How do you value stocks? Finance textbooks argue that you should look at their dividends. But many stocks don’t pay dividends, and even if they do, it’s hard to forecast what they’ll be in the future. And newspapers talk about a stock’s 'price-to-earnings' ratio which seems nothing to do with dividends.
This lecture will explore the essentials of stock valuation, explain what causes stocks to rise and fall so wildly, and demystify the jargon used by finance practitioners.
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A lecture by Alex Edmans
The transcript and downloadable versions of the lecture are available from the Gresham College website:
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- Good evening everybody. This is a chart of the stock prices of the largest companies on the UK stock market yesterday. But what causes some prices to go up and some prices to go down? And how do we know whether the prices fail or not? Whether we should buy shares or sell them? Well, we're going to look at these questions this evening in today's lecture on how to value a stock. It's the fifth in my Gresham College public lecture series on basic financial literacy called the principles of finance. And while today is explicitly about how to value shares, what we're going to look at will hopefully be applicable to anything that you want to value any financial decision. So what is an investment? An investment is spending some money now to get some benefit in the future. Now, we are going to look at shares. We will buy the shares now and get some dividends in the future. But there's many other investments that you might make buying a house, renovating a house, going to university. All of those things have immediate costs and long-term benefits. And hopefully what we're going to look at today will be applicable for all of those situations. But we might think haven't we heard this a bit before? Because those of you who came to my lecture three on how to make financial decisions, we did look at how to value lots of these investments, but we're going to go beyond lecture three in two important ways. First we're going to take risk into account. So when you buy a share, the dividends are risky. And indeed, when you buy a house, you are not sure how much you can solve that house for in the future. So risk is something we absolutely need to take into account. We looked at how to look at risk last time in lecture four, but we're going to going to do is now combine that with the prior lecture to value an investment when there is risk. And also we're going to look at more realistic cash flows. So what we looked at in lecture three was investments that gave the same cash flow every year. But we know with stocks, dividends go up then they go down in a pandemic, they bounce around a lot. So we're going to look at a lot of the uncertainty, which drives changes in the stock market. So let's go back to basics. How do you value a stock? How do you value anything? Well, what we've established is the value of any investment is the future cash flows from that investment. If we're buying a house, it's the future rental income. So we're buying a stock, what are the cash flows that we get from owning a stock? It's actually not that obvious. So let me look at the profit and loss statement of a company. A stock, a share is a share in a company and you own the company, but how much do you receive from owning a company? Well, let's take a clothes company, say it makes 1000 pounds a year from selling clothes. It has to pay 300 pounds in terms of raw materials and in terms of the staff. So after netting that off, it's got 700, but then it has to pay tax. And let's say the tax rate is 20%. That's 140. And so the profit after tax, the bottom line net income, that is 560. And so let's say there's 100 different shareholders. That 560 is split 100 ways. So we each are better off by 5.6. But we actually don't receive five pounds and 60, why? Yes, the company has made five pounds and 60 per shareholder, but it's not necessarily going to pay that out to everybody. Why? Because it might reinvest a lot of that money. So when a company's chosen to make money, does it choose to reinvest it and build another clothes factory or spend it on training its employees or does it pay it out and so that's the important difference. So out of that 5.6, I'm going to assume that 3.6 is reinvested and used to build another factory. And only two is paid out to shareholders. And what that two is known as is a dividend. We often hear the term dividends, but what does it mean? That means that is what is paid out to shareholders at the end of the year. But notice dividends are quite different from earnings. Earnings are the profits that a company makes, but we could choose to pay some of it out and choose to retain it within the company. Just like you achieve a salary every year. Your salary is every month, your salary is deposited into your bank, but you might only withdraw a partial amount of that salary and that is known as dividends. And so the actual cash received by a shareholders is only the dividends. It's only the two, it's not the overall profit that a company makes. So the first important point for today is that when we look at valuing a company or valuing a stock, it's only dividends that we need to take into account. Go back to the formula we looked at in lecture three, the value of any investment is the present value of all of those future cash flows from now until the end of time. For a house, again, that's rental income. For a stock it's only its dividends. And so what we'd need to do to forecast the price of a stock is to estimate all of the future dividends that the stock will pay from now until the end of time. If I buy a share now I'm entitled to