JAMES WESTON: 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 is a question that we ask of NPV. NPV, remember, our first capital budgeting tool was whether or not the present value of the cash coming in exceeds the 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 equal to 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 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 a crummy project. But if I can smash that NPV with a cinder block, 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 a measure of resiliency of the cash flows. The harder I discount, the more that drives down the NPV. How hard do I have to hit it and still stay bigger than 0? That's what IRR is designed to tell us. This decision rule is very similar to our net present value decision, as we'll see graphically in a few slides. What we're really going to do with internal rate of return is take the net present value, which was a nominal figure, and squish it into a percentage, which makes it more heuristically, naturally, intuitively, more appealing. I could tell you that the net present value of a project is 2,632. That number's hard to-- 2,632 million, 2,632 thousand? 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 intuitively, oh 25% is a good return. It takes that net present value and smushes it into a percentage, which is nice. We'll have to be cautious about doing that. But it's nice. It gives us a more intuitive and appealing 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 weighed against all of the cash flows coming in off the project in future years. 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 0? 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 it in Excel or in a spreadsheet model or on a financial calculator. They usually have IRR functions built in. 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 could 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 NPV 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 0. The point at which that crosses 0, the discount rate that sets the NPV equal to 0, is the IRR. Now look at what we've done. We've bisected the project into discount rates higher, where the NPV is negative, and discount rates where the NPV is 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's 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 smushed it into 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 that might be easier than saying the net present value is 1,613,672, which might be a hard number to figure out, because it's a big nominal number. And I don't really know what it means. But I tell you the return is 10%, you're like, 10% relative to a 5% cost on capital. That's a 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. 36 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 at 10%, discounted at 20% instead of 10%, that would give me a net present value of minus 336. So what must have happened in the middle? Somewhere that net present value crossed from positive to negative. If we solve it, that actually happens at exactly 16%. That's the trade off where discounting it hard enough, just to draw all the value out of it. It's actually a 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 says equals 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 root, sets it to 0, 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 equal to 0. Finding that 16% is relatively easy. To wrap up, internal rate of return is very similar to NPV. But it scales that NPV into a percent. 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 cost, 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.
