Most investors are familiar with the humble price to earnings ratio (PE), which simply measures the relationship between the current market price and earnings per share (EPS).

PE = price / earnings per share

In essence the ratio simply seeks to identify the relative value of an investment by comparing its price to its earnings: a low PE signals a 'cheap' stock, while a high PE implies an 'expensive' stock. While this makes a great deal of sense, the fact is that this seemingly innocuous ratio can be a mine field of misinterpretation. Largely this is due to the difficulties in applying broad generalisations to specific cases, and the failure of most investors to quantify metrics in an objective and pragmatic manner.

So rather than discuss some broad truisms that have limited practical value, let's have a look at how we can employ the PE ratio more intelligently. The starting point is to understand that the PE ratio can be used as a means to indirectly forecast future share price, and in turn the expected rate of return you can expect as an investor. Importantly, we can do this by invoking fewer forecasts than most other models and the result is less sensitive to small changes in the input variables. In the parlance of mathematics, the model is more stable.

**Price is a function of two variables**

Rearranging the PE formula, we can see that share price is a function of EPS and the PE:

Share price = EPS x PE

In plain English, the share price is always a function of what premium the market places on earnings.

Therefore, you can use estimates of EPS and the PE to forecast the future value of the stock. (There are some serious considerations to be made when making any forecast, or indeed on relying too much on the output of any model, and we will return to these issue later. For now, let's just examine the theory).

We will illustrate the concept using Woolworths (WOW) as an example. Last year Woolworths reported EPS as $1.632, and is forecast to increase this to $2.13 over the next three years (based on current consensus estimates). Next we need an estimate for the PE.

Over the past 5 years, Woolies has traded with a PE between 15 and 27, and it is currently trading with a PE of 16.2. To begin with let us simply assume that the PE will essentially be the same in 2013. Therefore, we can calculate a forecast price by multiplying expected EPS ($2.13) by the expected PE (16), which gives $34.08.

Given that Woolworths also pays a dividend (with a consistent payout ratio of approximately 70%), we can also expect an additional $4.43 in dividends over the next 3 years, or a total yield of 16.7%. Combining capital and income, and based on the current market price of $26.46 we get a total return of 45.7% or 13.3% per annum (I have not reinvested dividends to keep the calculations simple, but doing so would increase the overall return).

If we assume our two forecasts are accurate, we now have an objective basis for making an investment decision. Essentially the question becomes: "is a 13.3% average annual return sufficient to compensate me for the risk of investing in Woolworths"? And indeed this is precisely the kind of questions that teaminvest members ask.

**Coming from the other direction**

If 13% is too low a return for you, given your view on the prospects for the business, the question then becomes: "what rate of return do you require to make Woolworths a compelling investment"?

Let us say for the sake of argument that you feel as though 15% is the minimum return you would require based on your perceived risks of the business. We can back calculate the necessary current share price at which 15% then becomes achievable (I won't go into the calculation, but it's essentially a rearrangement of the previous method).

If we do this we get a share price of $25.48. In other words, if your estimates for EPS and PE are valid, and if you want an annual average total return of 15%, then you should only purchase Woolworths shares at $25.48 or less.

Although we have further to go, we are already acting in a far more rational and objective manner than most investors. To simply desire 'high' returns without any notion of likely capital and income returns is highly risky: we are far more susceptible to reacting emotionally and irrationally to chaotic short term share price movements.

**Double dip investing**

What you may have noticed from the above example is that by holding the PE steady we have essentially tied all investment growth to the growth in earnings per share. Indeed, over very long stretches of time this is largely how it goes. Nevertheless, changes in market mood will obviously have a big impact on potential returns, regardless of underlying earnings growth. In fact, it is entirely possible for companies to experience very solid EPS growth while the share price either stagnates or goes down.

Consider again the case of Woolworths. Its earnings per share have consistently grown over the past decade, yet the share price has essentially gone sideways since early 2008.

