 The decision, this is Professor Farhad in which we would look at the price earning multiples or the price earning ratio or simply put price divided by earning. This is the most widely quoted ratio in the real world. So if you listen to CNBC Bloomberg radio, read the Wall Street Journal, Business Insider, any of these outlet, they will mention the PE ratio day in and day out for many companies. Now, as you can see, it's pretty simple. It's the price of the stock divided by the future earnings and specifically earnings is EPS, the future earnings of the company. Now, in this session, we're going to break it down. We're going to explain how do we construct this ratio, although it looks, it appears simple. It is simple from this perspective, but it's very important to understand what's behind the ratio. How did we come up with this PE ratio and what does that mean? What is a PE ratio of 10 versus 20 versus 15 means to you. Before I start, I would like to remind you to connect with me only then, if you haven't done so, please subscribe to my YouTube channel, where I have plenty of resources. And on my website, farhadlectures.com, you will find additional resources, whether you are a finance accounting, especially if you're studying for your CPA or taken accounting courses or taken the CPA exam. Also, if you want to know how well is your university performing on the CPA exam, you could check out, I have this data. So let's go ahead and get started to figure out where the PE ratio is coming from. First, to be able to compute the PE ratio, we need to estimate earnings per share. Once you hear the word E estimate, it means estimate could be wrong. So that's one of the weakness of the PE ratio. It's based on future estimate. Now, how do we estimate earnings? Well, we have to estimate sales. We have to estimate cost of goods sold. We have to estimate operating expenses. We have to estimate taxes, depreciation. Then we find earnings. So there's a lot of estimation that goes on. So this is one of the weakness in those. All these estimates are based on accounting rules. And if you don't know anything about accounting, if you know, if you don't know anything, I will tell you one thing under gap. You can you can treat revenues, expenses, cost and in very different ways. So managers can easily manipulate this EPS. The other issue with the PE ratio is deciding on appropriate multiple. What do we mean by appropriate multiple? Let's assume we have a stock price that's trading at $50 and the company in the future will earn $2 per share. Well, 50 divided by 2 equal to 25. So the multiple, the multiple is $25. It means you are paying for to pay $50. You are paying $50 for the share. What are you buying? You are buying their future earning. So for every dollar in earning, you are paying $25. So you have $1 in earning, $2 in earning. Those are the $2 and that's $50. This is what it means. Now, is this a high multiple or a low multiple? It all depends on the company prospect. If the company in the future is going to grow, what we do, let's assume it's a technology company. And what happened is they have a bright future. They're going to gain more market share because they have a new innovation. So what's going to happen is, if that's the case, then rather than $25, what we need to do, what we need to do, if the company is making $2 per share, the $25 may not be an appropriate multiple. Maybe the multiple is $30. Therefore, the price becomes $60. So although we kind of figure out this is multiple of $25, but if we think there's growth, more growth in the company, if we think the multiple should be $30, then the stock price should be $60. Actually, it's a good buy now. If you think the multiple is $30, if you think the multiple is $30, then you should buy the stock because it's only trading at $50 and eventually the market will realize that's the case. So let's go back to the basics of what we learned here and we'll come back and we'll revisit those P-E ratio with real-word examples. I have few examples for you. So if you remember, we learned about the price of the company, P0, equal to the expected earning divided by K, which is the required rate of return. And we learned that this component of the equation called the no growth value per share. So earning divided by K is the no growth earning. It means with no growth, the company will be valued at that much, dividing those two figures together. Now, if the company is going to grow, we add to that the present value of growth opportunities and the no growth plus the growth opportunities equal to the price per share. Now, the P-E ratio is basically P0 divided by E1. The price today divided by E1, it's going to give us this multiple, multiple. Now, all we have to do now is rearrange the formula, rearrange this formula. And if we rearrange this formula, we'll come up with this formula. Now, you could rearrange the formula on your own, but I could assure you, I don't want to take two, three minutes to rearrange the formula. You will come up with P-E ratio, the price P0 divided by the future earning equal to one divided by K times one plus the present value of the growth opportunity divided by earnings divided by K. So this is basically, we went from this formula to this formula. All we did is we rearranged the formulas, taken four, five steps to come up to this. Let me show you how this work. Let's assume the forward P-E ratio of Google is 23.54 in mid-2017. If the market capitalization K is about 10%, it's about 10%, here's what we can do. We can figure out what's the no growth and what's the growth component of the stock or yes, of the P-E ratio, not the stock, the P-E ratio. So here's what's going to happen. We're going to take the number one divided by K, one divided by 10 multiplied by the number one plus the present value of the growth opportunity divided by the present value of assets in place, which is E divided by K. That's going to give us 23.54. If we solve for the formula, we come up with that this component here, this component here equal to 1.35, 1.35. So this whole component here in the bracket is 2.35. Simply put, we have 10%, well not 10%, one divided by 0.1 equal to $10, $10 times 2.35 will give us $23.54. What does that mean? It means the P-E ratio, the