We have one period, 0 and 1, then indeed NPV and

IRR is the same because clearly what is it?

We can say that here we have -C sub 0, here we have C1.

Then the MPV is C1/1 + IRR.

Here I put IRR by force minus C sub 0.

And that should be equal to 0.

And I solve that and get one and the only IRR.

So that will be the same criterion,

and that will lead to this approach.

So far so good, and if all projects would be one period and the NPV calculation

would be as simple as it is here, then we would not need anything else.

And strictly speaking, we would not need any other criteria by NPV, and

this whole discussion that we had so far and

that we are proceeding right now would be redundant.

However, the reality is different.

And on the next, what I will show right now is what happens when we

deal with the actual more general formula for the NPV.

Well, we know that in general NPV =

-C sub 0 + C1/1 + r + Ct/1 + r to

the tth power, where I already made

the simplification, I put the same r.

Now if we set that to 0, then clearly,

this equation is of the tth power,

and it has t solutions, which is kind of bad.

Well, luckily, the majority of these solutions are bad solutions without

going deeper in what that means.

That requires some mathematical advancement.

But for now, what I will start to do, I will start with an example.

Because oftentimes we do have one good solution.

But then, if we said that we identified this IRR,

whatever it is, and then we said that we have to take into

account projects with the return that exceeds this IRR.

Well, let me give you a very simple, but

an example of a two period projects with these following cashflows.

So let's say this is 0, this is 1 and this is 2.

Here it will be -2000.

Here it will be +1000.

And here it will be +2000.

So what's NPV?

NPV is equal to -2,000 + 1,000/1 + IRR,

because we are solving with respect to that,

+ 2,000/ 1 + IRR squared.

Well this is the quadratic equation,

and solving that we get two solutions.

One solution is negative, but

the positive solution will give us IRR of 28%.

So if we proceeded in a straightforward way, we should have said, well,

now we have to take only the projects for which, whether it's a good or bad project.

Well, we can say now we have to take projects with IRR which is greater

than that.

And that will be, So

we just got this number, and now let's see what happens with NPV.

Because we know that the more general NPV criterion says

that the project should have an NPV that is greater than 0.

Well, let me draw a chart of NPV.