Clear with this? Clear with this? Now, let's take another concept called as. You have any doubt? Okay, let's take another concept called as annuity. Let's take a concept called as annuity. I'll tell you what this is. This is not that annuity I told you, no, summation of all your interest factor. This is not the same annuity. Why? That is called annual. I will just tell you. Okay, just branch it into two. Just branch it into two. This is also your foundation syllabus. You have heard this deferred annuity, annuity due. Yes or no? Whatever you say. Anyways, I'm going to do. Don't worry. Okay, so please write down. Effort annuity, deferred annuity, and and you read you. Deferred annuity and annuity due. What do you mean by default annuity? When the cash flows arrays at the end of each year. Annuity do, do means when the cash flows arise at the beginning of each year. Now, cash flows can arise at any time. Yes, certain cash flows can arise at the end of the year, or certain cash flows can arise at the beginning of the year. Now, I know you might have one doubt. Sir, what happens if it occurs during the year? Yes, obviously, in real life, during the year, let's say on 25th July, I received so much amount of cash flow. So, discount factor should exactly consider that date and all. No, so I should discount for a proportionate year or not? See, if you see at the end of the year, I receive. I know, okay, fine. When I'm discounting for one year, I will do. Let's say I'm receiving after one and a half years, then I should use the discount factor pertaining to one and a half years. Correct? Till you know, what we have seen, first year, then at the end of second year, then at the end of third year, and so on. So, basically, you've taken only at the end of the years. Correct? What will happen if it is in between a year? In real life, that scenario will arise. But in exam, in exam, they cannot ask you because for that, you need some tools, some mathematical tools. You need some Excel spreadsheets, or you need some specific tools that calculates. In real life, cash flow can generate at any point of time. No, let's say today, your customer comes. What is today's day? 27th December. You today, he comes with a check of online. Sir, only then I will do because only then I can calculate the discount rate. Will you do that? So, basically, in real life, cash flows can happen at any point during the year, any day, specific day, it can do. It can happen. But for the educational purpose, we will either take it at the beginning of the year or the end of the year. Are you clear with this? How does this affect, sir? When you are calculating the discount rate, no, yes. So, 1 plus r, the whole power n is there, no? 1 plus r, the whole power n. Future value divided by 1 plus r, the whole power n. If you see n, till now, we would have seen only n can be one year, two year, three year. If you have received it in the middle of the year, let's say after one and a half years, then the n will be 1.5, you know, correct? One and a half years. Suppose in between, let's say 15th of March, then proportionately that n will also change, you know, three and a half, two and a half months divided by 12 months. For exam, for all the limited, uh, educational purpose, all those things are not that. Either the beginning or the end of the year only cash flow gets generated. That is the assumption with which we are going. In real life, it's easy. It's easy for you to do if you have all these tools. If you have these tools, one click of a button, you can do it. Best tool is Excel. You can easily do anything you want in Excel. If you're good at Excel, this finance, all the finance career opportunities I told you, no, one basic requirement is Excel knowledge from basic to advanced, you should be knowing in Excel. So, they call right now, they're calling it as financial modeling. Financial modeling means bringing up with models in Excel, in Excel, coming up with your own templates. That is called as financial modeling. That's the order of the day. So, coming back to our discussion, we will assume for all the purposes in our classroom, that is also applicable for your syllabus. That is only applicable for your syllabus. So, cash flows can arise only at the beginning or at the end of the year. Clear with this? Clear with this? Clear with this? Now, deferred annuity can also be called as adios. You just note this down. If you find the word, 100 rupees received in arrears. Okay, when I wrote my intermediate, this this came in. This came in. Thank God. Day before the exam, I just went through something, but somehow that also came. Arias, if they, if they use the word received in arrears, means what? Received at the end. You're postponing it. So, you're postponing something to the end. So, received in arrears. This can be also called as received in advance. In case, in case, in an extreme scenario, where they use these jargons, you should be able to, you should be able to handle it. Are you clear with this? Now, example one, example is salary payments. Salary payment, when will they pay you? Work for this month. Yes, at the end of the period, I will pay. Correct? So, can I say one example for this is salary? Is one example? Now, where advanced concept comes in, or where they will ask you to pay upfront. Huh? Then before the next month starts, you pay in the beginning, and then you occupy. Correct? Correct. Some people can also allow. Otherwise, if you've seen lease payments and all, lease payments and all, they would have made it in an agreement clearly. You pay and use. That's