Hi welcome back. We have had time and opportunity to do many different problems, and I've taken the time to go really deep into them. And I've spent a lot of time today with you, because I believe the value add in online is the explanation one on one. And today is a lot of real world applications which will help you further in the class, so just bare with me for a little time. We'll do one interesting problem but before we go there let's do my favorite financial concept. And my favorite financial concept is called a perpetuity. A perpetuity is simply something that pays you C dollars, roughly the same amount or a PMT which goes on forever. Right? It's pretty remarkable. So what do you get? You get CCCCC forever and it could be with or without growth. So when I saw this the first time I said this is really dumb to the extreme. This is a textbook idea. When am I ever going to see something like that, right? So let me just first of all think of some examples of perpetuities, right? So there are borns out there. There is something that pays you, say, one pound. For a long period of time. So, that's one example. The second example which is much more complicated but much more intuitive is what is called a stock. A promise as opposed to a bond. I promise we'll spend a couple of weeks on stocks and bonds. But I want you to raise this. What's the basic difference between the stock and bond? This is limited in maturity. And this hopefully goes on. Forever. So for example, when John Ford started the company, he didn't say we'll be there only for five years and I'll pay you some money and then we are gone. That's not a company. That's not an idea. Great ideas last forever. Great things last forever. What I want you to recognize in all of this is that forever actually doesn't mean forever. What do I mean by that? So take the example and show you the power of perpetuities. Now let me ask you this. Suppose I gave you something. Suppose I gave you something that paid $10 forever. Guess what the power of perpetuity is? At times 0, guess what its PV is. We won't derive this. I"m going to give you this one formula. When we have time towards the end, I will do stuff that's kind of nerdy and, you know, interesting for derivations, if you have the time. But, I will tell you that it turns out to be C over R. So, the simplest formula in the world is the formula for perpetuity which is the most complex thing to comprehend. So what could the perpetuity be? It's a perpetuity that lasts. It's like a stock that pays you 10 bucks every year, and is expected, a company that's expected to survive for the reasonable future. So, it turns out, what would be the answer for this? Suppose the interest rate is 10%. This would be $10, divided by 0.10, is $100. Okay? What could be simpler? And would you like this $10 to grow over time? Sure. If it is growing over time at the rate of g, is the growth rate. So suppose the growth rate is 10%. So in the first year, how much is this paying? $10. In the second year, it's paying 1.1, and so on. By the way, these things in real life, are called growth stocks. So, something like what Microsoft was in the beginning, or Google, or technology firms that are successful. They grow and pay out over time. Their growth rate is extremely high. What does the formula become? C over R minus g, right. So because this growth rate is 10%, I can't use this formula. So let's make this growth rate 5%. So what is R? 10%. What is g? 5%. And what is C? 10 bucks. Again, very simple to calculate. The reason I'm introducing these now is not so much to start doing a lot of examples, I just want to introduce it now because it's a linear process. We went from annuity which ends after a certain interval, you take loans and you pay them off. Then you think of another concept that goes on forever. And we'll come back to this stocks. And as I showed you right now. If the growth rate is 10%, and you're interest rate is also 10%. You can't use this formula. That doesn't mean you can't calculate the number. You'll have to go the long way. That emphasises one more important issue, don't use formulas blindly. Formulas are at your disposal, not the other way around. Okay? So, we'll come back to perpetuities in the future, but for now, I would say just keep it at the back of your mind. That there is something real world that looks like a perpetuity and it's very common. It's what are called the share in the company or a stock of a company because it will last for a very long period of time. And in the real world what happens is you don't know how to value things beyond say ten years or thirty years, it's just too far because the world is too uncertain. Such formulas C over R minus g are really useful in approximating what you think is going to happen. There is no point in getting too refined after the five, six years. Because it's about the future. So actually these formulas, when I saw first time, I said, what are they talking about? Are the most useful ones in real life. Because you want to get a sense of value. You don't want to get it so precise when you know it's wrong, right? So approximate formulas like C over R minus g are actually so useful in grabbing the basics of what finance is trying to offer. Okay, as promised I'm going to spend a little more time today and this time is not on the next three slides. The next three slides that you see here, don't worry about them. I'm just emphasizing them to remind myself and to remind you that if you are oriented to words formulas, which I would encourage you to be. Because formulas reflect in the end your understanding of what's going on, not the other way around, I would encourage you to walk through these formulas. And as I said, I'm not going to spend the time for you to read them. This is one part of this overhead slides that I've used are visuals that I will provide you as a resource. As I said I want the main resource to be the videos but I am providing you resources like the course syllabus with chapters from various books written by wonderful people. I also want you to learn from them not just from me. I don't have the control on learning. Your learning is you are in charge. But I'll give you some formulas so that you can go back and confirm your knowledge. So I just wanted to remind you and me we'll do that. That will put everything together, but I want to end today's class by doing a problem with you, and I would say I'm going to read this problem first with you. Try to understand the context and then I encourage you to take a break and hopefully you've taken several breaks over different days during this content because I'm committed in week two to make you understand why we do things the way we do. And the reason is we can learn a lot in ten weeks. And I've taken a lot of time today simply to make you understand how real things are even though they are problems written on a little spreadsheet or in a little PowerPoint. So let's go through it. You're 30 years old. You believe that you will be able to save for the next 20 years, until you are 50. And why am I saying that? Typically that's when a lot of people earn money and save. But after that, for 10 years, till your retirement at 60, you will have a spike in your, I shouldn't even call it a spike, in your expenses. Many spikes in expenses. So that you would not be in a position to save for the next ten years. So remember what's going on. You're starting at 30, 50 and then under the break is 60. These are artificial but believe me very useful points in your life. After 60, what are you going to do? You want to retire but you want to be able to live. Right? And you want to be able to live at a standard of living which in this problem is pretty high. Because most people in the world can not afford even one tenth of this 120. But that's, I want big round number so that I don't have to deal with decimals. And I'm not trying to make a statement about what my expectations or yours are. So you'll retire at sixty, and then you'll expect to live until eighty. And you want to take care of the next twenty years at the rate of one hundred thousand dollars. Right? Not what is happening now? You were saving between 30 and 50 so that you could do this between 60 and 80. And the fact that both are 20 years is just an artifact of the example. Who controls all of this? You do. Who controls now the next decision? What interest rate will you earn on your savings will depend on you. It'll depend on what type of risks you are willing to take. And for convenience, or for just fun, I'm assuming that you are a person inclined to invest in risky stuff. And therefore you'll be rewarded on average in the long run at 8%. So this is the nature of the beast. This is the problem. I'm encouraging you now to do two things. Thing about it for about five to ten minutes and do the most important thing in life. Which is more important than even finance. I can't believe I just said that. But draw time line and put your problem on that time line. If you can do that we can do this problem in five minutes. If you can't do that, remember it's not a problem of finance, finance is going to help you not hurt you. It’s because common sense is not that common. Is finance is full of common sense, but the word common sense is a wrong expression. I found whenever I look at common sense, it's pretty complicated. That's why after a while it becomes common to you, but finance is only going to help you. So do that, I'll come back in about five minutes, and we'll do this problem together, and that'll be the end of today. And I promise you, this will enable you to do the assignment and crank up the heat in the assignment. I want this week to be intense for you. And the purpose fully so. And the reason is we can go very far, we can go very far not in the mechanics but in the understanding of the world. Okay, so break for five to ten minutes and I'll come back and do the problem. See you soon.