dividends next year and the year after and the year after that, and I should forecast all of those future dividends. And that will tell me how much the stock is worth. But you might think well doesn't that assume that I'm going to sort of live forever and stay around until the end of time and collect all of those dividends. Oasis sang in 1994, you and I going to live forever, but nobody's actually figured out a way of how to do that. So is this sort of unrealistic that we are not going to stick around to receive every single dividend. And even if you could live forever, it might be that you would not want to keep the stock forever. It might be that I'm buying shares now to finance my children going to university in five years time. So you might think, well, do we really care about what the dividend will be in 15 years time if I only intend to hold it for five years. And in fact, surprisingly, the answer is yes. Why is that? Okay, so let's look at this example where I'm going to buy a stock now. And I know that I'm going to sell it within two years, because I want to use the money to deposit a house. So what am I going to receive when I buy the stock? I'm going to collect the dividend after the first year, and I'm going to collect the dividend after the second year. I'm just going to assume dividends paid once a year to make things simple. So I've looked at the first dividend and the second dividend. And after the second year I'm going to sell my shares because I need to use the money to put a deposit on my house. But when I sell my shares, let's say I sell them to Simon. When Simon comes along and offers me money for my shares, what is a fair price that Simon is going to offer? Well, he's going to say, well, if he buys the dividend the share at the end of year two, the future dividends he will get are going to be dividends from year three, year four, year five and so on. So even though I don't care about the dividends in year three onwards, because I'm not receiving them, I do care because this affects what Simon is willing to pay. Okay so when Simon comes along at the end of year two, he's going to forecast the company's future profits from year three onwards. And he says, well, if I'm going to have the share at the end of year two, I'm going to receive dividends from year three and four and five and so on. And so if you work through the math, which I'm not going to bore you with, what this means is that I care about every single dividend. So even if I'm only going to hold the shares for two years, I will only receive two dividends, but because Simon will receive dividends three, four, five and so on, what he pays me at the end of year two will reflect all of the future projects and the future dividends of that company. And so let's just strip back from all of these equations and think about what this means in terms of the real world. So why is Tesla such a valuable company? Tesla makes electric cars and those electric cars will be really profitable in the future. Yes I know that Tesla is already profitable now, but why it's worth so much is that people are thinking about the future in 15 years time, this is going to be massively profitable. Now, many people who hold Tesla shares have no idea whether they're going to be still holding them in 15 years time. Life changes, you might want to buy a house. You might have children and send them to university, but why it's worth so much is even though the world is so uncertain and we have no idea when we're going to sell the shares. As long as we have confidence that when we sell the shares that people we'll sell them to, we'll look in the future and see Tesla as a stream of all of these future profits from electric cars, we are willing to invest in electric cars today. And I can't stress enough the importance of this insight. By anybody who wants to criticize finance and the stock market will say, the stock market is short termist. People only hold their shares for one or two years. And that's true, people don't hold their shares for a long time, but why is it that companies with quite low earnings are worth so much money? It's because they're worth what their value is in the future. And even if I'm not sticking around to explicitly receive those future profits myself, I still care about them. Why? Because anybody who buys my shares in the future will be thinking about the long term prospects of the company. So this is why it's entirely fair to value a company by trying to forecast all of the dividends right now until the end of time. So if it is a possibility that we're going to have a huge carbon tax, I don't want to be investing in fossil fuel companies, because I know that maybe 10 years from now, this business might not be sustainable. If there's a company which mistreats its workers, doesn't invest in a diverse workforce, then I will know that maybe in 10 years time that this company will not have as strong human capital. Therefore I might not value it highly today. And indeed, when you see some companies with incidents like Sports Direct and Boohoo and so on, this is something that affects the company's valuation today. So I've just spent a while stressing how the stock market does take into account all of the future dividends of a company. But that seems to be a bit of a hollow victory, because it means that in order to estimate the price of a stock, we would literally have to forecast every single dividend from now until the end of time. And that's a really arduous task. It's going to be really difficult to do that. But some of you might remember if you came to lecture three, that there was a nice shortcut formula that we can use to avoid having to forecast from now until the end of time. So we have some settings in which we have a growing perpetuity. What