all. You pay and then you can use. Clear with this, guys? Clear with this? Some software subscription and all, OTT platforms, 12 years, 12, I mean, 12 months, one year subscription. Yes, you guys, you guys have this Amazon Prime, all this, OTT Netflix and all that? Yes. Now, for one year subscription, can you say I will use for one year and then pay? Obviously not. Fine. You pay today, and then you can use for the next one year. This is where the, this is where the concept of annuity due comes in. Clear with this? This is also very logical. This is also very logical. Clear? Now, let's just take an example. Let us just take an example. Please write down. Concept number 10. Present value of multiple equal cash flows within bracket annuity due. Till now, we saw what? Till now, we saw what? Deferred annuity only, no, guys? Till now, we saw deferred annuity. What is that? All the cash flows occur at the end of the year. Correct or not? Now, in this, in this concept, you are going to see what will happen if the cash flow arrives at the beginning of the year. Are you all clear with this? Shall we proceed, guys? Shall we proceed, guys? We will finish this and we'll wind up for the day. Happy? Biggest motivation of life. Yes, great. So, let us, let us continue. Please, at least then you stay motivated. Let us continue. Yes, so, example. Take an example. Take an example. Here, case one, deferred annuity, and case two, annuity due. Annuity due. Now, what happens is, they are saying cash flows will be every year. Cash flow will be rupees 100. Okay, guys, guys, just listen. Every year, cash flow will be rupees 100. Correct? Now, let me see if you guys have understood this conceptually. They are saying every year, the cash flow generated for the next five years, every year, the cash flow generated will be what? 100. Every year. Clear? Clear? If I am following deferred annuity, deferred annuity means what? So, when will I receive these figures? Let's say year 0, 1, 2, 3, 4, and 5. Can you fill this? Can you fill this? Can you fill this? Year 0, what will it be? Huh? Nothing. Not principle. Forget that loan concept. Please forget that loan concept. I am just telling you, you got some, someone is saying I will pay you 100 rupees. Okay, someone is saying I will pay you 100 rupees every year. Case number one, for the next five years, I will pay 100 rupees based on deferred annuity model. Correct? Today is year zero. Correct? There is something called year zero as such, but today I should put it right. That is already in present value. Year 0 is already in present value. Correct or not? Correct or not? Today, do I receive anything? No, because he's following a default annuity concept. At the end of year one, Helena, fear 100. Similarly, 100, 100, 100, and 100. Correct? Correct, guys? This is how your cash flows will look like. Again, these can't be added pertaining to different periods. You need to discount everything, arrive at the present value, and only add. But I'm just framing how it will look like. Correct? Now, another guy says, I will pay 100 rupees every year based on annuity due, which means at the beginning of every year, I will pay you what? 100 rupees. Tell me, how does this stream of cash flows look like? For the first year, today itself, I will receive 100. Correct? So, this 100 is pertaining to the first year's cash flow. Correct? Then, second year's cash flow will be received at the beginning of no, no, second year's cash flow will be received at the beginning of second year. Correct? Or can I say, beginning of second year is same as end of first year? Correct? First January, 31st December, both are literally one of the same. Don't tell me one day difference. Yes, literally that meager thing can be ignored. Correct or not? Can I say, can I say, beginning of the next year is same as the end of the current year? So, can I say, year, 100 rupees in year 0, 101, 100 into 100 in year 3, and 100 in year 4. Year 5, I will receive nothing. It's actually in year 5, beginning, you would have received that got accounted here as end of year 4. So, for year 4, you would have received something that got accounted as end of year 3. Clear? And so on. And the first year, whatever you received, that got accounted as if it was received today. Are you all clear with this? Now, this kind of scenario, we have already seen in length and brick. Clear? Now, if this comes in, if this comes in, what to do? It's very simple. Right? It's very logical. Can anyone, can you guys frame the cash flow equation here? First, let me put this case one. Let me put this case one. Please write down. Deferred annuity already covered, which concept? Concept number, no, deferred annuity in case of this is, uh, equal cash flows, definite year concept six. Please refer concept six. Concept 6 already done. Every year at the end of every year, I'll be receiving 100. I told you, you can accumulate, take 100 in common, accumulate the interest factor. That is called as present value interest factor of annuity and all. I told you, yes, I showed you the table also. Clear with this? Clear with this? Fine. So, this is present value is nothing but 100 into present value interest factor annuity of 10 percentage for 5 years. Now, go to the table. Tell me how much is this? Or you can also do it to calculate. You can calculate it manually. Tell me, go to the table, present value interest factor of annuity, 10 percentage for five years. How much is it, guys? If you look at this, if you look at this, which table is it? Present value interest factor of annuity, 10 percentage for