majority of the growth of Google stock, the majority of the growth is due to this component right here, the growth component, not the no growth component. The no growth component is only 10. The growth component is the remaining, which is 13.54, which is a bigger component. Okay, so notice a company like Google will have high P-E ratio, not very high, but it's relatively high because it has future prospect. So the P-E ratio reflect the market optimism concerning a firm's growth prospect. So how much are they going to grow? The higher the P-E ratio, the higher is the growth opportunity, assuming you believe the growth is going to actually occur. So an analyst must decide whether they are more or less optimistic than the belief implied by the market multiple. If they are more optimistic, they would recommend buying the stock. So here's what happened if you recommend buying the stock. Let's assume a company like Tesla, maybe it's earning for the sake of simplicity $2 per share. And here's what's going to happen. If the price right now is 100, 100 divided by 2 equal to 50. So the multiple is 50. If investors think Tesla in the future, they will have more earning. If they have more earning, it means they should have higher multiple. Then what they do is they drive the price up to 200. Once they drive the price up to 200 divided by 2, the multiple becomes 100. So when you drive the price up, supposedly that you drive the price up before the earnings because you want to buy the stock before they report the earning, after the earning gets too late, the price already reflected that earnings. So you want to buy the price before. So what happened is we noticed that companies like Tesla, companies like Netflix and FLX, they will have a high PE ratio because the anticipation is they're going to have more in the denominator. Therefore, if they're going to have more earnings, the numerator will increase now, not when they have the earnings. You want to be in front of the earnings, not behind the earning. For example, a company like Netflix, Netflix used to have PE ratio of 400. Okay. And who am I kidding? 800 at some point. Okay. Now the PE ratio is 78. So it's, it's still growing. Just to kind of give you a comparison, the normal ratio over for the S&P 500 on average for over the past 50 years is between 15, 10 to 15. Let's say 10 to 15 as a range to 20 to 25. So let's say low and 10, high end 25. This is the normal. This is the normal range, the overall average. So you could imagine that 78. So you simply put to buy Netflix today, and Netflix went down today because they reported yesterday and they did not, you know, they did not report their future subscription is not as as, as, as, as optimistic as investors thought. So the stock price dropped. Otherwise, this ratio was higher yesterday. Okay. So now the stock price went down three, 3.9% today. This is around 250 PM on what's today's date, October the 22nd, 2020. So simply put, if you notice, Netflix is the high. So when you buy for Netflix, you are paying a lot of money for Netflix. You are paying a lot of money for their earnings, which is what? Where's the earnings, earnings date? Beta, this is beta. Yeah, $6.19. For the $6.19, the future earning, you are paying 78 times. If you take 78.35 times 6.19 will give you the stock price. So the earnings right now, the PE is 78. If somebody think Netflix should have a higher PE ratio, if they think they should have 100, then 100 times 6.19, the price should be $619. So it all depends on what do you think is going to happen to Netflix? All the Netflix still growing. For example, a company like Alphabet, this is at the same time as well, they have a PE ratio of 35. Again, Google, which is Alphabet, all is going to call it Google. It used to have a very high PE ratio until they started to earn. Now they're earning $45.49 per share and investors think a multiple of 35 is appropriate, or at least that's what the market thinks today. Let's assume Google, they're going to have a cure for COVID, right? They're researching something about curing COVID, right? Let's assume that's the case. Then what happened automatically, the multiple will go up, then say, oh, the multiple should be 100. If the multiple should be 100, then we're talking 100 times $45.49. Now we're talking about $4,500 stock, okay? But if they have nothing to, they have no abnormal growth, then, you know, they're going to grow and the multiple is appropriate 35. Notice Apple will have also a multiple of 35. So simply put, we're saying Apple and Google, Apple and Google, they have a, you are paying, they're basically, in a sense, if you think about it, although, although you think Google is more expensive than Apple because it has a price of 1,600, 616, not at all. They are both practically almost the same price for every dollar in earning, you're paying $35.52 for every dollar in earning, you're paying $35 and then sent for Apple. This is how you value a stock based on their, on their multiple. So this is why the PE is important because it tells you, if you think Apple is going to have higher growth, then you will commend more multiple. So you pay more for their future earnings because, because you think in the future that 3.30 is not appropriate. It should be $5. So let's assume, let's assume you want to keep at 35, but you think earnings will be five and if you take 35 times five, this should be the new price for Apple, whatever that price is. So that's 30 times five is 150, 150, five times five is 25. So you think the price should be 175 if Apple can earn $5 with an appropriate multiple of 35. So for every dollar, you should pay $35 for future earnings. Okay. So that's how you look at the PE ratio. Also, we can look at the PE ratio from another formula that we learned. And this is the constant growth dividend, dividend model, which is the price of a stock equal to the future dividend times K minus G. The K is the required rate of return minus the growth rate. Now recall that dividend equal to the earnings that are not reinvested in the firm. Of course. So what is dividend equal to? What can we replace this, what can we replace this with this part? Dividend equal to the expected earning times one minus B. Remember, B is the plowback. So