is that for those of who didn't go to the third lecture, that is when the dividends of a company will grow at a constant rate over time. And that is quite realistic. Like once a company is mature, it might increase dividends let's say by 2% per year, pretty much every year. So a rough guess, and also a pretty reasonable guess might be for a mature company that it's going to grow at the same rate forever. And so how can you value that? Well, what we can do is we can just take next year's dividend. We divide it by the discount rate, which we got from lecture four. So that is the rate of return on alternative investments minus that perpetual growth rate. And therefore that will give us the valuation. And I'm going to look at example very, very quickly. But before I look at the example, let's just see, does that make sense? Yes. So what is the discount rate? That is the rate of return available in other investments? So when the Bank of England puts up interest rates, which it did recently, the stock prices will typically go down. Why? It's less attractive to hold stocks because it's more attractive to put your money in the bank because the interest rate is higher. So what determines the rate of return available on other investments, the greater the alternative investment opportunities, the lower the price of the stock. That's why I'm so grateful that so many of you have come up to today's lecture. The alternative opportunity was the assumption outside and that's something which will affect the value to many people coming to today's lecture. And so the growth rate, the greater the growth rate, the smaller the denominator, the smaller the denominator, the greater the value. And that's why intuitively companies that grow faster like Tesla have higher stock prices. So let's try to look at this and apply this with a practical example. Let's take Tesco, a company that we all know. So these numbers are just made simple deliberately. Tesco has just paid a dividend of three pence per share, and its beta is 0.5. Remember what is beta, that's just the risk of a company. And it'll become clear why we need it. Even if you didn't come to the last lecture. Analysts are expecting the dividend to grow by 2% each year forever. So it's just paid three P per share. And that three pence is going to grow by 2% forever. The current risk free rate. That's what the Bank of England sets is 1%. And the expected excess return on the FTSE is 4%. What should Tesco's share price be? So let's use those simpler formulas to see how we can value a large company like Tesco. So the first thing we really want to do is you want to estimate the discount rate, the rate of return that we would use to discount Tesco stock because it's something risky. And so you might remember the capital asset pricing model from lecture four. So what that says is that the return that Tesco gives you above the risk-free rate, depends on the market's return above the risk-free rate, multiplied by the beta of Tesco, how risky Tesco is. The riskier the stock, the greater the return you require to invest in that stock because it needs to compensate you for that risk. So let's plug in these numbers. I'm going to plug in the number of 0.5 for the beta, 1% for the risk free rate and the return on the market, 4% minus 1%. But in fact, that's wrong. Why is that wrong? Because the question says the excess return on the FTSE is 4%. So the excess return is already, after subtracting the risk-free rate. So actually 4% is what the FTSE stock market is giving above the government risk-free rate. And therefore we don't need to subtract the 1% because that 4% is already after subtracting this 1% to begin with. So you might think, okay, let's fix that problem. And so what is the required return on Tesco? Well, the market is giving you 4%, but because Tesco is not that risky, Tesco only requires half of what the market gives. And therefore the required return on Tesco is 3%. So that does make sense. The interest rate for investing in something very safe, like government bonds is 1%. Tesco is risky so you do demand more than 1%, but it's not missed as risky as the market. So you only require a 3% return for investing in Tesco. So let's now apply that to the dividend. So we said Tesco has just paid a dividend of three pence per share. And we know that the discount rate is 3%. That's what we just calculated. And because it's growing by 2% every year, let's take that three, subtract the two, and I'm going to get three over one that gives me three pounds being the stock price of Tesco. But that's also wrong. I'm not having a good day today. Why? Because I've said Tesco has just paid a dividend of three pence. But when we look at the valuation of a stock, we don't care what's happened in the past. We care about what's happening in the future. When I buy that share, I don't get the dividend that was paid last year, I'm going to get all future dividends. And this is something which is common to all aspects of finance. Finance is always concerned about the future. And that's true not just to finance, but any type of investment. Let's say you are the manager of a football team and you want to buy a striker. You don't really care about the goals that the striker scored for his current team. When you buy that striker, all you care about is how many goals he will score for your team going forwards. Yes, you might still care about his track record to the extent of which the track record predicts the future. But remember, we only care about the future and the track record is only a guide. Similarly here, yes, we do care about the dividend that Tesco just paid. Not because we actually receive that dividend, but because it affects what Tesco is going to get in the future. And so we said Tesco