five years. How much is it? 3.791. Correct or not? This cash flow equation, directly if they give this, I can multiply and arrive at the present value. Correct, guys? It's that simple. It's that simple. Yes. So, tell me how much is this? 3.791. So, this is going to be how much? Rupees 379.10. Some students said they didn't get this point one zero. Forget it, right? Are you all able to understand this? This is already done. This is already done. Are you all able to understand this? Now, our focus is on case two. This is logical, right? This is also logical. This can be done. Yes. So, write down annuity due. Please write down annuity due. With this, we'll be winding up today's session. So, please focus. Let's close it up. Let's close it properly. Now, tell me, how will your cash flow equation look like? How will your cash flow equation look like? I'm talking about this scenario. I am talking about this scenario. I am talking about this scenario. Can I say this is 100 divided by 1.10 to the power 0? Correct? Because it is in year 0, and anything to the power 0 is 1. So, can I say this is 100 into 1? Why is it 1? Because it's already in present value. Correct, guys? Are you all able to understand? Are you all able to understand? You just apply the formula. It will say 1 divided by 1 plus r to the power n. What is n? 0. Anything to the power 0 is 1. So, 100 into 1. So, why is it 1? Because it's already in present value. Year zero only, no? Are you all able to understand this? Then, 100 divided by 1.1 to the power 1. 100 divided by 1.1 to the power 2. 100 divided by 1.1 to the power 3. 100 divided by 1.1 to the power 4. Shall we just frame the equation? So, just frame the equation. So, write down, please write down. This is where the conceptual understanding of the subject comes in. Please always write this cash flow equation. It helps you logically approach the subject. Uh, yes. You have any doubt? Sure, guys. Are you all cleared what's happening here? Yes. Okay, fine. So, now this is going to be 1 plus 0.10 to the power 0 plus 100 divided by. Guys, answer, please. Tell and write. Tell and write. 1 point, uh, 1 plus 0.10 to the power 1 plus 100 divided by 1 plus 0.10 to the power 2 plus 100 divided by 1 plus 0.10 to the power 3 plus 100 divided by 1 plus 0.10 to the power 4. Are you all clear with this? Are you all clear with this? This is actually the year one cash flow. But since it was received today itself, I am marking it as zero. This is year two's cash flow. Since it was received at the beginning of year two, I took it as if it was received at the end of year one. Are you clear? And so on. Are you able to understand this? Are you able to understand this? So, can you tell me, you can look at that present value table now. You don't look at this, uh, you know, don't look at the annuity table. You can just look at the present value table, or you can do the calculation. Fine. Can you tell me this is 100? I can take this out in common. One divided by one. One point one to the power 0 is only one, right? Okay, fine. Let me do this. 100 into 1 divided by 1.1 to the power 0 plus 100 into 1.1 divided by 1.1 to the power 1 plus 100 into 1 divided by 1.10 to the power 2 plus 100 into 1 divided by 1.10 to the power 3 plus 100 into 1 divided by 1.10 to the power 4. Correct? Correct? This is what it is. And all these things, you can just take 100 common. Just take 100 common. So, one, one divided by 1.1 to the power 0 is how much? 1. Plus 1 divided by 1.1 to the power 1. Use a calculator trick. How much is it? 0.909. So, 1 divided by 1.1 is equal to how much? 0.909. Then click one more equal to. How much does it come? 0.826. One more equal to 0.751. One more equal to 0.683. Correct? Or can I say this is simply, or you could have directly taken it up from the table? 100 into 1 plus 3.169. Correct? Correct? This 3.169 is nothing but present value interest factor of annuity at the rate of ten percentage for four years. Correct? I could have taken it common. That I could have taken it from the table itself. Are you able to understand, right? So, you were able to understand. So, tell me how much is this? 100 into 4.169. How much is this, guys? 416.90. Are you all clear with this? Are you all clear with this? Or, or in other words, can I say, or in other words, can I say, when I have this annuity due concept, can I say present value is equal to? Present value is equal to in case of equal cash flows, can I say the cash flow into 1 plus present value interest factor of annuity, or whatever is it, our percentage for n minus 1 year? Correct or not? Because this we took it only for four years, no? You guys saw this, one, two, three, four. Only for four years we took. Correct? Why? Because the first year's cash flow was received today itself. Correct? And so on, it happened. It is as good as I received in year 0, 1, 2, 3, and 4. Correct, guys? Correct, guys? So, they would have told that I have received in five years, but I received it in annuity due at once. So, 5 minus 1 only with respect to four years annuity table we need to look at this. Can we just go check this on the table? Yes, can we just go check this on the table? So, go to the table. Here, whereas the annuity table, 10 percent for four years, right? 