CF 6-5A – Crossover Rate – Corporate Finance

So let's have a look at problem six, five, a, an interesting question, and a lot of interesting math going on here. Uh, in fact, the math is challenging enough because it's a lot of calculating of rates. And when we calculate rates, I advise you to use Excel or a financial calculator. Doing it by hand is just trial and error. I'm not going to do anything by hand here. Everything is going to be in my financial calculator. So if you're not a financial calculator user, this might be of limited use to you, but in any event, it's still a good problem. Involved management is debating between two projects. The company does not have the capacity to do both and must choose the best option or neither. Cash flows for the projects are laid out in the table below, and there are some cash flows. Now this is the start, this type of question, let's just do some math here, uh, three 40. So I'm looking at project X three 40 negative plus 200 plus one 75 plus one 55. If we do the project just purely based on a cash basis without thinking of, um, time value of money, we end up at 190 grand and looking at project Y three 40 negative plus one 60 plus one 70 plus two 10. We end up $200,000 ahead on project Y just pure cashflow, just calculating the numbers, but time value of money matters. And the fact that you're getting a bunch of money early with project X and less with project Y and more project wise money comes in late and less than project X means even though project X has less raw dollars, it might be more attractive. So anyway, that's sort of important in these calculations. And what we'll find is if the discount rate is zero, in other words, there's no such thing as time value of money project wise way bigger, better if the discount rate is high, like 20%, for sure project X is going to be better because we're discounting the future cash flows and there's more future cash flows with Y. The question is what's that point where they cross over, right? What's the crossover rate? So that's the big question of the problem. That's the name of the game here. And we're going to figure that out. But before we can figure that out, we're asked the IRR to compute IRR. That's the point where a net present value of a project is zero. What is the rate at which the net present value is zero? We're going to enter these numbers into our calculator and compute IRR. Let's do it. So I clear, I go CF, second function, clear work, make sure there's nothing in there. CF. So CF at time zero, I'm doing project X now, 340,000 negative, enter. Down error cash flow at time one, 200 grand positive, enter. Frequency of that is one. I only have one $200,000 cash flow. So everything here, that frequency is going to be one, 175 for cashflow at time two, enter. Cashflow at time three, 155, oops, screw that up, 155, glad I caught that, enter. And then I just hit IRR, compute, and the IRR is very high, 27.3%. What's the IRR? Well, actually, before I do IRR project Y, I've got all those numbers in my calculator. Let's do the MPV at 10%, which is part two, assuming a discount rate of 10%. What's the net present value? It's going to be a big number and it's going to be positive. How do I know it's a big positive number? Because my IRR is 27%, if my discount rate's 10, it's got to be positive. If the IRR was 27% and the discount rate was 30, this would be a negative number. Okay, let's go ahead and solve. So I go MPV, the discount rate is 10, so I put 10 in as my I, hit the down arrow. I compute MPV, 102,900. Okay, project X in the bag, let's do the same thing for project Y. Click, click, clear, CF, second function, clear work, CF, 340 negative, enter. Cashflow at time one, 160, enter. Down arrow, down arrow, cashflow at time two, 170 positive, enter. Cashflow at time three, 210 positive, enter. Now I just had this sneaking suspicion. Did I put in my cashflow at time zero as a negative number? I did. Okay, so you can just hit up and down and go through your cash flows, but they're there. So I've got everything in. Now I want to compute IRR. So I just hit IRR, compute, 25.82%, I guess I'll just call it 25.8%. So a lower IRR for project Y, slightly. And well, let's see what the MPV is, the net present value. Is it also lower? I don't know. So I go MPV and it's the MPV at 10%. So I is 10, hit enter, down arrow, compute, 103, 726. Oh, interesting. So the IRR is actually 727. The internal rate of return is higher for project X, but the net present value at a 10% discount rate is higher for project Y. And just eyeballing this, it, as the net present value goes from 0%, you know, if we're just not the net present value discount rate, pardon me, goes with 0%. We really prefer project Y because it's 200 versus 190 at 10%. We still prefer project Y, but at some point, because look at the IRR, it's higher for project X, at some point, we're going to start to prefer project X. The question is at what discount rate do we switch from project Y to project X? In other words, it's climbing everything below 10%, certainly project Y, everything up to a certain number. We're going to like project Y better. At what point do we cross over? Here's how we do that. You subtract your two, you just find the difference between the two. So 340 minus negative 340 is zero. There's no difference. 200 minus 60, that's 40,000. 175 minus 170, that's 5,000. And 155 minus 210, that's negative 55,000. And we just enter these as cash flows into our financial calculator. So let me clear CF, second function clear. So I put them in as cash flows. So CF at time zero is zero using that one. Cash flow at time one, 40,000 positive. Enter cashflow at time two, 5,000 enter. And the cashflow at time three 55 negative enter. And now I'm going to compute the IRR of those cash flows, those differences in cashflow. IRR compute, and it's 11.18%. That's the moment we cross over. That's the moment we go from preferring project Y as we did for those first 10%. So we prefer project Y up to 11.18%. And then we cross over at 11.18%, we're indifferent. And once we're over 11.18%, we prefer project X. So that's the crossover rate, 11.18%. So just to draw this on a chart from 0% to 11.18%, we would pick project Y from 11.18% to I guess, 27.3%, we prefer project X and after 27.3%, we prefer neither. We would just say, don't do either. Cause we're losing money. Cause 27.3% is the internal rate of return of project X above that. The net present value is zero. In fact, above that it's negative 27.3% is where a net present value is zero. So above 27.3%, we would just not do either project. So the question goes on, is the interest rate increased above your answer in part C? No, in part, yeah, above 11.18%. So above your answer in part C, which project would you prefer? We would prefer project X. Why? Because it produces a higher net present value than project Y does at that level. And we sort of explained why in that little graphical chart I put on the bottom. Okay, folks, we've done it. Congratulations. Not an easy concept, but the math's not too bad. If you know how to use your financial calculator, I suppose. Thank you as always for watching. I really do appreciate it. I work hard on these videos for you. I hope they're helpful. And if they are helpful, I hope you'll give me a thumb or a sub. Have a great day. Thanks for watching. See you in the next one.