*Figure 1. EPS for Woolworths, 2001 - 2010*

*Figure 2. Closing share price for Woolworths, February 2008 to present*

The explanation for this is that the market has, right or wrong, discounted its premium on the stock. In other words, the PE multiple has decreased, essentially offsetting any growth in underlying earnings. (For buyers this is actually a great thing! For existing shareholders, and especially those with an income focus, there is likewise little to complain about: Woolworths has never decreased its dividend, and in fact has raised payments by an average of 18% EVERY year for almost two decades).

Of course, it is also entirely possible that market sentiment and hence the PE multiple could increase over your investment period, even if earnings are stable or decreasing. The optimal situation of course is when both EPS and the PE multiple increase: it's a double whammy that leads to truly spectacular returns.

Consider our previous example with Woolworths. Let's maintain all of our assumptions, however let us assume that in three years the stock will be trading at a PE of 18 (instead of 16). Plugging this into our equation gives us a target price of $38.34, or a total annual average return of 17.06% if dividends are included. The point to note that although EPS growth has been exactly the same under both scenarios, any change to the expected price multiple will have a significant impact.

The potential for 'double dip' effect should motivate investors to choose stocks that are likely to achieve both solid earnings growth AND are currently trading at a low valuation (which is essentially what Warren Buffet looks to do). If either of these considerations are not met, you are essentially limiting your potential investment returns.

It is all pretty obvious stuff when you think about it, but the problem is that many investors simply fail to understand this important relationship. The result is often a focus on speculative stocks that have no or low earnings and trade at a high PE multiples. (The justification is that when the company in question hits the jackpot, so to speak, it will validate the current high price multiple).

Sadly though, even in the rare cases where these stocks do see a sudden and significant improvement in earnings, the fact that their valuations are already high preclude any meaningful double dip effect. Needless to say, should those lofty earnings growth expectations fail to materialise, as they most often do, investors can suffer a double dip effect in reverse: falling or worsening earnings and a drop in the PE multiple. Ouch.

**Garbage in, garbage out**

This all makes a lot of sense, but the fact is that we can be as pessimistic or optimistic as we like, and can curve fit the data to suit our individual biases. Two analysts, using the exact same model, can come up with wildly different valuations simply by making seemingly benign changes to the input variables. In other words any valuation is only as accurate as the forecast used; garbage in, garbage out, as they say. This is in fact a problem associated with all valuation models, and deserves close scrutiny.

The first point to make is that such an exercise is only ever valid if you are dealing with a company that has highly reliable earnings and there is high confidence in growth expectations. Obviously, conducting such an analysis on a company with volatile or non-existent earnings will provide low quality or nonsensical results. However, companies such as Woolworths are well suited to such analysis: their earnings are amongst the most stable on the ASX.

We can remove our personal subjectivity by using a consensus forecast for EPS (available on most broker websites) or alternatively we can base our expectations on historical performance. While past performance is no guarantee of future performance, it is nevertheless a very good guide.

Next we have to decide on a suitable PE ratio. Long term historical market and industry averages are a reasonable starting point, although it's worth noting that there are many extended periods where PE's remain significantly divergent from the historical norm. Furthermore, different industries tend to trade at different price multiples. As such it is often a better approach to look at the historical performance of the stock in question, and place this in the broader context of the longer-term industry average.

**Margin of safety**

In all cases the sensible investor avoids anchoring on optimistic figures. We must be realistic and assume that we are rarely going to be exactly right in our forecasts, indeed it is almost a certainty that we will be wrong, and often substantially so.

Nevertheless we require forecasts for our model and as such they are a necessary evil. The sensible thing to do is to make a best guess, and then apply a conservative margin of safety. That is, we assume that we will be wrong and hence cut our estimates to account for any downside surprise. If the analysis still points to an attractive outcome then our confidence to buy should be that much greater. Of course there is still potential for a surprise, but more likely the surprise will be to the upside.

