The alert reader might trace through this
simple calculation to ask how we now arrive at a long-term S&P 500 return
of 4.42%, using the present value model. Here’s the trade secret:

Long-term Return of the S&P 500
= (10 year average of operating earnings/current
price of the S&P=4138) X 1.33

a) Ten year average of S&P 500 operating
earnings per share (**$137.78**, up to 9/30/22). For large companies,
depreciation ⁓ capital expenditures, so operating earnings ⁓ EBIT.
To get the operating earnings figure, as of this writing (ask S&P if this
changes), navigate to the S&P 500 site, click on: Documents, Additional
Info, Index Earnings. (This crucial Excel spreadsheet seems to move around a
lot.)

b) 1.33, here’s where this growth multiplier
applied to the above earnings yield comes from: Columbia Professor
Bruce Greenwald’s lapidary book *Value Investing ( 2001)*,
choose this edition, table 7.11, p. 144. The table contains two terms: ROC/R=
12%/7% = 1.7, the ratio of a company’s return on capital/the cost of its equity
capital (the rate of required investor return); and LTG/R the long term growth in distributable cash/the cost of its
equity capital= 4% */7% =
.57. Given these factors the multiplier for the above earnings yield is 1.33.
This is the nearest published multiple; an interpolated multiple would be
slightly higher.

*** This is the long-term growth of the
U.S. economy, 2% real and 2% inflation.**

c) How do we modify this multiplier to take
into account the __long-term__ effects of the COVID pandemic,
global warming and inflation? The answer is, we don’t. To derive what is the
present value (undisturbed price of the S&P 500), we use the ratios ROC/R
and LTG/R. All terms in these ratios can change proportionately due to
adverse events. Unfortunately, the long-term capitalization term which includes
additional inflation does not.

d) With the above formula, you can also
calculate the level of the S&P 500 given a certain required return.

e) The S&P 500 is also often disturbed by
positive or negative events.

In “Stock Prices, Earnings and Expected Dividends,”
Campbell and Shiller (1988) find, “Long historical averages of real __earnings__ help
forecast present values of future real __dividends__ (i.e. stock prices factoring out inflation).” But five
years of compounded dividends recapture only 10% of a large company’s inflation-adjusted
stock price. It is actually easier to estimate the level of real economic
growth into the far future, than it is to evaluate the effects of specific
circumstances on near-term earnings. (Here we use reported operating earnings
and therefore calculate the level of the S&P 500, that includes the effects
of inflation.)

Particularly for smaller companies, five years of economic growth
is important because it sets the __level__ from which a company is
assumed to grow at the same rate as the general economy. This also resolves an
apparent paradox of why short-term stock prices are so volatile; when looking
at the historical record, real growth in the long-term economy is much less so.