So in this example we have a cash of a $400,000 cash in the future.

Returned by the project and your r is 7% present value with

a simple net mathematical calculation of one divided by

one plus the discount rate times the future value of the project.

And that comes out to be in this example $373,832.

And don't take that as meaning that's a very specific number and

keep in mind that the $400,000 is an estimate.

So it's more $852 than the minimum.

I mean, if they took they are starting

with the number 400,000 which is the best guess.

Okay. It's just the mathematical calculation.

So now, we know what the present value is.

So what's the net present value?

Okay, the present value minus the required investment to generate

the $400,000 is the net present value.

So assuming in our example that we, that in order to generate $400,000,

in the future, one year into the future.

You have to invest $350,000 was the net present value.

We calculated the present value, that was $373,832.

The investment is 350.

So the net present value is a positive number of $23,832, right?

And you can express this formula as NPV equal

C0 plus C1 which is cash in the future,

divided by one plus the discount rate.

Now C0 is always a negative number.

C0 means what's the amount of investment okay, and that's always negative.

That's why you have a negative cash flow and a positive cash flow, okay?

So that represents an outflow.

Now the problem with this formula, I shouldn't say problem.

The thing you should remember, what I said a minute ago.

These formulas are assuming certainty in the numbers.

Well, the $350,000 is a certainty because you know you can invest $350, 000, but

the amount of $400,000 is not a certainty.

And that's one of the kind of traps that you can fall into,

thinking that these numbers are certain, okay?

So, how does the present value and rate of return relate?

Okay, so the present value equals the future income discounted at a regular

return offered by the alternative invested, the alternative investment.

So you can state this differently by saying, the investment is worth

making because it's rate of return exceeds the cost of capital.

So in our example we can state this in a different way mathematically.

We had a $400,000 return of cash in one year.

We invested 350.

It means we made $50,000.

If you divide $50,000 by 350,000 of what you invested.

That comes out to be 14.3%.

Say the discount rate is we already know that was only 7%, right.

So we've got a very good return on the investment which

is much higher than the opportunity rate.

Okay? So that's another way to express this.

The value or the potential interest in making these investments.

So it may sound complicated, it's not.

I would recommend that you go through the slides at your leisure and

just remember that it's a mathematical calculation.

And you simply come up with the final result and say.

Did my project return a net present value greater than my cost of capital?