 # infinite period DDM question

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!

5.6 magnitude, shook the whole building! http://quake.usgs.gov/recenteqs/Maps/SF_Bay.html