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Alan Cring Productions in association with Emergent Light Studio presents the Illinois State Collegiate Compendium, academic lectures in business and economics.

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This is business finance, FIL 341 for Autumn Semester 2024.

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Today, stock price valuation.

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I have a spreadsheet for this one.

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It, and some of the worksheets within it, a lot easier to use the Excel spreadsheets and to try to do these on your own.

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Trust me on that. You'll see why here in a little bit.

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But, so in your canvas, you're going to go to files, and once you're in the files, you go to spreadsheets.

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I said you go to spreadsheets.

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Find spreadsheets here.

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There we go.

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Go to your spreadsheets folder, and the one that you will want to download is stock valuation.

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Now, go over here to the three dots on the far right side of that line, and you click those and you download

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the stock valuation sheet.

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Enable editing.

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Go to the dividend model.

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I will take this from the simplest scenario, which is pretty unrealistic,

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on through to some scenarios that are more realistic.

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I'll show you how you deal with each one of those.

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There's a worksheet in that spreadsheet for each of the different scenarios that I'm going to start with.

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Along the way, I'm going to introduce some new terminology to you as well, just to make this a really rollicking lecture.

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Okay, we're good.

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First things first.

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I've said this part before.

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What we do in finance and in accounting hinges on an assumption, what we call the going concern assumption,

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that the company is going to stay in business for an indeterminably long period of time.

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In accounting, that is why we can do accrual accounting, not assuming that we have to pay all of our bills

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right away in cash.

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We allow accruals, accumulation.

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In finance, it plays its part through the assumption that a company's earning power,

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we hope positive but sometimes negative, continues for the foreseeable future.

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In other words, we don't have a terminal date for a company.

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Now, we may terminate our ownership of that company through selling the stock,

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but the company itself goes on forever.

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The first scenario you see up there is painfully simple.

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It's an easy scenario.

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This is where we would assume that the company, you're going to buy the stock,

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and you'll collect the dividends for a couple of years, and then you will sell the stock down the road.

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So we can start with a, and I will just give you a quick scenario.

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This first sheet is woefully easy.

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One thing I do want to promise you is that I won't take the models any further than examples that I do in class

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so that you don't have to do anything crazy to the spreadsheets.

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You buy a share of ZLT, common stock.

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You receive a dividend at the end of the first year,

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and again, this is a very unrealistic scenario, but it starts us off, of $1.60.

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In the second year, a dividend of $1.80,

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and in the third year, a dividend of $1.55.

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After that third dividend,

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you sell the stock for $18.75.

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If you discount the cash flows at 7.25%,

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what is the current price of the stock?

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I'll give you a minute to catch up there.

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Okay.

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Now, most of these, I'm going to, I think all of them, I will be drawing a timeline.

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It's not absolutely necessary to do it, but it helps clarify what you're after, what you're doing,

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and I do them to this day, not just for the teaching, the pedagogy of it,

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but just so I can keep my own brain straight.

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What we have here, you buy a stock, year zero.

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You got year one, year two, you got year three.

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So in this case, the first year was $1.60.

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You're going to get a buck sixty, 1.60.

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Above the two, second year, I'm going to put the $1.80.

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And above the three year, I'm going to put the $1.55.

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But I'm also going to put my sale price, $18.75.

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So what you are really doing here, to find the price right here,

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P zero is going to be $1.60 discounted back one period, what did I say,

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one plus.075 to the negative first, plus the second year dividend, $1.80,

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discounted back two years at 7.25, I'm sorry, I put it, 7.25, 7.25,

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one plus, to the negative second power, plus the third year,

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which will be the $1.80, but also plus the $18.75 discounted back one plus.0725

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to the negative third.

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That's how you're going to get the price.

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Now, you're just going to take each of these back,

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you're going to telescope each of them back to the present,

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and add them up, and that should be the price of the stock now,

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because that's the present value of its future expected cash flows to you.

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Again, it's kind of unrealistic, well how do you know the price in three years?

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It sets the stage for more difficult ones.

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But I promise I'll have one of these easy ones on a quiz or an exam,

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so that you can actually sort of have one that's an anchor.

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So in this case, on the worksheet one, the dividend model worksheet,

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I'll put in the dividends that we need to do, 1.60,

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the next dividend, year two, was 1.80,

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and the dividend three is $1.55,

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and then over here in the column C, where the sale price,

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you put that in, and I'll put in $18.75.

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There it is.

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Now I have to put my discount rate in.

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What did I say the discount rate was?

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7.25%, 7.25, and there's your stock price, $19.66.

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That easily.

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Now notice how the formula works, because if I gave you four years,

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you'd have to adjust this.

