ROE and expected return

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bchad

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I’ve thought about this a bit, but think there could be an interesting discussion:
What is the relationship between Return on Equity (ROE) and a stock’s expected return?
 
Using simple DDM
P = d/r-g
r = d/p + g
g = ROE*retention
So: higher ROE, all else equal higher g, all else equal higher r.
 
So:
E(R) = Div Yield + ROE*Retention = D/P + ROE*b
This implies also that if a stock pays no dividends, then D=0, b=1, and therefore
E(R) = ROE
But ROE is computed using the book value of equity So maybe this only applies if P/B = 1…
 
Thats kind of a circular argument - you apply DDM if the stock pays dividends, then you assume it doesn’t?
 
Apply l’hopital rule here. As dividend approaches .000000000001, b approaches .99999999.
 
You can take the limit as dividends approach zero. In this case the function is well behaved (no discontinuities or funky stuff like that). Alternately, maybe someone has a relationship between ROE and E(R) for a non-dividend paying stock. Capital growth=ROE*b where b=1 still seems plausible.
But what about the difference between book value and market value of equity. You have to buy stock at marks value (usually), so ROE will usually overestimate E(R), won’t it?
 
what’s l’hopital rule doing here. as dividend approaches .0000000001, b approaches .999999 and your DDM model approaches gggggggggarbage.
in the extreme case when a stock doesn’t pay out dividends, that means that they are able to reinvest the earnings in projects that give them a return higher than the cost of capital, so ROE>r
 
So if you know that you can invest at higher than the cost of capital, why would E(R) = Ke.
I’m not trying to be difficult. My intuition just tells me that there is some interesting (possibly profitable) financial concept in here.
 
P=d/(r-g)
GG model only makes sense if r>g. it gives you junk otherwise.
g=b*ROE, and you are trying to compute the limit b->1 a.k.a. g->ROE
so DDM will break down unless r>g=ROE in the limit b->1. but if r>ROE, then why is b->1? you are reinvesting all of your earnings, getting a return on equity that is less than the cost of capital? doesnt make sense
 
needhelp Wrote:
——————————————————-
> Apply l’hopital rule here. As dividend approaches
> .000000000001, b approaches .99999999.
Wow l’hopital rule.. Brings back memories of high school calc. I haven’t heard that word in over 10 years
 
Mobius Striptease Wrote:
——————————————————-
> P=d/(r-g)
>
> GG model only makes sense if r>g. it gives you
> junk otherwise.
> g=b*ROE, and you are trying to compute the limit
> b->1 a.k.a. g->ROE
>
> so DDM will break down unless r>g=ROE in the limit
> b->1. but if r>ROE, then why is b->1? you are
> reinvesting all of your earnings, getting a return
> on equity that is less than the cost of capital?
> doesnt make sense
Interesting… I hadn’t thought about it that way.
However, the idea that …
E(R) = dividend yield + expected capital growth rate
…doesn’t really require assuming GGM, does it? Nor does expected capital growth rate equaling ROE*b require starting with GGM. So even if there is this interesting contradiction that you brought up about GGM with 0 dividends, I’m not sure it’s necessary to start there.
Also, I am using expected return - E(R) - differently from the cost of (equity) capital, Ke. I see Ke as what the market demands on average for providing equity capital for a business with a given set of risks. I see E(R) as what you, the analyst, actually expect the rate of return will be. The two might be related, but I’m not sure they have to be.
 
Just yesterday i had a discussion w a colleague. This is the scenario:
Two similar companies A and B, the only difference is A pays a stable dividend rate every year but B says it will not pay dividend but reinvest back into company to grow earnings.
Question is, assuming all things else no change, would you, as an investor, give a higher expected rate of return for Company B relative to Company A.
My answer is as an investor, I would expect a higher return for Co B due to the higher risk (revinested amount need to generate a higher return than the dividend yield to compensate for the higher risk).
What is your view? Of course if you dont hold other things constant, there will be any changes like higher dividend growth rate from higher retention rate, higher ROE due to higher projected earnings etc. But suggest to keep these constant for simplicity sake. Thanks.
 
Interesting topic. Here’s my take:
Cost of equity is a subjective. It is different for every investor (unlike cost of debt). It does not appear in any financial statements.
Ultimately the cost of equity is your required rate of return to make investing in the project acceptable. From that perspective it is like an IRR or p-value. Just remember that when investing in listed equities, the average return is around 6%-7% in the long-run. Of course when you invest in a project, you would like to do better than average, hence why COE is often seen as 10% plus. In a standard equity DCF model, however, 6%-7% is the appropriate figure you should be using.
If ROE > Cost of equity then you are in the money. Happy days. And vice versa naturally.
The CFA curriculum lists several models for calculating COE, with basic CAPM probably the most commonly used in the market. Really though, you can use any number you feel like. Your valuation of anything is a totally subjective thing. There is no right or wrong answer, although clearly some answers would be so outlandish they’d be very hard to justify!
 
pmoonoi - it will depend on whether the company is earning a ROE > COE no? If so, I would want the company to reinvest. If not, the company should pay out dividends until it is only reinvesting in projects that at least cover the cost of equity.
Does that sound reasonable?
 