whatever, whatever, whatever you don't keep, you pay in dividend. So that's why it's the earning times. Let's assume this is 60%. So you take the earning times 0.4, which is one minus 0.6, 0.4 is the one, which is the dividend. So the equal to that. Also, we know that G to compute a G will take ROI return on equity times the plowback. The plowback is what you keep times ROI. Now we could substitute for D and G because we can take this G and substitute this G and this is the formula for G. We can substitute G and we can substitute D. Let's see how things would look like. So simply put, we can see the price of a stock equal to the future earning times one minus the plowback, whatever, which is, which is D one. Okay. Divided by K minus K, which is the required rate of return minus G, which is G reflected on ROI times the plowback rate. Now, again, we could manipulate this formula and we'll end up with the price earnings equal to one minus the one minus the plowback ratio divided by K minus ROI minus times B. Why are we doing all of this? Well, why are we doing all of this? Because if we can, we can easily verify now that the PE ratio increased with ROI. So if you plug in some numbers and you could increase return on equity and hopefully this makes sense. If you increase your return on equity, you're going to have a higher PE ratio, a higher multiple. Why? Because people are willing to pay for your, for your company because you have opportunity to earn more than the required rate of return. This makes sense because higher ROI project, project give firms good opportunities for growth. We also can verify that the PE ratio increases with a higher plowback. Now, if you can keep more money, that's not only that. As long as ROE exceeds K and you keep that money, you'll keep the money and you could make more than what's, what's required rate of return, then you should be better off. So it's not only higher B, higher plowback, higher plowback, as long as you can earn more than the required rate of return. Hopefully this makes sense as well. Okay. So when a firm has good investment opportunities, the market would, would reward it with higher PE multiple. If you have project, if you have product on the horizon, investors are willing to pay for your company more, which will increase your multiple. Okay. If it exploits those opportunities more aggressively by plowback, more earning into these opportunities. You put money back into the company. You have project to earn money. The investors will reward you ahead of time. Okay. Now let's take a look at a quick example just to kind of make sure we can, we can do the basic computation for these. ABC's FAC has an expected ROE of 12. So ROE equal to return equity is 12. Expected earning, expected earning E of one equal to two dollars and the expected dividend of dollar 50. So D one equal to dollar 50 per share. It's market capitalization K equal to 10%. What is the expected growth rate? So first, you know, the formula for the expected growth rate, which is B. This is the, not, not be sorry, expected, expected growth rate is, is G not be expected growth rate is G. What is G? G equal to ROE times B. Okay. So do we have ROE? Yes, we do 12%. Do we have B? B is the plowback. How much do we keep? Well, let's, let's, let's see if we could find this out. If we're going to be making two dollars and of the two dollars, we're going to making two dollars. We're going to pay dividend of dollar 50. It means what does that mean? It means we're keeping 50 cent. So if we take 50 pennies divided by two dollars, 50 divided by two, it's going to give us a rate of 25%. So 12 times 25%. Now we have the growth rate G equal to 3%. So we just computed G. What is the stock price of, what's the, what's the price? Well, what is the price of the, what's the price? The price equal to D one, which is we do have, we do have D, D one times, times K minus G. Do we have K? We do have K and we do have G. Let's plug everything. So P zero, the price of the stock equal to dollar 50 times K is giving 10 minus G minus 3. This is 0.1, 0.03. So if we do that, we find that the stock price should equal to 21 dollars and 43 cent. And what's the P E ratio? Now we have the price 21.43. And what's the future earnings? Future earnings is two. So this is P zero divided by E one, the future earnings. We find out that you are paying a multiple of 10.71. I mean 10.71. What does that mean? If we compare this multiple to Apple and Google, guess what? Apple and Google, they have a better prospect than this company. They have a better prospect. And obviously Netflix has better prospect than this company as well. So who would have a low P low P? It doesn't mean it's not good. Simply put, it means you're if we buy your what we're doing when we buy your stock for every dollar and earnings, we are paying ten dollars per share. That's all we're saying. Why are we paying ten dollars per share? Because this is how much we think you are worth your in your industry or your company should be should have a multiple of 10. Now, how do I know it's a multiple of 10 is good? Well, you have to compare to, you know, how well do you have? Do you have any growth opportunities? If you do, I'll pay more. So this is why your stock will go up. OK, and if you don't, you know, if I don't believe that, if you want to drive the stock price up, just let's assume 10, let's assume 10, and let's assume the market is not really treating you well. All we have to do earn $3 if rather than to earn three, then the stock price will be, you know, three times 10 is 30 and three times seven is to 10. So it's like it'll be around $32 and 10 cents. So if you don't give me a higher multiple, that's fine. You're going to miss out. I'm going to have more earning. But if I think you're going to have higher earnings, I don't wait until you have the higher earning. I'll pay higher multiple for you, for your company. So this is basically how the PE ratio work. Again, I'm going to invite you to like this recording, share it. And if you are a CPA candidate, I strongly suggest you check out my website, farhatlectures.com, especially if you're taking accounting. I have finance courses, CPA exam. You could always donate if you choose to. Thank you very much. Stay safe and good luck.