 Personal finance practice problem using OneNote. Estimated stock ROI rate of return, assuming constant dividends and growth. 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, 240, estimated stock ROI, assuming constant dividends and growth tab. Also, take a look at the immersive reader tool, practice problems typically in the text area too with the same name, same number, but with transcripts. Transcripts can be translated into multiple languages and either listened to or read in them. We're thinking about investments in stocks, stocks representing ownership interest in a corporation. Corporations being separate legal entities breaking out their ownership into fixed or standardized units of shares or stocks. We are also typically thinking about publicly traded companies, those trading on public exchanges, making them more transparent and accessible to individuals. And so we can see things such as their financial statements, for example, to make investment decisions upon. Also note that your investment strategies may differ when using tools such as mutual funds and ETFs, as opposed to say investing in individual stocks. We're considering individual stocks here when you're thinking about them, you're often drilling down on the trend analysis and the financial statements of the individual company as opposed to possibly sectors or sections of a market, for example. So the assumption here, we've got the dividends at your end are $7. The stock price is gonna be $80. Now the stock price will be determined by supply and demand because other stocks are trading for that amount. That's how we can determine what the current price is. We're gonna be assuming the constant growth rate of 5% and we're also gonna assume that the dividends are going out into the future at a constant rate. So we're using a method similar to what we use when we basically value the bonds, for example. So remember when you're kind of valuing the bonds, figure out the price of the bonds, you're typically looking at the cash flows that are happening into the future, discounting them back to the current timeframe, the cash flows representing a standardized, fixed income flow of interest in the future and annuity in essence, and then the payment at maturity. When we're talking about stocks, it's a little bit more complex because we've got two things that we're kind of looking at. One, we might get dividends, cash payments, cash flow, the company taking the earnings of their company and distributing them to the owners in the form of dividends. And we also might get an increase in the value of the stocks, possibly by the company taking those earnings, putting them back into the company and buying machinery and equipment, increasing the value of the company, hopefully being reflected in the stock price. We also do not have any maturity date in order to kind of figure out the future cash flow because the investments could go out indefinite, right? So we're kind of considering dividends, for example, in this assumption and a cash flow assumption as if they're gonna basically go out indefinitely into the future. We could make other assumptions, we could assume they're gonna go up periodically or something like that, but we're gonna assume that in this particular company, the dividends are going out into the future and that we have constant growth, meaning the value of the stock is gonna be going up in the future. And we know the stock price, therefore we wanna consider what the rate of return is. Okay, so we can use the ROI, just if there was just dividends, for example, would be the $7 of dividends and the stock price, meaning if we just have the dividends as our return and we're not basically considering the fact that the stock's gonna go up in value, we're just looking at what we're receiving in terms of dividends. We would be comparing the dividends, usually on a yearly basis to then the stock price, what's being traded at that current timeframe. And if we divide those two out, pulling out the trustee calculator, we've got the seven divided by the 80, which is gonna be moving the decimal two places over 8.75. So that's the ROI if it were just dividends. And then we're just gonna tack on that constant growth rate. Now that constant growth rate, the strategy is more and more effective when we're thinking about stocks that are kind of peeking out in their business cycle. So it's like utility companies, for example, that don't need to basically invest much anymore and they're just tracking along and they're just gonna be making money and giving out dividends, right? Or things that are closer to a standard growth rate, those are easier to use as cash flow kind of model with because when you think about the constant growth rate of 5%, for example, you'd like that to be, that's a pretty big assumption, right? If the growth rate was a lot higher than that, that would be a big assumption to basically make. So we're gonna say, so you gotta be kind of knowing which kind of companies you're gonna apply this model to when you're trying to look at the valuation through future cash flows. So if we assume that there's a 5% constant growth rate meaning the value of the stock's gonna go up by 5% and that means our stock price goes up by 5% and we can sell it and realize it if we wanted to, that would mean then that we'd have the return of, rate of return of 13% to 8.75 plus the 5%. Now to kind of get an idea of what we're doing here, remember we're taking, if I took an annuity calculation and I calculated an annuity based on this present value calculation in a similar way to get back to the stock price, we've done this in prior presentations, so this would be similar to kind of like a bond calculation. If I had my rate of return here was the 13.75, but I assume a constant growth rate of 5%, that means the rate of return for like just the dividends would be the 8.75. If I tried to present value that stream of dividends at the 8.75 for example, we do a present value of the rate, that would be the 8.75, the number of periods, I'm using a very large number, a thousand, because we don't know, there is no maturity, it could go on forever. So you could try to get a better idea or a feel for what's going on by making this number not so high out into the future and see if it has an impact on your price calculation. If you take it out like a thousand years into the future because