0:10

And I want to remind you that these breaks are more to kind

Â of give you my sense of where you probably need to stop,

Â but remember this is you, and many different ways of learning.

Â There are lots of you there.

Â So it's up to you to always take a break.

Â And if you don't understand something, you have other resources.

Â So you don't have to go to these videos until you feel comfortable moving forward.

Â I'm emphasizing this right now,

Â because the idea of a stock is not easy to comprehend.

Â 1:08

So that's all that it's saying.

Â Why dividend?

Â That's just a name for the way the stock pays stuff to you, right.

Â Like for example, for a bond it was coupon and then face value.

Â Why is there no face value here?

Â Because you expect when you buy a stock that the stock,

Â even if you're going to sell it, is going to have value.

Â 3:37

Turns out, and if you have the time, you can do these calculations for yourself,

Â and data for yourself, but I think it's very cool to derive this.

Â But imagine the formula is the simplest possible c over little r.

Â Actually I apologize because I sometimes use big r and little r but

Â r unqualified means the discount rate or cost of capital.

Â 4:34

So this is the formula.

Â What I'm going to do is I'm not going to try to derive it for you.

Â And this is where I think you need to

Â put in some work based on the level of curiosity you have.

Â You can look at the books I've recommended to you or

Â you can sit down if your curious, just derive it.

Â Remember this is equal to what?

Â 5:12

The only constraint I'm putting on this is these two variables are the same,

Â approximately.

Â And why do we use these formulas?

Â Because remember, a stock, you don't even know what the dividend is going to be in

Â the first year or the second year.

Â So getting too precise can be actually hurtful to your thinking.

Â You're doing a very detailed calculation of stocks.

Â Doesn't make that much sense, so

Â we will use formulas like these because they kind of capture both

Â 5:52

So we know that if it's dividend stock is a constant level of dividend,

Â whatever it is.

Â Let's do this.

Â Let's spend five minutes and

Â you do it with me, and I'm assuming the problem is relatively straight forward.

Â We can do it with each other.

Â Otherwise, just take a break, do it.

Â 6:13

And we'll come back to it, and I will try my best to

Â make sure that I'm making a good judgement about what is doable together and

Â what is you want to do a little bit of a break and test yourself.

Â And remember, you have always the opportunity to go to the assessments and

Â assignments to do similar problems and then come back, okay?

Â So this problem is relatively easy.

Â It says suppose Green Utility is expected to be at dividend

Â to pay a dividend of 50 cents.

Â Not to be a dividend but to pay a dividend of 50 cents per share for

Â the foreseeable future.

Â And the return on the business is 10%.

Â What does this mean, return on the business.

Â It means another way of saying that the cost of capital belongs not to you,

Â not to anyone, but the type of business you are in, and

Â that return is a function of demand, supply, everything, but together.

Â What should be the price of the stock?

Â 7:34

And I'm asking you what would the price of the stock be?

Â And I'm calling it a utility because it turns out utilities are regulated.

Â And it's very common to view them as income stocks,

Â as opposed to another example I'm getting to which is

Â at the heart of the rest of the session this week.

Â It's called Growth Stocks and I just love that stuff because

Â it'll convey what really is going on and how growth is good.

Â How growth could be bad and so on.

Â But let's stick right now with the stock that's not planning to grow but

Â is planning to pay $0.50.

Â 9:13

the assumptions behind the ease of the formula.

Â You just suddenly realize, how cool it is.

Â You know how people are so comfortable with numbers, seemingly,

Â in the financial world.

Â It's because they use formulas like this.

Â That's what's ingrained at the back of my head.

Â And therefore, I can feel very comfortable.

Â It's not that I'm very comfortable calculating complicated

Â formulas with numbers in Excel.

Â In fact, I shouldn't be and I have better things to do.

Â Okay, so let's just see,

Â what does forever mean?

Â Now many people get caught up in, nothing is forever, how could it be forever?

Â Let's just, this is not quite real,okay?

Â So let me ask you the following question.

Â Let me assume that forever means 30 years.

Â And by the way, that's not terribly long, right?

Â A lot of companies do survive 30 years.

Â That's not the important point though.

Â We are trying to price a stock that

Â is not expected to die tomorrow because there's no point in doing that, right?

Â So let's take this example, same example and

Â say, okay Gautham, forget about this perpetuity stuff.

Â It doesn't make sense.

Â So let's just assume it lasts for

Â 30 years and the dividend is 0.50.

Â 11:03

So just to recall what was the value of the perpetuity,

Â it was $0.50 divided by 0.1, very simple.

Â So 50 cents multiplied by 10 was 5 bucks.

Â Keep that in the back of your mind.

Â Now let's do this on a calculator.

Â You see what's going to happen, you can't do this in your head.

Â And that's part of the value proposition I was talking about.

Â So let's go to an Excel.

Â Let's do =, and what are we figuring out?

Â PV, I'm actually much slow than you probably, by now.

Â And you guys are just rolling along with this stuff and

Â saying, Gautham, come on, get, go fast.

Â I don't type very fast, that's the way I am.

Â Well anyways, so the rate is .05, that can't change.

Â And how much of my, sorry, rate is 0.1.

Â Right, there you go.

Â I'm talking and I'm messing up numbers.

Â The rate was 10%.

Â I think I got it right, 0.1.

Â The number of periods was what?

Â Not infinity, I don't like that, but 30 is fine.

Â And how much was my money?

Â $0.50, and I hope my fingers haven't done anything bizarre.

Â What's the answer or what's the value?

Â Look, it's $4.71.

Â Why did I do this?

Â Let's go back.

Â 12:44

Are you sure for the next 30 years, you'll get that dividend?

Â Because if it was exactly true, that you expected it and

Â you got it, there's something really magical about you.

