The stock price (per share) of a company divided by its most recent 12-month earnings per share is called its price-to-earnings ratio (P/E ratio). If this P/E ratio is then divided by expected earnings growth going forward, the result is called the price/earnings to growth ratio (PEG ratio). A lot of the information out there about how to determine a stock's proper ratios and use them to effectively value a stock discusses metrics like the stock's historic ratios, using them to compare industry ratios, or make statements like "a PEG below 1 is good."

This information isn't wrong, but if you need to understand and find these ratios for yourself, you'll need some extra help. Fortunately, with the aid of a simple hand-held financial calculator, there is a simple mathematical approach to finding rational P/E and PEG ratios.

**Earnings Yield**

The best way to understand the significance of the P/E ratio is to turn it upside down. If you divide the earnings by the price (E/P) you get the inverse of the P/E ratio, which is called the earnings yield. The earnings yield tells an investor how much return (on a per-share basis) the stock's shareholders earned over the past 12 months, based on the current share price. Remember that earnings, regardless of whether they are paid out in the form of a dividend or retained by the company for reinvestment into further growth opportunities, still belongs to the shareholders. Shareholders hope that these earnings will grow going forward, but there is no way to perfectly predict what that growth will be.

**Earnings Yield Vs. Bond Yields**

Investors have a vast array of investment options at their disposal at all times. For the purposes of this discussion, let's assume that the choice is limited to stocks or bonds. Straight bonds, whether government or corporate, pay a guaranteed fixed rate of return for some period of time, as well as a guaranteed return of the original investment at the end of that fixed period. The earnings yield on a stock is neither guaranteed nor of a definite time period. However, earnings can grow, while bond yields remain fixed. How do you compare the two? What are the key factors to consider?

**Growth Rate, Predictability and Fixed-Income Rates**

The key factors you need to consider are: growth rate, earnings predictability and current fixed-income rates. Let's assume you have $10,000 to invest and that United States government Treasury bonds of five-year maturity are yielding 4%. If you invest in these bonds, you can earn interest of $400 per year (4% of $10,000) for a cumulative return of $2,000 over five years. At the end of five years, you get your $10,000 investment back when the bond matures. The cumulative return over the five-year period is 20% ($2,000/$10,000).

**Example - Calculating a Stock's P/E**

Now, let's assume that you buy stock in XYZ Corp. for $40 per share, and that XYZ had earnings over the last 12 months of $2 per share. The P/E ratio of XYZ stock is 20 ($40/$2). The earnings yield of XYZ is 5% ($2/$40). Over the next five years, XYZ's earnings are expected to grow by 10% per year. Let's further assume that this earnings growth is 100% predictable. In other words, the earnings are guaranteed to grow by 10% per year - no more, no less. What P/E ratio should XYZ stock have to make it an equal investment opportunity to the five-year Treasury bond yielding 4%?

Using a present value/future value calculator, we can determine a mathematical value for XYZ. To do this, we take the 20% cumulative yield of the bond over the next five years and enter that as the future value (FV). Enter "0" as the present value (PV). Enter "5" as the number of periods (n). Enter 10 as the annual interest rate (i). Now, using a beginning period setting (BGN), calculate payment (PMT). The answer will show as -2.98. Drop the negative to find that the comparable earnings yield should be 2.98%. If we divide 1 by 2.98% (.0298) we find that the P/E should be 33.56. Because current earnings per share are $2, the price of the stock should be $67.12 ($2 x 33.56). The earnings yield is 2.98% ($2/$67.12).

*Note:*For the sake of simplicity we are ignoring the time value of money considerations of receiving cash flows earlier over the five-year period for the Treasury bond as opposed to the stock.)

What is the P/E if XYZ earnings growth is projected to be 20% per year? The answer would be 44.64 and the price of the stock should be $89.28. The earnings yield would be 2.24%. The earnings on your $10,000 (112 shares) investment would be $269, $323, $387, $464 and $557 for a total of $2,000. It seems intuitive that a stock with earnings growth that is projected to be greater than another's would trade at a higher P/E. Now you see why this is the case from a mathematical perspective.

**The Real World**

In the example above, the P/E of XYZ rose from 33.56 to 44.64, when earnings expectations rose from 10 to 20%. What happened to the PEG? At 10%, the PEG would be 3.36 (33.56/10). At 20%, the PEG would be 2.23 (44.64/20). All things being equal then, the PEG of higher growth companies will normally be lower than the PEG of slower growing companies, even though the P/E may be higher.

In real life, earnings are not perfectly predictable, so you must adjust your required earnings yield up from the guaranteed yield of bonds to compensate for that lack of predictability. The amount of that adjustment is purely subjective and fluctuates constantly as economic conditions change. In analyzing a particular stock, you need to consider how predictable that company's earnings growth has been in the past as well as possible interruptions to growth going forward.

In the example above, the price of XYZ stock is $40 per share. The reason it's trading for $40 probably revolves around uncertainties regarding the predictability of that expected earnings growth. As a result, the market, based on the cumulative subjective perspective of thousands of investors, has built in a higher return requirement. If XYZ does indeed experience a 10% earnings growth over the next five years, an investor buying the stock at $40 per share will be well rewarded as the earnings stream on $10,000 (250 shares) will be $500, $550, $605, $665 and $732 for a total of $3,052, rather than $2,000. The possibility of this additional return compensates the investor for the risk that the expected earnings growth rate of 10% may not materialize.

**Summing up**

Despite the subjective risk-assessment variables, P/E ratios and PEG ratios do have a mathematical rationale. First, the ratios are based on the earnings yield theory, which is married to current fixed rates of return. As interest rates rise, P/E ratios will tend to fall because they're inverse and the earnings yield (E/P) needs to rise to be competitive. As rates fall, P/E ratios tend to rise on average and earnings yields fall.

**The Bottom Line**

Over and above the fixed-income impact, P/E ratios will be higher for stocks with more predictable earnings growth and lower for stocks with less predictable earnings growth. If two stocks have comparable levels of predictability, the P/E will be higher for stocks with higher expected earnings growth and lower for stocks with lower expected earnings growth. PEG ratios for slower-growing companies will normally be higher than for faster-growing companies. Using a basic financial calculator, you can determine what these ratios should be at any given point under any given set of circumstances.