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Dividend and Growth Stocks

Dividend and Growth Stocks
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So we'll do special cases. But these two special cases I tell to everybody is basically life as finance. If you understand them deeply, you can go so far it's amazing. These formulas we'll do are the basis of multiples which is used in valuation. The basis of valuing stocks, the basis of valuing companies. And when you put things in spreadsheet, they look very complicated. But essentially this is what's going on. So let's start of. Suppose dividends are expected to remain approximately constant. Remember, what is the value of a stock the present value of all future? Dividends. Supposed the dividends are approximately constant. Do you know the formula for this?
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When you are a little and we met first, we talked about it. So you can actually show very easily that the present value for something called the perpetuity is the cash flow over the discount rate r. So what does the formula become? The formula becomes, and I'm going to write it, the price of a stock today will be D over r, assuming that D is approximately equals to D1 = D2 = D3. And set stocks that are dividend paying stocks. Isn't this school, this is so straightforward. So in life, we use spreadsheets because these are changing. Think about it that way. But you can always do that. But if it's approximately constant, why not just approximate.
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So let's do an example and you will see how cool this is. So suppose you expect a Dividend, Inc. How creative by me. Anyway, is expected to pay 1 buck per share for the foreseeable future and the return on it's business is about 5%. So how does 5% and the dividend is expected to be 1 buck. What should be the price? Now, you can get easier than this. So what do you do? If you noticed you write P knot = to 1 buck divided by 0.05. And the answer should be 20 bucks. So stock valuation can be very simple if you are kind of approx, you want an approximate value. So simple that it's just funny.
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So this is going to what does the start going to do? It expect you to last pretty much forever. Now, you miss a lot, that's impossible so let's just put some kind of finite life on it. So suppose, you actually think it last only 50 years and here's the beauty of that formula. That 50 years because of compounding or the reimburse of the discounting, what will be the value of this? And I would encourage you to figure this out. This is what kind of problem? This is a PV problem, with an r of what? 0.05, and the number of PV is 50. And what is PMT? 1, close bracket. Took a long time to do.
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[LAUGH] Do it in Excel, this approximately will be 18.26. What does this mean?
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Stare at it. So let me ask you this. The value we got for a perpetuity was 20, so 20 minus this is what? $1.74. And do you know what that is the present value of? Getting 1 bucks starting in year 51 forever.
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I mean, that's all it's worth today. You are getting 1 buck repeatedly every year forever. So on the other hand, now, let me change the example and try if you increase the interest rate to 10%, what will happen to this number? This number will become lesser and lesser. So how the interest rate, the more the discounting effect and the closer you're seal with r formula is to what you would need to do even with the spreadsheet, pretty cool. Let's do the second special case before we take a break, we'll do an example of it, too. So what happens if it's a growth stock? So what is a growth stock?
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Growth stock says, I will pay D1, and what will D2, we have done stuff like this, D2 will be D1 over (1+g) and so on. So suppose this is the kind of stock you expect to buy. How will you value it? It's pretty straightforward. Remember? P knot over = D1 over r -g. You can, of course, use it only if r is greater than g. So many times what happens is in the context of valuing a company, it may or may not be paying dividends. But you'll see later, dividends come from cash flows. And then, you decide to pay a dividend, as I said. You could not pay a dividend if you're growing.
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So suppose you're getting a dividend every year. This problem is pretty straightforward. But if g is greater than r then you use a spreadsheet until r becomes less than g and it won't take you long to figure out that r can't be less than g forever. I mean it's just not possible. So just think about this. Let's do an example, and see how easy it is. So suppose Growth, Inc., now I'm getting really creative, is expected to pay tomorrow's dividend of 2 bucks per share. Everything is per share because shares trade the whole company doesn't trade meaning there's no one share for the whole company, multiple shares.
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And private companies have shares and more than one held by a very small group of people. Actually, yesterday I was doing a case in class on a very famous company called Kohler. It makes kitchen stuff and all, and is a private company. And it had about 400 shares at the time the case was situated, all held privately. Some trading went on between people, but this is a publicly held company worth 2 bucks per share, expected next year. But after that, it'll grow at 2.50%. So D1 is 2 and g is 2.50%. And to make life a little simple, r is greater than g which is when you want to use this formula, otherwise you don't. What is P knot?
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P knot is 2 over 0.05 which is $40. And you see how simple this is, right? So both the propagate formulas with or without growth are pretty straightforward. If there is no growth, this formula would be what? This was what? D over r minus g, where r was 7.5 and g was 2.5. If g is 0, then of course the value of the firm drops. Why? Because a growth firm is more valuable all instruments remain the same getting more money. But the discount rate hasn't changed. So growth thinks price will be 40 bucks.
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