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OK, now we're going to talk about something which is probably

will be complicated to a lot of you that don't have a financial background.

But it's not that complicated.

I'm going to try to simplify it for you.

So you'll understand how investment proposals are evaluated within a corporate

entrepreneurship environment.

And the way it's done is by using something called a Net Present Value.

Now let's talk about in general, what that really means, okay?

A company will invest in an asset whose net present value,

which we'll talk about, we'll define that in a moment, exceeds,

or is greater than, or is positive versus the required investment.

So it's very simple.

A $100,000 investment let's say.

If my net present value of that project is 110.

That means it's positive and

that means it's a potential project to be invested in.

If the investment is 100,000 and the net present value is only 90.

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Obviously they would not make that investment.

So essentially net present value is positive if the rate

of return on the investment exceeds the opportunity

cost of capital, or the hurdle rate let's say.

So again that's not complicated.

The net present value of a project cash flows is positive if the rate of

return on that project itself is greater than your hurdle rate, okay?

And keep in mind that despite many people who

will theorize about what the overall objective of corporate finance is.

I think most people would agree, ignoring the social aspects of corporations but

looking at strictly the financial aspects.

The objective of corporate finance is to maximize the value

of the outstanding shares of the company.

And how do you maximize the value?

You invest in projects who's net present value exceeds the cost of capital.

Very simple.

Now let's get into more specifics.

How do you calculate the net present value?

Net assumes that I've taken something and I've deducted something from it,

and get to a net number, and that's exactly what we do.

So we calculate first something called the present value, okay.

The present value is equal to the future payoff.

Meaning what cash flow am I expected to get from this project

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in the future that I'm going to discount that back to the present

day at a discount rate which we'll call r.

r meaning the discount rate.

Rate meaning percent, okay.

Now as we know, or you should know.

A dollar today is always more valuable right, than a dollar in the future.

And that's because you can take the dollar today and you go invest it

in something called marketable securities and begin generating income immediately.

So a dollar today is always worth more to the corporation than a dollar in

the future.

So, you take the expected return on that project and

we're going to make it simple and say one year from now.

And you say okay, I'm going to return so much money in a year.

What is the present value of that money one year from now

at my current rate of return?

And the rate of return you use, is the reward that you demand, or

that I should say your investors demand, for delaying the receipt of that money.

And what does that r mean?

The r is essentially your hurdle rate.

Hurdle rate means I can invest I can take this money and

invest in marketable securities no risk at all treasury bill or whatever.

And I had no risk but I'm going to take that money and

I'm going to an alternative investment in your project.

So the r is the discount rate or the total rate or the opportunity cost of investing.

In your project versus the return that they had given up by investing in

your project, okay?

Not versus, but it's the opportunity cost

that they've given up by investing in your project versus that less risky.

So you calculate the present value using the r,

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It equals to the discount factor, which is the r we talked about, times C1.

C1 means cash.

C is always cash.

One means one year in the future.

So the discount value gives rise to the fact that

the value today of a dollar received in the future.

And this expresses a reciprocal of one plus the rate of return.

And I know that sounds confusing, but let's make it simple.

You take one over one plus r, and that gives you a rate.

And let's say If r is 7%, 1 / (1 + 7%) gives you number which you

multiply times the future value of your project to get to the present value okay?

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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?