IRR (Internal Rate of Return)

In this video, I'm going to be talking about IRR, otherwise known as the Internal Rate of Return. Now, the Internal Rate of Return is a way of evaluating a project and coming up with a decision to accept or reject that project. Okay, so this is very similar in a way to NPV. Now, when we think about NPV, we think if the NPV is greater than zero, then accept. That's the that's our decision rule. So IRR is kind of related in that sense and that ultimately it's going to lead to a decision rule. But first, in order to understand what IRR is, let's kind of work a problem here with NPV and then show how we do it with IRR. So let's say that we've got some project. So we've got an example here. We have a project and this project is going to be a one-year timeline. And at the beginning of year zero, right now, we're going to have a cash outflow. We're going to invest $100. So that's a negative $100. And then at the end of year one, we're going to receive a cash flow of $130. So this is a very simple project here, paying out $100 and then getting $130 back at the end. Now, in order to calculate this with our NPV, the other way, holding off IRR for a second and thinking about NPV, we're going to need to know the discount rate. Okay, little r, we'll call that. And so let's just say that the discount rate, let's say it's 8%. Now, I'm just briefly going to go through how we would do this under NPV and refer to the NPV video. If you haven't seen this yet, the NPV is going to be negative $100, that cash outflow, plus $130. But we're going to take that over one plus r, one plus that discount rate. And we need to do that because of the time value of money. So ultimately, the NPV, this is going to be 130 over 1.08. With this 0.08, that's just that 8% discount rate, we're converting it to a decimal and adding one to it. And ultimately, this is going to give us a net present value to this project of $20.37. So now if we think about our decision rule, well, is this greater than zero? Well, yes, it is. So then according to the NPV, you would accept this project and go ahead with it. But let's think about IRR now. Well, how is IRR different from NPV? Well, ultimately, what we're going to do with IRR, let me just say IRR, make this clear. I don't want you getting confused. So with IRR, we are going to set the NPV equal to zero. We're going to set the NPV equal to zero. So then we're going to still have that negative 100, the cash outflow, that thing from here, that's still coming down. And then we're going to have 130 over, and this time, I'm going to have one plus, but I'm going to put big R instead of little r. We're still going to have little r, little r over here being our 8% discount rate. You say, okay, well, what is this big R then? What is the difference between big R and little r? Well, what we're going to do is we're going to try and solve this and figure what is the big R that we would have to plug in that would make this equation so that the NPV is equal to zero. And then once we've determined what R is, we're going to take R and compare it to that 8%, and that's going to be our decision rule. So let's go ahead and let's just solve this for a second. So ultimately, we're setting the NPV equal to zero, and then we're solving for the R that would make this equation true. So ultimately, you can do some algebra here, but you'll end up with an R that is equal to 0.30. I'm going to say because we're going to convert that to a percent, just so we can easily compare these two. So we've got the big R is 30%, and then the little r is 8%. So what does that tell us? Well, we know that 30% is greater than 8%. Okay, what does that tell us? Well, if the big R, our decision rule, if big R is greater, if big R is greater than little r, then accept. That's our decision rule. Now let's think about what this means here conceptually. What we're trying to do is we're saying, okay, the NPV, we're ultimately going to say that's kind of our break-even point, so to speak, because when the NPV is zero, what does that mean? That means that wealth is neither being added nor destroyed at the firm, because you're just earning this opportunity cost however we want to think about it. You're just getting that 8%. So this NPV, when it's zero, that's our break-even point. And we're saying, what return would we have to have? What big R would there need to be in order to get the NPV to equal zero, to get to that break-even point? And we see that, okay, well, we have a return there of 30% would make the NPV equal to zero. And then we say, okay, well, let's compare that, let's compare that 30% to what our opportunity cost of the capital is or our discount rate, however we want to think about it, and let's see if it's larger. And then we look and we say, okay, clearly the answer, yes. So ultimately, we can think of IRR is the discount rate that makes the NPV equal to zero, that makes NPV equal to zero, to get us to that break-even point. We just ultimately say, instead of calculating the NPV directly, which we did under the NPV decision rule, we're just going to set NPV equal to zero, and then solve for the R, the big R, that would make this equation true. We find that big R that makes the NPV equal to zero, compare it to our discount rate, and if it's greater, then we accept the project.