The truth is that we know the assumption we've been working so far is not really

that we knew the forecasts, that's what we're going to learn now.

Really, what we were doing is we were using the expected value, okay?

All the numbers in our timelines, in our evaluations,

in our acquisition analysis, they represented expected value, okay?

So in this lecture, we are going to learn what an expected value means, okay?

The idea is that we were using averages, we were trying to

work with our best guess of what that number would be in the future, okay.

This is gonna be true for all the model parameters we worked with.

Cost savings, revenue increases, future investments, right.

We were always trying to forecast, to calculate this average value, okay.

So, our goal now is to learn how we deal with uncertainties.

The uncertainty is going to become more explicit when we think about investment,

and we're gonna talk about how we incorporate these uncertainties

into our evaluation exercise, okay?

So, the way I want to start is by actually going back to an example we talked about

in module three, okay?

The easiest one of the project evaluation analysis that we did.

We had an example where there was an initial investment.

The project was going to increase revenues and increase costs as well, right?

There is some depreciation.

All the numbers that you need to calculate the net present value of the project,

okay.

So in particular, we have forecasts about how much revenue the project

is going to add in the next ten years, okay.

So now what I want you to recognized is that every time a company is doing

this type of calculations, the company really doesn't know for

sure that the cash flow at time nine, for example,

is going to be exactly $6.3 million, okay.

We have to think about uncertainty, which is exactly what we're going to do now.

The first thing we need to do is to figure out what we mean by these forecasts.

What we mean by the numbers that we had in our spreadsheets, okay.

And as we discussed already in the introduction, these forecasts

should reflect what we think of as the project's most likely scenario, okay?

So for example, when the company was trying to analyze this investment,

right, trying to think about this product,

the marketing department may have forecasted the added revenues as

the product of the market price times the additional sales, okay?

So the added revenue worth $12 million because, sorry, $12,000,

right, because the price was $4 and you're selling 3000 units,

so $4 * 3,000 equals $12,000, okay.

So in the production department was probably responsible for

forecasting the cost, right.

And the way that the production department probably

forecasted the cost is by adding variable cost to fixed cost, right.

So the cost per unit times the additional sales

plus an amount of fixed costs, right?

Every project is going to have some costs that don't

depend on the amount that you sell, we call those fixed costs, okay?

So this is just to go a little bit deeper on the numbers, right?

So now let's think about uncertainty, right?

The truth is that the marketing department is making a guess, right?

The marketing department is trying to estimate

what the most likely value is going to be for the sales, for example, okay?

Let's take sales as an example here, right.

To make this more explicit, let's work with probabilities, okay?

The good thing is that, at this point,

we already worked with probabilities in this course, right.

So you already know how to do calculations with probabilities,

here is another example, right.