 Hello and welcome to the session. This is Professor Farhad and which we would look at the dividend discount model. Before we start I would like to remind you to connect with me on LinkedIn if you haven't done so and please subscribe to my YouTube. If you like my lectures please like them and share them if they benefit you it means they benefit other people. On my website farhadlectures.com you will find additional resources especially if you are studying for your CPA exam or if you are taking accounting courses. Also if you'd like to find out how well is your university performing at the CPA exam please check out my website. So what is the dividend discount model? It's basically a formula stating that the intrinsic value of a firm equal to the present value of all the expected future dividend. This sounds something that we learned about before. What does it sound like? It sounds like when we value stocks when we find the price I'm sorry not stocks bonds. When we find the price of the bond remember the price of the bond is the present value of the payment is the present value of the payments which is we call those in annuity plus the present value of the face value which is basically a single payment single payment. Simply put on a timeline if we're valuing a bond if we want to find the price of the bond the price of the bond we look at the payments and all these dashes are payments I don't know let's assume those are 30 payments it's a 15 year bond assume this is 15 year bond and each payment is a hundred dollars so each x each dash is a hundred dollar and at the end you'll get your face value therefore what you do is you discount your payment and you discount your face value to the present and this will be the price of the bond the dividend discount model practically sound the same basically it's the present value of all expected future dividend basically and for the bond the bond pays interest we discount the interest for the stocks the stocks pay dividend so basically you should be familiar with this overall concept also on the prior session we looked at the value of a stock or the price of a stock v you could say p0 the price of a stock we learned that the price of the stock to find the price of the stock if we can if we know the future dividend how much we're going to be paid in dividend and we can estimate the future price at p1 we discount at one plus k remember k is the required rate of return and this is what we can find the price of the stock today so simply put the price of the stock is the dividend discounted which is simply put it's d1 over one plus k plus p1 over one plus k so it's the discount of the dividend plus the discount of the price you discount those to the present and you will find the price of the stock today p0 so what happened if you want to find the price a year from now not not today you want to you want to know what's the price a year from now well the price a year from now equal to d2 the dividend that you're going to be receiving a year from now which is d2 notice this is p1 d2 plus the price of the end of the year again discounted at one plus k and hopefully you are starting to see a trend and let's kind of let's look let's put this trend on a timeline just as we did with the bond to see how this work from the stock's perspective so simply put if we have a timeline this is p0 and p0 is the day how do we find uh and this is p1 let's say this is p2 so on p3 p4 so on and so forth so how do we find p0 well we have to find for p0 we have to find we have to discount p1 and discount d1 discount those two how do we find p1 well to find p1 we have to discount p2 and d2 well how do we how do we find p2 think about it p2 is we have to find p3 discount p3 and discount d3 and how do we find p4 you got the point that p3 we discount p4 and d4 so simply put what's gonna happen is this so if this is p1 if this is the formula for p1 if we want to find the stock the stock price today two years into the future here's what we do we're gonna discount the d1 which is this part here this part here plus plus p1 plus the discount of p1 so so what we do is we discount so notice here this this area here that i highlight in green it's this part here plus p1 discounted well p1 notice p1 p1 in this formula equal to d2 plus p2 over 1 plus k so we can replace p1 so notice p1 here is replaced by let me use this a different color so p1 can be replaced by this circle here so p1 equal to d2 plus p2 divided by 1 plus k so it's going to be the dividend year from now plus the dividend two years from now plus the price two years from now so if we want to find the price if we're discounting the price two years from now now we could do the same thing for the price three years from now simply put if we want to find the price three years from now we can find the same thing simply put p the price today which is p0 would say value 0 or p0 equal to the this equal to the equal to the present value of the dividend d1 divided by 1 plus k which is discounted by the required rate of return d2 d3 d4 d5 now what happened in this formula we're only counting the dividend we kind of drop out the the price p2 is because we assume that the price is part of the