In this class, we will focus on investment decisions. So we need to understand what is an investment. We can define an investment as a project that requires initial cash outflows, and because of this cash outflows, it is going to generate probably in the future, some cash inflows. Some examples of investments can be the decision of a company to purchase a new equipment, a new asset, or to purchase a new software. So basically, everything that is going to change the asset structure of the balance sheet can be defined as an investment. We can be even more specific and identify some characteristics which distinguish an investment. These characteristics can be, first of all, the fact that the investment requires a cash outflows at the beginning, and we can define with a high level of precision, the amount of the cash outflows. The problem is that this kind of investment, and this is the second characteristic, is going to generate a future cash inflow, but we do not know exactly the payback time, where the payback time is the moment in which the investment is going to generate cash in. Moreover, we do not know the amount of the cash that is going to be received by the company. So we don't know the payback time, not even the amount of the cash in. These are basically the characteristics that distinguish an investment from the other decisions. Indeed, if we think of a company, we can have three main types of decisions, and we can classify these decisions on the basis of two main elements, where these elements are the time horizon and then the impact on the company, specifically the impact on the ability of the company to generate economic value. The first type of decision that we can have is represented by what is defined as short term decisions. If we have short term decision, the impact in terms of time horizon is limited. We are talking about an impact which is lower than one year. Examples are decisions that are related to the change in the production makes the change in the quantity, the change in the price. So something that affects the company for a period of time, which is the next month, the next week, the next semester or something similar, basically, lower than one year. So we are not touching the assets which are available for the company. Moreover, at the same time, let say this is a consequence, the impact on the company, specifically on the ability of the company to generate economic value, is limited. If we make the wrong decision because we define the quantity to produce, which is not enough, we have an impact, of course, but it is limited in terms of overall economic value which is not generated in this case. Then we have a second category of decisions which are what are defined as medium long term decisions. These medium long term decisions are exactly our investment decisions. So we are talking about some projects that are going to change the asset structure of the company, and they have an impact on a time horizon which is higher than one year. Think of the decision of the company of purchasing a new equipment or a new software. Probably, the company is going to use the equipment or the software for a period of time which is higher than one year, probably five years or 10 years. That's the reason why we're talking about an impact in terms of time horizon which is medium-high, and at the same time, the impact on the company, so on the ability of the company to generate economic value is medium-high as well. If you're purchasing the wrong equipment, or let's say, money in general, if you're making the wrong decision, we can have a significant impact on our ability to generate cash because we are influencing the cash for the next 5,6,7 years. Finally, we have a third category of decisions that are the so-called strategic decisions. In this case, we are talking about something that will have an impact on the company for a very long time horizon. We're talking about decisions that will affect the next, probably, a period of time which is higher than 10 years. Typical examples of strategic decisions are the decision to enter a new business or a dismissal of a certain business. So we are talking about something that can undermine the overall survival of a company, that's the reason why the impact on the company is very high. So we are talking about something that can affect the overall survival of the company, so a very high impact on the ability of the company to generate economic value. Starting from this classification of decisions, we can say that all of these decisions can be evaluated in terms of their ability to generate economic value, so their ability to generate cash for the shareholders, because we're talking about profit company, which is our focus. So we can say that if we want to evaluate these decisions, we can use as a metric, the so-called net present value. So the net present value of our decisions, whatever decision we're talking about, can be defined as the sum from the time, which is today until infinite, of the net cash flow that are generated by the decision at a certain moment of time discounted. That's the general formula. As I said, we can use this formula for evaluating all of these decisions. Our focus will be on investment decisions, so we can simplify this formula. If we think of the second category of investment, we can simplify the NPV formula and it will become the following: NPV, again, calculating at the moment zero, will be equal to the sum from zero to capital T of the net cash flow t, discounted, 1 plus k at the power of t, plus the terminal value at the instant of time capital T, discounted, 1 plus k at the power of capital T. So if we look at the differences between the general formula and the one that we apply when we have the investment decision, we can see two main differences. The first one is related to capital T, because basically, if we have an investment decision, rather than summing the net cash flow from zero to infinite, we just sum the net cash flow with reference to the expected life cycle of our investment. For example, if we think of the purchasing of an equipment by a company and this equipment is expected to be used for the next 10 years, then our capital T will be 10. So we will calculate the net cash flow for the next 10 years. So capital T is expected life cycle of the investment which operationally, represents the number of years for which we are going to calculate the net cash flow. The other difference is this second part of the formula, because we are going to add to the calculation of the net cash flow a terminal value. The terminal value corresponds to the value of the investment of our project at the end of its life cycle. For example, if we think of the purchasing of this equipment, and equipment is going to be used for the next 10 years, the value of the equipment at the end of these life cycle will be the terminal value. Of course, we could also have as a terminal value, zero, in the moment in which the company finishes the depreciation of the equipment, we will have as a terminal value, zero. The opposite instead, if the company decides to sell the equipment, we will have a certain value of terminal value that will be the selling price. If we want to generalize, this terminal value can be considered as the value of our project at the end of its life cycle, if any. So to conclude, we can say that if we want to evaluate an investment decision, we can use this NPV formula, which is the simplified, just because we are simplifying the calculation with respect to the time horizon that is limited to the number of years for which we are expecting to have an impact about our investment.