0:00

So, Professor,

Â if I was hoping we can go through the idea of the Gordon Growth Model?

Â >> Mm-hm.

Â >> And kind of how that relates to what we've learned in CAPM?

Â >> Myron Gordon, a half century ago, nearly told what,

Â he gave a formula for the present value of a growing quantity.

Â 0:24

Suppose we have an asset, let's call it land,

Â that is producing revenue for

Â you every year, and the revenue is growing in value.

Â So it produces x the first year, then it produces x times 1 + a growth rate,

Â the next year, and then it produces x times 1 + the growth

Â rate squared the next year, and then it does that forever.

Â So this is year, now it's times 0,

Â and then we have time 1, time 2, times 3,

Â time 4, it would be 1 + g cubed etc.

Â I say this might be land, because land, assuming that it's managed properly and

Â doesn't get depleted, will yield a crop every year.

Â And as time goes on, the crop will be worth more.

Â Partly because demand for it probably goes up in a growing economy and

Â probably because of technical progress.

Â And we're going to assume this land goes on growing like this forever.

Â 1:43

So the question is what do you pay for this land at time 0?

Â Okay, so Myron Gordon, he's famous for

Â this formula principally,

Â is that the present value = x/r- g,

Â where r is the rate of discount.

Â 2:08

What he's saying is that,

Â the present value is x/1 + r,

Â that's this first term here,+ x (1

Â + g)/1 + r squared + x (1+g)

Â squared/1 + r cubed, okay.

Â And if you calculate,

Â you can show that infinite sum

Â reduces to this simple formula,

Â as long as g is less than r.

Â If g is less than r, then each term is smaller than the one before it.

Â And it sums to a finite number.

Â If g equals r, then every term here is x/1 + r,

Â they are all the same, and so the sum would be infinite.

Â So as long as g is less than r this is a formula for pricing the value of

Â 3:14

a asset that actually yields an infinite amount, but

Â in the future It's actually growing forever.

Â [LAUGH] Right, so actually g can be negative also.

Â It doesn't matter whether it's positive or negative.

Â >> So that would be like you're losing some proportion every [CROSSTALK]

Â >> Yeah-

Â >> Every decade or something.

Â >> It could be that the land is being depleted.

Â >> Okay.

Â >> And so the growth rate of the value is negative.

Â So then this becomes r plus something because g is negative.

Â You still have a present value, and this is an important thing to recognize,

Â that even assets whose payments are running down to zero,

Â there still is a price for them today.

Â That's really important to recognize.

Â So some people think that businesses that are growing are the only ones I should

Â invest in.

Â 4:15

That's bad investing.

Â You can make a fortune investing in businesses that are declining.

Â You can fill up your portfolio with declining industries.

Â It doesn't matter, it's the question, can you buy them for

Â less than the present value?

Â And if you're buying them for less than the present value, it's a good investment.

Â >> I see.

Â And so, here, just to clarify, g is given?

Â >> Yes, I'm taking that as given, the growth rate, it might be like 2% a year.

Â >> Right >> And the interest, r might be 5% a year.

Â >> Okay.

Â 4:55

>> The value would be x divided by 5% minus 2% or x divided by 0.03.

Â >> Okay.

Â >> And this is a very useful

Â formula because a lot of possible investments have a growth rate.

Â In fact they usually do.

Â Usually you don't expect the earnings of a company, for example,

Â to stay exactly where they are today.

Â Some companies are expected to grow through time and

Â some are expected to decline through time.

Â So you end up using this formula all the time to judge.

Â You look at their earnings today and you think, well what is it worth?

Â What is the stream of future earnings worth?

Â And you can plug it into this formula.

Â >> I see, and r is that also given or

Â is that- >> Now, okay.

Â >> Being determined?

Â >> Now I haven't talked about risk in this equation.

Â I was saying the land is going to do this, we just know this for certain.

Â >> Right, that's just given.

Â >> But we don't in fact, often, we don't know the future with certainty.

Â So there's an amount of risk.

Â So if this growth rate is more uncertain than you thought,

Â that should lower the price.

Â 6:10

Right, so if the assets is riskless, if there's is no risk,

Â if we actually know all the future

Â payouts from the asset, then this r would be the riskless interest rate.

Â 6:38

You still use the same Gordon formula, but you have a higher r.

Â R is no longer the riskless rate.

Â >> Okay.

Â And I also found that to be a very fascinating statement you made that even

Â if most people I think typically think that if

Â there's a industry that's declining, I don't want to have that in my portfolio.

Â >> Right. >> But in this case we're kind of bringing

Â out the idea that even stocks of declining industries, those should be in your

Â portfolio if you kind of followed the- >> Right.

Â >> The standard traditional [CROSSTALK] >> I like to bring up the example of

Â railroads.

Â When the first railroads came in, well it was in the 1830s, but

Â by the 1840s, there was a big bubble in railroad stocks.

Â Lots of people thought wow, railroads are growing.

Â They were right.

Â Railroads were growing.

Â But people paid too much.

Â Even though they're growing, you can pay more than the present value.

Â So lots of famous people in the very beginning of the railroad era,

Â lost fortune, even including Charles Darwin, the great biologist.

Â He couldn't figure out present value.

Â He was a smart guy, but

Â he couldn't figure out what the real value of these railroad stocks were.

Â But then as time went on, railroads stopped being glamorous and exciting.

Â And they became old hat.

Â And then we got airplanes, and trucks,

Â and cars, and all these other alternatives to railroads.

Â So railroad stocks then became underpriced relative to this formula.

Â So one of the best investments to make in 1929 was railroads,

Â already people were thinking about Charles Lindbergh flew across the Atlantic Ocean,

Â everything is moving fast for airlines, and they just got overpriced.

Â The same thing happened in the year 2000.

Â In 2000, that was the peak of the dot-com bubble.

Â Everybody was investing in computer or software, or social media stocks.

Â 9:01

They made a mistake in thinking that they're worth more than they really were,

Â and the whole dot-com bubble collapsed.

Â The good thing to invest in, if you could go back in a time machine to 2000,

Â was railroads, [LAUGH] everyone was ignoring them.

Â But they're still chugging along, doing all this work.

Â And now, even being declining industry,

Â it wasn't living up to expectations initially,

Â in terms of earnings growth, but they made good investments.

Â Sometimes, not every time,

Â depending on how the price compares to the present value of their earnings.

Â