just paid three pence. But because that three pence is going to grow by 2% every year, what this means is that what I need to put in the top of this equation is three compounded by 2%, because of the last year dividend was three. The next year's dividend will be 3.06, because that will have grown by 2%. So this calculation is really simple. It's just plus times minus divide. So this is why finance is very easy in terms of maths, but in terms of the actual thought process behind it, that can be complicated, which is why I'm spending most of the time on the underlying economics and the intuition and the common sense. And then what would you do with this number? If that's what you thought the valuation of Tesco was, you can look up Tesco stock price. And I did that, and this is what it was last night. It was 286.70. So if you think that Tesco stock is worth 306, then you would want to buy it. And this is indeed what stock analysts do in real life. The calculation won't be as simple as this, but their general methodology is this. They will try to find what they think the company's worth. They will compare it to the current price. And they will say, we think the stock is a buy, or we think the stock is a sell. So what causes stock prices to change so much from day to day? Well, let's say we suddenly think, well, the world is now different. Maybe we think there's going to be another wave of the virus. Hopefully not, but let's say that happens. And we think that actually now the dividend will only grow by 1% per year because there's a change in the economic environment. So what is that going to do? It's going to change the 1% both here and here, and it's going to really reduce the stock price of Tesco down to 151.5. Okay so just one small change in the growth rate can change the value of Tesco, can half it from 300 down to 150. And so this is why stop prices can go up and down so much because if there's a change to a growth rate and it applies every year until the end of time, this can have a massive effect on the long term value of a company. So, so far what we looked at, we've found two different formulas to try to value a company. One of them is the exact academic formula where you value every single dividend right until the end of time. It's correct, but it's impractical because we can't forecast so far in the future. Then we just had a quick and dirty formula is that if you can assume that a company's dividends grow by the same rate every single year, then we can use the shortcut. But in reality, we can't make that assumption. Some companies don't yet pay dividends like Tesla, or even if you do pay dividends, maybe that might be grown really fast for two years, and then it's going to settle into a steady state. So in reality, what would you do? Well, you'd have to use a bit of both. So let's say I can't forecast my dividends until the end of time, but I can forecast them for the next five years or so. So what I do is I would explicitly forecast the dividends for the next five years. And then after those five years, I will ask myself, what is the company worth at the end of that fifth year? And that is something known as terminal value, which is the value of the company at the end of the fifth year. So what is the stock worth for me today? It's worth the dividends over the next five years and the terminal value. What is the company worth at the end of that five year period? Okay that sounds well and good. So how do we estimate terminal value? How do we know what the company's worth after those five years? Well, how do we estimate terminal value? Let's think about, well, how do we estimate value? How do we estimate the value of anything? And what is perhaps something that you will all have practiced in trying to value? Perhaps the most important investment you'll ever make is the value of a house. So how do we think about how much a house is worth? Well, there's two ways we can think about the value of a house. The first is the fundamentals. What does a house actually get you if you buy it? The house gets you somewhere you can live. What is that worth? That's worth the rent of the house. Because by buying the house that saves you having to pay out rent. So what a house is fundamentally worth is what you could rent it for. This is regardless of whether you're going to live in it, that saves your own rent, or if you're going to be a landlord and rent it out and you're going to be receiving the rent. What you care about is the rental income from the house. And so what a house is fundamentally worth, and this is what estate agents might partly look at is indeed how much it rents for and how much those rents will grow in the future. But I said, that's what partly estate agents look at, because the main thing that estate agents might look at is comparables, what they will look at is other similar houses. So if other similar houses of similar size in the same neighborhood are trading in a certain amount, then that will guide us on how much our house should be costing. And so these two principles for valuing a house, fundamentals, how much we can rent it out for and comparables, what other houses are worth. Those are the two same principles for stock valuation. And so why I like to look at analogies is people think, oh, stocks they're really complicated, the stock market is really cumbersome, but the principles of valuation that we can understand with more simple things, every day, things like houses, they will also apply. So let's look at these two things in turn. So the first thing we might do is go back to the fundamentals. We are valuing the house by looking at the rental income we can get, translate that to the company. We are trying to look at the terminal value act at the end of year five and the house that