dividend it's discounted as part of the dividend but basically what we do this is what in its simplistic format this is the dividend discount model which is the dividend all the dividend equal to the present value of all the expected dividend when we when we take the present value of the dividend and we discount them to the present value we find the price of the stock based on the dividend discount model so this is the idea you'll take your dividend and you discount them to the present value. Pretty simple in a sense that it's very similar to the bond. Simply, if we're comparing it strictly to the bond, think of only discounting the interest, not the face value. Now, here's the question to you. Do dividends stay constant? So simply put, here we are saying D1 plus D2 plus D3 plus D4. But do dividend stay constant? And the answer is no. Dividend, they don't stay constant for many reasons. The company makes profit. As they make more profit, they distribute more dividend. Also, we have something called the dividend yield. As the stock price goes up in value, the company will have to increase the dividend to compensate for the price. So the normal thing, dividend, they trend upward. So we're going to assume dividend trend upward at a stable rate that we call G. So G is the growth rate of dividend, because dividend don't stay the same. Here we are assuming the dividend, you know, D1, D2, it's all the same. For example, if the growth rate of the dividend is 5%, simply put, the company will increase their dividend for 5%. And the most recently paid dividend, D0, is $3.81. What can we say about D1? Well, D1 equal to D0, which is 3.81 times 1 plus the growth rate, which is 5%. So D1 equal to $4. D2, D0 plus 1 plus G raised to the second power, which is 3.81 times 1.05 raised to the second power. What is the third dividend? Well, it's D0 plus 1, 1 plus the growth rate raised to the third power, 441, so on, and so forth. This is assuming the growth rate, the growth rate is constant. It means it's the same growth rate, which is at 5%. So here's what we can say. We can say that V0, now this is we're going to be including the growth rate. V0, again, when I say V0, VALU0, it means the price, the price today, P0 equal to the D0 plus 1 plus the growth rate divided by 1 plus K. So basically, you'll take the future, the present dividend, you grow it, and you discount it. You will take, I'm sorry, not the future dividend. Yes, the future dividend in a sense that it's D times 1 plus G, which is the current dividend plus the growth raised to the second power divided by 1 plus K raised to the second power. Again, D0 plus 1 plus G, the growth rate raised to the third power, so on and so forth. Now we can simplify this equation into this equation. V0, we can say equal to the future dividend, which is the dividend growth, D0 plus D0 times 1 plus G divided by K minus G. So this formula here basically can turn into this formula. And basically, it can be simplified to the price of a stock, so we can find the price of a stock today, which is equal to the future dividend based on the dividend growth, 1 plus G divided by K, and we'll take it into account the growth at the denominator 1 minus G. So simply put, from all of this, you need to understand the price of the stock equal to its future dividend divided by K, the required rate of return minus the growth rate of the stock. Now we can compute the intrinsic value. Again, once we say the intrinsic value, it means we're calculating the stock price today. By dividing D1, not D0, the future dividend by K minus G. So of the market capitalization, which is the required rate of return, K is 12 percent. The equation implies that the intrinsic value of the stock is as follows. We have $4, which is D1. All we have to do, find D1 divided by the required rate of return minus the growth rate minus G. It means the stock, the intrinsic value of the stock, equal to $57.14. So this formula, so this basically, this is what we're going to go through. This formula equal to the constant growth model. It means the growth is constantly at 5 percent, or sometime it's not sometime. It's called the Gordon model after the Merriam Gordon, who popularized this model. So this is basically the basic idea of the dividend discount model or the constant growth model. Now let's take a look at an example. Preferred stock, if you're not aware of them, they pay a fixed dividend that can be looked at at a constant using the, we can find the price of the preferred stock by using this constant dividend discount model. Why? Because the growth rate is simply zero. The preferred stock, they pay you a fixed dividend. So when you buy a preferred stock, they will tell you, we're going to pay you $2. That's it. $2 forever. In a sense, it's part of the contract. Therefore, for example, the value of preferred stock, well, they also use the $2. Paying $2 when the discount rate is 8 percent, notice we don't have G, G equal to zero. So the price of the stock P zero equal to the dividend, and it doesn't have any growth. It's $2 divided by 0.08 minus zero, which is K minus G. We have no growth. Therefore, the price of the dividend, the price not of the dividend, the price