EARNINGS PER SHARE

To the uninitiated, a company's future profits seems the obvious place to start. Each shareholder is entitled to a part share of the company's profits based on how many shares they own. Sounds sensible, but it isn't the right way to go. That's because what a company reports as a profit is a different figure from what it makes. Reported profit is an accounting construct, a figure concocted according to a bevy of accounting rules. Hence ‘net profit' is not synonymous with ‘cold, hard cash'.

This means the figures in the accounts often need to be adjusted to better reflect economic reality. The steps to achieve this are well covered in other books, so it's not the aim of this one to comprehensively cover this area. But here are a couple of examples to illustrate the point.

There are two main areas where the Income Statement strays from reporting real cash flows. The first is how income and expenses are classified; the second is how they are timed — that is, in what period they are reported.

Firstly, classification. A simple example will suffice. During the 1980s Aussie entrepreneur Alan Bond built a listed company, Bond Corporation, using a minimum of equity and a mountain of debt. To soften the damage that the debt inflicted on the balance sheet, Bond Corp used the old trick of classifying expenses as assets. It's a neat trick that not only improves the appearance of the balance sheet but boosts the reported profit. A look at Bond Corp's 1989 accounts shows an asset of nearly $400 million classified as ‘other assets'. A closer look shows that $280 million of these other assets related to advertising expenditure. Bondy's company owned a brewery, which produced Swan beer. He'd spent millions on an advertising campaign trying to capture market share from Foster's. Despite the TV attack, Swan Brewery lost further market share. So one could say, all else being equal, its goodwill was declining. But rather than expensing these as ‘advertising costs', Bond Corp's accountants argued the advertising had enhanced an asset, the goodwill in the brand. The savvy analyst, on valuing Bond Corp, would spot the sleight of hand and correct the accounts accordingly. Assets down, expenses up.

Secondly, timing of income and expenses. Companies need, for example, to maintain the equipment they use (termed ‘capital expenditure' or ‘capex') — planes for Qantas, warehouse capability for Costco, port facilities for Toll Holdings. Failure to maintain equipment means a business is going backwards, but ironically failing to maintain its equipment means a company can overstate its earnings — at least for a short while.

The wearing out and associated devaluation of equipment already owned by a company is recognised in the accounts as the expense item ‘depreciation'. Depreciation is calculated by allocating a proportion of the original purchase price of the equipment as a cost to each year it remains in service. But depreciation can understate the true cost of maintaining operational capability for a given year. For the investor the more relevant figure is the annual investment in capital equipment necessary to leave the company in the same productive shape at the end of the year as at the beginning. This requires an intimate appreciation of the operations and dynamics of the business. It also requires an informed judgement call, so the analyst is relying on judgement rather than the financial statements to determine the most appropriate cost for that year.

DIVIDENDS AS INPUTS

So there are classification and timing problems in using reported net profit as an input to valuation formulae. What's more, managements typically retain a healthy proportion of the profit each year before they distribute dividends to shareholders. What shareholders receive, then, rarely equals the net profit.

What investors do receive is dividends. In fact, apart from possible capital returns, dividends represent the only money they do receive during the time they hold the stock. So why not use dividends as a cash flow input to valuation formulae? It's an argument that's been put forward by many investors for a long, long time. The Dividend Discount Model (DDM) is a valuation formula based on this very principle. It asks the analyst to consider only future dividends when valuing a stock.

On face value the DDM seems like an appealing formula to use, but proponents of non-dividend formulae might mount the following counterargument. If management retains a proportion of profits, don't these retained earnings grow the value of the company? Therefore don't they drive capital gains for shareholders? And aren't capital gains realised by the shareholder when the shares are sold? Therefore don't retained earnings also have a value? The answer is ‘yes' to all these questions, but retained earnings only have a value if management reinvests them profitably.

