Hi, the last technique to learn in this module is called Internal Rate of Return, or IRR. The IRR is defined as the discount rate that makes NPV of the project exactly zero. The definition is not so easy to understand, right, the discount rate that makes NPV zero. First of all, we need to understand that IRR is not the actual discount rate of the project. In previous examples, we were already given the actual discount rate of the project when we calculated the NPV. 20%, remember? In real world problems, a project's discount rate is estimated mostly based on project level of risk and that is the rate we use to calculate the NPV. Then do we have another rate here? Yes, the IRR is the hypothetical rate which would have made the NPV of the project zero, if the discount rate had been equal to IRR. To better understand the concept, lets think about the relationship between NPV and the discount rate. Do you remember what the NPV was for the project in our example? Yes, it was $113.63. But please let me rephrase it. The project’s NPV is 113 when the discount rate is 20%. If we have to change the discount rate because, for example, we just realized that the project is riskier than we thought, will the NPV of the project change as well? Yes, because NPV is a function of the discount rate. Let's say the new discount rate is 25%. Now, will the NPV be higher than the current NPV or lower than the current NPV? As you see, the NPV decreases as the discount rate increases. This is because future positive cash flows are more heavily discounted under the higher discount rate and that negatively affects the NPV. What if the discount rate decreases? Now, we have got a higher NPV than the original one. Future positive cash inflows are now less discounted under the lower discount rate. To summarize, the NPV changes as the discount rate changes. This table shows possible NPVs of the project in our example under different discount rates. Remember that our actual discount rate is 20%. In this table, you can see that the NPV decreases as the discount rate goes up. It's getting smaller and smaller and even becomes negative when the discount rate is 24%. That means between 22% and 24% there should be the point where the discount rate would make the NPV of the project exactly zero. The rate which makes the NPV zero is the definition of the Internal Rate of Return, or IRR. For this project, if the discount rate were 23.8% that would give us the NPV of zero. That is, the IRR of this project is 23.8%. But remember, in this example, the actual discount rate is still 20% no matter what the calculated hypothetical IRR is. So how do you find the IRR using Excel? In Excel, we use the function named IRR to calculate IRR. We have only one input for the IRR function which is the range of cells where you have cash flows of the project. Unlike the NPV function, we include all cash flows starting from the cash flow in Year 0 with the IRR function. So we can just select all cells with cash flows when using the IRR function. This time we should include the initial cash flow in cell C5. The IRR is very easily calculated in Excel. The IRR is 23.8%. So what does this number tell us about the project? The decision rule of IRR is that we accept the project if the IRR is greater than the actual discount rate. IRR can be interpreted as the average annualized rate of return of the project. In the previous example, the project is expected to have the annual rate of return of 23.8%. On the other hand, the actual discount rate is the hurdle rate required by investors or the owner of the firm. Given the level of risk of the project, they demand that the minimum acceptable rate of return from a project should be 20%. If the project's rate of return is expected to be higher than the hurdle rate, we should accept the project. Now it's time to ask the three good decision rule questions. First, the IRR rule not only considers the time value of money but also adjust for risk. From the case of NPV, we have learned that the use of the discount rate r, implies that the rule considers both the time value of money and risk. Although we do not use the discount rate in IRR calculation, we do use it when making a decision by comparing the calculated IRR with the discount rate. In that sense, we could argue that the IRR rule also considers both the time value of money and risk. Okay, then how about the last question? Does the rule let us know whether the project creates value for the firm? The answer's no. IRR is just a measure of the rate of return and does not tell us about the amount of value that the project will create. Finance professors argue that IRR is the most important alternative to NPV. First, knowing the rate of return of a project is intuitively appealing. The NPV analysis let us know the dollar amount of the value of the project, $113 for example. However, many corporate managers would also want to know the profitability number as well. Such as the rate of return of 24% per year. Second, if the calculated IRR is high enough, it becomes obvious that the IRR will be greater than the actual discount rate, whatever the number should be. In this case, you may not need to estimate the discount rate which is, in the real world, a difficult and time consuming process.