of the preferred stock equal to $25. How did we find this out based on the dividend discount model? We discounted the dividend using the required rate of return, and this dividend, don't grow. Don't grow. Simply put, a preferred stock pay you a fixed dividend. Hmm, sounds like interest on a bond. Exactly. Sounds like an interest on a bond. So let's take a look at another example. High flyer industries had just paid annual dividend of $3. This has just paid it. The dividend is expected to grow at a constant rate of 8 percent indefinitely. That's G. The beta of the high flyer stock is one. The risk free rate is 6 percent, and the market risk premium is 8. Why are they giving us all this information? Because they want us to compute the required rate of return, which is using cap M, using cap M. So what is the intrinsic value of this stock? Well, because a $3 dividend had just been paid, and the growth rate is 8 percent. The forecast for the year end is $3.24. So this is D1. So we find out already the numerator. The market capitalization rate, or K, or the required rate of return equal to D, using the cap M, risk free rate of 6 percent plus 1, the beta times times 8 percent, which is the 8 percent is what? 8 percent is the, what is the market, what's the, oh, risk premium, 8 percent right here, risk premium. So basically K equal to 14 percent. Therefore, what we can say is D1, which is 3.24 divided by K minus G, 14 percent required rate of return minus the growth rate. So the price of this stock is $54. What would be your estimate of the intrinsic value if they believe, if you believe that the stock was riskier with the beta of 1.25? Well, guess what? Now we're saying the beta is 1.25. What do we have to do now? We have to recompute, recompute this. Recompute the required rate of return. Let's do so. So if we recompute the required rate of return, we notice that K equal to 16 percent. What happened is K become 16, 16. What happened here? The stock goes down. It's because it's riskier. You buy it at a discount. So you, because it's riskier, you want to buy it at a discount. So because risk comes with return, you want a higher return. So now 16 minus 3.24 divided by 16 minus 0.08, which is 0.08 equal to $40.50. So if the stock is riskier, you want to buy it at a discount. So you have a higher rate of return, more risk, more return. How would you earn more return? You pay less for the stock. So when it, when it gives the return, you have a higher return when you pay less. Constant growth dividend, constant growth dividend, dividend implies that the stock value will be greater under those three conditions. Just basically they're common sense, but you have to know them. Obviously, the larger it's expected dividend per share. So the larger is the denominator. Think about it. What we say, we say D1 divided by R minus G. If D1 is higher, P0 is higher, right? That hopefully this makes sense. The lower the market capitalization. So as this goes down, as this goes down, this goes up. The price goes up. So the required, the required rate of return goes down, which is what we saw in the last example, because it means the stock is riskier. Therefore, we pay, I'm sorry, implied that the value will be greater. Yes, the value will be greater. The lower is the K. If the K is lower, the price is greater. Actually, it's the opposite. We're taking less risk. The higher the expected growth, the higher the expected growth, the higher the P0. So hopefully just make sure you understand this. And basically, if you don't understand or memorize them on the exam, just jot some numbers down. Say, well, what if I put 10, let's assume my dividend is 10, and my rate of return equal to 20.2 and my growth rate equal to 0.1 or 0.1, which is 10%, and start to change and see what happened to your stock price. So that's the easiest way to deal with. This is one sum of the implication of this model, the constant growth dividend model. Another implication of the constant growth dividend model is what, and hopefully you're already thinking about this, is that the stock price is expected to grow at the same rate as dividend. Why? Because we assume the dividend is what's driving the stock. So to see, suppose that the steady stock, steady state stock is selling at intrinsic value of $57.14. So simply put, that's the intrinsic value, P0 equal to D1, K minus G. Notice that the price is proportional to the dividend. Therefore, next year when the dividend is paid to steady stock holders, where they're expecting a 5% growth, let's see, if they're expecting 5% growth, what will be D2? It's $4 now, increased at 1.05, the future dividend is 4.2. Well, let's find the stock price, the future dividend, which is P1 equal to D2 divided by K minus G, 12 minus 5, and equal to $60. What does that mean $60? $60 means if the stock moved from $57.14 to $60 compute the percentage increase, that's equal to 5%. That's equal to the growth rate, it means of the dividend, it means the stock is growing in proportion to the dividend. So we can say that P1 equal to D2 divided by K minus G, D2 equal to D1 times 1 plus G, because D2 will take the previous year dividend plus the growth. Also, if we simplify now, if