Proponents of the DDM can fire straight back, arguing that the DDM also takes retained earnings into consideration. To appreciate their line of argument you need to answer the following questions:

• How do you obtain a capital gain? Answer: you sell.
• Who will deliver the capital gain to you when you sell? Answer: the person who buys your shares.
• How will that person value the shares they purchase if they too are using the DDM? Answer: the present value of the dividend stream they expect to receive in the future.

Put another way, the capital gain you receive forms part of the new owner's dividend expectation. If management has invested the retained earnings during the term of your ownership, the company's capital base and/or its operational efficiency will have increased, enabling it to deliver larger dividends in the future. So it's possible to deliver a valuation by considering dividends alone.

Confused? Then it might be clearer if you ignore ownership changes altogether. Imagine that only one person ever holds the shares. To simplify the example even further, ignore capital raisings and capital returns. All that one person will ever receive is dividends. The underlying value of the shares won't change just because ownership does.

Sounds great, so what's the catch? Here are three biggies:

• Who knows what those future dividends are going to be? It's difficult enough predicting next year's dividend, let alone those well into the future.
• Money changes in value. In an inflationary environment future dollars will be worth less than today's dollars, which means each future dividend has to be discounted by an appropriate factor to bring it back to a present value (the appropriate factor is called the ‘discount rate', but more about that soon). After all, it's present value you're attempting to calculate, not future value.
• The sheer logistics of the calculation are daunting. The DDM asks you to perform a separate calculation for every dividend yet to be received. Assuming an infinite company life, that's a lot of dividends to throw into the formula — clearly a mathematical nightmare.

John Burr Williams' name is often linked with the DDM, and, while it's wrong to give Williams full credit for the concept, he did discuss it extensively in his 1938 book The Theory of Investment Value. In 1939 Ben Graham was asked to review Williams' book for the Journal of Political Economy. He expressed concern that in order to apply Williams' method one needed to make some very large assumptions: ‘One wonders whether there may not be too great a discrepancy between the necessarily hit-or-miss character of these assumptions and the highly refined mathematical treatment to which they are subjected.'¹²⁵

What an eloquent way of saying ‘garbage in, garbage out'.

Keynes had expressed similar sentiments regarding people's capacity to forecast future earnings yields just three years earlier in The General Theory:

Our knowledge of the factors which govern the yield of an investment some years hence is usually very slight and often negligible. If we speak frankly, we have to admit that our basis of knowledge for estimating the yield ten years hence of a railway, a copper mine, a textile factory, the goodwill of a patent medicine, an Atlantic liner, a building in the City of London amounts to little and sometimes to nothing.¹²⁶

So if plugging prospective dividends into the DDM is unlikely to deliver the results we're hoping for, let's move on.

GROWTH OF EARNINGS AND DIVIDENDS

Valuation formulae need to be practical and easy to use. It's cumbersome work deriving an estimate for every future cash flow that share ownership bestows, so simpler formulae have been developed. They ask for a current earnings or dividend figure and a growth rate to apply to that number. This neat simplification then accounts for all potential future cash flows.

But while this simplifies the calculation it doesn't solve the problem of having to deliver predictions. Now you are being asked to deliver a growth rate for those future earnings. The selection of appropriate earnings growth rates is not a recent frustration. Reports from the time of the South Sea Bubble in 1720 show that it was frustrating analysts even then. As discussed in chapter 17, at the height of this 18th-century financial fiasco a number of analysts attempted to derive their own intrinsic values for South Sea shares. Their valuations varied widely despite the fact they were using essentially the same valuation methods. It was their different earnings growth estimates that caused the variations. That was 300 years ago, but it's still a problem today and will likely remain so 300 years from now.

So how do analysts go about selecting an appropriate rate of growth for a company's future earnings? Probably the wrong way. Too often they extrapolate recent past performance, and when I say recent past, I mean recent past — so stock prices can swing from one quarter's profit result to the next. The problem is that the recent past can provide a poor view of the future, particularly for companies operating in a dynamic and changing business sector.