Â Oh the real world, the real world doesn't operate like that.

Â It's approximately that, right?

Â So getting very precise about 5 bucks for 30, I mean, $0.50 for

Â 30 years would make sense if you were exactly sure that it's going to happen.

Â 13:27

And this, by the way, seemingly a very simple example, but it's a very deepish,

Â right, so this shows you why finance is both art and science.

Â All your numbers are wrong.

Â So what's the point of getting very precise about being wrong, right?

Â So let's compare these two.

Â 14:41

Infinity.

Â But you see now the power of, pause again, compounding.

Â At a 10% rate of return,

Â the money that you get at the 31st year, it's almost trivial.

Â It's only $0.29, even though it's forever.

Â So recognizing that the interest rate is positive, and

Â for stocks, stocks are risky relative to bonds.

Â They're likely to be high.

Â You know that formulas like perpetuities will bring you so close,

Â that you don't need to necessarily be very precise.

Â I am not saying don't use Excel, I'm saying most of value

Â of the framework comes from your thinking not from your answers, they are wrong.

Â I hope you found this little example very useful because

Â formulas like c over r are used all the time.

Â They are bases of are what are called multiples in finance.

Â Venture capitalists, people in I banking,

Â people who value stocks, don't try to get too precise.

Â On the other hand, bond pricing, I just touched upon a little bit,

Â can get very, very technical and precise.

Â And the reason is.

Â There's uncertainty only in one thing.

Â Fundamentally, in government bonds, for example.

Â If you expect the cash flow to be paid,

Â the uncertain interest rates is driving everything.

Â So you can get really precise in trying to model that.

Â But anyways, here in stocks, everything's uncertain.

Â [LAUGH] So what's the point getting too precise about?

Â Pretty much everything, because you can't.

Â 16:35

And this is called a growth stock.

Â And I'm sure you have seen examples of these and

Â things happening as we speak, which is the biggest company in the world

Â right now in terms of value of their stock?

Â Remember, when I say, value for company, I could mean many things.

Â The first thing I could mean is being a finance guy,

Â what is the market cap, which is the value of their stocks.

Â But companies also have debt.

Â So when I say a value of the whole company,

Â people would want to include that, which makes sense.

Â So anyway, so which is the company whose stock value is the most in the world?

Â It's Apple.

Â Apple has almost gone and survived, almost died and

Â survived and then grown rapidly in different phases.

Â So I would call it a growth stock, but it depends on where is it in its lifecycle or

Â new idea generation, regeneration or whatever.

Â So let's see how this would be priced.

Â Look what I am saying here.

Â Your Po here, where the first dividend is DIV1.

Â You can also call this generically, C1.

Â You see, that's what I told you, the nice thing about finance.

Â Once you know time, value and money, then we'll do risks at a fundamental level.

Â You can do any problem.

Â Because the beauty is the same framework, same tools, just the symbols change.

Â The names change.

Â So the first is C1.

Â 18:26

And in this case, DIV2

Â is DIV1(1+g) and so on.

Â Now obviously, we'll see and I'll show you the formula again.

Â It looks very similar to the previous one.

Â Let me first show you the formula.

Â But remember genetically, what will DIV2 be called?

Â C2 and so on.

Â So let me write the formula down and then we'll, by the way,

Â this is the only form of it, I haven't derived it for you.

Â And the reason, it'll just take up too much time.

Â The generic formula is C1 over r-g.

Â What is g?

Â 19:16

In this case, expected dividends.

Â What is C1?

Â The first cash flow.

Â So this is very important.

Â First cash flow is C1, the g is the growth in the cash flows not in r.

Â R is already a percentage.

Â So these are both percentages.

Â R and g are both percentages.

Â So, I'm not subtracting dollars from a percentage.

Â 19:53

You'll have to go the long way to do C1 divided 1 plus r,

Â C2 divided by 1 plus r square till such point that r is greater than g.

Â And that will always happen, think about it.

Â If g was greater than r, you would own the world.

Â It's not possible in a steady state, but

Â those are things that you get to practice in your assessment.

Â So let's call this the formula and

Â replace it by DIV1 over r-g.

Â And I'm going to use examples where r is greater than g.

Â But as I said, again don't use the formula when it doesn't make sense to use.

Â For example, if r is equal to g, what are you going to do?

Â Sit there, stare at the formula.

Â You have something divided by zero, go figure.

Â We use the long method.

Â And that's another thing I don't like about the way we get taught math and

Â algebra is we are never taught in a context.

Â I shouldn't say, never.

Â I was lucky in high school.

Â I was taught math always in a context and I've benefited so much by it, instead many

Â times we are taught stuff and all we see is the backside of the person teaching.

Â And that's not very interesting, anyways.

Â So let's get started with the formula and

Â I'm going to now let you take a little while to do it.

Â This is a good time to take a break, but let's first read the formula.

Â Suppose Moogle, Inc, I apologize my sense of humor is limited.

Â Is expected to pay, Ryan is laughing with me.

Â Is expected to pay dividends of 20% next year.

Â You see how I have to specify the first dividend?

Â And the dividends are expected to grow indefinitely at a rate of 5% per year.

Â Again, the word indefinitely doesn't literally mean forever.

Â Remember, it's reusing formulas as an approximation.

Â Stocks of similar firms are earning an expected rate of return of 15% per year.

Â Why am I saying this?

Â Because I want to repeatedly remind you

Â that the 15% is not owned by you.

Â In fact, it doesn't belong to anybody, it belongs to the marketplace.

Â Businesses get different rates of return due

Â to a fundamentally different set of risks.

Â What should be the price of a share of Moogle, Inc?

Â So just take a minute and try to do it in your head.

Â When we come back, we'll do it together and see how easy it is.

Â Take a break.

Â See you soon.

Â