 Personal finance practice problem using OneNote. Stock price calculation assuming constant growth and dividends. Prepare to get financially fit by practicing personal finance. You're not required to, but if you have access to OneNote, would like to follow along. We're in the icon left-hand side practice problems tab in the 12 to 20 stock price calculation assuming constant growth and dividends tab. Also take a look at the immersive reader tool, the practice problems typically in the text area too. Same name, same number, but with transcripts. Transcripts that could be translated into multiple languages either listened to or read in them. We're thinking about investments in stocks, stocks representing an ownership interest in a corporation. Corporations being separate legal entities that have the ownership interest broken out into fixed units of stocks or shares. We're also typically thinking about publicly traded companies. Those traded on public exchanges, allowing more transparency and access to individual investors to things such as the company's financial statements for example. You also wanna keep in mind your investment strategy when investing in individual stocks as opposed to say mutual funds and ETFs. We're focused in on the individual stocks at this point analyzing for example, the trends and the underlying fundamentals of the actual one actual company or corporation. Also, you wanna be thinking about these types of analysis in terms of how they fit into your overall investment portfolio, which again, you might be using say tools like mutual funds and ETFs or if you're using individual stocks, then those individual stocks would need to be thought of in total to think about how they fit in your overall investment strategy. So now we're trying to think about the value of a stock, say the price of the stock or what we think the value of it is so that we can compare it to the current price that's being determined by the market and see if it's over or undervalued possibly helping us out with investment decisions or selling decisions at that point. So we're gonna do so using a strategy similar to what we tried to do with the bonds. What we would like to try to do is think about the future cash flows that are happening, present value them back to the current period to help us to determine the price. It's a little bit more difficult with the common stock and then with bonds to do that because with bonds, everything is set within the fixed income of the bonds meaning we know exactly what the interest payments will be, we know exactly what the maturity date will be, we know exactly what we're gonna get at maturity and then we just have to figure out what we think the appropriate discount rate would be and then discount the annuity of the interest payments and discount the present value at the end of the maturity date and that would be how we can kind of value the price of the bonds. With the stocks, we have two ways that we're expecting to get a return on the stocks, you'll recall. One would be that we're hoping to say get dividends, which would be a return of the earnings in the corporation to the owners with the distribution of dividends which is similar to draws for a partnership or say a sole proprietor for example, except that in say a partnership the different partners could get different amounts for draws and the partner themselves might be facilitating the draw that they would like to have whereas with the corporation, all stocks need to be uniform, no one stock can take a bigger dividend than another stock although one person could own more stocks than another person therefore the stock strategy or dividends to be distributed would be determined by the board of directors and by management by in essence the company. And then we also might get a return for say the increase in the value of the company, possibly they're growing and that would be reflected in the stock price so that we can sell the stock at a larger amount in the future. So remember between those two strategies in a normal business cycle if the company went all the way through the business cycle it would look maybe something like this and more of the growth stocks would be down here where we would expect not to have as much dividends but the growth would be much higher at this point that would be like when Apple was growing and they're not gonna give a lot of dividends but they would be giving a lot of value in the shares going up so that you could sell them at a higher amount. If you're talking about this flat area up here that would be like Apple now possibly or say like a utility company that's well established they don't need to reinvest but they're well established and we would expect dividends to be somewhat more constant up here. So we talked about a situation before that would be a little bit more easy for us to apply this strategy if we make the assumption that the dividends are gonna be somewhat constant and that we're not gonna have as much growth because we have a well established company. If we're looking at companies down here and we're using this strategy to try to value future cash flow streams then we gotta think about dividends way out into the future what's gonna happen once they become established and what will be the dividends so that we can discount back or we try to take into consideration the growth that is happening and that's what we're gonna determine now adding that added level of complexity. Okay, so we're gonna say then that we've got the annual cash dividends are 10 paid each year we're gonna assume that those are constant but we're also gonna assume that there's growth meaning the value of the stocks