So, Professor, if I was hoping we can go through the idea of the Gordon Growth Model? >> Mm-hm. >> And kind of how that relates to what we've learned in CAPM? >> Myron Gordon, a half century ago, nearly told what, he gave a formula for the present value of a growing quantity. Suppose we have an asset, let's call it land, that is producing revenue for you every year, and the revenue is growing in value. So it produces x the first year, then it produces x times 1 + a growth rate, the next year, and then it produces x times 1 + the growth rate squared the next year, and then it does that forever. So this is year, now it's times 0, and then we have time 1, time 2, times 3, time 4, it would be 1 + g cubed etc. I say this might be land, because land, assuming that it's managed properly and doesn't get depleted, will yield a crop every year. And as time goes on, the crop will be worth more. Partly because demand for it probably goes up in a growing economy and probably because of technical progress. And we're going to assume this land goes on growing like this forever. So the question is what do you pay for this land at time 0? Okay, so Myron Gordon, he's famous for this formula principally, is that the present value = x/r- g, where r is the rate of discount. What he's saying is that, the present value is x/1 + r, that's this first term here,+ x (1 + g)/1 + r squared + x (1+g) squared/1 + r cubed, okay. And if you calculate, you can show that infinite sum reduces to this simple formula, as long as g is less than r. If g is less than r, then each term is smaller than the one before it. And it sums to a finite number. If g equals r, then every term here is x/1 + r, they are all the same, and so the sum would be infinite. So as long as g is less than r this is a formula for pricing the value of a asset that actually yields an infinite amount, but in the future It's actually growing forever. [LAUGH] Right, so actually g can be negative also. It doesn't matter whether it's positive or negative. >> So that would be like you're losing some proportion every [CROSSTALK] >> Yeah- >> Every decade or something. >> It could be that the land is being depleted. >> Okay. >> And so the growth rate of the value is negative. So then this becomes r plus something because g is negative. You still have a present value, and this is an important thing to recognize, that even assets whose payments are running down to zero, there still is a price for them today. That's really important to recognize. So some people think that businesses that are growing are the only ones I should invest in. That's bad investing. You can make a fortune investing in businesses that are declining. You can fill up your portfolio with declining industries. It doesn't matter, it's the question, can you buy them for less than the present value? And if you're buying them for less than the present value, it's a good investment. >> I see. And so, here, just to clarify, g is given? >> Yes, I'm taking that as given, the growth rate, it might be like 2% a year. >> Right >> And the interest, r might be 5% a year. >> Okay. >> The value would be x divided by 5% minus 2% or x divided by 0.03. >> Okay. >> And this is a very useful formula because a lot of possible investments have a growth rate. In fact they usually do. Usually you don't expect the earnings of a company, for example, to stay exactly where they are today. Some companies are expected to grow through time and some are expected to decline through time. So you end up using this formula all the time to judge. You look at their earnings today and you think, well what is it worth? What is the stream of future earnings worth? And you can plug it into this formula. >> I see, and r is that also given or is that- >> Now, okay. >> Being determined? >> Now I haven't talked about risk in this equation. I was saying the land is going to do this, we just know this for certain. >> Right, that's just given. >> But we don't in fact, often, we don't know the future with certainty. So there's an amount of risk. So if this growth rate is more uncertain than you thought, that should lower the price. Right, so if the assets is riskless, if there's is no risk, if we actually know all the future payouts from the asset, then this r would be the riskless interest rate. But if it's greater, if there is risk. And that would be measured by beta in the capital asset pricing model. Then r would be increased reflecting that risk. You still use the same Gordon formula, but you have a higher r. R is no longer the riskless rate. >> Okay. And I also found that to be a very fascinating statement you made that even if most people I think typically think that if there's a industry that's declining, I don't want to have that in my portfolio. >> Right. >> But in this case we're kind of bringing out the idea that even stocks of declining industries, those should be in your portfolio if you kind of followed the- >> Right. >> The standard traditional [CROSSTALK] >> I like to bring up the example of railroads. When the first railroads came in, well it was in the 1830s, but by the 1840s, there was a big bubble in railroad stocks. Lots of people thought wow, railroads are growing. They were right. Railroads were growing. But people paid too much. Even though they're growing, you can pay more than the present value. So lots of famous people in the very beginning of the railroad era, lost fortune, even including Charles Darwin, the great biologist. He couldn't figure out present value. He was a smart guy, but he couldn't figure out what the real value of these railroad stocks were. But then as time went on, railroads stopped being glamorous and exciting. And they became old hat. And then we got airplanes, and trucks, and cars, and all these other alternatives to railroads. So railroad stocks then became underpriced relative to this formula. So one of the best investments to make in 1929 was railroads, already people were thinking about Charles Lindbergh flew across the Atlantic Ocean, everything is moving fast for airlines, and they just got overpriced. The same thing happened in the year 2000. In 2000, that was the peak of the dot-com bubble. Everybody was investing in computer or software, or social media stocks. And because they saw the growth rate. But they made a mistake. You have to use this formula. They made a mistake in thinking that they're worth more than they really were, and the whole dot-com bubble collapsed. The good thing to invest in, if you could go back in a time machine to 2000, was railroads, [LAUGH] everyone was ignoring them. But they're still chugging along, doing all this work. And now, even being declining industry, it wasn't living up to expectations initially, in terms of earnings growth, but they made good investments. Sometimes, not every time, depending on how the price compares to the present value of their earnings.
