This is part three in a multi-part series on the most misunderstood investing concepts with this edition covering that classic valuation short-hand, the PEG Ratio. As a brief review, article one discussed many in the investment business do not fully understand fair value, while article two expressed my belief that time horizon is also a classic source of confusion.

Despite having authored an extended deep dive research paper on the “The Fallacy of PEG Ratios” way back in 2011 for the Journal of Private Equity, I still hear the PEG ratio used in analyst team meetings, on business news, and as an actual data point that may be downloaded.

First, before proceeding let me define the bloody misguided concept. The PEG ratio is a company’s price to earnings ratio divided by its growth rate. This growth rate can be the forward 1-year earnings growth rate, or 3-year, or 5-year, and so on. The idea is that if the P/E ratio is less than the growth rate, a value of < 1.0, that the company is undervalued. Oppositely, if the P/E ratio is greater than the growth rate the company, a value of > 1.0, is overvalued. This understanding is in defiance of these concepts, as well as mathematics. Ouch!

So, what is it about the PEG ratio that makes it misunderstood? Principally, it is that when you pay, say a P/E of 25.0x for a stock you are trading $25.00 for just $1.00 of earnings. Lost to most investment pros is that there is a time value of money problem embedded in this tradeoff. By incorporating the earnings growth rate assumption in the PEG ratio this is supposedly accounted for, and well, it kinda is accounted for, but its interpretation is massively, massively misunderstood.

Yes, PEG ratios include a growth rate assumption, but the interpretation is to look for PEG ratios of less than 1.0x. But this interpretation misses the fact that the higher the PEG ratio, the much higher growth rate necessary to compensate me due to the time value of money. As an example, let us consider Facebook back in the day.

Facebook Case Study

In the early days of Facebook it traded at a P/E ratio of 105.6x. Using the PEG ratio as a valuation shorthand we would invest if the expected earnings growth rate (let’s assume it is a five-year time horizon) for Facebook were at least 105.6%. This is, of course, the vaunted PEG ratio of 1.0x.

However, whether this is turns out to be true depends mathematically on a number of conditions being met. First, Facebook actually has to deliver earnings growth for five years at a rate of 105.6%. If we assume a 0.0% rate of return on reinvested earnings, Facebook in this scenario would generate a return to you of 106.3%, and obviously a great result.

But there are other important mathematical assumptions that I have made that may not necessarily hold. For example, the majority of that 106.3% return is earned, not from actual earnings growth despite the assumption of 105.6% growth for five years, but because I have assumed that Facebook’s lofty 105.6x P/E holds flat for the entire five years. This is a highly unlikely scenario.

If, on the other hand, I assume that Facebook’s multiple contracts just 5% per year for that five-year investment time horizon then the return drops to 96.2%. Clearly a wonderful result, but that is a much lower rate of return than the PEG ratio of 1.0x and its 105.6% embedded growth assumption would imply.

Also, and crucially, earlier I assumed a 0.0% required rate of return. What happens if I assume Facebook’s multiple stays flat (an aggressive assumption), but that you have a 10.0% required rate of return? Your return in Facebook drops to 87.6%. Again, not bad, but definitely not 105.6%; in fact, you would underperform by 18.0% based on PEG ratio assumptions.

If you understand the dynamics of CAGR math then you know if you lengthen the investment time horizon that returns usually will increase. But if I lengthen the investment time horizon out to 10 years then the returns on Facebook actually decrease slightly to 87.3% from 87.6%. The reason is that when the required rate of return is lengthened out, it impacts the return dynamics of Facebook to a greater extent. More importantly, for this scenario to hold, a single dollar of earnings at the beginning has to grow to $1,349.68 at the end of year 10. I consider this to be a nearly impossible feat that stretches credulity.

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 I am 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? The result is a CAGR of 89.6%. Most of us would welcome that return, but in comparison to the understanding most of us have of the PEG ratio, it would have to be considered disappointing.

In summary, PEG ratios are misunderstood because of the following five key issues:

1. Flat multiple assumed
2. Missing reinvestment assumption
3. Missing required rate of return
4. Missing time horizon
5. PEG ratio homogeneity assumed

I would love it if you would receive notification of my new articles – sign up here 🙂 Don’t forget to comment on the article in the space below. Thanks!

Flat Multiple Assumed

The PEG ratio assumes that the multiple paid at the outset holds flat until sale. This is clearly a bogus assumption because multiples bounce all over the place during a holding period. Not only that, but high earnings growth rate businesses eventually experience a slowdown, and a commensurate shrinking of their multiple.