The limitation of relying on recent past performance is further magnified if a company is currently enjoying a high level of earnings growth. That's because high growth rates typically taper, leading to lower economic values than an optimistic analyst might have anticipated.

Given that it's a difficult issue, I'd like to take a look at how three great investors have dealt with the earnings growth dilemma.

Ben Graham used to place a lot of importance on historical data, but not just on the recent past. He preferred to include at least 10 years of financial data, since he felt this better reflected a company's financial performance as it moved through the business cycle. He related this data to the needs of what he called the ‘defensive investor' and the ‘enterprising investor'. He said that companies suitable for the defensive investor should, over the last 10 years, have demonstrated an increase in earnings of at least one-third (33 per cent). In order to smooth out anomalous years, Graham insisted that the beginning and the end figures are the three-year average earnings figures of years one through three and years eight through ten respectively. For the enterprising investor (willing to take on more risk), Graham suggested the most recent annual earnings figure must be greater, by any percentage, than that of seven years ago.

That's all very interesting, but should one assume a similar rate of earnings growth for the next seven to ten years? A judgement needs to be made whether that's a safe thing to do. If the industry is stable and mature, and the company being valued has a sustainable position within its sector, then possibly so.

On now to Warren Buffett. Reviewing the prices Buffett has paid for investments over the years, I've come to the conclusion that he doesn't use high earnings growth rates in his valuations, no matter what the company's track record shows. This was confirmed to me in 2014 on one of my trips to Omaha. An analyst who'd worked alongside Buffett for several years addressed a group of 30 investors, of whom I was one. He put it succinctly: ‘Buffett doesn't pay much for growth.'

What's more, Buffett appears to solve the problem of having to extrapolate earnings into the distant future by simply not doing it. Author Bob Miles told the 2014 ‘Genius of Buffett' class in Omaha that Buffett expects any investment to be paid back within seven years and that he assigns little value beyond ten.

This line of thinking appears to be equally embraced by other value investors. For example, Henry Singleton, the co-founder of Teledyne, Inc., one of America's most profitable conglomerates, simply never paid more than 12 times earnings for an acquisition. And given that the companies typically demonstrated explosive growth rates after he acquired them, one could say that at 12 times earnings he didn't pay up for growth either.^a

LINKING EARNINGS GROWTH TO RETENTION OF EARNINGS

Earnings-based valuation formulae assume a direct link between the growth rate of earnings and the reinvestment of retained profits (that is, those profits not paid out to shareholders in the form of dividends). Here's how the thinking works.

Imagine a hypothetical company that has $200 million of shareholders' capital tied up in its operations (referred to as book value or shareholders' equity). Put another way, shareholders would need to stump up $200 million to reproduce the company. There are 10 million shares on issue; hence each share has a book value of $20. Let's assume the company has earned a net profit of $20 million in the most recent year of operation — that's $2 of earnings for each share. The company's directors decide to retain half of this profit and to distribute the other half in the form of dividends. Here's the same information in mathematical form:

Because the company retains $10 million of earnings, rather than distributing the money to shareholders, the shareholders' stake in the business (shareholders' equity) has increased from $200 million to $210 million.

Question: If the company made $20 million this year, then how much do you expect it to make next year?

The simple answer is that next year's profit, just like any future profit, is unknown. It will be subject to a nearly endless list of variables — everything from shifts in demand for its products to changes in wage rates and currency fluctuations. But our simplistic valuation formulae don't allow for a large number of inputs. They ask for a few all-encompassing measures such as return on equity, earnings growth rate and discount rate. And for the simplest formulae these inputs are stated as single, unchanging numbers. So, aware of these limitations, let's calculate the earnings growth rate for our hypothetical company.

If it delivered a profit of $20 million using $200 million of shareholders' equity last year, that's a return of:

And if the company can achieve the same rate of return in the coming year it will make:

That's an extra $1 million or 5 per cent on the previous year.

