0:12

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

Â we looked at the simple case of a perpetuity.

Â That's an asset like land that lasts forever and

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

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

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

Â and the proper discounting of cash flows.

Â So here we go. Suppose that instead of

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

Â the asset generates a different amount of income each year.

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

Â eternity like our indestructible apartment building,

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

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

Â Now to put this in a business context,

Â here's an example of just such an investment;

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

Â and that your company is considering replacing

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

Â New machines won't come cheap.

Â The price tag is a cool $2 million.

Â Note however, that your chief economist forecasts of

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

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

Â Also, at the end of five years,

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

Â Now from this date, it may seem pretty

Â obvious that the company should make the investment.

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

Â they will generate an even cooler $3 million in

Â revenues and salvage value over the five year period.

Â But wait, not forget about the time value money.

Â How can we account for that?

Â Well, here's the formula commonly used

Â to calculate the net present value of this investment.

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

Â try to understand underlying intuition formulas Russell.

Â Here in this equation,

Â the first term is I sub-zero,

Â it represents the initial investment at time period zero.

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

Â indicate that it must be subtracted in

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

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

Â discounted by the interest rate feature in the denominator.

Â Specifically R is the interest rate.

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

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

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

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

Â So let's do that now.

Â For the proposed investment in

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

Â Remember, in our example the machine costs $2 million

Â and will generate $500,000 per year,

Â over its five years service life.

Â Then, there's another $500,000 for

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

Â So please try to work this problem out,

Â as we pause the presentation.

Â 4:05

Okay. So what's our answer?

Â Here's the math; we start off with

Â our initial $2 million investment which has a negative side because it is an outlet.

Â Then we must discount the income stream of $500,000 per year plus the $500000,

Â the company will receive at the end of the fifth year as salvage value.

Â This gives us a net present value or NPV of

Â $1,924,664 just for the stream of income.

Â Of course from that,

Â we have to subtract our initial $2,000,000 investment.

Â And when we do that,

Â we find that the actual NPV of the total investment is a negative sum, minus $75,336.

Â Wow! Did you get that right?

Â And here's the punchline;

Â because the net present value of the investment is actually negative,

Â your company should definitely not make the investment.

Â And this is despite the fact that over the life of the investment,

Â the machines will generate an undiscounted sum

Â of a half million dollars greater than the initial investment. [MUSIC].

Â Now, here is the real power

Â of the net present value equation in concept.

Â It allows you to evaluate investments under different interest rate assumptions.

Â And as you will learn in our companion course in macroeconomic,

Â interest rates constantly move up and down as the economy expands and contracts,

Â and central banks around the world conduct their monetary policies precisely,

Â to influence interest rates and rates of investment and economic growth.

Â So here is the last question of this module.

Â What if the interest rate on our loom investment is 5% instead of 15%?

Â What does your intuition tell you right now?

Â Will the loom investment be more or less attractive at a lower rate of interest?

Â Will your company now make that investment in

Â new machinery if the cost of borrowing money is cheaper?

Â We use the NPV formula to crank out the new numbers and

Â find some answers now as we pause the presentation.

Â [MUSIC]. Did you

Â get the calculation right?

Â At the new and lower interest rate,

Â the investment actually generates

Â a very nice positive net present value of more than a half a million dollars.

Â Thus, by making the investment,

Â your company would increase its profits.

Â Of course from an intuitive perspective,

Â what's happening is this;

Â the lower the interest rate, that is,

Â the cheaper the cost of borrowing money unless one has to discount the revenue stream.

Â This in turn increases the present value of

Â the revenue stream and makes the investment more attractive.

Â So if you got all that right,

Â way to go, if you didn't,

Â you may want to cycle back and redo this model before moving onto the next module.

Â This is important stuff here.

Â You will indeed find the concept of the time value of money,

Â to be a valued friend throughout your personal and professional life.

Â