FIN 37 - Mod 6 Intro - Payback Period IRR and Net Present Value

Welcome to module six of our finance course, one of the most important modules of the semester. I don't think it's one of the hardest though, but it's a very useful module. So we're going to cover payback period, internal rate of return and NPV, net present value. And we'll start actually by doing an example with all three of them, uh, just in this video to explain each of them. So net present value. If you've been following along with our course so far, really is straightforward. You just figure out what the cash flows related to whatever the opportunity is, the project or the investment or whatever, and you just take the present value of the cash flows. So typically it's going to be like, we spend some money at the start, some cash flows to us. And we're saying, well, was it worth it? Uh, that's the very typical, uh, net present value question. And here is a typical example. I drive Uber and I'm thinking of replacing my gas car with an EV after trade in the EV is going to cost me $35,000 out of pocket today. I estimate that it's going to save me $10,000 a year for the next six years. By the way, you know, these numbers are totally made up. If you are an EV super fan and I've underestimated this too bad. If you're a gas lover and I've overestimated the savings too bad for you to this, just back of the napkin, guesswork calculation to serve finance problem. Um, so I spend $35,000 upgrading my car, getting a new, uh, EV, and it's going to save me $10,000 a year for the next six years. And the discount rate here is a big one, 12%. Uh, so we'll start by calculating the net present value. We'll go over what it means. We'll talk about IRR and last payback. Let's start with net present value and let's just track the cash flows. Pretty straightforward cashflow number line here. We've got one actually time zero zero one, two, three, four, five, six years. There's my timeline. And at time zero, it's negative 35 K time one. It's plus six K or plus 10 K six, six years. I had the number six in my mind time two it's plus 10 K times three. Sure. I got to squeeze this in, in a nicer spot, but here we are. I'm committed to it. And I'm six plus $10,000. And what we're saying is do the plus tens outweigh the minus 35. Again, we're saying you're saying likely, of course, you know, it's plus 60 minus 35, but time value of money matters. And in fact, having such a big discount rate is going to mean this $10,000 six years from now is like worth half in today's dollar. So it's not so obvious an answer. And so what we need to do is figure out, well, what is the value of our 10 K cash flows over the next six years? And does it beat the negative $35,000 today? And so it's present value of an annuity, right? This is a $10,000 annuity for six years. We know the math. I can do it in my financial calculator fairly quickly. I'll do this one by hand because we'll do some financial calculator work in a second, but let's do the present value of that annuity we've looked at. It is a $10,000 savings. So my C is 10,000. Here's the formula for an annuity. You've seen this before. Uh, one minus one over one plus R. So 1.12 to the power of six, the power of T, um, all divided by 0.12. All right. So get my calculator out and we'll solve for this. Uh, or no, I won't start with a $10,000. Click, click clear. Uh, let's start with a 1.12 to the sixth power. 1.12 Y to the X six 1.97. Uh, I go one divided by that. So one over X. So now I'm at 0.5. Then I go one minus that. So I make that number negative plus one. So now I'm at 0.49. I divide by 0.12 and I multiply by 10,000. So it's 41, 1, 1, 4, 41, 1, 1, 4. So looking at my, uh, uh, NPV, I have to put out $35,000 today, but the present value of those $10,000 cash flows is 41, 1, 1, 4. So overall I'm up 61, 1, 4. In our class, if the net present value is positive, we say, do it, go ahead with the project. It has a positive NPV. It is worth doing. That's what we would say here. If you want to do this maybe more quickly in a financial calculator, what I would do if you, if I was using the BA two plus is you enter cashflow. So you go CF. Oops. Uh, let me clear this out. I'd done this in preparation. So my cashflow at time zero is negative 35,000. I hit enter down arrow. My cashflow at time one is plus 10,000. And since all the cash flows are the same, I can use this frequency and I can say the other six of them. So I hit six enter. That's it. I've got all my cash flows in the calculator. I compute NPV. It says, well, what's your discount rate? My discount rate is 12 enter. I hit the down arrow and I hit compute again. And there it is 6, 1, 1, 4. And that's the number I had calculated by hand. So just to show you, you can do this by hand or, uh, in a financial calculator, IRR. I'm a believer. You're going to need a financial calculator. It's, I don't have the math chops, uh, to do this one by hand. Uh, maybe you do, maybe your instructor does IRR is calculating, solving for a rate. And what IRR says is what discount rate is needed to show NPV of zero. So we know it's got a positive NPV when our discount rate is 12, it's going to be a higher discount rate to show an NPV of zero. Meaning if our discount rate is lower than that, or, uh, then you know, if IRR is higher, uh, gives us a higher discount rate than the one in the question, uh, this is a project worth doing. In other words, the project's internal rate of return is higher. And we know the project internal rate of return is going to be higher because NPV was positive. So if NPV was zero, uh, what, uh, would the discount rate need to be to make NPV zero? Uh, how do I do that? Well, again, financial calculator, it's easy. You just go IRR compute, right? We got all our cash flows in it's 17.97%. So a required rate of return is 12%. The internal rate of return of this project is about 18%. Again, you would say, do the project. Um, and we'll see some curious examples where NPV and IRR give us, uh, uh, interesting results. Anyway, uh, the last one payback is the simplest payback. I think of ski pass math, maybe because I, I mean, I'm from Canada and I ski, uh, here's ski pass math in a nutshell. Uh, ski pass costs $1,200 at my local hill. Uh, or I can go just without a ski pass and it costs $100 per trip. So you go, okay, it's $1,200 for all you can eat, all you can ski pass, or it's $100 for a trip. Well, the ski pass pays for itself after 12 times, right? That's payback period math. The payback period is 12 ski trips. Well, the payback period here is it costs me $35,000 and I save $10,000 per year. What's my payback period? 3.5 years, right? This is ski pass math. Couldn't be simpler. And this is like early days when you're thinking about a project, this is back in the napkin math. And of course, the faster the project pays you back, the less risky it is. If the payback is 10 or 20 years, well, the world changes in 10 or 20 years. So you would generally think shorter payback means less risk for me. All right. And by the way, the thing about payback is you can see it does not take into consideration, um, the discount rate. Now there is such a thing as discounted payback, but that's for a future video. So there you go. The big topics of the week, payback period, very simple. IRR probably the trickiest. And the one that I, I do think you're going to want to use a financial calculator to solve or Excel or something like this and net present value, a core concept in any finance course. This one is going to be a key concept for you. All right. Thanks so much for watching lots of examples ahead. See you in the next video.