CF 6-8A – Comprehensive Calculations – Corporate Finance

Let's examine problem 688. This has us doing lots of calculations. It's a great practice question because you've got to do payback period, you got to do net present value, you got to do profitability index, and you've got to do IRR, internal rate of return. This is a kitchen sink type of a problem, but it's a nice sort of summary problem for most of the things we've learned this chapter. So the question says Vertex Business is debating between two projects. The company does not have the capacity to do both and must choose the best option or neither. The company's required rate of return is 19%. Cash flows for the projects are laid out in the table below. And the first thing we're asked to do is to compute the payback period, which is the simplest, I consider this back of the napkin calculation, where we just go, how many years does it take for this project to pay off? So this one that costs us 240, well, we make 110 up in year one, so that means we're still at minus 130, right? Just negative 240 plus 110 is minus 130. Minus 130 plus 100, okay, we're still $30,000 in the hole after two years, but we come out of the hole sometime in year three, because we go from negative 30 plus 80, we go to plus 50. So we can stop when we go positive. That's, you know, you don't need to keep doing a running tally. So we took one full year to come out of the hole. We took two full years to come out of the hole, but we didn't take the full third year to come out of the hole. We had 30 grand that we needed, and we made 80. So it took us a partial year, 30,000 divided by 80,000. It took us about 0.375 of a year. So the answer here is 2.375 years. That's how long it took us to pay back, 2.375 years, and this is project two. Let's do project one. I'll do it in blue ink. So again, we're 700,000 down. We make 90, so we're 610 down. We make 180, so we are, what is that, 430 down. We make 190, so we are 240 down, and then we, sorry, these are negatives. We make 800, so we are like 560 up, and that's where we go positive. So it's one, two, three years plus a partial last year. We had 240 to make. We made 800, so 240 out of 800 is 0.3. So it's 3.3 years for project one. So what would you rather take to pay back your project? Two years or three years? 2.3 years or 3.3 years? You'd rather your project pay back faster. So definitely a check mark on the side of project two, which is better, project two for sure. Okay, let's do net present value. Now, to do net present value, I'm not going to do by hand just because we've got our financial calculator, but I'll show you how to do it by hand. I'll show you the calculations I would do for project two. So you divide, so you've got to discount your cash flows. That's the thing with a payback period. There's no discounting of the cash flow. So that's why we call it back of the napkin math, because it's rough work. But here, this 19% discounted cash flows, right, is our required rate of return is big here, 19%. It's going to make a huge difference. So you divide, to discount the cash flows, you divide by one plus the discount rate, 1.19, to the power of however many years you want to discount the number. In this case, it's zero, 1.19 to the power of one, divide by 1.19 to the power of two, divide by 1.19 to the power of three, and divide by 1.19 to the power of four. Now, 1.19 to the zero is one. I'm not going to do these all by hand. 1.19 to the zero is one. So 240,000 negative divided by one is 240 negative. You don't need to do that step, right? I just was showing you how it works. So there's our cash outflow. I'm going to do the present value of all of these cash inflows in the financial calculator. You can just do it, like you can add them up, you know, do the math, add them up. I'll do it in the financial calculator, save us all some time. So cashflow at time zero, I'm going to just put in a zero because we've already dealt with it. Cashflow at time one, 1.10, enter cashflow at time two, 100, cashflow at time three, 80, and cashflow at time four, 70. So I'm going to compute the net present value. My discount rate is 19. Hit the down arrow, hit compute, 245,433. Now, again, you could have done this by hand and you can do it all in one step. The reason I've separated it into two steps is having the inflow and the outflow is really useful for profitability index. So I'm sort of thinking ahead to part C. You could have put all the numbers in here and NPV'd it and you would have got 245 minus 240. You would have got 5, 4, 3, 3, which is our net present value. 