A company’s reported earnings in a given year can give a misleading picture of a its demonstrated earnings power, which I will refer to in this article as *sustainable earnings per share*. One source of inaccuracy is that reported earnings will often contain components – such as gains or losses on asset sales, litigation gains and losses, and charges for acquired in process research and development – that are unlikely to be repeated in the future.

Even without the effects of non-recurring charges to earnings, a company’s reported earnings in a given year can be a misleading indicator of the company’s sustainable earnings when the company’s earnings growth is cyclic. The earnings of many companies will tend to follow an industry specific or economic cycle, where profits are lower at the bottom of the cycle and higher at the top; this can sometimes obscure the company’s underlying earnings growth rate (with the effects of the cycle removed). To illustrate, consider the following chart that plots the adjusted earnings per share, revenue per share, end of year price, and price to earnings ratio (using the end of year price) of Caterpillar (NYSE:CAT).

**Figure 1:**

Sales of Caterpillar’s products – primarily mining and construction equipment – are correlated with the economic cycle, and the nature of this industry is that it is not possible to quickly adjust costs to match changes in demand. This results in earnings volatility that is much higher than revenue volatility. This volatility often results in a situation where a company’s shares are a better value at a high price to earnings ratio than at a low price to earnings ratio. For example, at the end of 2002 Caterpillar’s price to earnings ratio was 23, but only because the company’s earnings were temporarily depressed. A similar situation occurred during the recession of 1992, where the company’s earnings completely disappeared. Both of these times were, in retrospect, a good point to purchase shares. At the other extreme, the company’s price to earnings ratio was 12 at the end of 2006, but only because earnings were at a cyclical high, fueled by the construction boom. In retrospect, despite the relatively low price to earnings ratio, this was not such a good time to buy. Not shown on the chart is what is likely to unfold in 2009, where the company expects revenue to fall by over 30%, and earnings per share (adjusted for redundancy costs) to fall from $5.66 to $1.25.

Clearly, this example illustrates the need for a better method of establishing a company’s sustainable earnings than a single year’s adjusted earnings. So how can we account for the company’s business cycle? First of all, we are going to need more than this year’s earnings to do this; ideally we would want enough years of adjusted earnings to cover a complete business cycle. One problem with this is that a business cycle is not apparent until it is over, and even then identifying it can be a bit subjective. To illustrate, how can we be sure that the year 2008 in Figure 1 is actually the peak of a business cycle? A partial solution to this problem is to use either ten years of adjusted earnings data or enough years to capture at least two peaks or troughs in the company’s business cycle. Referring again to Figure 1, ten years would suffice, as it captures a trough in the earnings time series in 1992 and a trough in 2002.

Once we have gathered at least ten years of a company’s earnings with non-recurring charges removed, and we believe this captures a full business cycle, how do we now determine the company’s sustainable earnings? Can we just average the ten years of earnings? If the earnings growth rate underlying the cyclic component of earnings is zero, then this approach would work fine. But if the company has a positive underlying earnings growth rate, then this approach would be pessimistic, in that earnings would be reduced more and more by this underlying growth rate as we go back in time. If this is not clear, then picture a company that has no cyclic component to its earnings, but has grown earnings at exactly 10% a year over the last ten years, and the earnings per share in the most recent year is $1.00. Averaging this company’s earnings will give a value of $0.68.

Now let’s compare this to another company which has earned $1.00 per share over the last ten years, which would give an average of $1.00 – higher than the company which has been consistently growing its earnings per share, although both have earned $1.00 in the most recent year. Surely we do not want to penalize the company that has grown its business over the last ten years, yet that is exactly what happens if we just average ten year’s worth of data.

Evidently, we need to somehow remove the underlying earnings per share growth rate from the earnings per share time series before taking the average of the time series. This is known as *de-trending* the earnings per share time series. De-trending a time series of earnings with a constant earnings growth rate trend equal to G is accomplished by multiplying each value in the original time series by (1+G)^{N}, where N is the difference between the current year and the year corresponding to the earnings value in the time series. Going back to our example of a company that has grown earnings per share at 10% over the last ten years, we would multiply last year’s earnings by (1+0.1), the year before that by (1+0.1)^{2}, and so on. If we do this for the company in our example, and then take the average of the de-trended time series, we find that the company’s sustainable earnings per share would be $1.00, the same as the company with zero earnings growth.

So far this sounds pretty easy, the catch is that a company rarely grows its earnings at a constant rate, and the situation is further complicated because there is almost always a cyclic component to the earnings history as well. One solution that probably comes to mind is to use the geometric earnings growth rate over the period as our de-trending rate. Unfortunately, since the calculation of the geometric earnings growth rate only uses the first and last elements of the time series, we could get a spurious growth rate in certain situations. As an extreme example, imagine ten years of earnings data with the least recent earnings per share equal to $0.25, and the other nine elements equal to $1.00 per share (1,1,1,1,1,1,1,1,1,0.25); the geometric earnings growth rate over ten years would be 15%, and using this to de-trend the earnings time series would give sustainable earnings per share of $1.75, which seems a little high for a company with earnings of $1.00 per share for every year except one. So what about using the arithmetic average growth rate, which uses all elements in the time series? This is actually worse, as it suffers from being overly sensitive to one or more years of earnings growth that are not really representative of the overall trend (i.e., outliers). In this example, using the arithmetic average growth rate to de-trend the time series yields sustainable earnings of $4.03 per share.

We clearly need a better technique to determine the underlying earnings growth rate; the technique should take into account all data points (not just the beginning and end of the time series), and should not be overly sensitive to the growth rate during any one year. Using the slope from linear regression would meet these criteria, except that the growth trend is not linear, but geometric. As part of our solution, let’s first define an optimally de-trended data series as a data series with a slope close to zero, as determined by linear regression (once the series is de-trended, linear regression works fine). We could then keep guessing (in practice, we will use a binary search algorithm to aid in our “guessing”) at the value of the underlying growth trend until we find one that, when used to de-trend the data series, produces a de-trended data series with a slope of zero, as indicated by applying linear regression. We can then take the average of this de-trended data series to determine sustainable earnings; alternatively, we can directly determine sustainable earnings from the regression intercept, both yield the same result. Applying this technique to our example (1,1,1,1,1,1,1,1,1,0.25) yields sustainable earnings of $1.15 per share, which seems fairly reasonable.

This technique usually works well, but can produce spurious results when the earnings time series is extremely volatile. I have found through experience that when the lower 95% confidence internal on the regression intercept falls below 75% of the regression intercept – which often occurs with companies in cyclical industries - it is better to go with an alternate approach, where we take the average of the de-trended revenue per share time series (which is more stable), and then multiply this by the average profit margin (adjusted earnings divided by revenue) over the ten-year period.

It turns out that Caterpillar is a company well-suited to this technique. Using this approach, we can plot Caterpillar’s sustainable earnings per share, reported earnings per share adjusted for non-recurring items, and the price to sustainable earnings ratio. Here we see that by valuing Caterpillar’s shares as a multiple of sustainable earnings per share gives a better picture of when the company’s shares are over or under-valued.

For some examples of using a company’s sustainable earnings to value a company’s shares, feel free to look at Chapters 3 & 4 in my book, which can be downloaded from my website.

If there is any interest, I can make the Perl code for the de-trending algorithm available on my website.

**Disclosure: I do not own any shares of Caterpillar (CAT).**