company's worth what the future dividends will be from year six onwards. So why is that so powerful? Because it might be that the company's immature for the first five years, dividends are bouncing around all the time. So we cannot assume a constant growth rate, but maybe after five years, the company has matured. And then we can use that shortcut formula that assumes a constant growth rate. Let me repeat myself, the shortcut formula that we use for Tesco that is really attractive if you can assume a constant growth rate, but you might not be able to assume a constant growth rate from the start. Maybe you can only assume it from year five onwards. So if so, we will explicitly forecast the first five dividends and then use the shortcut formula from year five onwards when Tesco is mature. And then we can make that simple shortcut assumption. So what we have is the value of Tesco or any company, it's the first five years of dividends. And then the terminal value is the future dividends from then on which we're going to assume are growing at a constant rate. So again, let's just try to apply this with an example. So let's go back to Tesco, I'm going to try and keep the numbers exactly the same as possible to the extent that I can. Dividend of three last year, beta is the same. The dividend grows by 2%, but we're now going to say the dividend only grows by 2% for the first two years. Why is it growing so quickly? Because of the recovery from the pandemic, but then we're going to say actually after two years, it's going to level off and only grow at 1.5% from then on. So how do things change? What we can't use that constant growth formula from the start because dividends were by 2% and then by 1.5. So what we're going to do is we're going to explicitly forecast the first two dividends and then use the shortcut afterwards. So let's do that. So what we could do is we could just make a table projecting the dividends of Tesco. It was three just received me. It grows by 2% for the first year. Grows by 2% for the second year. And then from year three onwards, it's grown by 1.5% until the end of time. So how do we do the calculation? What we're doing is we're going to first look at what is the stock price comprised of. The first dividend 3.06, the second dividend, that's also grown by 2%, 3.1212, the third dividend of 3.16. And that is then growing by 1.5% per year. So if you look at the numbers, we're going to value the first dividend, the second dividend, and then the third dividend, which then grows at 1.5%, and because that is constant, we can now use that simple shortcut formula. And at the end of the day, this leads to the price being 205. And if you remember, what was it when the growth rate was 2% forever, it was 306. It's now gone down a huge amount to 205. Why again small changes in the growth rates can have huge changes in the stock price. And again, this is why people will disagree so much in the value of a stock. This is why so many people will trade stock every day. I might think Tesco can sustain its growth of 2% forever. Simon might think I'm a fool. They could only sustain it for two years and then it tails off and therefore Simon will sell and I will buy, we will trade with each other. And so if you are then to compare that to Tesco's current price, you might say, no, let's sell it. Why? Because we don't think it's actually worth it when we take into account the fact that growth is going to tail off. So that was the fundamental method. But remember I said that the other way in which you value a house is you look at comparable houses, look at the prices of other houses and then see what our house is worth. But the big question is what is it to have a comparable house? What is the important dimension of comparability? Is, my property's address is 15 Peninsula Court. Do I compare my house with other houses which are number 15? No. Because the number 15 is irrelevant. What is the value of a house based on, what is the value driver of a house? The main driver of value of a house is its square footage. So what I would do is I would look at other houses in the same region and look at their price per square foot. Why? Because the square footage of the house is the main thing that drives the value of the house. So let's say you want to take a holiday home in Whimple, Exeter. You find this house and this house is worth 295,000 pounds. And you see on the estate agent website, this is 847 square foot. That is what you care about, you don't care about its number. You might not even care about the number of bedrooms so much as the size of the house. That is the main thing people are concerned about. And so you'll say this costs me 348 pounds per square foot. And so that's interesting because if there was another house which was 1,000 square foot, well, you'd say, well, the fair price is then 348,000 pounds. So the strength and the beauty of this method is you can actually compare houses of different sizes because when you put them all under the same common denominator, then you have that ratio, which is comparable. This is why when you go back to Tesco. Now, not to value Tesco, but to buy stuff from Tesco, let's say you want to buy some cereal, like cereal boxes. They come in all different sizes, but how do we know what cereal is most affordable? They'll put the price per 100 grams. And this whole idea of price per square foot for a house is the equivalent of your price per 100 grams. So going back to the prior example, what drives the value of house? It is the square footage, that's what we care about. Just like when we buy cereal, we don't care about the size of the box. We care about the amount of cereal that it contains. It could be there's a massive box with not much cereal. So what we're paying for is the