hello this is module eight in this module we are going to look at stock so the title is stock valuation so what we need to learn is how we will compute the price of the stock using dividends then we will compute the price of the stock using some multiples and then finally there is a discussion on about the stock market so basically there is three section common stock feature of stock and preferred stock and the stock market so let's get started with common stock so it's important for us to remember the principle it's here here the basic principle that we've been following so the price of the stock is the present value of the expected cash flow that's exactly what we did when we look at advance so since the price of a stock is the present value of the cash flow all the questions is what are the cash flows or the cash flows include the dividend when the company pay some dividend and when you sell the stock hopefully you will sell the stock for more than what you paid for so you will then realize a capital gain okay and you will realize the capital gain hopefully whether you sell the stock back to the company or whether you sell the stock to somebody else on the secondary market so let's illustrate how we are going to calculate the value of the stock so we're supposing that we are thinking about purchasing a stock from Moore or incorporated we expect that the company will pay a $2.00 dividend in one year and you think that we will be able to sell the stock for $14 and that time so if you require a return of 20% much or what is the maximum you will be willing to paint so on the following slide I just draw a timeline and you can see so the question is how much will I be willing to pay today assuming I am expecting to receive a dividend of $2 and I am expected hoping that I will be able to sell the stock for $14 so this become a time value of money problem we have no to cash flows right that will be receiving the future and the question is how much will I pay today so we can compute the present value of those cash flow as we did before so 2 plus 14 is 6 that's the future value the required rate of return is 20% the cash flows will be receiving one period and we compute the present value so 1333 should be the fair value now let's extend this problem to to period so let's assume that instead of keeping the stock for just one year we will keep the stock for a second year and we believe that the company will pay another dividend a little bit higher of two dollars and ten cents and then we believe that at that time we'll be able to again sell the stock and we will sell the stock for 1470 the question again well what is the value of the stock today and as you can see this is again a time value of money problem so you can use the cash flow function and in that case you will input cash flow 0 is 0 cash flow 1 is 2 and the frequency is 1 is only one time this cash flow and then cash flow 2 is 210 plus 14 70 which is 16 80 again this cash flow is only going to be received once then net present value you know read the rate of return the discount rate is 20% and you will compute the net present value and you obtain again 1333 so that's important that you realize that the price does not change right what is changing is the strategy and investors will have again we obtain 1333 and then one last time so now let's assume that we want to keep the stock for three periods and we have the dividend that are listed here we believe that the price will be fifteen and again we calculate the present value and again the price is 30 so what can we see here if we generalize but it does not matter the number of period I'm working with if I plan to keep the stock one period is going to be 13 - period thirteen three period thirteen now you can imagine that we could calculate what will happen to the price if I kept the stock for four period or five period or six seven eight nine ten and on and on and on and on and on and in fact because the stock does not have a maturity you could imagine that you will keep the stock until infinity but each time the price will still be thirty territory so we can continue to push back the years in which we will sell the stock the value will always remain the same so we can generalize this and here's what's happening instead of using our calculator like we did here go here or here and can you imagine if I had to use my calculator when I have 200 cash flow we need to just find an approximation or a formula that will help us to calculate the price without having to just introduce the cash flow like this and we are very lucky that somebody called Myron Gordon who has studied this problem and suggest is the Gordon model so here's what he has shown so when a company is paying a dividend and when the dividend is constantly growing so you can see that this line here so this is a constant growth right instead of just using all those cash flows like we just did here but we could use a formula and the formula will be here the price of the stock is equal to D oh that's the first dividend that was paid times 1 plus G G is the growth rate of the dividend divided by r r is the discount rate the required rate of return minus G repeat P o is the price of the stock now and this here so P o is the price the value how much people are willing to pay do is the dividend that has already been paid and then D 1 D 2 D 3 and so and so on are the future dividend now if we look at the growth model well since the dividend are all growing at the same rate D 1 is d o that has been growing at the rate G once D 2 is do that has been growing at the rate G twice the tree is do that has been growing at the regi three times so G is the growth rate so knowing this what do times 1 plus G is indeed D 1 that is correct this is exactly the same thing and highlight this dist make sure you see this right so that's D one right here the formula see that and then R where R is the required rate of return your discount rate and G is the growth rate now this formula that you have here can be used for a positive growth like here the dividend increase increase but we could use the exact same formula if the dividend was decreasing decreasing decreasing decreasing or we could use the same formula if the dividend was not changing right if the dividend was not changing well G will be zero so you can imagine that the formula then become D divided by R take a look here is the dividend are not changing I don't need to identify which dividend I'm talking about it doesn't matter whether it is D 1 D 2 D Twitter all the same so we just put D and then since G is 0 well then we divide by r minus z0 which is r so this is how we will calculate the price of the stocks let's illustrate suppose Big D incorporated just paid a dividend of 50 cents per share so clearly this company just paid a dividend so this is D o that's the dividend that has been paid to dividend it is expected to increase its dividend by 2% per year so this is clearly the growth rate dividend will increase by 2% as G if the market requires a return of 15% on assets of this risk so this is the required rate of return and is capital R oops on assets of this risk how much should the stock be selling for well we can apply the formula the price so I can just copy the formula right here gonna copy that on the next slide to make sure we have the formula in front of us all the time so it is d o times 1 plus G divide it by our point 15 minus G when that gives you three dollars and 92 cents of course if the company does not pay a dividend the model should normally be used although we could make a case of why in the long term company will always pay a dividend but in that if the company does not pay a dividend or if you want another idea of what the price should be well you could use a multiple such as the p/e ratio so in that case the price will be a benchmark the p/e ratio times EPS and I remind you that EPS is earnings per share and the benchmark p/e ratio will often be the industry average or you can use the company as well if you want and you can use then this to approximate if you know the p/e and if you know the earnings per share were just multiply the two and that will allow you to calculate D price illustration suppose the company had earnings per share of Twitterers over the past year the industry average p/e is 12 while using this information 12 times 3 which is 36 well you can evaluate or estimate that that will be the price of the stock so this is the end of the first recording for this lecture