we simplify now, we find that D1 basically just break this formula down, put 1 plus G on the side. So notice here D1 times 1 plus G. So D1 divided K minus G equal to P0. Remember to find this formula here gives you P0, D1 divided by K minus G equal to 0. Simply put, the price is the price today equal to the price plus the future growth. So the price, the P1, it end up to be P0 times 1 plus the growth. All we have to do, if you know the growth of the dividend, take the current stock price multiplied by the dividend growth and you will find P1. This is what basically, what this formula, just you can go back and just see how we break down this formula, that this is what it breaks down to. So make sure you know this formula, this one right, this one right here. Therefore, DDM implies that when dividend are growing at a constant rate, the expected rate of price appreciation in any year will equal to the constant growth rate G for a stock whose market price equal to the intrinsic value. Obviously, the stock, that's assuming the stock price equal to the intrinsic value, which we find the intrinsic value based on the dividend growth. So they should equal to each other. Therefore, what we can say, the expected return equal to the dividend yield plus the capital gain yield. And hopefully, we remember this from the prior session. So if we want to find the return on the stock, the expected return, the expected return has two components, the dividend component, which is again, if you let's assume we have a stock stock, we paid for a stock, we paid $50 for a stock and it pays $2 per share. So two divided by 50 equal to 4%. That's the dividend yield. That's this formula here. Plus, let's assume the growth rate, we assume the growth rate for the stock is 2%. 2 plus 4 equal to 6%. So the expected return equal to the dividend yield plus the growth rate of the stock. If there's any growth rate. If there's any growth rate for the stock. Let's take a look at this example. IBX stock dividend at the end of this year is expected to be 2.15. So read this problem carefully. It's at the end of this year. It means this is D1. They're not talking about D0. They're giving you D1. It's expected to be $2.15 and expected to grow at 11.2. 11.2 is the growth rate. If the required rate of return is 15.2, that's K. What is the intrinsic value? What is the intrinsic value of the stock? Basically, simply put the formula is D1 K minus G. So what's the intrinsic value? We're giving D1 $2.15 divided by K 15.2%, which is 0.152. Let's use decimal 0.152 minus 0.112. So if we do this computation, we find out that the price today is $53.75. We call this P0 or V0 or the price today or the intrinsic based on the intrinsic value. Now we can compare this to the market price. We don't have the market price, but this is the intrinsic value. Well, the second question is this. If IBX current market price equal to the intrinsic value, that's good. What's the next year expected price? Wow, that's easy. Why? Because if we are already told that the intrinsic value equal to the market value, it means the only growth is the growth of the dividend. It means if we take $53.75, which is the current price P0, all we have to do is multiply this by 1 plus G, 1 plus the growth rate. That's all, which is equal to $53.75 times 1.112, which is equal to $59.77. So basically taking the P0 and multiplying by a growth rate to find P1. P1 is the price next year. That's all because they're equal to each other. If an investor were to buy IBX stock now and sell it after receiving the $2.15 a year from now, what is the expected capital gain? It means the price appreciation and percentage term. What is the dividend yield and what would be the holding period? Now, what we have is this. We have how much is the stock price today? How much? So the stock price today, let me put it today. Stock price today is $53.75. One year from now equal to $59.77. Okay, so we have this information and we know the dividend for this equal to $2.15. Now, we have to find out the dividend yield, the capital gain yield. Well, let's start with the dividend yield. The dividend yield is you're going to be getting $2.15 and you paid for this stock, $53.75. If we take $2.15 divided by $53.75, let me just do this calculation real quick, that's going to give us 4%. So the dividend yield is 4%. Now, we need to know the capital appreciation, how much did that stock increase in value? Well, we have to find the difference between $59.77 minus $53.75 divided by $53.75. Let me find the rate on this. So if I take this computation, the numerator is $6.02, so this is equal to $6.02, divided by $53.75, let me do this, $53.75, that's equal to 11.2%. So what is the, what would be the holding? The holding is 4% plus 11.2%, 11.2%. Well, think about it. This is the growth, 11.2%. This is the, this is remember, growth rate is 11.2% and the dividend yield is 4%. So the total holding period, the total holding period is 15.2%, 15.2%. As always, I'm going to remind you to visit my website, farhatlectures.com, if you have, if you need additional resources and if you're studying for your CPA exam, this topic is covered on the exam. Study hard, good luck and stay safe.