then clearly this in general is going to be a different rate of return.

Not because of the length, but also because of the fact that maybe

the expectations for a two year investment are different.

We have to compare returns that are sort of normalized to the same period.

So here r2, in order to get the PV of that, you have to square that.

Then the NPV of this will be equal to -C sub 0 plus

C1 over 1 + r1 + C2 over 1 + r2 squared.

So we generalized for two periods.

But, again, now we can make the general formula.

We can say that the general NPV is equal to

-C sub 0 + C1 over 1+r1 + the general

term Ck over (1+rk) to the k-th power.

And then plus because that doesn't have to be finite.

So this is the general formula which we reached very quickly.

But the problem is that, in order to find MPV,

you have to know all the C sub 0, C1, Ck, and so forth.

And also you have to know r1 rk, and so on and so forth.

So, well, you can always say that In reality you can make investments not only

at point 0 but then later on 2.

But for the sake of simplicity, we can always think that these

investments can be treated sort of like costs at these points.

So we will not delve deeper into that for now.

We discuss these differences between capital expenditures and

some kinds of costs.

Not only in what follows in this course, but

also in some greater detail in our third course.

But for now, we've reached this formula and that all sounds great.

We know that unfortunately we posed more extensions than we have answers.

Because you say, great, if I only knew all Cs and all Rs, I would be great.

However, we do not always know them.

And starting from the next episode, we'll start to see how this formula works

if we do know some of these Cs, or we have a good forecast of them, or

if we make some special cases that will simplify the use of this formula.

Let me tell you right away that although some of the examples are, not only widely

known but seem to be very much made up to make the formula look simple.

But the key story is that actually people do use these simple

results in actual corporate evaluations and evaluations of some real assets.

So our examples from the next episodes will not be so irrelevant, if you will.

So starting the next episode, we will study these short cuts.