**Real Implied Growth Rate (RIGR) reveals market expectations for long-term earnings growth implied in an individual firm’s stock price. Comparing RIGR for a single firm to the overall market and its industry can help investors identify over and undervalued firms and sectors. This analysis reveals dismal growth expectations for Microsoft (Nasdaq: MSFT) with an expected long-term decline putting Microsoft in the bottom 11% of S&P 500 companies. Is that reasonable?**

RIGR is derived using the Risk Premium Factor Valuation model (RPF Model). The RPF Model has shown very strong correlations with actual S&P 500 Index levels for the past 50 years. You can read a summary of the model on Seeking Alpha (here) or the full paper on SSRN** **(here).

While using the RPF Model to determine the stock price for an individual company is not practical, simply because it's probably impossible to derive the long-term growth rate necessary to derive valuation without creating a multi-year projection, the model is useful in deriving market expectations. In other words, based on the current share price, how fast does the market expect earnings to grow or shrink?

Implied growth is determined by simply rearranging the equation, P = E / (R_{f} x (1+RPF) – (R_{f} – Int_{R +} G_{R})) to solve for growth as shown below:

** Real Growth (G _{R}) = (R_{f} x (1+RPF) – (R_{f} – Int_{R})) – E/P**

Please note that this is real growth; inflation has been stripped out. Looking at the S&P 500 as a whole we can determine the expected real growth rate:

Closing Price (P) = $1,163

TTM Operating Earnings = $80.00

R

_{f}= 3.7%Int

_{R}= 2.0%RPF = 1.48

We find that the implied real growth for the market is only 0.6%. It’s hard to believe that the perpetual growth rate for S&P Index earnings, which should parallel the overall economy is under 1%, so we probably have a problem with one of our input variables. Is the market undervalued? Are interest rates too low? Are operating earnings too high? Has the RPF shifted?

While there is no way to be sure, it does not really matter if we are making relative comparisons. How does a company’s growth expectations compare to its peers and the entire S&P 500?

According to the CAPM model, Cost of Equity = R_{f} + β x ERP. We know that by definition the Beta (β) for the entire market is 1.0. For convenience this term is usually left out of the RPF Model when evaluating the entire market. When evaluating individual companies we can insert β to derive the company Risk Premium. Under the RPF Model:

** ERP = R _{f} x RPF**

So the company risk premium is simply R_{f, } x β x RPF. Therefore, to apply the RPF Model for an individual company we only need to substitute β x RPF for RPF in the original equation.

** P = E / (R _{f} x (1+RPF x β) – (R_{f} – Int_{R +} G_{R})) **

** Real Growth (G _{R}) = (R_{f} x (1+RPF β) – (R_{f} – Int_{R})) – E/P**

This was applied to every company in the S&P 500 using data from I-Metrix. Since the model does not hold for negative and near zero earnings, companies with negative earnings and high P/E (>80) were eliminated along with low P/E companies (<5) as outliers. While based on aggregate earnings for the S&P Index the expected growth was 0.6%, median real growth was 2.1%. Not surprisingly, the largest firms with the most earnings have lower growth expectations. The chart below shows real growth expectations plotted against market value.

Source: I-Metrix data, Hassett Advisors analysis (Note that market value is on a log scale.)

You can see the concentration of large market cap companies with growth rates below zero (upper left quadrant), explaining why the median growth rate is higher than the aggregate implied growth for the index.

The next chart shows the distribution risk adjusted real implied growth rate for firms in the S&P 500:

Source: I-Metrix data, Hassett Advisors analysis

This distribution is useful for putting implied growth for individual firms in perspective compared to overall market.

Evaluating RIGR for an individual firm requires putting it in context relative to its peers and the overall market. For example, on October 7, 2010, Microsoft had the following:

Consensus P/E estimate 10.39

β = 0.81

R

_{f}= 3.7%Int

_{R}= 2.0%RPF = 1.48

So implied real growth = -2.9%; implying that investors expect Microsoft to suffer a long-term decline in earnings.

Is that reasonable? Obviously, it depends on your view of Microsoft's business. Since I don't have any special insights into Microsoft's operations, let’s compare it to the rest of the software industry. The chart below shows Microsoft compared to software companies as classified by Market Guide.

Source: I-Metrix data, Hassett Advisors analysis

Not only does Microsoft rank near the bottom of the software industry in terms of growth, but near the bottom of the entire S&P 500. The percentile rank is just 11%, meaning the market expects 89% of the S&P 500 to grow faster.

This alone is not a reason to put Microsoft on your buy list, but it does call for deeper analysis. Windows and Office make up the bulk of Microsoft revenues. Should we expect those products to go into long-term decline in volume and price? Will efforts in mobile and search continue to fail? Or will continued growth in computer power in the coming years (see What if Moore’s Law Continues for Another 40 Years) increase to need for Microsoft’s operating systems and tools to harness the power?

If Microsoft puts together a few quarters of revenue and earnings growth will market expectations rise? Even bringing RIGR up to 0%, just growing with inflation would expand Microsoft's P/E multiple by perhaps 40% to about 15. Some good upside.

Evaluating real implied growth helps identify companies that may be mispriced relative to the market or its peers and suggests where further analysis can be leveraged. In future articles, I will be applying this methodology to other sectors and companies.

**Disclosure: **Long MSFT