If one assumes the company can repeat this performance year after year, then the anticipated earnings growth rate will remain at 5 per cent. It's no coincidence that in this example the company retains half of its earnings each year and 5 per cent represents half of the company's return on equity (10 per cent). Put another way, the anticipated earnings growth rate equals the earnings retention rate times the company's return on equity.

Lovely and neat, isn't it? Earnings retained and reinvested. Result: a larger capital base. This produces more earnings. Result: earnings growth. And so the cycle continues like an efficient compounding machine, all of it being perfect input for valuation formulae.

This relationship has a name. It's called the ‘clean surplus relation'. Stated mathematically:

where:

• B_t = book value at the end of the period
• B_{t − 1} = book value at the beginning of the period
• E_t = earnings for the period
• D_t = dividends paid during the period.

In other words, the book value at the end of the period equals the beginning book value plus earnings minus dividends. The problem is, this neat equation rarely reflects real life. The two principal reasons for this are:

1. The adoption of generally accepted accounting principles means accounts aren't constructed in a manner that meets the needs of the clean surplus relationship. Put another way, reported earnings don't equate to real cash.
2. Retained earnings are rarely reinvested so efficiently.

More about point two. The formulae assume no leakage, no waste, when the retained earnings are reinvested. Again, this is a relationship that doesn't occur in real life. Let's take a look.

In November 1962 the Bulletin of the Oxford University Institute of Economics & Statistics published an article by Ian Little entitled ‘Higgledy Piggledy Growth'. Little followed this up with a small book, first published in 1966, titled Higgledy Piggledy Growth Again. He set out to determine whether a company's past earnings growth tells us what its future earnings growth will be.

Little was particularly interested in the impact of retained earnings on earnings growth. He used the term ‘plough back' to describe these retained and reinvested earnings. His findings weren't as neat as the valuation models suggest: ‘Our tentative conclusion is that there is no relation between plough back and growth.'¹²⁷ And Little had this to say about extrapolating historical earnings growth rates into the future: ‘Any unbiased reader of this chapter must come to the conclusion that there is no tendency for previous behaviour to be repeated in the future.'

While Little denied that past earnings growth could be extrapolated, he stopped short of suggesting that stock analysis was a waste of time. He spoke of the need to use ‘extra factors' as input to the analytic process, leaving it up to the reader to determine what these extra factors might be. But his comment touches on an extremely important point, one that's been made by some investment greats: it's an appreciation of these extra factors that distinguishes great investors (I'll be exploring what these extra factors might be later in the book).

A diversion is needed here.

WHY COMPOUNDING IS FINITE

Let's look at why retained earnings don't automatically convert into mathematically determinable rates of earnings growth.

For those of you who haven't heard the story of how the Dutch acquired Manhattan Island from the Lenape, here it is. Seventeen years after Henry Hudson cemented his place in history as the first European to set foot on the island of Manhattan, the Dutch thought they'd buy the whole island. In 1626 Peter Minuit, in his capacity as governor-general of New Netherland (a Dutch colony covering parts of what would become New York, New Jersey, Pennsylvania, Maryland, Connecticut and Delaware), traded a bunch of trinkets worth 60 Dutch guilders with the Lenape. They thought the trinkets were a gift, while Minuit thought he'd just struck the greatest real estate deal of his life. Now, 1626 was long before US dollars were issued, but in 1846 historian John Romeyn Brodhead equated 60 Dutch guilders to about US$24. Whether you put faith in his calculations or not, the $24 price tag has stuck.

When people first hear this story they think the Lenape got the thin edge of the wedge, but like many stories this one has a twist. This is because the story of Minuit's cheap land purchase is more commonly used to demonstrate the power of compounding. If the Lenape had refused the trinkets and instead asked for, and invested, an equivalent amount of cash, then today their ancestors would be rich beyond their wildest dreams. That's because $24 placed in a bank account (presumably a Dutch one) back in 1626 would have compounded to over US$1 trillion by 2015, assuming an annual compounding rate of 6.5 per cent. Not one additional dollar had to be added to the initial seed capital in order to achieve this result. All the Lenape had to do was reinvest the interest each year and resist making a single withdrawal for nearly 400 years.

