Welcome back to Finance for non finance professionals. In this video, I'd like to talk about using the Internal Rate of Return as a capital budgeting tool for deciding how to spend money within the firm. The Internal Rate of Return Earn is a question that we ask of NPV. NPV, you remember our first capital budgeting tool was whether or not the present value of the cash coming in exceeds that cash going out, the net of the present value of the cash flows. We're going to ask a slightly different question with the internal rate of return, we're going to compute an NPV and then we're going to ask what rate sets the NPV=0? And then our decision rule is we're going to invest if that rate is bigger than the discount rate we used to compute NPV. That sounds a little bit complicated, but it's actually kind of simple. What we're going to do is we're going to compute an NPV, and then we're going to smash it down. We're going to hit it hard, hard, hard with a higher and higher discount rate, and say, how hard do we have to smack down this NPV in order to drive all the value out of it. If all I have to do is hit that project with a feather and the NPV goes negative, that's kind of crummy project. But if I can smash that NPV with a cinderblock, a 20, 30% discount rate and it's still got a positive NPV, that's a good project. And so internal rate of return is saying, how hard do I need to smash down the cash flows in order to drive the value out of the project? So it's sort of a measure of resiliency of the cash flows. Okay, the harder I discount, the more it drives down the NPV. How hard do I have to hit it and still stay bigger than zero? That's what IRR is designed to tell us. Yeah, this decision rule is very similar to our net present value decision as we'll see graphically in a few slides. What we really going to do with internal rate of return is take the net present value which was a nominal figure and squash it into a percentage, which makes a sort of more heuristically, naturally, intuitively more feeling. I can tell you that the net present value of a project is 2,632. That number's kind of hard to, 2,632 million, 2,632. It's hard to think about nominal numbers, for all of us. If I tell you the internal rate of return on the project is 25%, it's easy to sort of intuitively, like, 25%'s a good return. It takes that new present value and smooshes it into a percentage, which is nice. We'll have to be cautious about doing that but it's nice. It gives a more intuitive, appealing sort of take on the NPV of the project. Let's think about the IRR in formulaic terms. When we had our net present value formula, the NPV was equal to the initial cost Weigh it against all of the cash flows Coming in all of the projects in future years. Yep, that was our formula for the NPV. All we're going to do now for IRR is we're going to take that exact same formula, the Initial Cost. And instead of adding up the cash flows, we're going to add on the cash flows instead of using r, the discount rate. I'm going to replace that with IRR. And I'm going to set that equal to 0. And now I'm simply going to say, what rate sets that equal to zero? And all we have to do is solve for the IRR. And the spreadsheet's going to help us do that. It's hard to do that with pen and paper, but it's easy actually to do in Excel or in a spreadsheet model or on a financial calculator. They usually have IRR functions built in. Okay, and so now we're going to solve this polynomial equation for the IRR and that's going to tell us if I had smacked down the cash flows, at what r would it drive all the value out of the project? We can think about this relationship graphically. So, if I think about a project that's got positive NPV if I don't do any discounting. So what I'm going to do is I'm going to graph the value of the net present value, how big the MPV is, against how hard I'm smashing it down. The discount rate. As I smash that cash flow down, that NPV down with higher and higher discount rates, that NPV is going to come down until at some point, it crosses zero. The point that which that cross is zero, the discount rate that set the NPV equal to zero is the IRR. Now look at what we've done. We've sort of bisected the project into discount rates higher, where the MPV is negative and discount rate were the MPV positive. If my discount rate for this project really ought to be here. Let's say this is 5% and my IRR is 10%, what is the IRR rule really told me? What it told me is, look, any time the discount rate is below the IRR. It's a positive NPV project. So in a sense IRR is just like NPV, except that I've smooshed it in to a percentage place, where the discounting just turns it negative. And so that gives us a nice, because now I can say, hey, the return on this project, the IRR is 10%. And not might be easier than saying the net present value is 13672, which is might be a hard number that sort of figure out because its a big nominal number that are really know what it means. But I tell you the return is 10%, here I call, 10% relative to 5% cost the capital that to good project. That's what IRR does for us. We could think that through in terms of a simple example. Let's say, I were spending $9,364. In order to generate cash of 10,000 in year one and 1,000 in year two. If I didn't do any discounting at all and just added up the cash flows, that would be 1,636. If I discounted the cash flows at 10%, I would discount the 10,000 back one period at 10%, discount the 1,000 back two periods at 10%. Give me a net present value of 553. If I instead of discounting a 10% discounted it 20%, instead of 10%, that would give me a present value of -336. So what must had happened in the middle somewhere that the present value of pros from positive to negative. If we solve it, that actually happens at exactly 16%. That's the trade off were this counting of hard enough to draw all the value out of it. It's actually really easy thing to do in excel, if I take the example that I just showed you and look at those cash flows, take the present value of those cash flows. Again, discounting the 10,000, discounting the 1,000, computing the net present value, summing them all up to get 553, all I have to do in excel. Is say, =IRR go and grab that set of cash flows right there, which is what the cell is doing right there and built into Excel is an easy IRR function, and so it spits it right out. It solves that polynomial equation, finds the route, sets it to zero, and spits out the 16% for me. So It can be conceptually difficult to think about solving big equations that have lots of roots, but Excel does it for us solving that setting that NPV to zero. Finding that 16% is relatively easy. Okay. To wrap up Internal Rate of Return is very similar to NPV, but it scales that NPV into a %. It's a more intuitive measure because it gives us a sense of what kind of rate of return the project is yielding, and it accounts for the timing, the opportunity costs, and the risk of the project in a very similar way to what NPV does. So IRR is one of our good capital budgeting tools. We should always compute it, alongside of our NPV.