Missing Reinvestment Assumption

The PEG ratio makes no assumption for how the business or you reinvest earnings. For the returns implied by the PEG ratio to hold, the reinvestment rate of return must equal the initial assumed growth rate in earnings. This is often an overly aggressive assumption.

Missing Required Rate of Return

The PEG ratio doesn’t explicitly account for your required rate of return. Instead, it assumes that your required rate of return is 0.0%. Clearly this is an untenable assumption. In the Facebook example, if you assume just a 10.0% required rate of return, returns fall from 107.51% to 89.02%. If you assume a more private equity-like 40% required rate of return then the return in Facebook falls to 49.78%. Fantastic, except the result is far below the initial expectations implied by the PEG ratio.

Missing Time Horizon

I noted with great interest that my piece in this series on time horizon was generally less appreciated than the one on fair value, but the fact is that time horizon is usually lurking in the shadows of every investment disagreement. The PEG ratio provides further proof of this fact as there is no investment time horizon in the conversation. But because of the time value of money, time horizon clearly affects the ultimate realized rate of return. Duh!

PEG Ratio Homogeneity Assumed

Very importantly, the PEG ratio treats all PEG ratios as being the same, when in fact they are very different. For example, a PEG ratio of 1.0x can be generated by a 10.0x P/E combined with a 10.0% five year earnings CAGR, or a 100.0x P/E ratio combined with a 100.0% five year earnings CAGR .

In this case the return profiles are very different for the two different 1.0 PEG ratios. For the 10.0x P/E with 10.0% five year earnings CAGR, with a 5 year investment time horizon, a 10.0% reinvestment rate, and a 10.0% required rate of return, your actual CAGR is 10.0%.

Yet, for the 100.0x P/E with a 100.0% five year earnings CAGR, with a 5 year investment time horizon, a 100.0% reinvestment rate, and a 100.0% required rate of return, your actual CAGR is 5.55%. This is a dramatically different result.

The results are even more dramatic for a PEG of 1.0x generated by a 5.0x P/E, with a 5.0% five year earnings CAGR, a 5 year time horizon, a 5% reinvestment rate, and a 5% required rate of return. Here the realized CAGR is a whopping 16.05%.

The culprit for these distorting effects and the source of massive misunderstanding about the PEG ratio is the time value of money. A P/E of 100.0x means that you are trading $100 for $1 of earnings. This is an exchange that you would likely not make at a Las Vegas casino. So that $1 of earnings has to grow very, very fast to make up for the disparity in what you paid at the outset to what you receive over the intervening years.

When Does the PEG Ratio Work?

So in what very special case do you actually earn the same rate of return that the company does? That is, if I buy a private equity interest in Facebook wanting my rate of return to equal Facebook’s 105.6% earnings growth rate implied by a PEG ratio of 1.0x, how do I do that? Unfortunately, the traditional PEG ratio heuristic of “companies are a value when the PEG ratio is less than 1.0x” focuses your attention incorrectly – it is close, but no cigar. The two things you want to focus on are:

• All three rates of return involved in the investment are identical, and without any deviation. These three returns are:
  • The company’s earnings growth rate
  • The rate of return on reinvested earnings
  • Your required rate of return on the investment
• The unified rates of return, from just above, when multiplied by the P/E must total 1.0

An example will help to make this clear. If you pay a 20x P/E then fair value is when the company’s earnings growth rate, the rate of return on reinvested earnings, and your required rate of return all equal 5.0%.

That is, fair value occurs here because 20 x 5% = 1.0. If these very special conditions are met, then your actual compound annual return will be identical to the three flows above, or 5.0%. Likewise, if you pay a 30x P/E then the three rates of return must all be 3.33% (30 x 3.33% = 1.0). If this is the case, then your return will be 3.33%. When these stars all align then your investment time horizon is irrelevant because this result holds for all investment time horizons.

Very importantly, the PEG ratios for these two scenarios are very different even though they both are scenarios where the stock is fairly valued. In the 20x case, the PEG ratio is 4.0x, or 20x P/E ÷ 5% Growth; whereas in the 30x case, the PEG ratio is 9.01x. So we have fair value with a PEG ratio of 4.0x and also at 9.01x. This clearly violates the “fair value is when the PEG is 1.0x” rule of thumb.

In Conclusion…

Do an actual valuation of a company before purchasing because PEG ratios are a bogus shorthand and also very distorting in screens. If you use them in screens try to remember that the growth rate must be much, much higher than the P/E ratio the higher the P/E ratio. Said another way, the PEG ratio must be much lower than 1.0x the higher the P/E ratio.

I would love it if you would receive notification of my new articles – sign up here 🙂 Don’t forget to comment on the article in the space below. Thanks!