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The way the formula works is I'm going to say equals NPV,

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that's for the present value, open the parentheses,

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and then the first entry will be your discount rate, B10,

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and then the second one will be your first dividend, comma,

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let me do it, I want to do it a little bit simpler for you to make it clear.

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Your first dividend, B2, comma, your second dividend, B3,

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comma, your third dividend, plus your sale price.

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Now obviously if I gave you four years, it'd be B2, B3, B4, B5, plus C5.

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I could do this with a macro so that it could tell how many years you were doing and all that,

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but like I said, macros are not very popular.

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And so close the parentheses, $19.51.

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Now I will allow for, obviously as I always do, a little wiggle room in your answer.

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Take the answer if it's plus or minus 25 cents or something like that,

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because you might glitch a number in there and cause a value to change,

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but there's all that you do, that's all you do.

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Now the second one, okay, you okay on that one?

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The second one, for this one I have to step back just a little bit here

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and go through a kind of stock that I've barely mentioned,

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and I think they mentioned it earlier in the book,

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but I have a specific purpose for doing it here.

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When we talk about stock, we almost invariably talk about common stock.

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But as I had mentioned earlier, there's another kind of stock called preferred stock.

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Preferred stock is odd, because to a certain extent it's like a bond.

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Let me just do an example.

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ABV cumulative preferred, I'm sorry, ABV, let's put in 2.65% cumulative preferred.

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Par value $80 per share.

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Here's how preferred works.

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Preferred, when you buy a share of preferred, as long as you own that share of preferred,

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you will get the dividend from the preferred every year forever, or they may divide it up.

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It is perpetual, it is what we call a perpetuity.

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The cash flow never ends, and it is the same.

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What is that dividend? D, the dividend, you take 2.65% times the par value.

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If you notice, that's just what you do with a bond.

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You take the coupon times the face value, the par value, $1,000, it's always $1,000 for a bond.

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Preferred, it's whatever is on the stock certificate itself.

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So I would take.02, what did I say there, 6.5, times $80, $2.12.

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So in other words, you're going to get a dividend every year for each share of $2.12,

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and that will go on forever. It will never stop.

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Now I won't beat this one over the head, but in your math class,

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you were shown a kind of addition of numbers called a series.

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It's an infinite, or maybe not an infinite, but in our case, an infinite sum of numbers.

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Usually something like 1 half plus 1 fourth plus 1 eighth plus 1 sixteenth, something like that, forever.

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And you saw, if you remember, that sometimes these diverts, they become infinite.

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But some of them converge, and the one we will be using here actually converges to a specific value.

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And there's a formula. You don't have to just keep adding up $2.12 times 1 plus the discount rate to the negative 1,

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plus $2.12 times 1 plus the discount rate to the negative 2 forever. You don't have to.

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Because the price of the share, adding up the discounted present value of $2.12,

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forever at higher and higher discount rates as the years go on,

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it comes out that the price of preferred stock is the dividend divided by the discount rate on the preferred stock.

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That's all it is.

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And in this case, that would be $2.12.

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Now, let me give you a discount rate for the preferred here.

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Let's say that its discount rate is 2.50%.

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So we would have $2.12 divided by.025.

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Survey says, divided by 2.5.

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And I ask, let's try that again. $2.12 divided by.025.

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$84.80.

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And you notice that the yield, what the market wants, is 2.5, which is lower than what the dividend is.

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So this price sell, this preferred stock sells at a premium to par.

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Just like a bond.

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Watch.

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Let me do discount rate and the price of the preferred stock.

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Now, we've done 2.50%.

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And we've got a price of $84.80.

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Let's try something like 2.80% for that formula right there.

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So I take the coupon, or rather the dividend, $2.12 divided by.028.

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And I get $75.71.

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It sells at a discount to par.

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Now let's see what would happen if I took a discount rate that was the same as the dividend rate, 2.65%.

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In that case, I take $2.12 divided by.0265.

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It sells at par.

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It's just like a bond.

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If the yield is below the dividend, then it sells at a premium to par.

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The market doesn't need 2.65, it only needed 2.50.

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So it's paying more than it should, so the market drives it up.

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If the market wants more than the coupon, 2.80% against the coupon, or the dividend, I keep saying coupon, 2.65,

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it will sell at a discount.

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But if the yield and the rate and the dividend rate are the same, it will sell right at par value.

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Just like a bond does.

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As the price goes, as the yield goes up, the price goes down.

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As yield goes down, the price goes up.

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The same inverse relationship.

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This formula right here.

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That formula for the price of a preferred share, D over R sub P, is actually a special case of a more general formula.

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I'll get to that in just a minute.

