[MUSIC] We just learned the concept of IRR, the rate of return of an investment. Right? Now we know how to calculate it, and we just did it for this specific example, the investment that requires 10,000 today, and then produces a yearly cash flow of $500 in perpetuity, okay? So, with a growth rate of 4%. In that case, we calculated an IRR of 9%. The question now is should we invest in this project or not, right? We know it has a rate of return of 9%. How do we know if we should make this investment or not, right? The answer is that you don't have enough information. Okay, to figure out whether a project is good or not we are also going to need a discount rate. All right, when we computed net present value for example, we needed the discount rate to discount the cash flows, right. And so now we also to make a decision using IRR, we're also going to need a discount rate, okay. An idea that it really is very intuitive it should make sense to you, is that in our case, we would invest in the project if the discount rate turns out to be lower than 9%, right? So you should think of the discount rate as the required return on a project, right? The discount rate is the minimal return that the project would need to have for the project to be a good project. On the other hand, the IRR is the actual return on the project. Okay? So if the IRR is bigger than the required return, if the IRR is bigger than the discount rate, that means this is a good project. Okay? We think of these as the IRR rule. The IRR rule says that you invest in a project if the rate of return is greater than the discount rate. That's what we think of as the IRR rule. Let's do an example here. Let's go back to our simple investment, which has an IRR of 9%. And now let's assume that the discount rate is 8%. Okay? Let me actually go over here. The discount rate is 8%. Okay? So the IRR is 9%, the discount rate is 8%. Okay? So that means this is a good project. Okay? That means this is a good project. Right? The IRR is bigger than the discount rate. Ask yourself what should be the net present value then? We just learned about NPV and we learned that when a project is good, the NPV should be positive. So in this case we know that even though we didn't compute NPV yet, we know that the NPV should be positive. Consider now a different case where the discount rate is 10%, okay? So now let's have a discount rate of 10%. You should be able to do this very easily, right? Since the IRR is lower than the discount rate, right? What should you do? You should not invest in that project. Right. So the answer is that this is a bad project, okay. This is a bad project because the discount rate is bigger the IRR. What should be the NPV, the NPV should be negative in this case. Okay? If we want to check that, of course what we could do is just to go ahead and compute the NPV. Right? Which is what I've done here. Okay? And I recommend that you go out and really try to do this calculation on your own. Compute the NPV, okay? And you will find out that this the discount rate is 8%. The NPV is 2,500 okay? If the discount rate is 10% the NPV is minus 1,667 okay? So this shows that if the discount rate 8% the NPV is positive. If the discount rate is 10% the NPV is negative. So here comes the question for you. There is a very important lesson here, there is a pattern, there is a general result that lies hidden in these number here. Not that hidden but I want you to think about this question and try to generalize you know what did we learn by doing this calculation. This is what we learned, okay? Another very important set of rules, okay? If the NPV is positive, right? So if a project is good, if it increases shareholder value, if the NPV is positive, these are all the same things as we've just learned. Then the IRR should be bigger than the discount rate. These statements are equivalent. Okay. Positive NPV, IRR bigger than the discount rate, good project, project that increases shareholder value, all of these are equivalent. Same thing for a negative NPV. Right? If an NPV is negative, then what this means is that the IRR is lower than the discount rate. And this result is great, because what this means is that you can use either NPV or IRR. So if you compute IRR of a project and you know the discount rate, you're going to get it right. You're gonna make the right decision. So maybe we don't even need to compute NPV, we can just compute IRR and compare the IRR with the discount rate. As we're going to learn next, this is actually not true. There are some cases where we're going to have problem to compute an IRR. That's our next lesson.