Let us return to Woolworths. The consensus forecast for EPS in 2013 is $2.13, but anything can happen over the next three years, so let's assume that the actual EPS figure in three years will miss current forecasts by 10% (a reasonable margin of safety for a defensive business such as Woolworths. If we were talking about a company with less reliable earnings, we may decide to further discount the forecast). This reduces our EPS forecast to $1.917.

In terms of the PE, the mid-point between the 10 year high and low is 21.2. However again we could err on the side of caution and assume that the PE will continue to track at the lower end of its recent range. Indeed our initial value of 16 now appears very reasonable indeed.

Plugging these figures into our formula gives us a target price of 30.67, and with dividends included, assuming again a constant payout ratio, this gives us a total investment return of 9.5% each year.

To many investors a near 10% average annual return is very reasonable, especially for a stock that represents very little risk. After all, a 10% annual return will see your investment double every 7 years or so. You may have a different view, and justifiably so, but the point to note is that we are making a decision based on a reasonable expectation of investment return, rather than undefined notions of 'cheap' or 'expensive'.

The beauty is that we have determined that Woolworths is an attractive investment even if the EPS doesn't grow as expected, and even if the price multiple remains at the lower end of its historical range. Should EPS or the PE come in better than our very conservative estimates suggest, then we have the potential for a lovely positive surprise. For example, even if we only change the PE to its long term average of about 21 we will get an annual average growth of over 18% for the next three years. At that rate you will double your investment capital every four years.

**Complex = good**

It is not uncommon to view such approaches as overly simplistic. Indeed, we all tend to assume that the more complex methodologies are necessarily better, although there is scant evidence for this.

Personally, I tend to hold the opposite view. The more complicated a valuation model, the more subject it is to error. The more variables that are invoked, the greater the number of forecasts that are required, and the longer the period for which such estimates are required, the more that can go wrong, and the greater the range of possible values that will be generated.

Of course you can certainly go too far in attempting to streamline the process but the goal should be to employ as few variables as possible. Scientists refer to this rule as "Occam's razor": a rule of parsimony that abhors superfluous and unnecessary inputs.

Consider the case with the discounted cash flow (DCF) model. This widely employed valuation model has the potential to deliver an extremely wide range of values, even with the smallest change to its inputs. The model can be employed in a simple one-step or multi-stage style, you can choose various fundamental metrics for discounting (eg free cash flow, earnings and even dividends), and users are required to discount items across an infinite series. Is it any wonder that analysts can differ so significantly in their estimates for intrinsic value?

More fundamentally though, time is not addressed; the method does not seek to specify how quickly the market price will move towards its 'intrinsic' value, which is essential if you want an understanding of expected rates of return.

**Conclusion**

The important thing for investors to understand is that whatever valuation you come up with, the market neither knows nor cares about it. Your price may rest on very sound philosophical ground, but shares are valued on an open market and are therefore entirely dependent on the sentiment of the day.

Nevertheless, there is great value in employing a sensible valuation model. The primary benefit is that it removes a lot of subjectivity and forces you to think about current share prices in terms of how they are likely to translate into investment returns. It is simply not tenable to call a stock cheap or expensive; we want to know how the price compares to a reasonable and conservative estimate of future price, and what that implies for capital and income returns.

Finally, we must accept that any forecast is subject to a wide variety of impacts, most of which will be difficult to anticipate accurately. So the pragmatic and sensible investor does the best they can and then applies a reasonable margin of safety. This doesn't guarantee that you will never make a mistake, but it does significantly lessen the impact of any negative surprises.

At the end of the day, investing in the share market is about finding good businesses that have attractive prospects and are trading at attractive valuations. Unless you are specifically seeking to speculate on market volatility, the idea should be to hold these assets for a meaningful time frame such that the underlying business has the chance to deliver on expectations.

Once you strip away the short term chaos of market pricing, it is ultimately earnings growth and a continuing (and improving) positive sentiment towards the business that will ultimately drive investment returns. As Benjamin Graham said; in the short term the market is a voting machine, in the long term it is a weighing machine.

*If you want to learn more about rational, value investing, visit www.teaminvest.com.au*