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But that more general formula for dividends that don't stay the same but grow at a constant rate, like some stocks do,

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the price of the stock will be the dividend in the next period, divided by the discount rate on the stock,

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minus the growth rate.

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Now the dividend in period one is nothing but the dividend they just paid, grown one period.

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One plus G.

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The formula for the preferred is just where G is zero.

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So watch this.

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If I want to price a share of preferred stock, if I wanted to price a share of preferred stock,

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I go to the constant growth rate formula.

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Well the first thing that I would want to do is I'd say this is a preferred stock so it has a zero dividend.

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And then I look at my discount rate.

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Let's try that 2.5% discount rate.

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And the current dividend, if I want to find the current dividend, I just say equals, what is the dividend?

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Well it's.0265 times $80.

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And there you go.

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So for preferred, all you do is set the growth rate to zero.

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That's basically all you do.

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Because dividends on preferred stocks don't grow, they just stay the same forever.

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Good times.

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And I could do the other one too where the current dividend, what do I say, discount rate.

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What did I do for that other discount rate?

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2.8075.71, just like I calculated.

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So this one, as you see, as I had said, you do a little more legwork in these worksheets than you did before.

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You have to just make sure that you have the right growth rate in, the right discount rate, and also what the current dividend is.

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And with preferred, all you do is take the dividend rate times the par value of the stock.

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And I'm going to put that here.

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And then you just get your answer.

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That one shouldn't be too bad for you to do on the quiz.

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The quiz will just be a series of these problems.

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Starting with the very simplest dividend model problem, and then going to the preferred stock.

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Now, let me step back a little ways here.

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Companies almost always start out not paying any dividends.

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That's one of the reasons they're risky.

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Their betas are high, and their prices are so volatile.

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We really don't have a whole lot of a model to figure out what the present value, the intrinsic value of the stock is.

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So we kind of feel around in the dark.

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However, most companies, the first thing that they want to do is to start paying a dividend.

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It's a signal that the company can afford to give the shareholders back some of what they have put in.

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So a company first starts by giving out a dividend, but it usually is one of those things where the dividend is all over the place.

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They give out a dividend of $1 the first year, $2 the second year, then they can't give a dividend the third year, then it's 85 cents the fourth year, something like that.

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So it's all kinds of, all over the place.

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However, companies want to try to stabilize their dividend.

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More precisely, they want to stabilize the dividend to a constant growth rate where there is a certain present value that we can find.

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And so the larger investors who want some way to see intrinsic value, the fund managers who want some anchor to know where intrinsic value is,

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so that they will be more willing to invest in this company.

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00:28:14,000 --> 00:28:23,000
That's why companies strive eventually to get to a constant growth rate of their dividends.

224
00:28:23,000 --> 00:28:28,000
Now, older companies have already gotten there.

225
00:28:28,000 --> 00:28:37,000
They are already in the phase of their life where their dividends grow at a constant rate per year.

226
00:28:37,000 --> 00:28:46,000
I wasn't sure if I bought that years ago, and then I started looking at dividends by year of some big old companies.

227
00:28:46,000 --> 00:28:52,000
Sure enough, from year to year, the dividend was growing at a relatively constant rate.

228
00:28:52,000 --> 00:28:56,000
Now, sometimes it was a little above that rate, sometimes a little below that.

229
00:28:56,000 --> 00:29:00,000
But the trend line was actually very tight around the data point.

230
00:29:00,000 --> 00:29:08,000
This company grows its dividend at 2.25% per year, or 1.2% per year.

231
00:29:08,000 --> 00:29:10,000
You can see it in the data.

232
00:29:10,000 --> 00:29:14,000
Companies really do have constant growth rates.

233
00:29:14,000 --> 00:29:40,000
So we can talk about a company, like for example, G.C.B. just paid a $2.50 dividend.

234
00:29:40,000 --> 00:30:09,000
That is expected to grow at a constant rate of 3.25%.

235
00:30:09,000 --> 00:30:22,000
For the foreseeable future.

236
00:30:22,000 --> 00:30:50,000
If we discount the cash flows at, let's say, 8.75%, what is the current price?

237
00:30:50,000 --> 00:31:18,000
Price per share of G.C.B. common.

238
00:31:18,000 --> 00:31:33,000
Now remember that this formula uses the dividend one year out.

239
00:31:33,000 --> 00:31:42,000
I'll let you get caught up with me here.

240
00:31:42,000 --> 00:31:54,000
So in order for me to get this price, I would take D0, which is the dividend they've just paid,

241
00:31:54,000 --> 00:32:20,000
and I would take the discount rate of $2.50 times one plus the growth rate of.02325 divided by the discount rate.0875 minus the growth rate.0325.

