Simple Present Value

Welcome back. We have talked about future value, we have seen the power of compounding. And I would like to now talk about present value, but we keep one thing still simple, which is we'll have a one time payment, or one time amount of money at a point in time. So in the previous examples, we had future values of what? A $1,000, or whatever the money is, at point 0 at different points in time in the future. So we increased them from one, and so on. Now what we are going to do is we are going to do the reverse of it, and present value is more difficult to understand, but not if you understand future values.

So many textbooks introduce present value first, which I find little bit counter intuitive, and tough for people to understand, especially with compounding. So let's do present value. So the question I ask is the following, and it's up on the screen for you. What is the present value of receiving $1,100 1 year from now? So let's again, make sure we understand the timing of it and draw the timeline. You are standing here. Our question is, asking what is PV? But I'm giving you money in the future. And for the beginning, time being, we will keep the period only one year. So I'm giving you 1,100, right. So can you guess, given what we have just did?

Turns out that the present value is, think of it as the reverse of future value. So if somebody gave me 1,100 in the future, will it be worth less or more today? Remember future value increases. Present value has to be less. So what will you do? You'll do 1,100, and you will do something called discounting. And the word discounting is everywhere in finance. And the reason is we make decisions today and calculate present values of our actions. But our actions affect the future, so we'll try to bring this 1,100 back today. Because that's when you make decisions, and it's good to think in present value terms. Nothing wrong in thinking in the future.

But what's the point if you're making the decision today? Turns out, what will you do? You'll divide this by 1 + r, and it'll become. $1,000. So let me explain why you divide, because the good news is you already know future value. That's why I like future value a little bit better in terms of beginning tool to understand. It makes sense, you can relate to it. And easier to do, dividing is more difficult than multiplying. Though with compounding, we saw that we need Excel as soon as we went beyond one year essentially. So, think about it while. One way to think about it is, suppose I put the 1,000 bucks here.

The present value, to check that my answer is right what do I need to do? To calculate its future value, take its future value to the future, how much will you get?

You'll get 1,100, which is equal to what? PV x 1 + r.

Yeah, we sometimes call PVP too, right? So what does FV become? So FV is PV x 1 + r. So think about it. What is PV? PV is FV / 1 + r. I kind of cheated, and did the calculation right here.

So, the reason it's difficult is you're not dividing by r, 1 plus r, you're dividing by 1 plus r, and this is a simple scenario. And the reason you're dividing 1 plus r is you get the original amount in the future, plus an interest rate, okay. So let's just keep going a little bit, and talk a little bit about the present value concept, which you already have. So PV concept is, you take something in the future value and you try to bring it back right? And the way you do it is you divide it by a number greater than 1. R, we'll assume throughout this course, is typically greater than 1.

So, what happens to the future value when you divide it by a number greater than one? It becomes discounted. It becomes less than the future value. One more time, let's write out the formula. Okay, so the PV formula = to FV over 1 + R. Sometimes I like lowercase. Sometimes I like caps. Don't worry about it, you know what I'm talking about? So in our example, it was 1,100. Divided by (1.10), and it was $1000. Okay? Let's take a break. We want to nail present value. We've nailed future value, at least for one payment, and then we'll come back and do more interesting stuff.