Could someone please explain the mathematics of why the stock price is expected to grow at the same rate as dividends in the infinite period DDM? Thanks in advance.

Sad, I’m fairly certain the assumption is that earnings are expected to grow at the same rate as dividends, not the stock price. You’re using the DDM to solve for the PV of the stock (i.e. its price, as justified by the DCF), assuming earnings and dividends grow at the sustainable growth rate (g = RR*ROE). I don’t think the DDM has any place in explaining the expected growth rate of a stock price. The DDM basically tries to explain the value of a stock by turning it into an annuity, one that happens to grow at a constant rate indefinitely. The reasonableness of this methodology is a debate for another time

Gun-man, I would tend to agree with you, but I encountered this question (see below) on page 175 of Schweser book 4. The answer seems to imply that a stock’s price must grow at the same rate as dividends do. What do you think? ************************************************************************ Holding all other factors constant, which of the following is expected to grow at the same rate as dividends in the infinite period DDM? A. Sales B. ROE C. Stock price D. All of the above Answer: C Explanation: The infinite period DDM implies that the stock price will grow at the (constant) growth rate of dividends. A crucial assumption of the DDM is that ROE is constant; sales growth rate could be the same as the growth rate of dividends and earnings, but this is not required.

I believe you are looking too hard into this… All the question wants to know is what the relationship is between dividends and the stock price using the DDM… Its not asking about various assumptions of a complicated valuation model…

I disagree, chad. The relationship between dividends and the stock price is P = D/(k-g). That’s not what the question was asking. The question was clearly asking what variable was expected to grow at the same rate as dividends in the infinite period DDM.

It’s not complicated chadtap, the equity valuation models in CFA level 1 are the the simplest models you can find and because of that they don’t work very well in practice. All the equity valuation questions they have in level 1 are trivial exercises in number crunching using a calculator.

Sad, interesting example question. I don’t know why I’m having trouble crunching this, it just seems like if we could predict how the stock price would grow, this would present arbitrage opportunities. And does the stock price even grow? I mean, aren’t all the future CFs built into the stock price already? With an ordinary annuity, it’s easy to observe its PV gradually increasing as it approaches its FV (at maturity). However, does a perpetuity even have an FV? The infinite period DDM basically turns a stock into a perpetual-growth perpetuity… It makes sense for earnings and dividends to grow in lockstep (w/ constant ROE), but when we throw in assumptions about the stock price growth, well, it’s just not registering for me presently… Anyway, maybe it’s back to Level I for me I’ll crack the books when I get back from the office.

I don’t see what is so complex about this. Look at the equation: P = D/(k-g) If g (the growth rate of dividends) increases, the denominator decreases which will cause P to increase.

Niblita, yeah, but who said anything about g changing? The sustainable growth rate (for dividends and earnings) is g = earnings retention rate * ROE So if there were an increase (or any changes in g), we’d be talking about a multi-stage DDM model (provided that k > g), ending with the terminal value when the company finally reaches its “sustainable rate.” Anyway, I’m done posting on this thread until I re-read some stuff.

Thats true, I read the question as only looking at G. If that grew, the the denominator blah blah blah.

I would have thought the answer lies in the equation P = D/k-g Which shows a direct relationship between stock price and Dividend, so an increase in dividend will cause an increase in price. So if we have growth factor of say 5 for Dividend we would expect the Stock price to increase by the same factor, hence the direct relationship. All other options/answers have no relationship with Dividend as far as Infinite Period DDM is concerned.

Glossary (G-49), 2006 LI CFAI Curriculum, Volume II: “Sustainable growth rate: A measure of how fast a firm can grow using internal equity and debt financing and a constant capital structure. Equal to retention rate x ROE.” webtwister, I just reread some stuff (including the excerpt above) and I’m still not convinced. All that constant growth you’re talking about is already built into the *current* stock price (i.e. its PV, a.k.a. “P0”, never changes). Notice there’s no “t” (for time) in the equation, we’re talking about a perpetuity here (albeit one that grows constantly forever). Let’s quickly revisit the PV of a zero-growth perpetuity: PV = Periodic Payment / Discount Rate = D1/k-0 So why should this PV be any different at t=0 vs., say, t=5 or t=1,000? So now we add in some growth, say 5%, so what? it’s constant and built into P0 too. Okay, I’ll let someone else settle this debate. And if I’m wrong, well hey, guess I learned something today. My position: g measures the sustainable growth rate of earnings and dividends (but not stock price), and the sample question above is FUBAR. Other position: g measures the sustainable growth rate of earnings, dividends, AND the stock price. You be the judge, I’ll concede defeat if necessary. Holy sh- we’re having a major earthquake in SF!