242
00:32:20,000 --> 00:32:24,000
Now if you do this by hand, for heaven's sakes, don't be like me.

243
00:32:24,000 --> 00:32:27,000
Put the bottom in parentheses.

244
00:32:27,000 --> 00:32:33,000
Don't forget to do that.

245
00:32:33,000 --> 00:32:36,000
One thing I should mention.

246
00:32:36,000 --> 00:32:42,000
You might see a problem where they're telling you what the next dividend would be.

247
00:32:42,000 --> 00:32:44,000
They'd be telling you the D1.

248
00:32:44,000 --> 00:32:48,000
So if they do tell you that, then you don't grow it.

249
00:32:48,000 --> 00:32:57,000
Like if I said, the dividend next year is expected to be $2.55, then you just put $2.55.

250
00:32:57,000 --> 00:33:02,000
You wouldn't grow it because it's already D1, the one they're giving you.

251
00:33:02,000 --> 00:33:05,000
But I give you this.

252
00:33:05,000 --> 00:33:22,000
I will use the current dividend they've just paid, so you will use it in the form that I've shown you there.

253
00:33:22,000 --> 00:33:25,000
Now here we go.

254
00:33:25,000 --> 00:33:30,000
We're using the same worksheet, constant growth rate model.

255
00:33:30,000 --> 00:33:36,000
The discount rate is first, 8.75%.

256
00:33:36,000 --> 00:33:41,000
The growth rate in this one is 3.25%.

257
00:33:41,000 --> 00:33:52,000
And the current D0 dividend is $2.50.

258
00:33:52,000 --> 00:34:00,000
And there's your stock price, $46.93.

259
00:34:00,000 --> 00:34:03,000
That is easy.

260
00:34:03,000 --> 00:34:07,000
Just make sure you put it in the numbers correctly.

261
00:34:07,000 --> 00:34:16,000
And I give you a little room in case you glitch on a little bit on the number, but $46.93.

262
00:34:16,000 --> 00:34:23,000
Now you can do it by hand, but you're fraught with little mistakes in parentheses.

263
00:34:23,000 --> 00:34:26,000
This way you just get the answer.

264
00:34:26,000 --> 00:34:27,000
No pain.

265
00:34:27,000 --> 00:34:31,000
And remember, if it's preferred stock, the growth rate is zero.

266
00:34:31,000 --> 00:34:36,000
That's all you have to remember is if it's preferred stock, the growth rate is zero.

267
00:34:36,000 --> 00:34:41,000
And you have to calculate the current dividend, the dividend rate times par value.

268
00:34:41,000 --> 00:34:54,000
But this takes you through the first more or less realistic stock pricing technique.

269
00:34:54,000 --> 00:34:59,000
Something I need to mention here is that growth rate.

270
00:34:59,000 --> 00:35:06,000
This formula would not work if the growth rate were larger than the discount rate.

271
00:35:06,000 --> 00:35:13,000
In other words, if I said the growth rate is 10%, all bets are off.

272
00:35:13,000 --> 00:35:18,000
Now that is not as much of a weakness as you might think.

273
00:35:18,000 --> 00:35:25,000
If you decided to take a course after this one because you just can't live without me teaching you finance,

274
00:35:25,000 --> 00:35:39,000
we have a term that at first it sounds like it was rejected and it's still rejected by some business people.

275
00:35:39,000 --> 00:35:43,000
We call it the maximum sustainable growth rate.

276
00:35:43,000 --> 00:35:46,000
And it's a mathematical formula.

277
00:35:46,000 --> 00:35:53,000
And we have found that this actually jives with the empirical studies.

278
00:35:53,000 --> 00:35:55,000
In other words, looking at companies.

279
00:35:55,000 --> 00:36:02,000
The maximum sustainable growth rate is a growth rate that a company,

280
00:36:02,000 --> 00:36:13,000
if it goes above that growth rate, it actually will die unless it pulls it back down below that growth rate within a year or two.

281
00:36:13,000 --> 00:36:26,000
The reasons might be all kinds of varied, but we know that you can't have growth rates that are just 50% over and over and over again.

282
00:36:26,000 --> 00:36:32,000
Because if they are, the company begins to get into terrible trouble and eventually it either goes bankrupt

283
00:36:32,000 --> 00:36:39,000
or it gets absorbed by a much larger company whose overall growth rate is sustainable.

284
00:36:39,000 --> 00:36:44,000
So it's not so much to say, well, the growth rate can't be as large as the discount rate.

285
00:36:44,000 --> 00:36:57,000
In fact, that comes into play from the results of maximum sustainable growth rate of a company.

