It is possible to calculate a “Justifiable” long-run P/E level that can be used to identify under-valued stocks.
This Justifiable P/E can be used to judge whether the stock market as a whole is trading at a Justifiable level. It can also be used to calculate an assumed selling price for any stock after a five or ten year holding period. This is important in performing implicit value calculations.
In performing implicit value calculations an investor may assume that after a five or ten year holding period all stocks will revert to some sustainable long-term P/E ratio such 12 to 15. This article examines how to estimate the justifiable P/E.
This Justifiable (or sustainable) P/E level will vary with the investors required minimum rate of return and with the growth and dividend policy of the stock. The Justifiable P/E can only be expected to work on average and will never work in every case.
For groups of stocks such as the Dow 30 stocks or the TSX index, it is possible to make educated and conservative predictions about the average future earnings growth. In contrast it is harder to do that for an individual stock. An individual stock is subject to many random events and risks that are, to a large degree, averaged away when we deal with a larger group of stocks.
Even with groups of stocks the level of the Justifiable P/E is quite volatile depending on the assumptions regarding growth, dividend policy, and required minimum return.
I calculated the following Justifiable P/E levels by “discounting” the expected cash flows that would result from holding a stock permanently.
| Required minimum rate of return | Company’s Return on Equity | Dividend pay-out ratio | Sustainable Growth rate of earnings and dividend (ROE * 1-payout) | Calculated Justifiable P/E |
| 7% | 7% | 30% | 4.9% | 14.29 |
| 7% | 8% | 30% | 5.6% | 21.43 |
| 8% | 8% | 30% | 5.6% | 12.50 |
| 7% | 8% | 50% | 4.0% | 16.67 |
| 8% | 8% | 50% | 4.0% | 12.50 |
| 7% | 8% | 100% | 0.0% | 14.29 |
| 8% | 8% | 100% | 0.0% | 12.50 |
| 7% | 10% | 50% | 5.0% | 25.00 |
| 8% | 10% | 50% | 5.0% | 16.67 |
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 ratio).
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.
Conclusions:
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.
Recommendations:
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.
Observations:
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 conditions.
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 years.
September 28, 2002 (minor edits to April 7, 2006)
Shawn Allen, CFA, CMA, MBA, P.Eng.
InvestorsFriend Inc.