gonna go up by the 7% the required rate of return for the common shareholders is 20% this is how much for example we think that could be received from other investments of a similar risk nature so that's the rate that we have to kind of clear in order to make it worthwhile for us to be purchasing these stocks. So we're gonna say okay so the annual cash dividend is 10 and this will be our quick calculation then we'll try to understand it with cash flows a little bit more in depth the return after growth so if the required rate of return we need to get a rate of return of 20 and we're thinking that the stable growth rate will be 7% now of course how would we know what this stable growth rate is? We don't right we're looking at the trend we might look at trend analysis in the past and see if we can extend that trend into the future we're gonna say we think the value of this stock is gonna go up the price of the stock for example is gonna go up we're gonna get a return in the value of the stock going up in addition to the $10 per year the $10 per year how do we know what that is again prior dividend policies that have been put in place and the company will most likely want to keep stable dividends into the future or possibly increase dividends they typically don't like to decrease the dividends because it's a bad signal to the market so that means that the 20 minus the seven there's a 13% return that's gonna be related to the dividends so if I take then the $10 dividend divided by the 13 we get to that $76.92 so we're gonna say 10 divided by the 0.13 which is the return we need after considering the stable growth would give us the price of the $76.92 let's see if we can think that through a little bit more here we can try to say okay one way we can kind of think about this and this would be similar to a bond calculation if I was trying to compare this to a bond what we do with a bond is we take the present value of the annuity payments and present value of the amount we receive at maturity and add them together here we have this stable growth so we can't really you know that that's gonna be the growth rate that's already kind of in place so what we're really doing is we can say okay let me try to present value first one way to understand this let's try to present value the $10 that we're going to be receiving using the 13% rate of return so in other words we're already getting 7% taking care of by the fact that we think the stock price is gonna go up let's try to use our present value of the stream of payments which would be similar to the stream of payments for say the interest portion of the annuity calculation for a bond so it would be present value of the rate and so we're using this 13% instead of the 20 so we're using the 13% comma the number of periods again we don't know what the periods are in a bond we would because we would know what the maturity is the maturity date so we're just gonna pick a large number because in theory this could go on forever but again this $10 like a hundred years out into the future discounted back at 13% will be a very small number so that's why we can kind of pick a large number for example then comma the payment is gonna be the $10 and once again we get to that 76.92 now we can also do if I do the present value using the 20% this will be I'll try to make this kind of feed in and see why it kind of makes sense to do this 20 minus seven like if I took the present value of the rate which is at the 20% comma number of periods we're gonna say 100 again and the payment then is gonna be the 10 we would get $50 so keep that in mind we're gonna use that in a second here but let's think about this in terms of breaking out now again you could get more complex than this and say well what if the dividend payments like changed in the future and I think they're gonna go up well you could actually map them out what you think the dividend payments will be in the future for example from year to year and then use the same concept but taking the present value of one of all future cash flow periods for example so that's one way you can build kind of a more complex model using the same kind of assumptions so we're gonna say okay so let's say that for example if I had the total dividends and we'll do the same kind of calculation but we're gonna map out periods or years one through 100 and we're gonna say okay if I took the 10% dividend and we did our present value calculation which I don't have right here but it would be the present value similar to this calculation it would be the present value of the rate which again I'm gonna take at the 10 what was it 13% and then discounting it or number of periods is gonna be one and then it would have two commas cause we're looking for the future value which is gonna be that $10 so if we brought that back then the $10 discounted back at 13% would be at the $8.84 and again if we did that all the way through as we've seen in prior presentations then we could discount two years out $10 would be at the $7.83 about and all the way out if we did that all the way out to the end for 100 years you could see as we saw in a prior presentation when we just did the $10 would be quite small 100 years out very small fraction of a penny right so then so that's why we can sum that up when we get to our $76.92 which we had up here so just another way to do that we can also do that I'm gonna now recalculate this number the $50 so we could say I'm taking the same $10 so it would be the rate is now gonna be the 20% the number of periods is gonna be one this time it would be one and then the future value would be the $10 so now we're discounting the $10 back one year but this