Oh you want to talk about the DDM in relation to the accounting now and not just the mathematics of the model? It’s been a couple of years since I’ve thought about this, but how about this for the intuition behind how g affects the stock price each year? Given g= retention ratio * ROE, then if retention ratio is ZERO they don’t reinvest any money in the business, so no growth in share value/business. If they retain some amount of earnings each year, that means they grow the value of the business itself by retained earnings. So if money is retained that means that g is greater than zero (assuming ROE is positive/not zero) and that additional money will be kept in the business and that you will have CAPITAL GAINS in the share price. Following is a mathematical example of how g is related to growth in stock price.

If g=5%, r=10% and dividend at time zero = $1… t0: D= $1, stock price= 1.05/(0.1-0.05) = $21 t1: D= $1.05, stock price = 1.1025/(0.1-0.05) = $22.05 t2: D = $1.1025, stock price = 1.157625/(0.1-0.05) = $23.1525 t3: D = $1.157625 Now: Growth in stock price from t1 to t2: 23.1525/22.05 -1 = 5% Growth in stock price from t0 to t1: 22.05/21 -1 = 5% And you could keep on doing this for every year into infinity… So the stock price has grown by 5% every year. It’s been a while and I’m a bit rusty on the ideas, but I believe it’s to do with retaining earnings which increases the asset base of the company and as you earn returns as a percentage of the asset base each year, if you keep retaining some amount of profits every year and don’t just pay it out as dividends then you keep growing that asset base and therefore you would think that the value of the company has to increase and you get capital gains.

Sean, You’re a genius. Thanks a bunch. Sad One

I’m the earthquake in SF. Fire everyone here and hire me, they don’t pay me enough at work.

sean, what you’ve demonstrated is four DIFFERENT PVs for four DIFFERENT COMPANIES (perpetuities), it doesn’t work that way. Your correct methodology should have been P_n = 1 * 1.05^n If I could use the DDM to model the exact growth in the stock price, why the F- would I ever buy the goddamn thing? Why don’t I just buy infinite f-ing call options on infinite margin and sell every goddamn put option on the face of the planet for the rest of my life, sitting on the beach earning 20%? The DDM is fraught with practical limitations, but it doesn’t pretend for a second to be some sort of magic 8-ball for predicting stock price growth (let alone constant stock price growth, forever, go find me a stock like that). Go revisit your books on this. It’ll instruct you on how to use the DDM to estimate a stock’s intrinsic value, which you then can compare to its market price and consider whether it’s over- or under priced. Better yet, quote me some passages that discuss using the DDM to predict stock price movements. Seriously, can someone else who’s actually passed LI step up to the plate here?

I think I’ve KO’d hired guns, I’ve got him swearing. You don’t need to pass CFA exams to work out what I’ve posted above. Well, getting back to the job at hand, I’m not really sure of what you mean when you say: "Your correct methodology should have been P_n = 1 * 1.05^n " IF the assumptions are correct and IF there isn’t any new information about the company and thus no new economic shocks, that means the DDM will allow you to predict the value of the stock if the assumptions don’t change (assumes inputs are correct). But just remember that it’s a prediction, not an assurance. You will have a distribution of estimates for each input and due to uncertainty (variance) you won’t be able to predict the price with 100% certainty. So any call options you buy will already have the possible growth input into it via the variance input. The calculations are for the same company it’s just done at different times in the future assuming that the assumptions hold. Try this out: $22.05/1.1 + $1.05/1.1 = $21 That shows that the present value of the stock at time zero equals the present value of the stock in one years time plus the dividend in one years time. Oh and there is heaps of research that makes use of the DDM to predict movements in the stock price, but it’s usually to show that there is mean reversion in market prices to theoretical fair value and usually focuses on the residual income model which is a method that is linked to the DDM. Can’t remember all the people that have published on it off the top of my head, cos I haven’t done any research in that area. Oh and don’t go editing that post afterwards, you post it, then you get to put up with what everyone thinks of you afterwards. Geez Joey must be asleep.

Obviously hiredguns has worked out that he is completely incorrect and has realised that he made a complete fool of himself. It is also quite obvious that he has not done any formal study in finance before and probably should stay away from finance if he can’t think about something as simple as the DDM model. I would hope that even my second year undergrad students could understand the examples I’ve posted above. But lets just put up some more information to show just how wrong he is: If the stock price doesn’t change as hiredguns assumes, then you will only receive return in year 1 in the form of dividends and this means that you will obtain a holding period return of: $1.05/$21 = 5% Now, if you include the capital gains as I’ve shown above you get the following HPR: ($1.05+ $22.05 -$21)/$21 = 10% (Your required rate of return!) So who do you think is correct? Receiving your required rate of return of 10% as I say, or receiving less than your required rate of return as hiredguns says? So if anyone wants some arbitrage make some bets against him about how fast he could bankrupt a hedge fund if he worked there. Hiredguns1, you still haven’t conceded defeat as you said you would if you’re proven wrong. So when is your apology for swearing on the this message board going to come as well?