Hi, so hopefully you've taken some time off. I'm going to shift to present value, but as I promised earlier, I'm going to stop with present value for very similar problems that we did earlier. And the reason I'm going to stop today, is I think the first week should expose you to the class, what it's all about, and some idea of time value of money. But we'll get things more complicated next session. Of course, I also want to remind you that we are trying to follow very strictly a week by week schedule. So I will let the video length be dictated by the week. So because today was introductory stuff and we did redoing of the content starting about an hour ago. What I'm going to do today is leave you with enough material of the content, you can always go watch the introduction to the class again anytime. But I wanted to give you enough today this week, so that you can start practicing, start doing assignments and so on. So now the next concept, which probably is more talked about, is present value than is future value. So again, let me start with the problem. So the question says, what is the present value of receiving 110 one year from now, and I think some of you, or all of you are smiling. Because you know why I am asking you this question with these specific numbers, the interest rate is 10%, and I'm giving you $110 one year from now. So think about this problem as something like this. You're going to receive $110 in the future, one year from now. You're trying to figure out what does it mean to you today? And this is a very important problem to solve, right, because most problems in life, you make effort today and you get money or pleasure in the future, right? So, you want to figure out what's the value of that today and present value, therefore is a little bit more important than future value for decision making. However, future value, I think, is easier to understand and it forces you to be a finance person. Finance people look forward, finance people don't look back, right, so that, hopefully, that's ingrained in you. I'll tell you a little bit about what that has done to me. [LAUGH] Because finance has changed me, in good ways mostly, but there are some elements of it which are pretty hilarious, which I'll get to in a second. Okay, so let's do this problem. And I'm going to use, again, just a simple way of doing it. And so, here you go. You have 0, you have 1. 1 period has passed. Remember always what connects 1 and 2 is time-value of money at 10%. I've made it very easy, and I have 110 here. So that's the problem. I think if you have paid attention and you've gone back, which you can do any time. You know the answer to this because I know what the future value of 100 bucks is at 10% interest, it's 110. So what is the value of 110 in the future today? Answer has to be, 100. Recall again, the first problem I did with you. I asked, how much would 100 become after one year? And we realized that 100 bucks would become 110. And I'll ask you exactly the same question, but in reverse. I'm saying, suppose you had 110, how much would it be worth? Obviously, to get the same 100 bucks, the interest rate has to be the same, right, and I've kept it the same. So the reason I find this problem very interesting, is it's easy to do. However, how do you go from 110 to 100 bucks? So this is where what I would recommend very strongly is that we try to do the concept before the formula. So if you look at my notes, I'll just go ahead one page, is that I never do the formula before the concept. So if you saw me toggle, I went to the next page and I showed you the formula after I did the concept. So let's do it again. Simple. Turns out that present value and future value, in this case, with one period of difference. Conceptually, I know what? I know already what this is. I know future value is equal to present value times one plus r. Right? Pretty straightforward. I know this, so how much would be the future value of 100 bucks at 10% after one year? We know the answer is 110. But now I'm asking you just the unknown element of this is this. So what would the PV be? PV will be FV divided by 1 plus r. In working the situation, it is very simple it is algebra. However, dividing something by one plus r, if I said it to you the first time, you would have said, why the heck am I dividing something by one plus something? And the reason is that one plus something is a factor that anything can be multiplied by. So, the future value factor is 1 plus r. What is the present value factor? One divided by 1 plus r, right? Because I'm taking the future value and multiplying it by 1, which is missing here because it doesn't matter, divided by 1 plus r. So this guy is telling me what? This guy is telling me, what is the present value of 1 buck if I got it one year from now? I have to divide that by 1 plus r. And if r in our examples is greater than 0, what will the value become? Less. So it's very straightforward that something in the future will become lesser in magnitude or value when I bring it today. And that's why this whole process is called Discounting. So when you read about finance we'll say, discounted cash flow or discounted money, and the reason is you're lessening it. And the key to that lessening is what? This r being greater than zero creates present to become larger in the future. But it also, therefore implies by definition that the larger in the future becomes less today. So that's the concept, right? But in doing the concept what have I also done? I have told you the formula. So I've told you the formula, which we can relate and you can write now you created the formula present value is equal to in our case 100 bucks. Sorry, $110, I apologize. It was the future value divided by 1.1. Why? Because R was 10%. So 110, pardon the, this is a 1 you know what I mean? I can make mistakes too. 110 divided by 1.1, and this becomes 100 bucks. How do you double check that? Very straightforward. That's what I love about finance. Ask yourself how much would 100 become in the future. And the answer you know is 110. So, future value and present value a kind of checking each other. They have to be consistent with each other. Because one is simply looking at the other inverse if you may. So, I hope this is useful to you and this itself is easy to calculate because I'm