It is shocking that in the modern era of computing, where people have the equivalent power of a 1980s-era super computer on their desktop, that so many investors continue to use an old, flawed, rule-of-thumb valuation measure, the PEG ratio.

What Is It?

In case you have never come across this quaint, and potentially dangerous, little valuation shortcut, let me provide a brief overview. The PEG ratio compares the price to earnings (P/E) ratio of a business to its expected future growth rate; this period is typically five years.

The thinking goes that a P/E ratio, even a forward-looking one, only accounts for the growth in an earnings stream one year out. By incorporating the company's expected growth rate for a longer period of time, it's believed that you get greater insight into whether or not a stock is fairly valued or not. Just like a P/E ratio, the lower the PEG ratio, the less expensive is the equity.

Should I Trust The PEG Ratio?

Importantly, does the PEG ratio have any basis in reality and can you trust it?  To both questions the answer is: sort of. In evaluating these answers, believe it or not, no subjectivity is necessary.  How can that be?

PEG ratios are actually based on mathematics, but shockingly, the PEG ratio is only accurate under a very specific set of circumstances that are rarely ever met in the investment market place.

Let's use the recent Facebook private equity offering to underscore and illustrate the above.

It has been reported that Facebook was valued at \$50 billion.

This value compares to sales and earnings for Facebook in the first nine months of 2010 of \$1.2 billion and \$355 million, respectively.

Since these figures are not for a full year we need to annualize them. Conservatively done, the 2010 sales and earnings for Facebook would be \$1.6 billion and \$473.3 million.

In turn, those numbers give us a price-to-sales ratio of 31.25x and a price-to-earnings ratio of 105.6x for Facebook, which we will use going forward.

If I were to invest in Facebook using the PEG ratio, I would normally conclude that I need at least a 105.6% earnings growth rate for five years for me to break even. This equates to a PEG ratio of 1.0x: P/E of 105.6x compared with a 105.6% five-year growth in earnings. However, mathematically this conclusion is not true.  Not even close.

An investor buying Facebook at the 1.0x PEG ratio would be sadly disappointed to learn that he needed a 396.4% five-year earnings growth rate in order to break even. This seems a highly unlikely scenario.

For starters, it is very difficult in the modern information era for a company to grow its earnings 400% every year for five years. Such success would attract fierce competition that would immediately dilute such miraculous profits.

Second of all, mathematically speaking, growing your earnings that fast is the equivalent of turning \$1 of earnings into \$3,014 in five years. No, I am not kidding. This is just simple, compound annual growth rate (CAGR) math.

The above calculation assumes that the Facebook multiple stays flat for the five years. That is, that there is no capital appreciation of Facebook relative to its level of earnings.

So what happens if we hold Facebook's earnings flat, and instead count on a rise in Facebook's price to compensate us for our investment? The P/E ratio of Facebook would need to be, get ready for it, 3,845.7x in five years! Again, this is clearly an impossible feat.

OK, if you understand the dynamics of CAGR math then you know if you lengthen the investment time horizon, say to ten years, the necessary earnings growth rates to break even should come down. You would be right. But how much further down? Earnings would only need to grow 215.4% each year.  But, and this is a big but, no company can grow earnings like that for ten years.

Alright, the last objection might be, "Did you account for the reinvestment rate earned on Facebook earnings?" In the above examples, no. That's because we are holding all variables fixed, but one.

So what if we now assume that Facebook reinvests its earnings at that initial earnings growth rate of 105.6%, and a 10-year time horizon? This is the BULL case for Facebook.

Earnings still have to grow at 190.7% each and every year for ten years.  More importantly, those increasingly huge earnings must be reinvested at 105.6% just to break even.

When Does The PEG Ratio Hold Up?

The above mathematical results are a bit shocking, yes?  So why is it that, contrary to conventional thinking the PEG ratio breaks down?

Here is a list of the principle PEG ratio problems to be aware of, as revealed by mathematics:

1. The PEG ratio doesn't account for the time value of money. That is, when you invest \$105.60 in Facebook in exchange for just \$1 of earnings, that \$1 has to grow rapidly for you to break even. That's because the PEG ratio does factor in your desired earnings growth rate of 105.6%.

2. The PEG ratio makes no assumption for how you reinvest your earnings. And even when you factor this in to your calculations, you still need much more massive earnings growth than the PEG ratio would imply you need, again due to the time value of money.

3. The PEG ratio doesn't factor in your investment time horizon unless you were careful in using an earnings growth rate commensurate to your preferred time horizon.

So what is the special case where the PEG ratio holds? The ratio holds when your desired rate of return and your earnings reinvestment rate are equivalent to the earnings yield of the business.

The earnings yield is simply the inverse of the P/E ratio. For example, if you have a P/E ratio of 20x for a stock, its earnings yield is simple 1/20, or 5%. If your desired rate of return is just 5% and if you are able to reinvest your earnings at 5% then your investment will break even. This is true for any time horizon.

PEG ratios also hold up in the negative sense. That is, if you buy any company, even one more conservative than Facebook, with a PEG ratio over 1.0x, you are overpaying. The problem arises for investors who think they are getting a bargain when they buy a stock with a less than 1.0x PEG ratio.

When Is The PEG Ratio Dangerous?

The PEG ratio is dangerous to use for businesses trading at high P/E ratios. Earnings growth rates simply cannot keep up with the high initial purchasing cost. In the above Facebook example, if all other variables are held fixed, including the 10-year earnings growth rate, but you pay only 35x earnings, then the growth rate needed to break even is "only" 150.8%.

What To Do?

We're not advocating complete abandonment of the PEG ratio. After all, in my very successful investment career as co-portfolio manager of the Davis Appreciation & Income Fund, we used PEG ratios on occasion as an initial screen to weed out overpriced businesses. Any business with a PEG ratio over 1.0x was completely ignored.

For businesses with PEG ratios less than 1.0x my caution rose in proportion to the magnitude of the P/E ratio. The higher the P/E ratio, the more dangerous is the PEG ratio; and the danger rises exponentially, not geometrically.

Jason Apollo Voss, CFA, recently authored the book, The Intuitive Investor: A radical guide for manifesting wealth. Prior to that, he retired at 35 from his hugely successful run as co-Portfolio Manager of the Davis Appreciation & Income Fund. During his tenure the Fund bested NASDAQ by 77%, S&P 500 by 49% and the DJIA by 36%; was named a Lipper Leader, and received Morningstar's highest rating for ethical stewardship of investor money. The Fund was ranked No. 1 in its investment category and was also a regular Morningstar "Analyst Pick."