So obviously that's a very simplistic idea, that you're going to receive a cash payment a year from now or you're going to give somebody some cash and they're going to pay you in a year from now. It may not always be a year it may be two years, it may be three years, it may be seven years. The present value of payout in two years from this slide. It's the cash payout divided by 1 plus the interest rates to the power of 2. So somebody said, hey, I'm going to pay you $100 two years from now, what would that be worth? 1 plus the interest rate squared or I can pay you $20 starting next year for the next five years. So $20 in one year, and then $20 in the second year, and $20 in a third year, and $20 in the fourth year, and $20 in the fifth year, what's that worth to me? Well, that would be the formula here, a cash payment divided by 1 + r to the t, 1 + r to the t + 1, 1 + r to the t + 2 etc., etc., etc.. I can write this using a really cool mathematical type, and this is what it would be. Present Value, is equal to the summation, the sigma, summation of my cash payment at period t divided by 1+r to the power of t, where t is from 1 to n. So it maybe one year, two years, three years, five years what have you. So, what we're going to do is let's go over to the Excel workbook and let me show you how to do this calculation, what it means, and we can play around with it a little bit. All right, here we are, at the Excel workbook. This is the tab that says NPV, net present value worksheet and examples. Let me just tell you what's going on in each one of these cells and then we'll work through a couple of examples. So, I've got this set up such that you can input some cells and it will spit out some results. Up here, in this cell, B9, I've got a place where you can change the interest rate, here I've got 5% you can change it to 10%, you can change it to 89%, 8%, 15%, okay? And as I do this you'll notice, here's what's happening. This present value factor is going to change as I change my interest rate. So here's 5%, you'll notice my present value factor changes. When I change it up to 10%, my present value factor changes, it's all automatic, okay? So, I'm going to move it back to 5%. So, what's happening is, that I've got this present value factor, I've got a little formula written here. And the formula is 1 + this interest rate, the information in cell B9, to the power of whatever the year is 1, 2, 3, 4, 5 what have you, okay? And what this means is that the present value factor shows you how much each dollar is discounted. For example if I have, If I have, let's try this again. All right, the present value factor shows how each one of these things is discounted. Given the fact that I'm using Excel do I have to go back through the whole thing over again or can I start from there? >> [INAUDIBLE] >> I don't like from the here's like the whole sheet, you know what I'm talking about, this workbook, you can paste and cut and right? [SOUND] >> [INAUDIBLE] >> Okay. >> [INAUDIBLE] >> Yeah, no. >> [INAUDIBLE] >> Talking about it but I think we can manage it. >> Okay, all right. Okay, let's talk about this present value factor. The present value factor is a function of my interest rate. You'll noticed that if I click on this cells, C14, inside the cell's a little formula, that's 1 over 1 +, $ B $9 to the power of C11. What that means is 1 + my interest rate, right there in B9 to the power of the number of years, then the present value factor like it's 5%. This present value factor after one year of 95% means that each dollar received one year from now is only worth 95% of it's value, at an interest rate of 5%. So an interest rate of 5% a dollar that I receive a year from now is not worth a dollar it only worth 95 cents. $100 I receive a year from now is now worth a $100, only worth $95. So the present value factor identifies how much a dollar in the future has been discounted. So, let's look at our example. Our example was what is the present value of a $100 received one year from now? Right here if I type in $100 my cashflow right now, one year from now you'll notice that right below here the cumulative present value, the present value of cashflow says 95. So this says is that if I'm going to get a $100 in one year, what is the present value? What is that worth right now? It's worth $95. What if I change this up to something else like 12%. So if I'm going to receive a $100 one year from now, but my discount is 12%, instead of 5%? And then a $100 is only worth 89. Here's how I can interpret that. If you tell me that you can only give me $100 in one year from now and my interest rate is 12%, I am only willing to loan you $89, that's it! And suppose my interest rate was 15% Then, if you can only give me $100 a year from now, I'm only willing to loan you $87, that's what this means. Let's do one more example, let's suppose you tell me that you could give me $100, but the $100 is spread out over 5 years, $20 in year 1, an additional $20 in year 2, and then in 3, and then in 4, and then in 5. Yes, it's $100, but it's not all at once. I don't like that very much. What am I willing to loan you if you can only give me this kind of cash flow? Certainly less than $100, how much less? That's where the present value comes in. In one year from now, $20 is really only worth $19 and then in two years, it's only worth $18, and then in three years, it's $17, and then in four years, it's $16. And in 5 years it's probably right around $16 again, according to this. So what happens is if I accumulate all the present values, the 19 plus the 18 plus the 17 plus the 16 plus the 16, this says that this cash flow at 5% interest, I would only be willing to loan you $87. That is the present value of this cash flow, $20, $20, $20, $20, $20 is $87. $87 is equivalent to the future cash flow of $20 at these times at 5% interest. Let's suppose my interest was 12%. Now, that $100 that spread out over five years, is only worth $72. This is a really useful formula that helps you understand the relationship between future cash flows and the present value of those cash flows. Obviously, I've given you some good pointers here. But what I want you to do is use this sheet and this formula to answer some of the questions that I've provided you on your assessments.