actual grams of the cereal. And so when we apply this to companies, we then need to think about what is the value driver of a company? What do we care about about a company when we are deciding to buy it? And here it's actually not so obvious. With a house, there is one clear dimension that we care about above all else, which is its square footage, but for a company there's many different aspects of a company that we might care about. So one thing you might care about is book value. So what is book value? That is the value of the assets of a company. Companies own things like buildings and factories. And you might think that the value of a company depends on its hard assets. And that is true for some companies. So let's say you are a real estate company. You own a lot of property. The value of that company really is the value of its property portfolio. So what you do is you would calculate the value of its property portfolio and compare that to other companies with similar property portfolios and look at the price per amount of book value per amount of property portfolio. So that works for some companies, but there's other companies which really don't have much in terms of hard assets. So let's take a tech startup. A tech startup, what are the main assets? They're the ideas or the people and people, you can't really have a value on. These people are never in the accounting statements of a company, they are never in the books of a company. That's why they're not part of book value. And so there's other industries where you don't really care about the hard assets a company has, but instead you might care about something like the earnings that the company makes, how much profit they make. Why? Because even if the assets are people, they're not hard assets like a machine, those people are still valuable because they generate your earnings. And so what you might care about is actually not how much hard assets you have, but how many earnings the company generates, because that takes an account are the earnings generated from smart people or great machines. And so indeed what most companies are valued at in reality is a price per earnings ratio. So many of you have heard of this. It's known as the PE ratio. When we're thinking about how to value a company, we value a company by its earnings, just like we value a cereal by the weight and we value a house by the square footage. Let's look at this. So let's take GlaxoSmithKline, the pharmaceuticals company. These are data as of last night, the price was 1755, the earnings per share, so how much profit the company made per share was 113. And if you divide one by the other, the price earnings ratio is 15.51. And so why is that useful? Well, you could compare GlaxoSmithKline to other types of pharmaceuticals companies. So we can look at AstraZeneca and we can look at further pharmaceuticals companies. And if indeed they're all trading at 20, we might think, well, actually this is a pretty cheap stock. Just like if the price per square foot on a house was less than other comparable houses, we might think it's a buy. So this is a really nice way to try to estimate a value of a company. You look at the comparable companies. But the tricky thing, let me just stress it again is that unlike with a house it's not clear what the value drive is, could it be book value? Could it be earnings? Well, whatever company doesn't really make earnings. So often startups, they don't make profits. So you might value it according to price per sales. Because maybe the main driver of some companies is the sales revenue and there's other companies which might not even be making revenue. So let's take WhatsApp when it first started out or Facebook, when it first started out, they didn't really find a way to generate revenue, but all they did was attract something like customers or subscribers. So in other tech companies, it might be price per subscriber. And so a lot of the skill in investment analysis is not the maths, this was simple, plus times minus divide, but to think about, well, what is the true value of a company, is that its book value, its hard assets, its earnings, its sales, its customers or something else? Some of you in this room might have read "Moneyball" by Michael Lewis about how to value baseball players. And so why Billy Bean of the Oakland Athletic was so successful is you realize that the value of a baseball player is not just how many times they hit the ball successfully, but how many times they get on base successfully. And it might be you get on base, not just by hitting successfully, but by walking because you are able to take some bad balls thrown at you. So let's now use this practically in an example, now that we've gone through the high level analogies, so we've got Tesco and Tesco's dividends grow by 2% per year. But then after year two, we are just going to say, we have no idea what dividends will be afterwards. It's really hard to forecast. However, we know that the earnings will be 12 pence and we know that other supermarkets are trading at a price earnings ratio of 20. That is the going rate for a supermarket. You take the earnings, you multiply it by 20, you get the market value. That's like looking at comparable houses. So how would your calculation change? It's going to be quite simple. What we're going to do as before is we're going to estimate the dividends for the first two years. And then after the end of the second year, what is the company worth? We're not going to say it's worth the future dividends because we have no idea what they are. Instead we're going to say, let's look at comparable supermarkets, they're all trading at 20 times earnings. And so it's going to be worth 20 times the 12 earnings per share. And that's going to give us our 240 