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Â Let's start with the NPV. The NPV has an expression.

Â I, I, I've been trying to stay away from expressions and

Â equations as much as we could.

Â Remember and it's important that you keep in mind once again,

Â that because our time in this course is very limited,

Â it's important that you keep in mind that each of these.

Â Sessions comes with a rating that you can do either before or after.

Â Typically, it's better to do it after.

Â In order to actually extend many of the formal content, the expulsions, and

Â the equations, we haven't actually covered here.

Â But they're covered in the readings.

Â And so it's important that you remember,

Â that after each session, there's going to be a reading.

Â And only after you do that rating you can go and work on the on the problem said

Â that will ask you to apply some of the concepts that we've been discussing here.

Â Now this is one exception, I do want to put there the expression for the NPV.

Â And not only because it is very important, but

Â also because we need to run a calculation.

Â And that calculation we can't really run unless we have the expression right in

Â front of us, as you're having there in your screen.

Â So on the left-hand side, we simply have the definition.

Â That we're going to calculate an NPV, that is, a net present value.

Â On the right-hand side,

Â we could have written what you see there in more than one way.

Â And by more than one way, I mostly think that, that you know.

Â We could have maybe used different notation.

Â The expression is more or less given.

Â So let's make a few comments to make sure that you understand what that

Â expression means.

Â Let's go to the first cashflow on the wrong, right-hand side.

Â That is CF0.

Â That is basically a, the first cashflow that because it happens today,

Â that's what the 0 means, that it's going to happen today.

Â You're not going to be discounting.

Â Remember what we discount are things that are going to happen in the future, and

Â we discount those things because a dollar that you receive one, two or

Â three years from now doesn't have the same value as a dollar you receive today.

Â So basically we can to apply that discounting.

Â In the complementary reading that comes with this session there's a little bit of

Â more discussion and a couple of examples that will help you

Â understand this whole idea of present value.

Â But for now and for our purposes it's a very basic idea that you know,

Â if I offer you what do you prefer a dollar today, or a dollar a year from today?

Â Or a dollar today, or

Â a dollar two years from today, the sooner you get that dollar the better.

Â Because the more you wait to get that dollar,

Â the more that that dollar will lose value to inflation.

Â And that's what we called before, losing purchasing power.

Â So we need to discount because of that reason.

Â The further away that dollar comes.

Â The higher the discount rate we need to apply.

Â Now, that first cashflow, not being discounted,

Â basically means that this is an amount of money that is related to today.

Â And I'm saying that it is related rather than it is positive or

Â negative simply because it doesn't have to be a negative cashflow.

Â Most people actually write a negative sign next to that C of 0,

Â and that basically means, well that's some sort of initial investment that we

Â need in order to start this particular project.

Â And that's typically the case, but it doesn't have to be the case.

Â You know, sometimes and you can think a typical example may be

Â executive education programs that are running business schools.

Â In those programs actually sometimes you first get the cashflows when people sign

Â up for the program.

Â And then you have to deliver and therefore bare the cost.

Â So it is not entirely clear and it doesn't have to be the case that

Â the first cashflow is negative, but more often than not, it is true that it is.

Â So if it makes you feel better and

Â you want to put a negative sign in top, in front of that cashflow.

Â And that is just fine, but for now just think of that as some sort of

Â initial investment that we need in order to get the project started.

Â Now, the other cashflows as you see,

Â all of them are discounted, and that DR is the discount rate.

Â We're going to get back to the discount rate later on.

Â For now, we could think of it as the cost of capital the company's cost of capital

Â and that is exactly what we've done before that is in sessions three and four.

Â We thought about and we calculated the cost of capital for Starbucks if you

Â remember, and we're going to go back to Starbucks a little bit later on.

Â Those cashflows as you see are being discounted by a discount rate, but

Â also notice that as we move from the left to the right that there's something that

Â increase and that is the power at which we raise 1 plus DR.

Â Well, what that means is that that discount factor is getting bigger and

Â bigger and bigger, and that is just a little technical way of saying what

Â we said before, that the further away the cashflow is in the future.

Â The higher the discount rate we're going to apply.

Â Second thing that is important about all the other cashflows that

Â are being discounted.

Â Remember, if the discount rate is the cost of capital, but if it's not,

Â it could be any discount rate.

Â That discount rate is always going to be positively related to risk and

Â that is an important thing to keep in mind,

Â because it tells you that everything else equal the riskier the project that

Â we evaluate, the higher that discount rate is going to be.

Â So everything else equal, if we were comparing two projects which

Â deliver the same cashflows, but one is riskier than the other, then the discount

Â rates we're going to be applying to the riskier ones are going to be higher.

Â And as you see in that expression, the net present value is going to be lower.

Â Third and final thing.

Â And this is probably the most important things about those about those cashflows.

Â And that is, all those are expected cashflows.

Â We wish that we knew those cashflows with certainty.

Â But in real life, we never know.

Â You know, we make investments, we have an expectation of what we're going to

Â get out of those investments, but any corporation, you know,

Â any corporation at any given point in time can only expect,

Â can never actually foresee exactly what those cashflows are going to be.

Â And here's, you know, something for you to keep in mind.

Â When you're evaluating a project, the throwing numbers into an NPV expression,

Â that's the very easy part.

Â You know, if I tell you,

Â let's evaluate this project as we'll do a few minutes from now.

Â And I'll give the expected cashflows and

Â I'll give you the discount rate, then throw in those numbers into excel and

Â coming up with a net present value that is not very difficult.

Â The difficult part in real life,

Â obviously, is to forecast, to foresee what those cashflows are going to be.

Â So, I, I didn't put an expected sign, when, you know, technically speaking,

Â I should have put an expectation before each of those cashflows from one to t but

Â I didn't want to over complicate, unnecessarily the expression.

Â But remember that anything that comes in the future cashflows one to all the way to

Â t where t is any number, it could be five years,

Â ten years, 15 years, whatever you think is the length of this project,

Â whatever you think is the number of periods from where you can foresee.

Â What the cashflows are going to be.

Â