In this lecture, we will first learn the definition of NPV, the most popular capital budgeting technique, and then study how to measure a project NPV using Excel. NPV is defined as the difference between the present value of cash inflows and the present value of cash outflows of the project. As you can see from its definition, NPV is measured in dollars. Also it can be either positive or negative, depending on whether the benefit of the project outweighs the cost of the project. Finally, you should remember that we need to know the discount rate to calculate NPV. Because we use the discounted cash flows in the calculation process. If we use a formula, we could write the definition of NPV as follows. Here in the formula, we measure the NPV of a project that has the life of n years. Note that cash flow in year zero, CF0, doesn't have to be discounted while all other cash flows in the future from CF1 to CFN are discounted using the discount rate r. In previous courses, you learned that the discount rate, r, is determined based on the risk of the project. That is, cash flows from a risky project should be discounted using a high discount rate. Next, about cash flows. Of course, the cash flow in any given year, can be either positive or negative. However it is also true that many projects have conventional cash flows. We say a project has conventional cash flows if the initial cash flow of CF0 represents a relatively large cash outflow and all other future cash flows are cash inflows. This is pretty standard form of the stream of cash flows of a project. Because many projects, in reality, requires a huge initial investment at the beginning and will bring that cash inflows in future periods in return. So let's try to calculate the NPV of the following project. This is a project with a life of five years, and it has conventional cash flows in a sense that only the initial cash flow of CF0 is negative. Also after examining the risk of your new project, you concluded that the appropriate discount rate for this project is 20%. Now it's time to calculate the NPV to see whether this project is a good one. In Excel we can use the function named NPV to calculate NPV. I believe it won't be too difficult for you to remember the name of the function, just NPV for NPV. In the NPV function There are two inputs. The first is the discount rate and the other is the range of cells where you have cash flows of the project. However, there is a problem with Excel's NPV function which requires our attention. NPV function assumes that the first cash flow in the range of cells occurs in Year 1, not in Year 0. Hence, when we use the NPV function, we need to leave out the initial outlay, CF0. Then we have to add the initial outlay manually outside the NPV function. Now let's see how it works in Excel. If you already have the range of cells with cash flows, as in row five, and the cell with the discount rate, cell C2, you can start calculating NPV using the NPV function. In the NPV function, you first reference cell C2 for the discount rate, and then enter the range of cells for cash flows. However, if you start from Year 0 in the NPV function, you'll get a wrong value because of the problem of Excel's NPV function we discussed earlier. Instead, when choosing the range of cells for the NPV function, we should start from Year 1's cash flow in cell D5. Then, we add Year 0's cash flow in cell C5 manually in the same cell. So the NPV of this project is $113.63, but what does this number suggest? Does it mean that we should undertake this project? The very simple decision rule of NPV is that we accept the project if the NPV is positive. A positive NPV means that the project will add value to the firm. For example, if a firm accepts a project with the NPV of $60, the firm value will increase by $60 because the manager just added the project to the firm where it has a positive value of $60. In the previous example, you'd also want to accept the project because the NPV of the project was $113, which is positive. In that example, the project had a positive NPV because the present value of future cash inflows was greater than the initial cash outflow in Year 0. Which suggests that the project was a good value-creating one. As the final task of this lecture, let's find out whether NPV is a good capital budgeting decision rule based on the three questions we saw in the previous lecture. First, does the rule consider the time value of money? The answer is yes. We always calculate NPV by discounting future cash flows. Second, does the rule adjust for risk? The answer is also yes, because the discount rate we use in NPV calculation reflects the risk of the project. Finally, does the rule let us know whether the project creates value for the firm? Yes, just recall that NPV is measured in dollars, and shows the value that will be added to the firm if the project is taken. Now you'll understand a little bit better why people say that the NPV rule is not only the most popular technique, but also the best capital budgeting technique.
