[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. Okay. So what's our answer? Here's the math; we start off with our initial $2 million investment which has a negative side because it is an outlet. Then we must discount the income stream of $500,000 per year plus the $500000, the company will receive at the end of the fifth year as salvage value. This gives us a net present value or NPV of $1,924,664 just for the stream of income. Of course from that, we have to subtract our initial $2,000,000 investment. And when we do that, we find that the actual NPV of the total investment is a negative sum, minus $75,336. Wow! Did you get that right? And here's the punchline; because the net present value of the investment is actually negative, your company should definitely not make the investment. And this is despite the fact that over the life of the investment, the machines will generate an undiscounted sum of a half million dollars greater than the initial investment. [MUSIC]. Now, here is the real power of the net present value equation in concept. It allows you to evaluate investments under different interest rate assumptions. And as you will learn in our companion course in macroeconomic, interest rates constantly move up and down as the economy expands and contracts, and central banks around the world conduct their monetary policies precisely, to influence interest rates and rates of investment and economic growth. So here is the last question of this module. What if the interest rate on our loom investment is 5% instead of 15%? What does your intuition tell you right now? Will the loom investment be more or less attractive at a lower rate of interest? Will your company now make that investment in new machinery if the cost of borrowing money is cheaper? We use the NPV formula to crank out the new numbers and find some answers now as we pause the presentation. [MUSIC]. Did you get the calculation right? At the new and lower interest rate, the investment actually generates a very nice positive net present value of more than a half a million dollars. Thus, by making the investment, your company would increase its profits. Of course from an intuitive perspective, what's happening is this; the lower the interest rate, that is, the cheaper the cost of borrowing money unless one has to discount the revenue stream. This in turn increases the present value of the revenue stream and makes the investment more attractive. So if you got all that right, way to go, if you didn't, you may want to cycle back and redo this model before moving onto the next module. This is important stuff here. You will indeed find the concept of the time value of money, to be a valued friend throughout your personal and professional life.