Remember that if you are a taxable investor, dividends will force you to pay taxes (and usually at a higher rate than capital appreciation), whereas with capital gains, you pay taxes only when you sell (and therefore bank the time value of the tax). So if ROE = Ke or even a tiny bit less, you might prefer the company to retain earnings so you don’t pay taxes on dividends(and transaction costs on reinvestment) and have the company do it for you. This might to be one reason that excess cash is often used to repurchase shares rather than pay dividends (the other might be that management thinks shares are undervalued).
(yeah, it’s nit-picking a bit, but something to remember)
 
“However, the idea that …
E(R) = dividend yield + expected capital growth rate
…doesn’t really require assuming GGM, does it?”
the derivation above does - how would you derive it otherwise?
“Also, I am using expected return - E(R) - differently from the cost of (equity) capital, Ke. I see Ke as what the market demands on average for providing equity capital for a business with a given set of risks. I see E(R) as what you, the analyst, actually expect the rate of return will be. The two might be related, but I’m not sure they have to be.”
ok, but if you are going to be applying the DDM and starting with the market price and back-solving for the cost of equity, you will get Ke. if you are going to be back-solving in order to get your “expected return” E(R), then you’ll have to plug in not the market price, but whatever the price you think it should be. if your E(R) is different than Ke, you are assuming the security is over/under-valued, right
 
bchadwick Wrote:
——————————————————-
> Remember that if you are a taxable investor,
> dividends will force you to pay taxes (and usually
> at a higher rate than capital appreciation),
> whereas with capital gains, you pay taxes only
> when you sell (and therefore bank the time value
> of the tax). So if ROE = Ke or even a tiny bit
> less, you might prefer the company to retain
> earnings so you don’t pay taxes on dividends(and
> transaction costs on reinvestment) and have the
> company do it for you. This might to be one
> reason that excess cash is often used to
> repurchase shares rather than pay dividends (the
> other might be that management thinks shares are
> undervalued).
>
> (yeah, it’s nit-picking a bit, but something to
> remember)
that’s an interesting point, although as long as the tax on dividends is the same as the capital gains tax, it shouldn’t make a difference to you. aren’t they the same in the US?
 
Mobius Striptease Wrote:
——————————————————-
> “However, the idea that …
>
> E(R) = dividend yield + expected capital growth
> rate
>
> …doesn’t really require assuming GGM, does it?”
>
> the derivation above does - how would you derive
> it otherwise?
You can derive it this way: my expected return is going to be some income (dividends), plus capital growth. I’ll estimate the dividends with current dividend yield (which may be zero, if no dividends are paid). I’ll estimate that the capital growth portion will be equal to the rate at which the book value of equity grows (which implicitly assumes that P/B ratio stays constant). If I do that, then
E(R) = Dividend yield + capital growth = Div Yield + ROE*b
If you want to assume that P/B doesn’t stay constant, you can estimate with a term for P/B
E(R) = Div yield + ROE*b + (% change in P/B)
There might be an interaction term between cap growth and %P/B change, but it would be small.
This is related to why I started this thread. The biggest uncertainty in my mind is what drives changes in P/B ratio. Actually, I guess the L2 crowd probably knows that, because I remember it was part of the L2 exam, but some of P/B might be sentiment, and some might be “justifiable.”
Ultimately, I’m trying to put this together to see how you might try to value an index, but that’s a long way from here.
>
> “Also, I am using expected return - E(R) -
> differently from the cost of (equity) capital, Ke.
> I see Ke as what the market demands on average for
> providing equity capital for a business with a
> given set of risks. I see E(R) as what you, the
> analyst, actually expect the rate of return will
> be. The two might be related, but I’m not sure
> they have to be.”
>
> ok, but if you are going to be applying the DDM
> and starting with the market price and
> back-solving for the cost of equity, you will get
> Ke. if you are going to be back-solving in order
> to get your “expected return” E(R), then you’ll
> have to plug in not the market price, but whatever
> the price you think it should be. if your E(R) is
> different than Ke, you are assuming the security
> is over/under-valued, right
Yes, I am assuming that the security might be overvalued or undervalued and that something about my own research/analysis gives me a chance to identify it.
As for DDM, I wasn’t the one who started off with it; someone else did. I just ran with those results and then noticed that I could get to the same place without having to assume DDM (as derived above).
 
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