[MUSIC] In this class, we will focus on the NPV calculation by considering the external financing. So we will see how the net cash flow formula changes, in the moment in which we are considering the approach through which the investment is financed. Basically, we have two alternatives. We can use a shareholder's capital logic or an invested capital logic. In order to understand this difference in terms of approaches that we can use for evaluating the investment, let's start from how we can represent a company. Assuming that we have our company. And we know that given a certain company, we have the shareholders as the owners. And so the shareholder will put their money inside the company. So we are talking about the capital that in a certain moment of time is provided by the shareholder within the company, and the company is going to use this money in order to make investment, so in order to do some projects. So we have investments in a certain moment of time, and once we have the investments, our project investment will provide back hopefully we say, cash flow again at that certain moment of time, and then shareholders will receive back their dividend. So this is let's say, the traditional structure of how a company functions. Of course in this schema, we need to take also into account banks, because if shareholders do not have enough money to finance the project, the company will ask for some money to the banks. So within this schema, we need to take into account banks. So we will have that the company will receive the money from the banks, and of course, it will provide back the loan that it has received plus the interest. So basically, this is the overall schema in the moment in which we want to take into account how cash flows move from the shareholders, to the company, the banks, and then the final projects. We can evaluate therefore our investment, either by using a shareholder's logic or an invested capital logic. Let's start from the simplest case. So we're considering a shareholder capital logic. In this case, if we're considering a shareholder capital logic, we are analyzing the investment by considering the perspective of the shareholders only, which means that basically we are not including the banks, we're in our analysis. So basically our focus, we are analyzing the investment from this perspective, so from the shareholders. In this case, the value of the capital of K in the NPV formula, will be the cost of the capital that is defined as e, which is the cost of the capital. It is defined as the equity, which is the cost of the capital of the shareholder. So this is the level of the risk that is perceived by the shareholder. So the value of the K, we're in the NPV formula, will be just the level of risk that is defined by the shareholders. Another component that changes within the NPV formula, is the cash flow. In the moment in which we are adopting a shareholder's logic, the cash that is considered, is just the cash that is provided by the shareholders, and it is received back because of the product. So all of the relationships between the company and the banks, are not taken into account in the analysis from a shareholder's perspective. This means that the cash flow is calculated as the operating cash flow. So the EBITDA minus the amount of debt, that should be provided back by the company to the banks, minus the interests that are paid on the debt that is received by the banks. So basically, the cash flow should be adjusted by taking into account this relationship of cash between the banks and the company. I haven't specified the cash flow, either it is a gross operating or a net operating, because it is our choice. So we can decide to calculate our cash flow, either as a cash flow gross operating or net operating, depending on the fact that we are including or no taxation. But we need to keep in mind that if we want to adopt a shareholder's logic, we need always to deduct from the cash flow, the debts that are provided back to the banks, and then the interest on this debt. Let's move now to the evaluation of the investment by using an invested capital logic. In this case, the investment is evaluated from the perspective of everyone that has provided the money to finance the project. Who is providing the money? Both the shareholders, but also the banks. This means that the perspective, if we are adopting a capital Logic, this is the perspective of everyone that has provided the money which means that we are including the shareholders, but also the banks. So this is the perspective of everyone that has provided the money. So it is an invested capital logic, because it is everyone that has provided the money in the project. In this case, the cost of the capital is a little bit more complex to be calculated because the cost of the capital K, will be as you can imagine the level of risk perceived by the shareholders, plus the level of risk let's say perceived by the banks. So we can say that it can be calculated as a weighted average between the level of risk perceived by the shareholders, plus the cost of the capital as it is defined by the banks. How can we calculate a weighted average in a very simple way? Actually, this K is defined as weighted average cost of the capital because as I said, this is a weighted average between the cost of the capital of the shareholders, and the cost of the capital of the banks. So we need to consider the cost of the capital of the shareholders whose formula is K of the equity, multiplied by the incidence of the portion of the money that is provided by the