[MUSIC] Okay. In our last module of this lesson,

we looked at the simple case of a perpetuity.

That's an asset like land that lasts forever and

pays a certain amount of dollars per year from now to eternity.

What we want to do now is a slightly more complex variation on the idea of a perpetuity.

The goal is to get us finally to the promised land of learning about net present value,

and the proper discounting of cash flows.

So here we go. Suppose that instead of

an asset generating the same amount of income each year like a perpetuity,

the asset generates a different amount of income each year.

Further suppose that instead of generating a stream of income from now for

eternity like our indestructible apartment building,

the asset generates a stream of income over a fixed period of time;

maybe five years, maybe 10 years, maybe 50 years.

Now to put this in a business context,

here's an example of just such an investment;

suppose you are the chief executive officer of a textile company,

and that your company is considering replacing

your old mechanical looms with a set of highly computerized looms.

New machines won't come cheap.

The price tag is a cool $2 million.

Note however, that your chief economist forecasts of

these new machines will increase revenues by $500,000,

for each of the five years of the service life of the looms.

Also, at the end of five years,

the machines will have a salvage value of another $500,000.

Now from this date, it may seem pretty

obvious that the company should make the investment.

After all, while the machines will cost $2 million,

they will generate an even cooler $3 million in

revenues and salvage value over the five year period.

But wait, not forget about the time value money.

How can we account for that?

Well, here's the formula commonly used

to calculate the net present value of this investment.

As you look at this formula, don't just memorize it,

try to understand underlying intuition formulas Russell.

Here in this equation,

the first term is I sub-zero,

it represents the initial investment at time period zero.

Note, the minus sign in front of this initial outlay,

indicate that it must be subtracted in

the net present value or NPV calculation as it is money out.

Now, the next set of terms feature the net receipt in any given period in the numerator,

discounted by the interest rate feature in the denominator.

Specifically R is the interest rate.

And sub one is the net receipts from the investment in the first period or year.

And sub two is the net receipts in the second period or year and so on.

So to get the NPV or net present value of any given investment,

is simply you have to plug in your numbers and in this one.

So let's do that now.

For the proposed investment in

the new machinery that we outlined for your company just a bit early.

Remember, in our example the machine costs $2 million

and will generate $500,000 per year,

over its five years service life.

Then, there's another $500,000 for

salvage value waiting at the end of the five year period.

So please try to work this problem out,

as we pause the presentation.