Corporate profits and their associated cash flows are at the heart of why investors buy shares in companies. While investors tend to understand the origin and importance of profits for individual companies, few have an understanding of how the economy in aggregate generates corporate profits, and thus don't know when analysts' estimates for profits and share prices are irrational. In today's brief, we attempt to remove some of the mystery from these economic concepts.

At the most basic level, corporate profits are revenues less expenses. But we are not interested in the microeconomics of this issue, which is to say the specifics of how individual companies generate profits. We want to look at profits from a macroeconomic level - how do profit forecasts tie in with broad economic trends?

Revenues at the macroeconomic level are simply Gross Domestic Product.  GDP attempts to measure the total value of goods and services produced in a given period, but does so by measuring sales and then subtracting inventory changes, so while it's called Product, it's actually measuring sales, and thus has a direct link to revenues.

To get from GDP to profits, we need a similar macroeconomic equivalent for expenses; here it gets a bit more complicated. First, we must subtract most of Personal Income - the assumption being that wages, salaries, and most other components of personal income represent corporate employment expenses. Items that are not paid by corporations to individuals such as government transfer payments are removed from personal income for this calculation.

Other items that must be subtracted from GDP to arrive at profits are depreciation, indirect business taxes such as sales tax, and Social Security taxes.

Finally, government subsidies and net income payments from the rest of the world - both of which boost profits - must be added to our equation. We can then display these concepts in a formula:

Corporate profits = GDP - Personal Income (excluding interest, dividends, and transfer payments) - depreciation - indirect taxes - Social Security taxes + government subsidies + net income from rest of world.

This formula then gives us a framework in which to judge the link between profits and economic growth as defined by GDP. Though many variables beyond GDP help to determine profits in any given quarter or year, none of these variables tends to shift much over the years in terms of its relative importance to the profits/GDP relationship.

Put more directly, over time, profits track GDP. In the post-World War II era, nominal GDP growth has average 7.1%, while profit growth has averaged 7.4%. As the following chart illustrates, profits as a percentage of GDP have not changed significantly for generations. Or put another way, profit growth has matched GDP growth.

Over shorter time frames - even periods of several years - profits can vary significantly relative to GDP, owing to the variables in our formula above. The most common source of this variance is Personal Income. In plain English, profit growth can differ from GDP in the short-term because the relative slices of the economic pie taken by employers and employees change.

Changes in the pie slices occur primarily for cyclical reasons. Corporations tend to win a larger slice of the pie early in a recovery and through the middle of an expansion, with employees faring better late in the cycle and particularly in recession (better in relative, not absolute terms).

The aging of the business cycle tends to benefit employees as the unemployment rate falls and their bargaining power increases. The recession benefits them in relative terms as corporations tend to bear the brunt of any downturn, with sales always falling faster than companies can cut expenses (i.e. wages). This shift reverses early in the recovery, as revenues ramp faster than expenses due to employer reluctance to add much to payrolls early in the cycle.

An example of how the shifting slices of the pie affects corporate profits was seen in the 1990s. From 1993-1997, corporate profit growth averaged 13% while nominal GDP growth averaged just 5.7%.

Such swings have always been temporary, both for economic and political reasons. If the corporate slice of the pie sustained a large increase at the expense of wage growth, it is not hard to imagine that a political response (i.e. shifting tax burdens) would result. Even without such a political response, these short-term cycles tend to resolve themselves, as the mid-1990s episode did. The recent swoon in corporate profits has brought the relative economic pie slices for corporations and individuals back to normal.

The inescapable conclusion of all this is that corporate profit growth - over time - will match GDP growth.

Having made the link between profits and GDP, we can now make one final connection between profits and the determinants of real GDP growth. This part is quite simple - real economic growth can only be produced by two variables - the growth in hours worked of American workers, and productivity growth. This might not sound intuitive, but it is. We can only produce more stuff if we are either working more, or getting more productive in the time that we are working.

Growth in hours worked can only come about if Americans are willing on average to work more hours, or if there are more Americans. The hours component of this is relatively fixed - the average workweek has tended to rise in recent decades, but at a very slow clip.

Population growth is determined by demographics, which we can forecast with accuracy, and immigration, which has also occurred at a relatively predictable pace. It is generally assumed that total hours worked can grow 1% per year over the long term due to these two factors. There are substantial cyclical variations, but the long-term average is not likely to veer much from this 1% forecast.

The more difficult variable to predict in this equation is productivity growth. Readers are probably well aware of the great productivity debate that occurred in the late 1990s. Prior to that period, it was assumed that productivity growth could only average about 1.5% annual growth. But a surge in business investment in the 1990s propelled productivity growth well beyond this historical norm.

Though the debate still rages, almost everyone now agrees that productivity growth has accelerated to a new sustainable norm of at least 2.5%. That's the low end of the estimate range, with more optimistic new economy types positing that productivity growth could average as much as 4%.

If you assume 1% growth in hours worked and 2.5-4.0% productivity growth, real GDP will grow 3.5-5%. If you then tack on a consensus inflation estimate of 2-3%, you get a slightly wider estimate range for nominal GDP growth of 5.5-8%.

Even with the most aggressive forecast, we are looking at macroeconomic forces that only allow for 8% corporate profit growth over the next several years, and more likely it will be closer to 6%.

This does not mean that someone who projects profit growth and S&P 500 gains of 15% for the next year is insane. Indeed, due to the cycles in employer/employee pie slices noted above, corporate profits grew an average of 19.2% while nominal GDP was up just 9.0% in the first year of nine post-war recoveries. But this profit out-performance has never been sustained.

Investors should therefore ask hard questions of any analyst who forecasts 15% profit growth over the course of several years. Does this analyst assume that productivity growth will be 12% and GDP will grow 15%? Will Americans suddenly work 50-hour weeks? Will there be a flood of immigration? Will there be a large and sustained income shift to corporations from consumers?

There are explanations for such strong forecasts, but they had better be backed by a very persuasive argument, as history strongly suggests that 15% equity returns as far as the eye can see are a long shot at best, and are most likely being forecasted by someone who wants to sell you those same equities.