10 percent for four years. How much is it? Yes, this is 3.170. In our calculation, it came to 3.169. Yes, 169, 170 are more or less one and the same. Clear? So, this is what it is. So, can I simply say, if there is an annuity due, if there is an annuity due, you can also use this formula and say, cash flow into 1 plus present value interest factor of annuity of whatever is the interest rate for n minus 1 year. Or, if you want to do it logically, this way also you can do it. It is absolutely acceptable. Are you all clear with this, guys? Is everyone able to follow this? Is everyone able to follow this? Sure. Is everyone able to understand this? Clear with this, guys? Now, I will just sum up whatever we have seen till now. I will just sum up whatever we have seen till now. Now, first, we saw the introduction that I told you that I told you 100 rupees today, 102 rupees tomorrow at the end of one year are not comparable as such. Correct? Then, how will you compare using what? Time value of money techniques. Convert today's value into tomorrow's money. Sorry, convert today's money into tomorrow's value using compounding or future value. Or, if they've given the future value, find the present value using your discounting. That is your present value techniques. Clear with this? This is what we saw. Then, we saw what happens in case of single cash flow. That's what we use the formula, right? Present value is equal to future value divided by 1 plus r. When there's a single cash flow, we just did it directly using the formula. We did single cash flow. Then, we went on to a series of cash flow, which I call as multiple cash flow. Multiple cash flow. In multiple cash flow, broadly, we saw there could be definite period. There could be definite period, or there could be indefinite period. Indefinite period is also called as perpetuity. Correct? Correct? This is also called as perpetuity. Now, now, indefinite period. In case of a definite period, the cash flows can be either unequal or equal. Correct? If they are unequal, what will you do? Respective years cash flow, you use the discount rate using the present value interest factor table. Correct? If the cash flows are equal, what will you do? Take the cash flow common, accumulate all the discount factors. That is called as present value interest factor and new T table. Are you clear with this? Yes. This is what we saw. Now, in case when they have not given a definite period, they are saying it goes on till infinity. Only two possible scenarios can arise. What are the two possible scenarios? Equal cash flow till perpetuity, or there could be a growth in the cash flow. There cannot be unequal cash flows and all in this case because if there is unequal cash flows, they should tell you know, in which year they receive how much. If they are able to tell that, that is not called as indefinite, only correct or not? Correct or not? In case of equal cash flows, what is the formula? Cash flow divided by discount rate. Logic, geometric progression, a by 1 minus r. Clear? Clear? Now, in case of a growth, in case of a growth, what is the formula? Cash flow at the end of first year divided by discount rate minus growth rate. Logic, the same geometric progression, sum of infinite geometric progression series. Are you clear with this? And then, we went on to see a concept of annuity. Annuity where annuity can be of two types, effort annuity and annuity due. And deferred annuity is already seen. Annuity to, we just saw right now, where the first cash flow happens, happens at year zero. So, the beginning, it means cash flow occurs at the beginning of every year. What I will do is, cash flow occurring at the beginning of year 2 will be taken as if the cash flow happened at the end of year 1, and so on. And with this normal logic, you can just do the entire question. Are you all clear with this? Are you all clear with this concept that has gone behind the entire discussion? Clear with this, guys? Clear with this? I humbly request you all to revise this. Revise this. And in case some of your friends have missed the first lecture, without this lecture, second lecture, directly they cannot enter. They cannot enter it directly unless and until you know this, you cannot enter into the subject. So, these are some basics. These are some basics. Right now, we have taken a long time. Full class, we have taken just so that, just so that we can just understand this concept. Few future, from the future classes, I will just be giving references. I will just be giving references. If there is a series of cash flows and all, I will not be again going back to the time value of money. Ideally, we have not even entered into FM. We are just covering the basic concepts involved in FM. This is ideally a part of your foundation syllabus. Still, I just wanted to set the ground so that we can easily build upon the subject. Are you clear with this? You will see in the next class, you will see in the next class that entire, whatever sums that have given you, all the sums will finish in a very short span of time, provided you revise everything and come to the next class. Clear with this, guys? Please revise thoroughly. If you have doubts, keep asking me. I don't mind. Please keep asking me. And of course, you guys have my number, right? On the WhatsApp group, you guys have my number? Yes. You can just keep asking me any doubts you have. You can just ask me on the group, whatever it is, you want. Please get it sorted then and there. Please get it sorted then and there. Only if you are clear with these fundamentals will you be able to move ahead in the subject. Clear with this, guys? So, thank, thank you all so much. Have a great day. Thank you.

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CA Inter | Financial Management Demo - 1 | 100% English | Nov 2023 & May 2024 |Time Value of Money

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