286
00:36:57,000 --> 00:37:05,000
I mean, you should see the growth rates of companies, older companies when they were young,

287
00:37:05,000 --> 00:37:09,000
those growth rates were insane, really high.

288
00:37:09,000 --> 00:37:16,000
But also their discount rates were very high too because they were risky and young.

289
00:37:16,000 --> 00:37:22,000
So rarely do we see a G that is larger than R anyway.

290
00:37:22,000 --> 00:37:32,000
But when we do, if that does not come under control relatively quickly, the companies just don't survive.

291
00:37:32,000 --> 00:37:43,000
It would be sort of like in a situation where you, good man, when you were a toddler, you were a little chunky,

292
00:37:43,000 --> 00:37:46,000
but you were going to grow out of it, but you didn't.

293
00:37:46,000 --> 00:37:53,000
You grew at a foot every month and 20 pounds every month.

294
00:37:53,000 --> 00:38:01,000
My God, by the time you were two and a half years old, you were eating my cats.

295
00:38:01,000 --> 00:38:06,000
But you can't live that way. I shot you. You ate my cat.

296
00:38:06,000 --> 00:38:12,000
But you understand that this is actually a part of a much larger principle.

297
00:38:12,000 --> 00:38:20,000
Growth cannot exceed a specific place because intervening factors go into it.

298
00:38:20,000 --> 00:38:22,000
But anyway, that's just a side note.

299
00:38:22,000 --> 00:38:24,000
You don't have to worry too much about it.

300
00:38:24,000 --> 00:38:27,000
Certainly not for my quizzes and tests.

301
00:38:27,000 --> 00:38:41,000
Okay, enough of that.

302
00:38:41,000 --> 00:38:48,000
Now, the most realistic scenario.

303
00:38:48,000 --> 00:38:51,000
I can't remember whether I mentioned this or not before now,

304
00:38:51,000 --> 00:38:57,000
but companies don't start out paying dividends.

305
00:38:57,000 --> 00:39:04,000
And when they do, the dividend is going to be all kinds of different things.

306
00:39:04,000 --> 00:39:13,000
I had a few, some of my consulting jobs that lasted for more than a couple of years.

307
00:39:13,000 --> 00:39:19,000
There would come a time when they were profitable and there was pressure from the shareholders.

308
00:39:19,000 --> 00:39:22,000
Will you please start paying a dividend?

309
00:39:22,000 --> 00:39:28,000
We've put money into this company, and all you do is take the profits and plow them back in.

310
00:39:28,000 --> 00:39:32,000
You don't give us a little bit to keep us going.

311
00:39:32,000 --> 00:39:35,000
And sometimes it can get kind of ugly.

312
00:39:35,000 --> 00:39:42,000
Companies, I was at shareholders' meetings, and they'd have me, the consultant,

313
00:39:42,000 --> 00:39:46,000
answering the shareholders' questions at the annual shareholders' meeting,

314
00:39:46,000 --> 00:39:51,000
while they sat behind me in chairs looking down at their papers.

315
00:39:51,000 --> 00:39:55,000
And you get, there was one, the woman was just furious.

316
00:39:55,000 --> 00:40:00,000
She had her time and she used it to just, where are the dividends?

317
00:40:00,000 --> 00:40:02,000
We have not had a dividend.

318
00:40:02,000 --> 00:40:05,000
We put all this money in, and you keep giving us promises,

319
00:40:05,000 --> 00:40:09,000
and now you're bragging about a profit and you don't have a dividend for us?

320
00:40:09,000 --> 00:40:11,000
What is going on here?

321
00:40:11,000 --> 00:40:13,000
And she's just yammering, she was.

322
00:40:13,000 --> 00:40:15,000
And I had to be diplomatic with her.

323
00:40:15,000 --> 00:40:20,000
Bitch, I don't, there's nothing you can do.

324
00:40:20,000 --> 00:40:23,000
We're moving money back in.

325
00:40:23,000 --> 00:40:32,000
But sooner or later, the question comes up at the C-suite meeting,

326
00:40:32,000 --> 00:40:35,000
do you think it's time we started paying a dividend?

327
00:40:35,000 --> 00:40:38,000
And my answer is two-part.

328
00:40:38,000 --> 00:40:43,000
One is that your shareholders want it.

329
00:40:43,000 --> 00:40:49,000
And two is they don't really matter as much as the big dogs on Wall Street

330
00:40:49,000 --> 00:40:52,000
and the fund managers and the heavy investors.

331
00:40:52,000 --> 00:40:58,000
They want you to show them that you can afford to pay a dividend.

