Hi, in the previous lecture, we learned that sometimes there can be a conflict between the NPV result and the IRR result when we evaluate two mutually exclusive projects. In the next videos, I'd like to tell you some more details about NPV technique and IRR technique and more importantly, show you why they sometimes yield different results, specifically in the next videos, we'll study the following topics. First, we identify the multiple IRR problem and its implication on the decision making process. Then, we study things to consider when we compare projects with different sizes. The third topic is comparing projects with different lives. Finally, we analyze implicit assumptions of NPV rule and IRR rule on reinvestment rates and study why they should matter. So far, it was really natural to believe that there is one NPV one IRR, and one payback period per project. That is actually true for NPV and the payment period, but sometimes a project can have more than one IRR. In previous examples though, we did not suffer from the multiple IRR problem and that was because projects we have seen so far had a conventional cash flow. Okay, so what is a conventional cash flow? If a project has a stream of cash flows where the sign of cash flows changes only once, we say the project has a conventional cash flow. A typical cash flow of a project, that we can imagine, is actually conventional, because we usually assume that a big cash outflow is incurred at the beginning for year zero, and then starting from year one, the project generates multiple cash inflows. Just check how many times the direction, or sign, of cash flow, has changed in the stream of cash flows we just described. Just once. Can you see which project has a conventional cash flow between A and B now? Project A has a typical conventional cash flow as the sign changes only once between year zero and one, while project B has a non-conventional cash flow, because it has a negative cash flow in year two. In fact, we can easily imagine a situation where the project would have a negative cash flow in the middle of the project just like in case of project B. If the project requires a maintenance cost in year two, and the cost is greater than the net cash inflow from the operation, we'll have a cash outflow in that year. It is known that a project has only one IRR if its cash flow is conventional. That's why we did not have to worry about this problem, in previous examples. It is also known that a project has multiple IRRs if its cash flow is non-conventional. When we have say two IRRs, we can no longer use the IRR rule to make a decision. What if the actual discount rate is 10% but the project has 2 IRRs, 5% and 35%? In this case, IRR becomes useless and the NPV rules should be used in project analysis. Now, we talk about issues in comparing projects with different sizes. We know that the NPV is a dollar amount, while the IRR is the rate of return. Here, I'm letting you know in advance that both project A and B have positive NPVs when we use the discount rate of 10%. Which project do you think will have a greater NPV, A or B? Project A has a much greater NPV than project B, but is this result surprising to you? Probably not, NPV is the dollar value so NPV should be likely to be greater for large projects. On the other hand, IRR tends to be greater for small projects. You'd often find small high IRR projects in the real world, but large high IRR projects are rare. One of the reasons why this is happening would be the law of diminishing marginal productivity. It is an economic principle that as you increase your input, the output per unit of input will eventually diminish. Do you remember the general principle we should follow when you have a conflict between NPV and IRR? We learned, we should follow NPV rule because we want to maximize value not the rate of return. Now that we know the effect of project size on its NPV and IRR, can we really say NPV should be always preferred? As a matter of fact, IRR could make more sense to some companies, depending on their situation. You are more likely to prefer IRR as your decision rule, especially if you run a startup company. As a startup, you may have limited resources and more opportunities to invest in profitable projects. If that is the case, it might be optimal to undertake a series of small but high IRR projects, rather than to undertake one very large high NPV project. This is one of the examples which shows that a general principle that is usually applied to normal stable companies may not be necessarily a correct one for a startup company.