Now the next concept, which probably is more talked about, is present value than is future value. Again, let me start with the problem. The question says, what is the present value of receiving 110 one year from now? I think some of you or all of you are smiling, because you know why I'm asking you this question with these specific numbers. The interest rate is 10 percent and I'm giving you $110 one year from now. Think about this problem as something like this. You're going to receive $110 in the future one year from now and you're trying to figure out what does it mean to you today? This is a very important problem to solve because most problems in life, you make effort today and you get money or pleasure in the future. You want to figure out what is 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. Hopefully that's ingrained in you. I'll tell you a little bit about what that has done to me, not 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. Let's do this problem, and I'm going to use again, just a simple way of doing it. Here you go, you have zero, you have one. One period has passed. Remember, always what connects one and two is time value of money at 10 percent. I made it very easy and I have 110 here. That's the problem. I think if you've 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 percent, it's 110. So what is the value of a 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. I'm asking you exactly the same question, but in reverse. I'm saying, suppose you have 110, how much would it be worth? Obviously, to get the same 100 bucks, the interest rate has to be the same, and I've kept it the same. The reason I find this problem very interesting is it's easy to do. However, how do you go from 110 to 100 bucks? This is where what I would recommend very strongly is that we try to do the concept before the formula. If you look at my notes, I'll just go ahead one bit, is that I never do the formula before the concept. So if you saw me toggle, I've went to the next page and I showed you the formula after I did the concept. Let's do it again. Simple. Turns out that present value and future value, in this case with one period difference. Conceptually, I know already what this is. I know future value is equal to present value times 1 plus r. Pretty straightforward, I know this. So how much would be the future value of 100 bucks at 10 percent after one year? We know the answer is a 110. But now I'm asking you the unknown element of this is this, so what will PV be? PV will be FV divided by 1 plus r. I'm just inverting this equation, its very simple, its algebra. However, dividing something by 1 plus our 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? The reason is that one plus something is a factor that anything can be multiplied by. The future value factor is 1 plus r, what is the present value factor? 1 divided by 1 plus r. 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. This guy is telling me what? This guy is telling me, what is the present value of one buck if I got it one year from now? I have to divide that by 1 plus r. If r in our example is greater than zero, 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. That's why this whole process is called discounting. When you read about finance we'll say discounted cash flow or discounted money. The reason is you're lessening it, and the key to that lessening is what? This r being greater than 0 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. I've told you the formula, which we can rewrite and right now you created the formula. Present value is equal to, in our case, $110, which was the future value divided by 1.1. Why? Because r was 10 percent, so $110, this is a one, you know what I mean? I can make mistakes too,$110 divided by 1.1 and this becomes $100. 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? The answer you know, is a $110. So future value and present value are checking each other, they have to be consistent with each other because one is simply looking at the other in reverse, if you may. I hope this is useful to you and this itself is easy to calculate because I'm dividing by 1.1 and the value is, if you notice was $110. However, let's do this problem. Suppose you will inherit $121,000, two years from now and the interest rate is 10 percent. How much does it mean to you today? In other words, ask yourself the following question. If you were to put $100,000 in the bank, how much would it become $121,000? I'm giving you the answer already. The reason is, I know, because I've created this problem that the answer to this question turns out to be a $100,000. Let's see how I got that. I'm keeping the problem simple because you need to understand the concept better than the actual calculations, because the calculation, if they are simple you'll focus on the concept. So let me ask you this. Can you tell me the value of this $121,000 in year one? Can you? I hope you say yes. Why? Because we've done it. We have done a one-year problem. That's why I said in finance, if you can time travel, watch Star Trek, watch Star Wars, watch Matrix, if that's part of who you are, finance will be easy. Let's time travel to period 1, how much will it be? Well, I know it'll be $121,000 divided by how much? 1.10. That's the amount it will be after how much? One year. But you're looking at two years from $121,000. This is very easy to divide. That's why I took it. So what is 1.1 into $121,000? How much will I be left with? Well, one, one, 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 a $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 a $110,000 and I know how to divide a $110,000 by 1.1, the answer has to be a $100,000. Just this simple example tells you how hurtful present value process can be and why do we call it discounting if you're taking the future of a $121,000 and boiling it down to only $100,000. The reason is very simple the interest rate is pretty high. But a lot of people in business in particular, they tend to use high interest rates, and I find that a little bizarre at times. But anyway, just wanted 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. Let's do it. What's the formula of present value? The present value formula turns out to be future value of, in our case 121, divided by one plus r raised to power what? In our case it was two, 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 two, but could be anything. 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. I'm going to do one more thing before we go today. 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 where we are headed. We've 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. Let's show you Excel again, and the problem I will do is the two year problem. Let's do. Now, what is it that we are trying to calculate? The critical thing to remember is, put the function that I'm trying to solve for. I'm doing PV, and the rate was what? 10 percent. Number of periods was two, PMT remember, is a flow every year. We don't have any of that. Now, I'm supposed to tell you the future value, I'll tell you meaning the Excel. So 121,000, I think I got it. If I didn't shame on me, and let's see $100,000. I want you to see if one last thing and I'll show you the power of compounding in reverse. Let's make this a 121,000 stay the same. Let's keep 10 percent 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 a $121,000, your inheritance, suddenly you realize that there was a typo. Sorry, not two years, but 10 years now you are thinking, no big deal. Well, you're probably wrong by a huge amount. Your amount of money you are 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. Hopefully we have a relationship now, but you're not waiting for me to make a mistake, because I will make mistakes. Your goal here is to try to learn for yourself even if I am. What's happened? I have reduced the value of my inheritance to less than half by simply taking two years and making it 10. 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. To do that slowness, the major way I'm going slow is by keeping risk out of the picture. If I throw risk in and you started messing with that at the same time, life would become quite complicated. But just so that it satisfies your curiosity, remember, high risk high return, high risk high return tend to go together. Even though we're not talking about risk right now, and that being at the back of your mind in that simple, powerful way is not a bad thing. 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. I think if that has power, that's awesome. Because even when I teach classes live, I cannot do that. 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. I'm hoping that online, though it has limitations obviously, online has this huge benefit that 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.