332
00:40:58,000 --> 00:41:01,000
So yeah, but the second part of that is,

333
00:41:01,000 --> 00:41:05,000
once you start paying a dividend, you damn well better just keep paying it

334
00:41:05,000 --> 00:41:09,000
because you pay it once and then you say, we can't pay it this year.

335
00:41:09,000 --> 00:41:13,000
That's even worse than if you didn't pay it.

336
00:41:13,000 --> 00:41:16,000
So the second thing is, once you start paying a dividend,

337
00:41:16,000 --> 00:41:20,000
you should keep going with the dividends.

338
00:41:20,000 --> 00:41:24,000
Now, they don't have to be the same every year, not for a while.

339
00:41:24,000 --> 00:41:29,000
But eventually, you need to have a horizon

340
00:41:29,000 --> 00:41:35,000
where the shareholders can count on a constant growth rate.

341
00:41:35,000 --> 00:41:40,000
They get a dividend and they know it will be that plus a little more scratch the next year.

342
00:41:40,000 --> 00:41:43,000
And then after that, a little more scratch the next year.

343
00:41:43,000 --> 00:41:49,000
That is when the fund managers get really interested in you.

344
00:41:49,000 --> 00:41:51,000
You have shown one, that you can afford a dividend,

345
00:41:51,000 --> 00:41:57,000
and two, that you can sustain it, and three, that you can grow it.

346
00:41:57,000 --> 00:42:01,000
And that is not going to happen this year or next year.

347
00:42:01,000 --> 00:42:05,000
Your horizon could be out there five, seven, ten years.

348
00:42:05,000 --> 00:42:09,000
But there is a point right now where you say,

349
00:42:09,000 --> 00:42:17,000
we have this goal of getting the dividend under control and growing at a constant rate.

350
00:42:17,000 --> 00:42:24,000
That's when we are a big boy company or a big girl company and we can do this.

351
00:42:24,000 --> 00:42:29,000
So that takes us to the last of the models,

352
00:42:29,000 --> 00:42:37,000
where we say the company may pay dividends that are kind of all over the place for the next few years,

353
00:42:37,000 --> 00:42:42,000
but then we have a place where we have hit the horizon.

354
00:42:42,000 --> 00:42:52,000
So that you have dividends, but they are out of control for a while.

355
00:42:52,000 --> 00:42:55,000
So I'll draw a timeline of a company.

356
00:42:55,000 --> 00:42:57,000
Here is now.

357
00:42:57,000 --> 00:43:07,000
One year from now, the company pays its first dividend of let's say 75 cents.

358
00:43:07,000 --> 00:43:16,000
And then two years from now, the company pays a nice dividend of $1.50.

359
00:43:16,000 --> 00:43:28,000
And then in the third year, it pays, let's say it can't pay a dividend.

360
00:43:28,000 --> 00:43:40,000
And then in the fourth year, it picks dividends back up again at $1.60.

361
00:43:40,000 --> 00:43:48,000
And then from there, it is committed to a constant growth rate of the dividends,

362
00:43:48,000 --> 00:43:57,000
let's say of 2.4%.

363
00:43:57,000 --> 00:44:00,000
So ever after that, the dividends will be growing.

364
00:44:00,000 --> 00:44:19,000
So this dividend out here, year five, will be the $1.60 times 1 plus.024.

365
00:44:19,000 --> 00:44:28,000
Year four is called the horizon.

366
00:44:28,000 --> 00:44:34,000
And we can find the price of the stock at year four.

367
00:44:34,000 --> 00:44:46,000
Because that would be the dividend one period further out divided by R minus G.

368
00:44:46,000 --> 00:44:50,000
Because we can use the constant growth rate model now.

369
00:44:50,000 --> 00:45:13,000
We've hit a horizon where the constant growth rate formula kicks in.

370
00:45:13,000 --> 00:45:16,000
And I can tell you right now, that can be a pain in the butt.

371
00:45:16,000 --> 00:45:20,000
Especially if you have like a seven, 10-year horizon.

372
00:45:20,000 --> 00:45:24,000
You've got to take the present value of 75 cents discounted one year back,

373
00:45:24,000 --> 00:45:29,000
plus the present value of $1.50 discounted back two years,

374
00:45:29,000 --> 00:45:33,000
plus the present value of zero discounted back three years,

375
00:45:33,000 --> 00:45:38,000
plus the present value of $1.60 discounted back four years,

376
00:45:38,000 --> 00:45:49,000
plus the horizon value discounted back those four years.

377
00:45:49,000 --> 00:45:55,000
So that is where we can use the horizon value model.

378
00:45:55,000 --> 00:46:06,000
But this is the one where you have to customize it.

379
00:46:06,000 --> 00:46:15,000
You clear out your dividends and the horizon value.

