[MUSIC] Last time we looked at drawbacks of using payback period and some possible ways of addressing those drawbacks. In this video, we will continue looking at drawbacks of other decision tools. In this context, we will also look at ways of addressing al least some of these drawbacks. The couple of things we will talk about are the modified IRR and the profitability index. We will also talk about a couple of other ways of addressing these drawbacks in greater detail later in the course. First, we discuss the drawbacks of IRR. One of the main assumptions with IRR is the idea of compounding. It assumes that all cash flows generated over the project's life are reinvested in the project. And these cash flows also earn the same IRR over the remaining life of the project. How are this may not always be possible for two reasons. One investment in a project maybe made only at fixed points in time over its life. We can reinvestment cash flows on an annual basis. Reinvestment of the project means the project scale is constantly increasing over time, which may not be feasible or also may make the project unattractive. Even if one were able to reinvest the cash flows in the project, there is no guaranteed that those cash flows would continue to generate the same internal rate of return. So the IRR may actually always state the return a project generates. One lead to address the problem is to use the modified IRR, MIRR in short. For this, we are to calculate the future value of all cash inflows at the end of the projects useful life using its cost of capital. The initial investment is already in present value terms, and nothing needs to be done to it. For a project with a useful life of n years, then the MIRR is calculated as the future value of cash flows divided by the present value of the initial investment. The whole thing raised to the power of 1 over n minus 1. Let's go back to our original example with an initial investment of $1 million followed by annual cash flows of $200,000 for 9 years. The project had a cost of capital of 15% and an IRR of 13.7%. The future value of the annual cash flows can be calculated using the FV function in Excel. For us to input that the function is the cost of capital which is 0.15. The number of cash flows is 9 which is the second input. The third input is the annual cash flow of $200,000. This gives us a future value of $3,357,168. Now the MIRR is 3,357,168 divided by the initial investment of $1 million the whole thing raised to the power of 1 over 9 minus 1. The MIRR of the project comes out to 14.4%, which is higher that the IRR of 13.7%. The MIRR still has to be compared to the hurdle rate of 15%. Since, it is lower than the hurdle rate, we will still reject the project. A second problem with IRR is there are times of project may have multiple IRR. This is especially true when cash flows change sign more than once during the project's life. Let's look at a very simple example. A two year project requires an initial investment of $6 million at year 0. Generates cash flows of $15.5 million in year 1 and has a net outflow of $10 million in year 2. This project has two valid IRRs, 25% and 33.3%. See the graph to understand what is happening. The graph has NPV on the vertical axis and the discount rate on the horizontal axis. The curve cuts the horizontal axis at two points, which means that the project has two IRRs. For projects where the cash flows change sign more than once, it is better to use NPV as a decision tool. Alternatively, we could use the MIRR and compare it to the hurdle rate. A third drawback of IRR is that times an IRR may not even exist. This happens when all project cash flows are of the same sign. These are however rare instances, in such cases too, it is better to use NPV as a decision tool. A fourth drawback is something we saw earlier. IRR and NPV may give us contradictory decisions when trying to select one projects from among many, in which case, it is again better to use NPV. Finally, when we look at the drawback of NPV, remember NPV depends on future cash flows, most of which are unknown. This requires us to estimate what these future cash flows are likely to be. Regardless of how well we estimate these cash flows, there's always uncertainty in the cash flows. This uncertainty in the cash flow forecast leads to uncertainty in NPV. This requires further analysis on identifying our assumptions that critically impact our NPV calculations. This is what sensitivity analysis is all about which we will discuss in a later video. Another drawback of NPV analysis is that it assumes the decision to accept or reject a project cannot be revisted. A project may have a positive NPV today, and the company decides to go ahead with the project. After a year or two, the company realizes that the project isn't doing as well as they expected it to do, because sales revenues did not pick up, our costs were higher than anticipated. At this point, the company may be better off abandoning the project rather than continuing with it. Traditional NPV analysis assumes that such outcomes are not possible. This is the idea of real options, which we will also cover in a later video. A third drawback of NPV is that it ignores the scale of the project, which project should one select? One with an initial investment of $1 million and NPV of $10 million or another that requires initial investment of $100 million and NPV of $12 million. NPV analysis says that we should accept the second project. But clearly the first project allows us to earn more bang for the buck. Further because of limitations and the amount of capital a firm has. It may not even have $100 million to invest. A fix for this is to use a profitability index. It is defined as the NPV of the project divided by it's initial investment. It measures how much NPV is generated for each dollar invested. The two projects have profitability indexes of $10 million divided by 1 million which is 10, and 12 million divided by 100 million which is 0.12. Clearly, the first project gives the bigger bang for the buck, and should be selected over the second one. Next time, we will look at free cash flows which are necessary to calculate MPV and IRR. We will discuss how we go about calculating free cash flows and their relation to net income. [MUSIC]