**Reader's Question:** I have a started to pay attention to PEG ratios. Can you please explain how to calculate the PEG ratio for a stock? Can you show how Apple's (Nasdaq: AAPL) PEG is 1.6, as you indicated in an earlier post? How can PEG be used to value stocks? What is a good source for finding estimated five-year growth rates?

## Calculation of PEG

The PEG ratio is a straightforward way to combine two fundamental aspects of stock analysis for the purpose of gauging how cheap or rich a stock is trading:

Earnings:Traditional value-oriented analysis looks at price ratios, the most common of which is the price-to-earnings, P/E, or "P/E ratio." At a given level of earnings [E], a lower price (NYSE:P) results in a lower P/E ratio, providing investors with a "cheaper" investment.Growth:Extension of P/E ratio analysis to include growth can be accomplished by simply dividing the P/E ratio by the earnings growth rate [G], which gives (P/E)/(100 x G), or the "PEG ratio." The factor of 100 is included to convert the growth rate from a percentage to a number of percentage points (e.g., 15% = 0.15, becomes 0.15 x 100 = 15). Since P/E ratios are typically around 15 to 20, and growth rates are often in the 10% to 15% range, the PEG ratio is often numerically around 1 or 2 (note that the S&P 500 has a PEG ratio of 1.64, according to data from the Yahoo! Finance Stock Screener). As with the P/E ratio, a lower PEG ratio generally indicates a "cheaper" stock.

**To run through an example for Apple (Nasdaq: AAPL):** In the earlier post that you refer to, from back in early September, when Apple was priced at $144 per share, the trailing 12 months (July 2006 to June 2007) of reported earnings were $3.55, the one-year forward (to Sep-2008) consensus earnings estimate was about $4.40, and the consensus earnings growth estimate for the upcoming five years was 22.5%. At that time, I calculated the PEG ratio for Apple as follows:

PEG = {$144/[($3.55 + $4.40)/2]}/(100 x 0.225) = 1.6 (as of close on 04-Sep-2007),

where I use the average of the trailing 12 months [ttm], and one-year forward earnings to generate a proxy for "current" earnings on an annualized basis.

Today, with Apple trading 21% higher at $174 per share, and the one-year forward consensus earnings estimate having been raised to $4.58 through revisions reported by the 27 analysts covering the company, the PEG ratio calculates to:

PEG = {$174/[($3.55 + $4.58)/2]}/(100 x 0.225) = 1.9 (as of close on 18-Oct-2007).

The higher PEG, caused by the rise in the stock price, reflects Apple's richer valuation, versus a month and a half ago. Surely, we would be measurably wealthier today if we had bought Apple in early September at $144 (corresponding to the lower PEG of 1.6), and held our shares through today's close of $174 (corresponding to the higher PEG of 1.9).

## PEG and Returns

Now, if succeeding at investing were as simple as buying low-PE or low-PEG stocks and selling out at higher P/E and PEG ratios, it would seemingly be easy to make money. Generally, what we, as investors, really want to do is maximize our return-on-investment. In other words, while P/E and PEG are convenient price ratios that help to describe a stock, ultimately we are more concerned with the compounded annual return, R, in the formula:

(Price at 5-Year Horizon) = (Price Today) x (1 + R)5,

where we select a five-year investment horizon to match up with the standard five-year term used in earnings growth estimates provided by Wall Street analysts.

It is instructive to understand how P/E, growth rate and PEG all relate to return-on-investment. By definition of the P/E ratio (i.e., PE = P/E), we can write:

(Price at 5-Year Horizon) = PE5 x E5 = PE5 x E0 x (1 + G)5,

applying, in the second equality, the definition of earnings growth from today to the end of year five.

Setting the right-hand sides of the above equations equal to one another and rearranging, we can write:

(1 + R)5 = (PE5/PE0) x (1 + G)5,recognizing that (Price Today)/E0 = P0/E0 = PE0.

Although analysts report estimated five-year earnings growth rates [G], the terminal P/E ratio at the end of the five-year investment horizon (PE5) is not a commonly reported figure. Since the purpose of this discussion is to look at five-year returns, I am going to assume for the scope of our calculations that *the terminal P/E ratio equals the analyst consensus five-year earnings growth rate* (multitplied by a factor of 100).

To see why this is a reasonable assumption to make, let's again look at numbers for Apple:

since G = 22.5%, we are assuming that PE5 = 100 x G = 22.5.

Today, Apple's P/E ratio based on current earnings is about 43. We are essentially assuming that over the next five years, as the company's iPod and iPhone product lines mature, and both revenue and earnings growth decelerate, Apple's relatively high current P/E ratio of 43 will fall to a terminal five-year value of 22.5, which is about half of where it is today.

Our terminal P/E assmption allows us to rewrite our return equation as:

(1 + R)5 = (100 x G/PE0) x (1 + G)5 = (1/PEG) x (1 + G)5,

which tells us that return, R, is high when the PEG ratio is low and the earnings growth rate [G] is high. In other words, in order to maximize our investment return, we are concerned not only with low PEG - we will also want to pay close attention to companies that have high earnings growth rates.