here and that will give us our current valuation. So to close out before the questions, well, let's look at well, what determines the price earnings ratio to begin with? So I've said, the supermarkets might trade at a price earnings ratio of 20, but why is it 20? Why isn't it 15, why isn't it 100? Just like how you know the price per square foot of a house should be 1000 pounds, it might be that the whole street might be overvalued. So what determines that, why does it fluctuate? So the main thing which is going to drive it is the growth of a company. So let me get to the punchline first, the faster growing the company is, the greater the price earnings ratio of that company. So for houses, why are prices per square foot different? That depends on the neighborhood. The better the neighborhood, the higher the price per square foot and for companies, the equivalent of the neighborhood, what people really care about is the growth potential of that company. So let's again show this with hopefully simple examples. So let's take NatWest and it generates 10 pounds per share forever. And it pays this out entirely as dividends. And its discount rate is 10%. What is its share price? Take the similar formula to before we take the dividend in the numerator, 10%, 10 pounds, divide it by the cost of equity of 10% minus the growth rate. And the growth rate is zero because NatWest under this situation is not growing at all. It's just paying that 10 pounds forever. And so it's worth 100 pounds. The price earnings ratio is 100 over 10, which is 10. So if indeed NatWest does not grow at all, it's just paying out its 10 pounds forever. It's worth 100 pounds, its price earnings ratio is 10. But now let's say NatWest has the opportunity to reinvest these earnings at a profitable reinvestment rate. So 20% of its earnings, it can reinvest and it can get a return of 15% on those reinvested earnings. So how do we use that number? Well, it affects the growth rate because you might think, well, I gave you the growth rate being 2% or 1.5% but I plucked that out of thin air. How can we estimate how fast a company's dividends will grow? Well, actually we can put some science behind it. How fast a company grows, it depends on how much you are reinvesting multiplied by the return on the reinvestment. So if we are reinvesting 20% of the company's earnings and that 20%, we can earn a 15% return when we reinvest, that gives us 20% times 15% gives us 3%. So we're going to go through the exact same calculation as before, but two things change. First what is the dividend in the first year? It's no longer 10, it's only eight because we're reinvesting 20% of it. So that reduces the valuation. But on the flip side, the growth rate now is no longer zero it's three. And overall we're getting a higher price than before, which is 114, before it was 100. Now it's 114. And as a result, what we have is that price earnings ratio is 11.4. Now this looks expensive. You are having a price earnings ratio of 11.4 when other banks have a price earnings ratio of 10, but why is it expensive? It's because the earnings are growing in the future. I am quite happy to buy NatWest even though it's more expensive than other banks, because I know that the earnings that they have right now are not going to stay at that level. They're going to be growing in the future by this 3% rate, just like houses in different neighborhoods will have different prices per square foot, but is it expensive for a house in Noting Hill to trade at a higher valuation than maybe a house in Bristol? Not necessarily. Why? Because the neighborhood is more attractive. And the analogy of the neighborhood for companies is the growth rate. And just to show you how this might work in just real numbers. These are numbers that I took from an industry website, banks have a low price earnings ratio of about 30. They don't grow that quickly. Pharmaceuticals is about 34. Internet 48, biotech 75. So the faster the growing the company, that means even if they have very few earnings today, you might pay a massive amount for them. Why? Because they're earning so much in the future, they've got such high growth potential. So let me just have one final wrap up to reconcile everything I've done in this lecture before opening up to questions. So at the start of this lecture, I said, we value a company based on the dividends. A company makes profits, it generates some earnings, but we only care about the dividends that actually pays out when we value the company. We don't count the earnings that you reinvest. However, when I just talked about the price earnings ratio, when we think about comparing companies with each other, we compare the price per earnings. That is the equivalent of the price per square foot of the house. And you might think, well, isn't there some inconsistency. On the first level I've said we value the company by its dividends. But then when we compare, which companies are cheap or not, we look at the price to earnings. And in fact, there's no inconsistency. Why? Because when I said we value the company based on its dividends, we value all of the future dividends of a company from now until the end of time. That is what we did in the calculation. But the price to earnings ratio, that's something we're comparing the price just to the earnings right now. We're only comparing it to one number. And why is the earnings the correct number to think about right now, rather than dividends. It's because some companies might not pay dividends at the moment. Now, if a company's not paying dividends at the moment, it will be paying dividends in the future. So this is why the valuation will take the future dividends into account. But remember right now, when we're looking at whether a company's cheap or