380
00:46:15,000 --> 00:46:21,000
Now what we're going to do is first get in our discount rate.

381
00:46:21,000 --> 00:46:24,000
I didn't give you a discount rate here.

382
00:46:24,000 --> 00:46:27,000
Oh, 2.4%, that's right.

383
00:46:27,000 --> 00:46:30,000
No, I didn't give you the discount rate.

384
00:46:30,000 --> 00:46:44,000
Let's say that the discount rate is 9.1%.

385
00:46:44,000 --> 00:46:47,000
Now once you have the data, for heaven's sakes,

386
00:46:47,000 --> 00:46:49,000
I give you a word problem.

387
00:46:49,000 --> 00:46:54,000
I'd say the same thing that I've said 43 years ago in math classes.

388
00:46:54,000 --> 00:47:00,000
Get the numbers out of the word problem and throw away the words.

389
00:47:00,000 --> 00:47:05,000
The discount rate, I see that that is 9.1%.

390
00:47:05,000 --> 00:47:08,000
The growth rate of the dividends is 2.4%.

391
00:47:08,000 --> 00:47:13,000
We get those in there, thank God.

392
00:47:13,000 --> 00:47:17,000
Now you go back in, I've made this one for six years.

393
00:47:17,000 --> 00:47:20,000
That's the worst that I would do to you is six years.

394
00:47:20,000 --> 00:47:25,000
It's not that bad, but still, I could write a macro

395
00:47:25,000 --> 00:47:29,000
that you could just key in the number of years and the table would adjust.

396
00:47:29,000 --> 00:47:32,000
But it would be a macro and that would be a problem.

397
00:47:32,000 --> 00:47:37,000
So year one, 75 cents.

398
00:47:37,000 --> 00:47:42,000
Year two, $1.50.

399
00:47:42,000 --> 00:47:46,000
Year three, zero.

400
00:47:46,000 --> 00:47:49,000
Year four, $1.60.

401
00:47:49,000 --> 00:47:53,000
Now we're going to do the horizon value,

402
00:47:53,000 --> 00:47:56,000
rather the dividend one year further out,

403
00:47:56,000 --> 00:48:05,000
which would be equal to the dividend one period before times,

404
00:48:05,000 --> 00:48:19,000
or in parentheses, one plus the growth rate.

405
00:48:19,000 --> 00:48:22,000
Now for the horizon value.

406
00:48:22,000 --> 00:48:33,000
Remember that the horizon value is the first dividend

407
00:48:33,000 --> 00:48:38,000
where constant growth is going to happen.

408
00:48:38,000 --> 00:48:40,000
Be sure that you see that.

409
00:48:40,000 --> 00:48:45,000
The horizon value here is in year four.

410
00:48:45,000 --> 00:48:49,000
We need year five because we need the dividend in year five.

411
00:48:49,000 --> 00:48:56,000
So we say equals that year five dividend,

412
00:48:56,000 --> 00:49:14,000
which I calculated here, divided by R minus G.

413
00:49:14,000 --> 00:49:21,000
So in other words, at year four,

414
00:49:21,000 --> 00:49:34,000
the dividend is paid and the stock price at that time is $24.45.

415
00:49:34,000 --> 00:49:38,000
Now I do appreciate this is a little more robust.

416
00:49:38,000 --> 00:49:41,000
You're having to do a little modification.

417
00:49:41,000 --> 00:49:48,000
But now we're going to say equals NPV to find the present value.

418
00:49:48,000 --> 00:49:49,000
Close the parentheses.

419
00:49:49,000 --> 00:49:51,000
Open the parentheses.

420
00:49:51,000 --> 00:49:53,000
First thing with the NPV formula,

421
00:49:53,000 --> 00:49:58,000
you use the discount rate, comma.

422
00:49:58,000 --> 00:50:03,000
And then each year of dividends, one after the other,

423
00:50:03,000 --> 00:50:07,000
year one dividend, that's B2, comma,

424
00:50:07,000 --> 00:50:10,000
year two dividend, that's B3, comma,

425
00:50:10,000 --> 00:50:15,000
year three dividend, that's B4.

426
00:50:15,000 --> 00:50:22,000
And then in year four, I'm sorry, that's year three,

427
00:50:22,000 --> 00:50:31,000
it is the dividend that year plus the horizon value that year.

428
00:50:31,000 --> 00:50:35,000
We put them together, close the parentheses,

429
00:50:35,000 --> 00:50:38,000
and there's your Uncle Bob, $20.34.

430
00:50:38,000 --> 00:50:44,000
Now if it was six years, five years, and then it went constant,

431
00:50:44,000 --> 00:50:48,000
I'd do the year six, and then I'd put the horizon value there

432
00:50:48,000 --> 00:50:57,000
with the year five.