While our last result is conceptually appealing, it turns out that PE and PEG ratios are more readily available in online databases than the growth rate, G.

Consequently, for convenience we use the definition of PEG to rewrite the return equation as:

(1 + R)5 = (1/PEG) x [1 + PE0/(100 x PEG)]5,

or, solving explicitly for the return-on-investment:

R = [1 + PE0/(100 x PEG)]/PEG0.2 - 1.

To help visualize what this equation means, I provide the graph below, showing contours of constant PE. Observe that calculated returns are higher for lower values of PEG. Also, for a given level of PEG, a higher PE ratio (implicitly indicating a higher earnings growth rate) produces higher returns.

*click to enlarge*

We can also take a look at contours of constant return, as indicated in the plot of PEG ratio versus current P/E ratio below.

*click to enlarge*

**Now, let's get back to our example for Apple:** If we had bought the stock in early September at $144, when the current PE ratio was 36 and the PEG was 1.6, our pro forma five-year annualized return would be 11.4%. The same calculation today with Apple's share price at $174, current PE ratio of 43, and PEG ratio of 1.9 gives a pro forma return of 7.7%. Since the stock price has risen 21%, while our assumptions about future earnings growth remain unchanged, anyone buying the stock today should, of course, reasonably expect to earn a lower return, compared to having bought Apple shares when they were cheaper in early September.

## Application to Dow Component Stocks

To build our intuition about the relationship of return to P/E and PEG ratios, it is helpful to look at actual market data for familiar stocks, such as the 30 components of the Dow Jones Industrial Average. The scatterplot below shows the P/E and PEG ratios for each of the Dow 30 component stocks. JP Morgan Chase (NYSE: JPM) has the lowest PE ratio, at 9.5, while McDonald's (NYSE: MCD) has the highest P/E ratio, at 25.6. AIG (NYSE: AIG) has the lowest PEG ratio, at 0.78, while Pfizer (NYSE: PFE) has the highest PEG ratio, at 2.74.

*click to enlarge*

Using our expression for return, R, we can proceed to calculate the pro forma five-year returns based on the P/E and PEG data, again assuming that the terminal P/E at the five-year horizon equals the five-year earnings growth rate as projected by the analyst consensus estimate. Results are plotted below.

*click to enlarge*

Notice that there is a very strong correlation between low PEG and high pro forma return. AIG, trading at a low PEG of 0.78 (PE = 9.9, G = 12.7%) produces the highest pro forma return, a very respectable annualized rate of 18%. At the other end of the spectrum is Pfizer, with a PEG of 2.74 (P/E = 10.3, G = 3.8%) that leads to a strongly negative pro forma return of -15%. It is the measly estimated growth rate of 3.8%, coupled with the assumption that the terminal P/E equals this growth rate (indeed, a P/E ratio of 3.8 is awfully low!) that produces the substantial loss on a pro forma basis.

*click to enlarge*

## Cautionary Remarks

As with most (maybe even all) analytical frameworks for valuing stocks, the formulation presented above has its shortcomings. The pro forma returns are calculated by relying on two key underlying assumptions to make the otherwise formidable problem tractable:

Consensus Earnings Growth Estimates:Analysts periodically revise their earnings and earnings growth estimates, based on new information about a company's business plans, the competitive landscape, industry pressures, and the overall economic outlook. Five-year growth estimates, though the "best available" at any point in time, can and do vary considerably from quarter to quarter and year to year.

Terminal P/E Ratio:While our assumption that the terminal P/E ratio at the five-year horizon equals the five-year earnings growth rate may be a reasonable one that allows for a "ballpark" comparison of pro forma returns for investment in many different stocks across diverse industries, it simply is not possible to determine P/E ratios so far forward in time with any degree of confidence and accurary.

Consequently, we cannot and should not expect the calculated pro forma returns to end up closely predicting the actual returns that will materialize over the next five years. The financial world is complex, and continually changing and, with this change, our assumptions themselves need to shift as the months and years go by. Think of stock forecasting models as being like "the man who is always 100% confident, except that his opinion changes from day to day." You see, on any particular day it is possible to peer five years into the future; but you must realize too that our predictions today about future years will generally be very different from our predictions next month about these same future years.

Nevertheless, the P/E and PEG ratios, while having limited predictive power, do remain useful tools for assessing the cheapness or richness of stocks - at least in the current market environment, and at least relative to other stocks in the same or similar industries. For an analysis of potential returns offered by leading U.S. and Chinese Internet stocks, applying techniques explained in this article, please see my recent post highlighting prospects for Baidu (Nasdaq: BIDU) and Google (Nasdaq: GOOG).

## Data Source

A comprehensive source for stock data is Yahoo! Finance. The Key Statistics page for any listed stock includes the trailing 12-month P/E, forward 1-year P/E, and PEG ratio. From these P/E and PEG ratios, we can obtain the five-year earnings growth rate, G, by working through the definition, PEG = (P/E)/(100 x G). The consensus five-year earnings growth estimates, G, are given on the Analyst Estimates page for any listed stock, along with P/E and PEG ratios.

*Disclosure: Among the stocks mentioned in this article, the author holds or manages long positions in Baidu, and Google.** *