dividing by 1.1 and the values if you noticed was 110. However, let's do this problem. Suppose you will inherit $121,000 two years from now and the interest rate is 10%. How much does it mean to you today? In other words, ask yourself the following question. If you were to put 100 bucks, right, $100,000 in the bank, how much would it become 121,000? I'm giving you the answer already. And the reason is, I know because I've created this problem, that the answer to this question turns out to be $100,000. So let's see how I got that And I'm keeping the problem simple, because you need to understand the concept better than the actual calculation. Because the calculation, if they're simple, you focus on. So let me ask you this, can you tell me the value of this 121? In year one. Can you? And I hope you say yes. Why? Because we have done it! We have done a one year problem, so that why I said in finance you can time travel. Watch Star Trek, watch Star Wars, watch The Matrix. If that's part of who you are, finance will be easy. So let's time travel to period one, how much will it be? Well I know it will be 121,000, divided by how much? 1.10. That's the amount it will be after how much? One year, but you are looking at two years from now, 121 this is very easy to divide, that's why I took it. So what is 1.1 into 121, how much will I be left with? Well, 11, 110, so this is 110,000. But that's not what I'm asking you. I'm not asking you what is the value of $121,000 inheritance one year from now. I'm asking you today. So what do you do? You take 121,000 divided by 1.1, and then I divide it again by 1.1, right? So how much does that become? I know this guy is 110. And I know how to divide 110 by 1.1. The answer has to be 100,000. So just a simple example tells you. How hurtful present value process can be and why do we call it discounting? You're taking the future of 121 and boiling it down to only $100,000. And the reason is pretty simple. The interest rate is pretty high. But a lot of people in business in particular tend to use high interest rates, and I find that a little bizarre at times, but. Anyway just want to, to give you a flavor of what's going on and now I'm going to do what I promised you is I'm going to tell you the concept formula together. So let's do it. What's the formula of present value? So the present value formula turns out to be Future value of, in our case 121, divided by (1+r) raised to power what? In our case it was 2, because future value of 121 was occurring when? Two years from now. In this case, it'll be raised to power n, where n, in our example, was 2, but could be anything, right? You could be getting an inheritance 50 years from now. You could be retiring 30 years from now. So, this problem doesn't have to be two or three. That's why I wanted to emphasize that and I'm going to do one more thing before we go today, and what I'm going to do is, before I get into multiple payments, that's what next time is. So just to give you a sense of what and where we are headed. We have talked about a single payment carrying back and forth, now I will do something that's much closer to reality. Which is multiple payments. But before I do that, what I want to do is show you Excel again. So Okay. So, let's show you Excel again and the problem I will do is the two year problem. So, let's do. Now, what is it that I'm trying to calculate? The critical thing to remember, is put the function that I'm trying to solve for. So I'm doing pv. Right? And the rate was what? 10%. Number of periods was 2. PMT, remember, is a flow every year. We don't have any of that. And now, I'm supposed to tell you the future value. I'll tell you, meaning the Excel, okay? So 121,000. I think I got it. If I didn't shame on me, and let's see. $100,000, right? So I want you to see if one last thing and I'll show you the power of compounding in reverse. Right? So let's make this 121,000 stay the same. Let's keep 10% interest the same. But let's just mess with this number two. So I'm going to make the two. Ten, so what am I saying? Instead of giving you $121,000, your inheritance, suddenly you realize that there was a typo. Sorry, not two years, but ten years. Now you are thinking, no big deal. Well, you're probably wrong by huge amount. The amount of money you're left with, if I've gotten all the numbers right, and by the way part of your problem is to double check what I'm doing. Not to second guess me but, to get the problem right, right? So hopefully, we have a relationship now. We are not waiting for me to make a mistake. [LAUGH] Because I will make mistakes. Your goal here is to try to learn for yourself, even if I am. So what's happened? I have reduced the value of my inheritance to less than half by simply taking two years and making it ten. So bless you. I hope you've enjoyed today. I hope you recognize that finance has both technology, power of thinking and bringing it all together. Hope you also recognize that we are going to go slow in the beginning, and part of the reason is so that you feel comfortable with time value of money. And to do that slowness, the major way I'm going slow is by keeping risk out of the picture. If I threw risk in, then you started messing with that at the same time, life would become quite complicated. But so that it satisfies a curiosity, remember high risk, high return. High risk, high return tend to go together. So even though we're not talking about risk right now that being at the back of your mind in that simple powerful way is not a bad thing. I look forward to you next week and I'm really excited about this class. And the reason is, believe it or not, I feel like I'm teaching each one of you separately and I think the power, if that has power, that's awesome. Because even when I teach classes I cannot do that. My thing, I feel, I struggle many times because I feel like I wish I could be a perfect teacher for everybody. But I'm not. I haven't met anybody who is. Because we all have different ways of learning. And I'm hoping that online, though it has limitations, obviously, that online has this huge benefit. I feel like I'm talking to you. You're there. I can feel you. And remember, whatever beats here is the same thing that beats here. So, if I see you or I don't see you I can feel you. Take care and see you next week.