FIN 38 Payback Period and Discounted Payback Period

In this video, we're going to work on a problem you can download from TonyBell.com. Go to the website, click the PDF link, and you'll notice there's no sign in, no sign up. The PDF just pops right up. You'll scroll down and find whatever problem it is that we're working on. As you scroll through the problems, you'll notice many are free and open, like the one you're watching now, but some are members only. I think the free and open ones are enough for most people, but if you can't get enough of me and you'd like to join and get access to those members only videos, click the join button underneath the YouTube play box. All right. Thanks so much for watching. Let's get started. Let's examine problem six one, a payback period. When I think of payback period, I think of like gym memberships, or for me, I ski, I'm from Canada, so we have good skiing nearby. And here's my ski pass situation. It costs a thousand dollars to buy a ski pass to my local hill. It also costs a hundred dollars if you just want to buy a ticket for the day. So the math is pretty simple. I say to myself, if I'm going to ski more than 10 times, I'm getting my money's worth out of the pass. In other words, the payback period for the pass is 10 ski trips. We all have these types of things, and it's a very basic, I consider it a back of the napkin calculation you can do. And companies do it on their projects. They go, okay, well, this project costs us this much, but this is how much it's going to bring in. How soon does it pay itself off? Right? How, how much do I need to use the project or whatever? How many years does it take to pay the thing off? So that's what we'll look at with problem six, one, a, a payback period. So horizon strategies is considering a project with the falling cash flows. It costs us 60 grand up front and you can see the paying back over time. So the question is how long until it pays back? And the way I do this is I just do a running total. So I go, okay, after year one, I'm minus 60,000 after year two, well, minus 60 plus 20. I'm still minus I'm minus 40,000, right? It was minus 60. I've made 20 grand, but I'm still in the hole on the project. After year three, I'm still in the hole by 10,000. After year four, I go positive. I go to 5,000. So I can stop there. Once I've gone positive with my little running total here, we can figure out the payback period. So it takes us one full year there. We still haven't paid back two full years here. And then sometime in year three, we pay back because we go positive. Now the math here is fairly straightforward. You just go, well, um, I was $10,000 behind and I'm going to make $15,000 this year. So you take this number, divide by that number. So you go, okay, well, it's $10,000 is what I needed to make up. And that year I make 15,000. So it's 0.667. So how many years is it going to take me one full year, two full years, and then two thirds of year three to break even. So my payback period is 2.667 years. Okay. And again, you would be evaluating this against other projects, right? You have more projects typically than you have resources to do them. And so you'd say, well, this is, you know, 2.67, you know, if all the other projects are taking four and five years to pay back, you'd say, oh, this is a pretty safe project to tackle. But something that is lost here because it's such a simple calculation is the time value of money. The fact that these future cash flows, uh, they, they are, you know, money in the future is not the same as money today. So part B says, well, why don't we discount those cash flows? So I'm going to move, uh, and erase this stuff and actually I'm going to erase everything and just sort of start over. I trust you can rewind if you need those numbers and we're going to do a discounted cash flow. So how do I discount them? Well, it's a 10% discount rate. The first number, well, you divide by 1.1 to the power of zero, which of course is just dividing by one, this one divided by 1.1 to the one, because it's a year from now, this one divided by 1.1 to the power of two divided by 1.1 to the third power divided by 1.1 to the fourth power, then divide by 1.1 to the fifth power. And we're going to figure out what our discounted cash flows are. So again, uh, 60,000 divided by 1.1 to the zeroth power is just 60,000 divided by one. You can see I did it in my calculator there. And so it's 60,000 and of course, $60,000 in today. That's what it is in today's dollars. 20,000 divided by 1.1 to the first power, 20,000 divided by 1.1, 18, 182, that's positive. So the first one I put a little negative, it might be hard to see there, but I did squeeze a negative in. This is a positive number. Every other number here is a positive cash flow. Uh, 30,000 divided by 1.1 squared. So 1.1 squared, I go one over X times 30,000, 24,793, 24,793, 15,000 divided by 1.1 cubed, 1.1 to the power of three, one over X times, uh, 15,000, 11,270, 8,000 divided by 1.1 to the fourth power 1.1 to the power of four, uh, 8,000 divided by that. So one over X times 8,000, five, four, six, four, and 4,000 divided by 1.1 to the fifth power for a 1.1 X five, and then one over X times 4,000 times 4,000. Okay. So finally I've got my numbers two, four, eight, four. Now, just as I did last time, I'm going to want to do a running total, but this time with the discounted cash flows to figure out, well, using only discounted cash flows, how many years or periods does it take me to kind of come out even or come out ahead? Uh, so negative 60,000 plus 18, 182. So 60,000 negative plus 1, 8, 1, 8, 2. After one year here, I am still in the hole minus 41, 8, 1, 8. Uh, let's add 24 grand to that plus 24, 7, 9, 3. After two years, I'm still in the hole minus 1, 7, 0, 2, 5. I'm digging myself out of this $60,000 hole I've made for myself plus 11, 270 plus 1, 1, 2, 7, 0. So after, uh, uh, three years, I'm still in the hole minus 5, 7, 5, 5. And after four years, you can see I'm still going to be in the hole plus, uh, 54, 64 minus 2 91. And so it's not until sometime in year five that I climb out of this hole 291, uh, negative plus 2, 4, 8, 4 positive is 2, 1, 9, 3. Okay. So I go positive in the fifth and final year. So it's going to be four point something years, right? Because I got one full year, two full years, three full years, four full years being negative before I finally go positive. You take 2 91 divide by, uh, the discounted cashflow of that year to figure out which fraction of the year you're going positive in. So 2 91 divided by 2, 4, 8, 4 says 0.117. So let's call it 0.12. So 4.12 years, we're being overly precise for something that's going to happen four years from now. Will it be exactly 4.12 years? You know, 0.1 of a year is whatever a month or something like that. A little bit. It's about a month, four years in one month, you know, it's maybe a little overly precise when we're making projections that far into the future, but that's how you do it. So we've solved the problem, uh, using the discounted, uh, cash flows. It's going to take us 4.12 years to, uh, uh, pay back. Right. And so that's, that's useful information to have, right? The time value of money becomes highly relevant. You know, the numbers were sort of manipulated to make that the case with our lower cash flows later. So that's, that's why that's happened that way, but it's, it's a useful calculation, a useful tool to have in one's toolkit. I hope this video was useful to you. I hope it was a use. I hope I was a useful tool. No, that doesn't sound right. I hope the video was useful to you. Have a great day. Thanks for watching. See you in the next video. Bye-bye.