Hi, my name is Artem Anilov. I'm a senior manager in oil company LUKOIL. Also, I am an assistant professor here, in the School of Finance of Higher School of Economics. Today, we are going to discuss with you the process of decision making when considering investment projects. Our primary focus will be on uncertainty and risks. However, we will also cover some basics and theoretical aspects of this question. Later in the following lectures, my colleague Pavel Lvutin will discuss with you more practical cases of implementations of the concepts that we will discuss today. Today, our agenda is the following. First of all, we will discuss different criteria for making investment decisions. These criteria typically include net present value, internal rate of return, payback period, and profitability index. Then we will switch to the cases of uncertainty and how to incorporate uncertainty in our evaluations of investment projects. Let's start with discussing different criteria of investment projects. The first criteria and the most popular one is the net present value, and we will start with this criteria. To calculate different criteria of investment projects, basically you need two ingredients. The first one is cash flow or free cash flow. The second one is discount rate. Basically, you have two types of the cash flows, free cash flow to the firm and free cash flow to the equity. You also have two types of discount rates. The first one is weighted average cost of capital and the second one is cost of equity. Here in this lecture, we won't dive into the details of calculating both cash flows and discount rates because these elements of evaluating investment projects has been discussed previously in the course. However, make sure before proceeding to the following sections, that you understand the concepts of free cash flow and of discount rate, because we will talk about them more thoroughly during the next slides. Let's start with the net present value. Basically, net present value shows the difference between the discounted values of cash inflows and cash outflows. Here on the slide, you can see the scheme of the investment projects. You can see that at time t, we had some cash outflow, which is capital expenditures or investments and then during four years, we have some cash inflows, which may be our revenue or it's some economy of the costs or whatsoever. To calculate the net present value, we need to, first of all, discount these cash flows, as you can see on the formula on the slide and then summarize all these elements. This formula may be shortened to what you see on the bottom of the slide, which is just the sum of the discounted cash flows. As investment is just the cash outflow, we can incorporate it in the sum. The NPV rule is quite simple, one should take investment projects with NPV higher than zero or should take projects with the highest possible net present value. These straightforwardness of this rule makes net present value very popular among practitioners from almost every industry. However, one can calculate net present value not only using cash flows, but also residual income or economic value added. The concepts that you may have already learned during the previous lectures of our course. The thing is that you just substitute cash flows with residual income and calculate net present value. We can consider the company's value is just the sum of NPVs of overall investment projects that of the company and residual income shows us if the company creates value or destroys it or if a separate project creates value or destroys. Here, you can see that this concept of net present value and residual income are interrelated. Here is an example of calculation of net present value using residual income. Consider a simple project of three periods where at time zero we have a cash outflow, the investment of one hundred, and then we have some cash inflows during the first and the second period. You can see the calculation of the residual income here. The residual income at time zero is actually zero because we only have investments and we don't have any income. At time one, we can see that our residual income equals to 50 because we have some inflow and we also have some capital charge, which is the rate of return over the investments and then the final period, our residual income equals minus 50 because we take into account investments only when the investment project is finished, in this case, at time two. Then we discount the values of residual income and obtain 45 for the first period and 41 for the second one, so the NPV of the project is formed. You can make sure using the standard process of calculation of NPV, that it will yield the same result. Here on this slide, you can see the concept of NPV profile. When we have our cash flows determined and we trust some of these cash flows. The only thing left to estimate is the discount rate and NPV, actually, will depend on the values of discount rate that we will use. Here on the slide, you can see the declining line of different values of net present values and the different assumptions about the discount rate. On the left part of the line, which is above zero, you can see the positive values of NPV and you can be assured that the projects in this part will be implemented if the discount rate is no more than about eight percent. The right part of the graph, you can see that NPVs turn negative and these projects won't be implemented if the discount rate will be above about eight percent, and you can see that this line intersects with zero at about the rate of eight percent and this rate is called the internal rate of return. This is another criteria for evaluating investment projects and we will talk about that more thoroughly in our next section. Thank you.