time at the full 20% rate of return and we get to of course a smaller number because this one we discounted using the 13% and so that's gonna be the 8.33 if we did that all the way across we get the same thing and again it gets quite small at the end so we get if I sum this up we get the 50 so we've recalculated this $50 now the reason I did that is just try to get an understanding of what we're gonna do with the growth so if we tried to say for example if we started with this $50 that's like let's assume that's the original price with no dividends and then we said that there's gonna be an increase in the value because I'm gonna try to represent in flows this 7% increase so in other words if I start at that 50 that we calculated up top and we said it's gonna increase by 7% each period and we do do this in Excel if you wanna do this in Excel 50 times 0.07 would be another 3.5 and then I'm gonna add that to the 50 which would be 53.5 or I can say okay one or 100 plus 0.07 7% would be 107% or 1.07 times the 50 and that would give us to the 53 about if I take that and I multiply it times 1.07 we get to the 57 about if I take that times the 1.07 you can see the increase that we are getting as we go forward. If I look at the difference then between periods we're gonna say okay the stock price went up from 50 to 53 because there was a 7% increase that's 3.5 which you can get by subtracting these two or you can get it by taking the 50 times the 0.07 right it was a 3.5 if I do that all the way across you can see we have a trend that's different than the dividends that's why this gets a little bit tricky to think about my future benefits here because and remember these are not actually realized it's not cash flow this represents the increase in the price over time which I would only actually receive in cash if I sold the stock. So we could say okay then you can see that's gonna increase and you can see this one actually goes up so you gotta be a little bit careful with this calculation because if it's a large increment of increase this number out into the future can be quite large whereas of course when we were taking the $10 it's the same all the way out into the future so if I discount that stream of value into the future we could say okay let's first I'll do the same thing with the dividends the dividends are at the $10 $10 so that means that basically the benefit into the future then if I add those two up is gonna be for example we had the 3.5 increase in the value of the stock plus the $10.13 and then in year two we got the 3.74 plus the $10 it's 14 and I didn't put the pennies down here but you can see how it you can see how it's gonna basically increase because this number right here is increasing because there's a rate of return of growth whereas this is a fixed dividend that we're assuming is going out into the future okay so then if we calculate then our present value of all the streams of future value that we're receiving at the 20% the full 20% now we got the 13 and the next period we're discounting it back 20% for one year so we're taking that 13 that we're getting in the next year in value part of it being the dividend part of it being the increase in the value of the stock we're discounting it back 20% we get to the 11, 25 and then in period two we're discounting that 14 something and change it's rounded discounting it back 20% for two years we get to the 9.545 and so on and so forth notice that as we get out into the future then of course because of time value of money we're gonna get less value but we can also see that this is increasing at 7% so we've got that kind of a little bit different of an activity if I go all the way out here to 100 time frames you still get a fairly small number because this rate of growth was only 7% but if this rate of growth becomes significantly high like if it was 20% or 50% or something then this number way out here is gonna be is gonna be quite large right because of that and that can kind of skew things out a bit now we're out here way out here saying a 7% increase so meaning before if my value of stock 99 years later was at 40,547 times times 1.07 we got the 43,386 minus the 45,47 that gives us our 2,838 so that's a pretty big number in and of itself but 100 years out it's still relatively small so that means that we can kind of use a similar the same kind of method discounting back here and if I add all that up that gets us to the 76,92 the 76,92 that we calculated up top so that's an attempt to try to see why this kind of simple calculation up top works and is somewhat similar to us trying to trying to look at the future cash flows or future value that we're gonna be receiving not just in cash flow and essence but instead trying to think about the constant growth that we're gonna get in the value of the stock and take into consideration the cash flows and again remember if you use a concept like this then you could get more complex calculations by assuming the dividend's gonna go up periodically I mean maybe it won't go up constantly maybe you're thinking 10 years it's gonna go up or something like that and you have a staggered growth if you break it out on a year by year kind of break out then you can have more complex kind of analysis of these into the future and again this is only one technique that you can use to value stocks obviously you might favor different techniques of the stock valuation and these kind of valuations typically are more solid if you're looking at established companies that have an established dividend because this assumption that there's a stable growth is a large assumption that you'd be based in on past data for example. So there's that.