not, we are looking at the price compared to what it generates right now. And if it's not generating any dividends, we can't look at a price to dividends ratio. So instead, what we're going to look at is the price to earnings ratio when we're comparing different companies, because those earnings, most companies will have them. And that is what's the sustainable value that the company creates. We don't really care about how much it's paying right now in terms of sustainability if a company's generating profits, those earnings are what we expect to be sustainable in the future. Okay, so let me just sum up and then open it up to Q&A. So earnings or profits. That's how much shareholders are better off by, at the end of the year, some of those earnings are reinvested in the company and the rest is paid out to shareholders as dividends. When we value a company, we value all of those future dividends from now into the future. And that applies irrespective of whether we intend to hold the company forever or whether we intend to sell it for two years. So this means that the stock market is not short termist. We always care about the long term prospects of a company, because even we're not going to be around whoever we sell it to will care about those future prospects. Now forecasting dividends until the end of time, that will take a long time, but there are shortcut formulas that we can apply. And even if we can only apply the shortcut formula after a certain period, then we do a two step process. First value a company for the first let's say five years. And then after the company is matured, we can use that shortcut formula if we can predict dividends and think they will grow constantly. And even we can't predict dividends, we will value a company by looking at other comparable companies. But the trick is how do we compare the companies? Is it going to be on the book value, the earnings, the sales, the number of customers, the subscribers, that's where a lot of the art finance is. And finally, how do we measure how expensive a company is? Just like we'd look at prices per square foot of a house. We would look at the price to earnings ratio, compare the price that the company's trading at to the earnings that it's currently having. And why might price earnings be higher in some industries than others? Not because they're massively overpriced. It could be that it's fair for them to have a high price because those industries are growing. Okay well thank you so much for your attention to a rather more technical lecture today, but this is really the essentials of stock valuation. Let me now open it up to questions. So let's welcome Simon to lead them.(audience applauding)- Great, thank you very much for another tremendous lecture. We've got quite a few questions online and we'll probably have a few from the hall as well. I'm going to start off with one of the online questions. It is have you ever applied these rules of thumb and found a stock has massively either under or overperformed its valuation?- I think stocks will often overvalue or underperform, but this is something this is often due to new news, which is not known at the time. So at the time that you apply evaluation, you will have your estimates as to the growth of a dividend. Now, after the fact, it might be that the growth rate ends up much higher or much lower, but the thing is at the time could we have predicted that and often you couldn't and had you been able to predict it, then everybody would've traded on it and been able to make money. So often people will say after the fact, oh yeah, I knew it all along, but actually that's often a bias because it's often that we didn't predict it after we see it. And that's why it's quite difficult to make money on the stock market. So if you went to my third Gresham series last year, the psychology of finance, a lot of times people think, oh, we apply these formulas and we're going to have a different valuation from the market. When in fact sometimes they'll be often getting it wrong because the market is up and actually getting a right price.- Do you think most people should be investing in stocks, given the complex maths involved?- I'd say they shouldn't be investing in stocks directly, but investing in mutual funds. So why, what is a mutual fund? You might buy a fund from Fidelity and they will hire a professional fund manager. And what she will do is do these calculations. So she will look at the risk, which determines the denominator. She will forecast the future growth, which determines the numerator. And she has a big team of analysts to do that. And in return you'll have to pay a fee, but that fee is pretty small compared to the amount of analysis required. And also what a fund manager does is she typically diversifies and holds multiple stocks. So as per my answer to the first question, you could have got the valuation right at the start, but then unexpected things happen like a pandemic. And if you are diversified, it might be that some companies in your portfolio might be the Amazons or Zooms that benefit from the pandemic, just as much as you might own some restaurants, which suffer in the pandemic. And so this is why it's much better to hold a diversified portfolio than individual stocks.- Well, Professor Edmonds, thank you very much for another tremendous lecture.- Thank you very much and the final--(audience applauding) Thank you so much, Simon and my final ever Gresham lecture series, before I retire and hand over to my successor will be next month. It's on how to finance a company. We're going to look at whether a company should finance itself with debt or equity. So that will be my final time addressing, but thank you so much to everybody who supported my lecture series.(audience applauding)