Investor Minimum Required Rate of Return:
With long term government bond yields currently in the range of 4 to 5%, equity
investors require a minimum expected return of about 7% to 8% to compensate for
the additional risk of equities. While we would all like to earn more than that,
supply and demand forces should cause the market to adjust prices to a point
where we can expect only 7% to 8%.
The only way that a company can provide investors with an 8% minimum return
over its life is for the company to make an average Return On Equity ("R.O.E.") of a minimum 8%.
This applies to the returns to investors as a group, it does not prevent
individual investors from making a high return by outsmarting other investors in
trading which is a zero sum game.
Limitations of Sustainable Growth:
Individual companies can grow at high rates, but only temporarily. No company
can perpetually grow faster than the economy - otherwise it would
eventually grow bigger than the entire economy (an impossibility). Economist
predictions for the long run growth of the economy are in the range of 4 to 5%.
There is also a relationship between investor required return and an average
company's R.O.E.. If investors require 8% then company's
should also find that the projects in which they invest are priced such that an
8% return results. In the long run other companies enter the industry and
compete for resources such that the return on equity to all companies is driven
toward the minimum required by investors, in this case 8%.
So, in equilibrium, investors require 8%, therefore company's returns
gravitate to 8%. The company's growth rate can then be calculated using the
sustainable relationship that growth = R.O.E. times (1 - the dividend pay-out
If mature companies tend to dividend out about 40% of earnings, then with an
8% R.O.E., they should grow earnings at 8%*(1-.4 )= 4.8%. Comfortingly, this is
consistent with the economists predictions of economic growth.
Some companies will consistently earn more than the average ROE, but this
will likely be offset by others that earn below average.
Assuming that investors require an 8% return, then it is prudent to assume
that sustainable company R.O.E.s will also be about 8%. A 40% dividend pay-out
ratio is then consistent with an economic growth of 8%*(1-.4) = 4.8%. This 8%
R.O.E., yields a sustainable justifiable P/E of 12.5. Interestingly, the sustainable P/E remains
at exactly 12.5 across a broad range of dividend pay-out ratios from 100% all the
way down to 10%. At a 100% dividend pay-out ratio this can also be calculated as the value of a
perpetuity, using a return of 8%, $1.00/.08 = $12.5 again a P/E of 12.5.
Similarly if investors require a 7% return and the sustainable ROE becomes
7%, then the sustainable P/E is 14.29. (Not coincidently 1/.07 = 14.29).
A stock market average P/E above 15 would then seem to require that either investors are satisfied with equity
returns below 7% or it requires an unsustainable assumption where companies
deliver a long-term ROE that is higher than the investors require.
My conclusion is that the equilibrium Justifiable P/E on a stock market index is
currently between 12.5 and 15. Given recent very low interest rates I would
focus on a required 7% ROE and a justifiable P/E of about 15. This is where it "should" be trading based on
"normalized" earnings. Note that if current earnings are thought to be
artificially and temporarily lowered by recession and unusual write-offs, then a
higher P/E can be justified.
In performing intrinsic value calculations, investors should assume that the
selling P/E, for a healthy company, after a five to ten year holding period
should be 12.5 to 15. A higher assumed P/E can only be assumed if the company
is thought to have unusually strong and enduring competitive advantages and barriers to entry
that protect it from competition. A lower P/E should be assumed if the company
is unhealthy or is exposed to unusually heavy competition.
As investors we are quick to demand a minimum 8% return from every company.
Given that many companies pay no dividend, this is mathematically equivalent to requiring that
the company grow its earnings by 8% annually. An 8% annual growth, rather than
being something to brag about, is then a minimum acceptable level for a non-dividend
paying company, if investors require an 8% return. Before you conclude that such
a company can meet your 8% return, you must consider if it can grow earnings per share at 8%
minus any dividend yield.
It has often been noted that a low interest rate environment can justify a
higher sustainable P/E. This is true. In a high interest rate environment of say
9%, if investors require a 12% return from stocks, then the equilibrium
sustainable P/E is 1/0.12 = 8.33 which is indeed lower than the sustainable 12.5
P/E that applies if investors require "only" 8%.
Justifying a stock market average P/E of 20 requires that either investors
require only a 1/20 =5% rate of return or that we were entering into a temporary
period where the market is expected to earn much higher than the investors
required minimum. At the end of both 1998 and 1999, the DOW P/E was at 24. It
seems unlikely that investors were signaling that they only required a 1/24 =
4.2% rate of return. Instead investors may have thought that earnings going
forward were temporarily going to grow at a rate much higher than their 8%
required rate of return. My math indicates that this would have required the DOW
earnings to grow at about 13% annually for 10 years before settling back to a
more sustainable 4.8% annual growth (calculated as an 8% R.O.E. times a 40%
dividend pay-out). A third possibility is that investors thought that companies
could perpetually achieve, through technology, an ROE that was above the
investors required rate of return. But, this seems to violate equilibrium
This was unrealistic. The market was simply greatly over-valued and investors
paid the price for that with the market crash of the early 2000's.
Exceptions to the Rule:
Individual companies can grow at very high rates temporarily, therefore the
above analysis does not suggest that very high P/E levels can never be
justified. The above analysis deals with sustainable P/Es in the long run for
individual companies and
with diversified groups of stocks in both the short and long run.
For individual stocks (as opposed to the market average), I have provided a separate
table of justifiable P/E ratios.
If investors as a whole become very pessimistic then they could, for example,
demand a 10% return even though the companies are only earning 7% in the long
run. This could be achieved (going forward) if investors bid the average P/E
down to 7.7. Today, this seems impossibly low but that is exactly where the DOW
P/E was on December 31, 1980.
Possibly technological advances and new research and patents can allow
companies to earn returns that are somewhat higher than the rate of return
required by investors. If companies can perpetually achieve 8% R.O.E.s while
investors only require 7%, then a P/E of 21.4 can actually be justified if the
companies pay-out only 30% of earnings. This scenario seems to violate equilibrium
conditions and is not something I would count on.
One always has to be cautious in applying theoretical rules to the stock
market index or (much more so) to individual stocks. The market can remain at
theoretically unsustainable low or high levels for many years as long as
investors keep it there. Eventually it "should" correct, but it could take many
September 28, 2002 (minor edits to April 7, 2006)
Shawn Allen, CFA, CMA, MBA, P.Eng.