Of course none of this ever happened. Even armed with these figures it's unlikely anyone would choose to do it today. Firstly, who would you choose as the beneficiary of the final pot of gold – some as yet unborn distant relative? Why should you care if some great-great-great (etc.) descendant of yours finds themselves in the Fortune 500 Rich List in 2404? Secondly, do you really believe that the 15 or so interim generations of descendants would happily act as custodians of the money for the next four centuries without dipping their hands in the till? And, finally, even if you luck it with honest descendants, do you really believe that future governments would be able to keep their fiscally irresponsible hands off the money?

The fact is that all forms of wealth suffer leakage, both at a personal level (in the hands of investors) and at a corporate level (in the hands of the directors). Real money doesn't lend itself to being plugged into mathematical formulae. Gerald Loeb gave a great example of this in his 1935 classic The Battle for Investment Survival. He refers to a Saturday Evening Post story in January 1933 written by US financier Frank A. Vanderlip that said:

If the rich Medici family in Italy just six hundred years ago had set aside at 5% compound interest an investment fund equal to $100 000, its 1933 value would be $517 100 000 000 000 000 (five hundred and seventeen quadrillions). The original sum could have been represented by a globe of gold about nine inches in diameter, and the final figure would be 46 million times the existing monetary gold stock of the world.

Why didn't it happen? Why didn't some 20th-century descendant of the Medici family own the world? There is one simple answer: real money, as opposed to hypothetical money, is dispersed.

Hetty Green, once the wealthiest woman in the world, provides another example. Just prior to her death in 1916, Hetty left her $100 million fortune to her two children, Ned and Sylvia. Neither Ned nor Sylvia had children of their own, which meant that upon their death the money was scattered far and wide. Hetty's money was compounded for less than two generations.

Consider also Cornelius Vanderbilt, the wealthiest American at the time of his death in 1877. He was the creator of the Vanderbilt dynasty, which burned brightly for several decades before being relegated to just an interesting story in history. Vanderbilt was a shrewd businessman and aware how fortunes could evaporate. So before he died in 1877 he put in place what he thought to be protection against this happening. He anointed his first son, William, as the sole perpetuator of the Vanderbilt empire. Cornelius had many children but it was William who received the bulk of his $100 million estate. The others each received token six-figure amounts — enough to keep them comfortable by the standards of the late 19th century. Even Vanderbilt's second wife had been asked to sign a prenuptial agreement in an effort to keep the fortune intact. But where is the Vanderbilt fortune now? Or for that matter the Astor, Carnegie and Rockefeller fortunes? Much of the money was returned to society in the form of charitable donations and, in the case of subsequent generations, hefty levels of government taxation. But it also seems subsequent generations didn't possess the business acumen, inclination or drive that these fortunes' originators did.

Okay, diversion over. Stories of the financial erosion of history's dynasties could fill a library. But what these examples highlight is that wealth is not some sterile figure you can simply plug into a compounding formula, and it's no different when valuing companies. After all, companies are run by people. The destinies of companies are determined by the same human frailties that govern the loss of family fortunes. There are massive leakages to corporate wealth — ill-timed and unprofitable entries into new markets, acquisitions undertaken to feed the CEO's ego rather than boost earnings per share, self-enriching managerial options schemes, heavy-taxing governments, sector-destroying shifts in technology … and the list goes on.

So what do we do? Do we simply ignore these realities and press on regardless? Do we continue to source figures from a company's financial accounts and plug them into simple compounding formulae? I think the answer is yes. Don't ignore the formulae, just handle them with care — appreciate their limitations, and use conservative inputs.

It's also a good idea to take your cue from Buffett: don't assume perpetuity. Work on having your investment repaid within a decade, then think of everything you receive beyond that as a bonus. And if you've chosen the right companies, it's going to be one very healthy bonus.