shareholders with respect to the overall financing of the project. So we have that the money that is provided on the project by the shareholders can be abbreviated with the E, that stands for equity, divided by the overall money that is put in the project. That is the money of the shareholders, so the equity, plus the money that is provided by the banks, which is abbreviated as D, that stands for that. So basically in this case, we are calculating the incidence of the amount of money that is provided by the shareholders with respect to the overall amount of our investment, that is given by the sum of the amount of money provided by the shareholders plus the amount of money provided by the banks. And this is the weighted average of the cost of capital with respect to the capital provided by the shareholders, plus the cost of the capital of the banks, which is basically the interest rates of the banks, multiplied by the incidence of the amount of money that is provided by the banks. So the incidence of the debts, so the amount that is provided by banks, divided by the overall amount of our investments. So basically in this case, we are simply doing a weighted average between the cost of the capital of who is providing the money, so shareholders and then the banks. If the calculation of the weighted average cost of the capital is a little bit more complex with respect to this case. We are lucky and said, in the calculation of the cash flow, because given that we are in the perspective of everyone that has provided the money, the cash flow is exactly the cash flow that we have without deducting anything. It can be either a cash flow gross operating, or it can be a cash flow net operating, depending on the fact that we are including or no taxation. But basically, we consider the overall operating cash generated by our investment. Again, also in this case, we will have different results in the calculation of our net cash flow, given by the fact that we are using the perspective of the shareholders only, or the perspective of everyone that has provided the money. Again, let's see what changes with a really simple example. Assuming that we have this data, we have an investment that is committed today. This is investment in the moment of time 0 of 1000 euros, and we know that given this overall amount of the investment, 600 euros are financed by the equity, so by the shareholders, and then the remaining 400 euros are financed by the bank, so it is a debt. And then we know the cost of the capital of both of them, we know that the cost of the capital of the shareholders is the 10%, while the interest rate from the banks is the 5%. And we know that the cash flow that is generated for the next year from our investment is equal to 300 euros, and we are required to calculate both, the cost of the capital and the cash flow by adopting both of the logics. So let's see what changes, let's start from the shareholders capital logic. As I've said, the cost of the capital in this case, is simply the cost of the capital of the shareholders. So K will be 10% stop, we have already done. Let's move now to the cash flow, the cash flow in this case is the cash flow that is generated by the investment, which is 300 euros. So this amount minus the amount of money that is provided back to the banks. So we don't have the repayment of the debt because we don't have the data. So we just need to take into account for the interest rates that are paid on this amount of the debt, that will be 400 euros multiplied by the interest rate. So basically, we are paying the 5% on the amount of money that we have received from the banks. So we will have multiplied by 5%, so we have that the cash flow that is generated in the year number one by our investment, will be 280 euros by adopting a shareholder's capital logic. Let's see now what changes if we are adopting an invested capital logic, we need to calculate K. And as I said, this is the weighted average between the cost of the capital of the shareholders and the interest rates from the banks. So we'll have that K equals the cost of the capital of the shareholders. So 0.1 multiplied by the incidence of the amount of money provided by the shareholders with respect to the overall amount of the investment. So it will be 600 euros divided by the overall amount of the investment, 1,000 euros plus the interest rates, the cost of the capital from the banks. So 0.05, multiplied by the incidence of the amount that is provided by the bank. So 400 euros divided by 1,000, that is the overall amount of the investment. If we calculate this value, we will have a cost of the capital of the 8%. Now, let's move to the calculation of the cash flow. The cash as I said is really simple because the cash flow with an invested capital logic, is the overall operating cash flow generated by our investment. So it will be 300 euros, and we have already calculated our cash flow. These are the two alternatives. Both of the approaches are allowed, so we can use either the shareholders capital logic or the invested capital logic, what changes is the perspective that we are adopting in order to evaluate our investment. Usually, the invested capital logic is the most precise because we are evaluating the overall investment, considered from the perspective of the overall amount of money that has been provided within our project. At the same time, if we are calculating the cash flow as a cash flow net operating, we have the more precise approach that we can have in order to calculate the net cash flow that is generated by the investment. [MUSIC]