it could indefinitely go out in forever, then you know, you get closer to basically this number here, the 80. So comma and then the payment is going to be the seven and that's gonna give us our $80 just to see that. If you took the present, the annuity ROI with the dividend and growth rate, so now I use the same calculation using this 13.75 based on just the dividends. So I took the rate, which is going to be this 13.75, the number of periods is 100 this time. I'm just picking up fairly large number, comma and then the payment is gonna be the seven. Again, you'd get to that 50.91. And we're gonna try to use that number here as we kind of think about it in terms of mapping out all the payments into the future. So we could do a similar calculation, try to map everything out into the future. You can actually do this a little bit more complex method if you're thinking the dividends are gonna go up not at a standard rate, for example. So then you can actually map out on the years into the future what's gonna happen and do a kind of a more complex model. So we'd have the dividends are seven all the way across. So if we went out 100 years, $7 dividends, that would total up to $700, but that's expanded over a long timeframe. If I was to discount each one of these dividends on a year by year basis, this is doing it year by year is what allows me to increase the dividends. If I wanted to use a model and assume that the dividends are gonna go up, say every five years or something like that. But then we're gonna say, if I took that $7 and discounted it back using the rate of just this 8.75% that would give us to the 6.43. And if I did that all the way across, of course it would get smaller and smaller as we discount, for example, $7 back using the 8.75% for four years, it's now at five. If I go all the way out to 100 years, I'm still getting that $7 because we're assuming that that is constant, but it's very small. It's a very small number once we go way out into the future. And that's why it's kind of indefinite, but they're becoming a lot less significant out there. And we get to something close to the $80, not quite 80. That's why we used a thousand up here. So you can see the impact on how far out you go when you actually map it out this way, which I think is kind of useful. If we did the same thing, but now we use the $7 dividend and we use the 13.75 rate of return, $7 discounted back at the 13.75, would give us the 6.15. And if I did that all the way across, then we can add all those up and we get to that 50.91, which is this 50.91 we got to here. And that's gonna be used because we could try to think about, okay, what's gonna be happening with this constant growth kind of idea? If I use that 50.91 as our starting point, and I assume that we're gonna increase by 5% constant growth, what does that mean from a cash flow? Now note, this isn't actually cash flow now because we're not getting the dividends. We're saying that the value of the stock is gonna increase by 5% each year, which means I could then have the option of selling it, but I may not, you know, if I sell it, then the constant growth stops at that point in time, right? So it's the potential for us to have it. It's unrealized gains until we sell the stock. But if it went up 6% or 5%, then I'd have 50.91 times the 0.05, that would be an increase of 2.54 plus the 50.91, which would be 53.45, or we can think about it this way. If I take one or 100% plus 0.05, that would be the 1.05 or 105% times the 50.91, that would get us to 53. So the stock price is gonna go up to 53.45 times the 1.05, it's gonna go up to 56.13 times the 1.05, and you can see the trend here. That's what we're assuming is gonna happen. But notice what happens to our return then that we're getting, it's not an even return like the dividends were, the return is actually going up. So if this rate is fairly high, it's gonna have a kind of confusing impact on our calculation, because it's not gonna be the same all the way across, meaning if I, for example, if I compare that to the dividends, which are right here, I'm just pulling down the dividends that we did up top, $7 even that we're assuming all the way across 100 years out, the increase in the stock price starts to get significant, right? So now you're looking at the difference here, if you had a stock price, if my investment was at the 6, 3, 7, 5.8 times the 0.05, we've got the 318, that's a significant increase in dollar amount, but it's still 100 years out into the future. So it's still a fairly, fairly small once we kind of present value it back to the current timeframe. So that's the two values that we're gonna get, if we add them together, then we've got the, just these two, the 2.55 and the seven, not the 53. So we've got the 2.67 and the seven, that's gonna be the amount of value we're getting into the future in terms of dividends and the increase in the stock price. And then if we discount that all the way across using the 13.75 now, so now we're gonna take period one, we're discounting this 9.55 that we're assuming we're gonna get back one year using the 13.75, a formula like this would be the rate, it'd be the 13.75, we'd say then the number of periods is gonna be this one and then comma, comma, because it's not an annuity, future value would then be that 9.55, bringing it back to the current timeframe, getting us to the 8.39 about, and then of course it goes down and down as we go into the future and as we go into the future all the way out, it still gets relatively small, not as small as the dividends, which are almost non-existent, they growth in them, because again this percent increase still has an impact out into the future. So it's kind of, if that rate of growth is high, then this calculation gets a little bit distorted, right? So in any case, so if I add all that up, that's where we're getting about that $80. So we're kind of recalculating the $80. And the reason I do these kind of present value things is to try to, this concept up here is a little bit abstract, people probably just kind of memorize this, but don't have any real understanding of what's going on and you can't get to more complex calculations by breaking out more complex assumptions unless you break it out on a year by year basis, it's also just really good for your time value of money calculations. So it's really good practice, Judy's in Excel highly recommended.