[MUSIC] So welcome everybody. Now that you've attempted the quiz on stocks, I'll walk you through what the correct answers are and how we arrive at them. Let's start with question number one and review each statement. Choice A suggests that the zero growth model assumes a 100% dividend payout. This is true since the firm has no growth opportunities and simply returns 100% of the earnings to the stockholders. Choice B however is false. In fact the opposite holds. Since at higher growth rates, share prices look like a hockey stick. In fact, they look something like this, if I can plot them for you here. Where we have growth rates over here. And we have the stock prices over here. So what happens is, that at low growth rate the prices are hardly being affected and they suddenly jump up as the growth rates start to approach the required rate. So that's really interesting, you can see that shareholders love growth rates and they are willing to pay very high prices at height growth rates. Choice C is true. Since all growth valuation models look at future dividends and price and they never include the current dividends. They've all ready been paid out to existing shareholders so you don't pay for what you don't get. And choice D and E are self explanatory. Let's go to question number 2. All of the choices here speak to shareholders rights and are correct, except for choice D. This statement is incorrect because stocks don't have a face value or par value, nor do they ever mature. It takes us to question number three. Here, we have statement A which is incorrect because the Dow has only 30 stocks. Statement B is also incorrect because the Dow is not a global, but it's a U.S. Index. Statement C is the correct response. Statement D is incorrect because the Dow has 30 stocks as I just mentioned, the Standard and Poor index has 500 stocks, and the NASDAQ about 3100 stocks. Statement E is incorrect even though Coca Cola is part of the DOW, a drop in the index value doesn't mean that Coca Cola went down. It depends on which of the stocks went down within the index that forced the whole index to go down. More generally stock price decreases do not necessarily mean that you should sell. You may want to wait. Maybe a whole bunch of other decisions you take, so we simply cannot take E as the correct statement. Again, the correct answer is statement C. Let's now go to question number 4. Here we are supposed to calculate the stock price three years down the road. This is when the company starts to pay $2 per year indefinitely. And it's at that point that we can apply the zero growth model. You'll recall the zero growth model, which is the price is based on future earnings, which are exactly equal to dividends and that is divided by the discount rate. So it's a perpetuity we value it today by dividing it by the discount rate. We have all the information we need in the problem. Before we do apply the information, let's keep in mind in this particular case. We are here in time zero. And remember that the dividends only kick in three years from now. Right. So, we're really computing the price in year three and that will look at next years dividend, which it doesn't matter because, it's flat, it's a zero growth model. So, you look at the dividend and then you divide it by R and this price, let's not forget we need to present value back to today. Right so then we apply this to a formula. The dividend we know is $2 and the discount rate has been provided to us 10% which give us a value of $20. Let's not forget, this needs to be brought back to times zero, and in order to do that we just have to take this value of 20 and bring it back, present value for three years. So that's 1 plus the discount rate raised to the power 3 and that gives us the answer, which is $15.03. And that corresponds to choice number e. Right. So that takes us to the next question, number 5. Here, where instead of using the zero growth model, we're going to use the constant growth model, so we have this was the zero growth model. Now we look at the constant growth model. And you recall the constant growth model to compute the price this time we look at the next periods dividend, which is D1 and divide that by the discount rate minus the growth rate. Keeping in mind that D1, next years dividend is this years dividend, D0 multiplied by one plus the growth rate. Now on a timeline, again, we can draw the information that we've given in this particular case what do we have for constant growth, we have time periods that continue on, where this is D0, this is going to be next year's dividend, the following year's dividend, the year after that, right until the dividend for period t. Right? And to compute the present value of all of these numbers All we have to do is to use this particular formula here. We've been given the data, easy to plug it in and get our results. So, what we have is the most recent dividend. The most recent dividend is $1.40 and that's growing at 5%. That's a growth rate divided by the discount rate of 10%, minus the growth rate. And that gives us a new price of $29.40. This corresponds to choice number E. Okay for question number 6 we can see that this is a non-constant growth problem because we have variable growths given in the problem. So what we can do is set up a little visual for us once again to see where the growth rates are changing. So what we have in the problem is for two periods we have a growth rate. Let's just put that over here. Period one and period two. We have a growth rate of 6% that's corresponding to this period here. And then from there on the growth rate dips down from here on to 3%, right. So for period 3/4 or indefinitely were at 3%. And, of course, we can compute the price at this point in time. That would be P2, which of course would be D3 using the constant growth of 3% divided by R minus G. And then we would, of course, forecast the next period's divided, the following period's dividend, and bring this dividend back here, and bring this dividend back here, along with this price. That's really what we're trying to do in this problem. Okay? What I've always recommended when you have different variable growth rate is to use a three step procedure. And that makes the visualization put very concretely into steps. So let's do the steps. The first step is to forecast the dividend until they become constant or zero growth. So, that's step number one, let's do that. Step 1. Forecast the dividends until there are zero or constant growth. In this example we have dividends becoming constant in period two. So we have to forecast d1 and we have to forecast d2. Let's do that. What is going to be dividend at the end of one it's going to be D0 into 1+g that's what D1 is. Right? [COUGH] And if we do that in our example we have $3 that's growing at 6% and that works out to $3.18. Let's do that again for period two, this is D2. D2 is going to equal to D1 into 1+G, because the growth rate is the same, we take this time 318 1 plus the growth rate and we get 337 that's dividend for period two. So we've really completed step one. Step one is simply to forecast d1 and d2, and we have done that right here. Let's do step 2. Step two is to compute the price at that point in time. Which point is that? Right over here, when the dividends become zero growth or constant growth. We've all ready noted that the price at the end of year two will depend on the following year's dividend divided by r minus g. So that's what we're going to do here. Calculate the price at the point where the growth rate becomes constant. In this case, we look at the third period's dividend, which is going to be d3, and divide that by r-g. So, what is d3? Well, d3 is going to obviously be d2 times 1 plus the growth rate. In this example, d2 is 3.37, this is now going to grow, note at 3%. 1 plus the growth rate, that gives us the new rate of D3. Divide that by the discount rate that is given in the problem, to be 16%, and notice we subtract now the constant growth rate of 3%. And that will give us the answer for step two which is $26.71. That is step two. That takes us finally to step three. Step three is simply the present value of steps one and two. So we want to bring this dividend back as I mentioned, this dividend back and this price back. Those are the three things we want a present value instead of three. So let's do that to present value leaves three amount. All we have to do is take the numbers which you see here. We take the first number D1 which is 3.18, bringing it back for one period at our discount rate of 16%. We do that right here. This is to compute remember, the price today. And then we bring the 2 and p2. P2 we've computed the dividend for the second period is 337. And we've computed the price, which is 26.71. Bring these back for two periods. And voila, we have the answer if we solve for this. You work this out you're going to get $25.17. Probably have a little rounding error. But that's because I've been rounding as we go along. And that should correspond to answer A. And that is it for this particular quiz. Thank you.