433
00:50:57,000 --> 00:51:25,000
This is the formula.

434
00:51:25,000 --> 00:51:33,000
I can't remember what the formula function is.

435
00:51:33,000 --> 00:51:35,000
But you can see it right there.

436
00:51:35,000 --> 00:51:39,000
All you do is first put in the discount rate, then comma,

437
00:51:39,000 --> 00:51:41,000
one after the other.

438
00:51:41,000 --> 00:51:47,000
Don't leave out the zero because it's keeping count of years.

439
00:51:47,000 --> 00:51:50,000
And then you just keep putting in the dividends until you get

440
00:51:50,000 --> 00:51:57,000
to the year when the dividends stop being random.

441
00:51:57,000 --> 00:51:59,000
That was year four because they're going to grow

442
00:51:59,000 --> 00:52:01,000
constantly after that.

443
00:52:01,000 --> 00:52:06,000
So I stop in year four, get that dividend, then I grow at one

444
00:52:06,000 --> 00:52:10,000
period so that I can have the formula for the horizon value,

445
00:52:10,000 --> 00:52:14,000
and you go back here and get your horizon value.

446
00:52:14,000 --> 00:52:16,000
There you go, that's close enough.

447
00:52:16,000 --> 00:52:17,000
Got it?

448
00:52:17,000 --> 00:52:18,000
That's the horizon value.

449
00:52:18,000 --> 00:52:24,000
Just be sure that you take the dividend one year past the last

450
00:52:24,000 --> 00:52:31,000
one you're given, and then you use that in the formula in column

451
00:52:31,000 --> 00:52:35,000
C of the cell right before that calculation.

452
00:52:35,000 --> 00:52:37,000
Let me do something here.

453
00:52:37,000 --> 00:52:38,000
There you go.

454
00:52:38,000 --> 00:52:39,000
That helps.

455
00:52:39,000 --> 00:52:40,000
That's a little better.

456
00:52:40,000 --> 00:52:45,000
So in other words, step one, get all your numbers in.

457
00:52:45,000 --> 00:52:50,000
Step two, get the dividend one period after your last number

458
00:52:50,000 --> 00:52:51,000
you're given.

459
00:52:51,000 --> 00:52:55,000
Step three, get your horizon value.

460
00:52:55,000 --> 00:53:00,000
Back up to the one where it all started to be constant and do

461
00:53:00,000 --> 00:53:02,000
the formula.

462
00:53:02,000 --> 00:53:04,000
Let me put this in here.

463
00:53:04,000 --> 00:53:06,000
Then I'll re-upload it.

464
00:53:06,000 --> 00:53:08,000
That should help you a little bit there.

465
00:53:08,000 --> 00:53:13,000
Okay?

466
00:53:13,000 --> 00:53:16,000
Now if you can remember how to do this, and I've got one more

467
00:53:16,000 --> 00:53:19,000
sheet here.

468
00:53:19,000 --> 00:53:25,000
That's just another horizon value problem for you to see.

469
00:53:25,000 --> 00:53:29,000
Now this one I've actually made it so it calculates it, but

470
00:53:29,000 --> 00:53:35,000
again, that wouldn't work if you had a different number of years.

471
00:53:35,000 --> 00:53:39,000
So there is that little bit of customization you have to do.

472
00:53:39,000 --> 00:53:43,000
But this one is big enough, this last little example here, is

473
00:53:43,000 --> 00:53:49,000
big enough that you could just delete a couple of the rows

474
00:53:49,000 --> 00:53:53,000
from this one for a problem that was fewer.

475
00:53:53,000 --> 00:53:58,000
I give you my guarantee that I would do no more than six years

476
00:53:58,000 --> 00:54:01,000
of dividends.

477
00:54:01,000 --> 00:54:02,000
Okay?

478
00:54:02,000 --> 00:54:05,000
That way, I mean, otherwise you're not proving anything to

479
00:54:05,000 --> 00:54:06,000
me.

480
00:54:06,000 --> 00:54:08,000
You're just typing extra numbers.

481
00:54:08,000 --> 00:54:11,000
So it'll be relatively limited.

482
00:54:11,000 --> 00:54:14,000
And all you need to do is be able to show me that you can use

483
00:54:14,000 --> 00:54:20,000
the formula the way I want.

484
00:54:20,000 --> 00:54:23,000
You all good on it?

485
00:54:23,000 --> 00:54:27,000
That is stock valuation in a nutshell.

486
00:54:27,000 --> 00:54:29,000
And that is all I have for you today.

487
00:54:29,000 --> 00:54:39,000
I thank you.