FIN 42 IRR, NPV and Crossover Rate

Let's examine problem 668. We're calculating IRR, we're calculating net present value, but the real key topic of this question is that of the crossover rate. So let's read the question and see what we are up against. Elevate Enterprises is debating between investing in two separate projects. Both have an initial cost of $75,000. The company does not have capacity to do both and must choose the best option or neither if NPV or IRR is negative. Cash flows for the projects are laid out in the table below. And so there's our table. I guess the one cash flow, I guess at time zero that isn't included in the table is that they both cost 75,000 bucks. Before I get into it, I always like eyeball the cash flows of the project. I do almost like a payback of it. And I sort of say, does this pay back? And if so, over what time period? So 40 plus 30 plus 20 plus 10, it's 100,000 positive to go against 75,000 negative. So this one, you add it all up, you're plus 25, not considering time value of money. And this side, 10 plus 20 plus 30, it's 105 versus 75. So this one, you're plus 30. And so you think, well, maybe project B is just better because you're 30,000 to the good where project A you're only 25,000 to the good. And that would be the case if there was no discount rate. If there was no such thing as time value of money, project B all day, it would be the winner. However, the fact is project A's cash flow is largely upfront and project B's largest cash flow is backloaded. And so the time value of money is going to become a factor. At 0% discount rate, it's project B, but at a large discount rate, it's going to be project A. You want your money upfront when interest rates or discount rates are high. So the question is, at what point are we indifferent? At what point do these rates crossover? So that's a million dollar question. But before we get to it, it asks us to compute the IRR of both projects. We'll do IRR of project A now. So I enter CF at time zero, 75 grand negative. My cash flow at time one gets entered as 40,000 positive. Cash flow at time two, 30,000 positive, enter. Cash flow at time three, 20,000, enter. And cash flow at time four, 10,000, enter. And now I compute the IRR. I hit IRR, compute 16.09%. So change my ink color here. IRR 16.09%. And we'll also compute the net present value at 9% discount rate. By the way, we're expecting this to be positive because the IRR is 16%. The net present value discount rate is 9%. It's going to produce a positive net present value. Let's figure out what the net present value is though. I go NPV. My discount rate goes in as nine, enter. I hit the down arrow. I compute NPV, nine, four, seven, six. Okay. So project A, we've done parts A and B. Let's do the same for project B. Let's compute the IRR of project B. 75,000. Oh, sorry. Let me, CF, sorry. Second function clear, clear, clear, clear. So I just wanted to clear everything else that had been in there before. 75,000 negative goes in at CF at time zero. My cashflow at time one is 10,000 positive. Cashflow at time two, 20,000 positive. Cashflow at time three, 30,000 positive. Cashflow at time four, 45,000 positive. And now I compute the IRR. So I go IRR, compute 11.91%. So significantly lower for project B than project A. If I were using IRR, which project would I prioritize? Definitely project A would be my answer to part A. Assuming 9% required rate of return, compute the NPV. Well, we've done it for project A. Let's do it for project B. NPV, I put nine in as my discount rate. I hit the down arrow. I compute NPV, 6052. So using NPV as a threshold, I like project A better also. NPV at 9%. So now the million dollar question, the whole purpose of this question was, you know, a little bit of practice for a net present value in IRR, but what is the discount rate where you'd be indifferent between the two? The way you figure this out, you subtract, you just figure out the differences between the two. So the 75,000 to 75,000, there's no difference there at the cashflow at time zero. 40 minus 10 is 30,000 positive, 30 minus 20, 10,000 positive, 20 minus 30, 10,000 negative, and 10 minus 45, 35,000 negative. We enter these all as cashflows and we calculate the IRR of this. This will be our point of indifference. This will be where we're indifferent between the two options. So let's do that. CF, second function clear work. CF at time zero is zero. Cashflow at time one, 30,000. Cashflow at time two, 10,000. Enter the down arrow twice. Cashflow at time three, 10,000 negative. Cashflow at time four, 35,000 negative. I compute the IRR. I had IRR compute 4.77%. Okay. Now we can take a bit of a step back. What's happening here? Project B, if there was no such thing as time value money, if our interest rates were zero, project B returns us 30 grand, project A 25 grand. We like project B at zero, but we saw at 9% we way preferred project A. So at what point did we go from preferring project B to preferring project A? The answer is at 4.77%. So the discount rate was zero all the way up to 4.77%. We like B. From 4.77% onwards, we like A all the way up to the point where A goes to its IRR. Anything above 16.09%, that's where the net present value of A is zero. Anything above that, the net present value of A is negative. We don't like it above that. We're not going to take either. So above 16.09%, from 16.09% to infinity, we would choose the option neither. Don't do any of these projects because they're money losers. So there we have it. We've answered part A, B, C. We've got the crossover rate of 4.77%. D says calculate the range of discount rates where you choose project A. There it is, 4.77% to 16.09%. Where would you choose project B? Everything up to 4.77%. And where would you choose neither or reject both? Anything above 16.09%. We've done it. We've made it to the end. You survived. A challenging topic, crossover rates, but an interesting one. I hope the video helped. And if it did, I hope you'll help me with a thumbs up. Thanks for watching. See you in the next video. Bye for now.