5, 4, 3, actually 5, 4, 3, 4. So this is a four because I should have rounded up. 5, 4, 3, 4 is our net present value of the project. The present value of the cash inflows minus the present value of the cash outflows. Let's do the other side. So I'm just going to do the inflows again, because it's useful for profitability index in a minute. So let me clear my work here. Cashflow, second function, clear. So cashflow at time zero, I'm not dealing with. Cashflow at time one, 90,000. Cashflow at time two, 180. Cashflow at time three, 190. And cashflow at time four, 800. All right. So NPV 19 is my discount rate. Hit enter, down arrow, compute NPV. 7, 1, 4, 4, 2, 4. That is my present value of the cash inflows. Present value of the cash outflows is negative 700. So what's the net present value? Just combine them. It's 14, 4, 2, 4, right? 7, 14 minus 700 is 14. 14, 4, 2, 4. So a pretty big win for project one, leaving me better off here. Okay. Compute the profitability index of each project. Now, because I split out my calculations the way I did, this is easy. You just divide the infos divided by the outflows. So divide 245 by 240, divide 714 by 700. So let's do the 714 divided by 700, 1.021. So that's part C. And 245 divided by 240, 2, 4, 5, 4, 3, 4 divided by 2, 4, 0, 0, 0, 1.023, 1.023. Okay. So what would you prefer? Well, it's close, but definitely project two is slightly better than project one, as far as profitability index goes. Next we do IRR. So we're going to enter our cash flows again. Now, if I could do a shortcut and sort of use the ones that are in memory, but I've cleared my memory to do this from scratch. I'll do project one first. 700,000 negative is my cashflow at time zero. So I do enter my time zero cash flows here. Cashflow at time 190. Cashflow at, and this one, there's no way to do it by hand. All the other ones I could have done by hand just as easily. It'd taken me two more minutes or maybe five more minutes, but you can definitely do it. This one, you just can't do by hand. Well, it's not easy to do by hand. Let's just put it that way. Cashflow at time 2, 180, cashflow at time 3, 190, and cashflow at time 4, 800. And now I compute the IRR. So I hit IRR, compute. I get 19.77%, 19.77%. And that's my answer to D. And by the way, the fact that the required rate of return is 19, this is 19.77. We'd say this is a project you can go ahead with. And that should be clear because it had a positive net present value. Okay. I'm going to re-enter some cash flows. So clear what's in there. And I'm going to enter the cash flows for project two. 2, 4, 0, 0, 0, 0, negative, enter. Cashflow at time 1, 110, enter. Cashflow at time 2, 100, enter. And remember the F that I'm sort of skipping past is frequency. And because these are cash flows that only occur once, the frequency is one, and that's the default. So I'm just skipping right past it. 80,000 for cashflow at time 3 and 70,000 for cashflow at time 4. And then I go IRR, compute, and I get 20.28%, 20.28%. So who's the winner here? Well, it's definitely project two is the winner here. So this is a weird question and it's framed kind of weirdly too. If we trust all these numbers as being equally true and, you know, if there's a hundred percent chance that this is all going to come to pass, because we're predicting the future here. Believe it or not, based on my answers above, I would choose project one. That's how powerful net present value is. How much money are you making, right? And if the answer is, well, these are mutually exclusive projects, I can only do one at a time. Maybe it's my staffing capabilities or my personnel. I would say do the one that makes you the most net present value. So that's how powerful net present value is. That's why it's such a fundamental corporate finance concept. Despite the fact that the payback is slower, the profitability is slightly lower, the IRR slightly lower. It's a riskier project, but I would still say if these numbers are trustworthy, I would pick project one. So a little bit weird, right? There's three check marks on this side. There's only one on that side. Shows you how powerful net present value is. Hard to go against net present value. You would need really good reason to, and this question hasn't given me sufficiently good reason to go against it. I would pick project one because it offers a higher net present value. Simple as that. All right. Thanks so much for watching. If this video helped, as always, you really do help me by hitting that thumbs up button. It tells the YouTube algorithm I'm doing good work and I hope it's good work. Anyway, thanks for watching. See you soon. Bye for now.