2.3. The Capitalisation of Current Maintainable Yield

Your answers to Activity 2 not only reveal the impact of different assumptions on a share's theoretical present value, but why basic price and yield data contained in stock exchanges listings published by the financial press favor the constant valuation model, rather than any other.

Think about it. The derivation and analyses of current share prices based on future estimates of dividends, ex-div prices and appropriate discount rates for billions of market participants, even over a single period is an impossible task. To avoid any weakness in forecasting characterised by uncertainty and to provide a benchmark valuation for the greatest possible number, stock exchange listings therefore assume that shares are held in perpetuity and the latest reported dividend per share will remain constant over time. This still allows individual investors with other preferences, or information to the contrary, to model more complex assumptions for comparison. There is also the added commercial advantage that by using the simplest metrics, a newspaper's stock exchange listings should have universal appeal for the widest possible readership.

Turning to the mathematics, given your knowledge of discounted revenue theory based the capitalisation of a perpetual annuity (where PV = Ct / r) share price listings define a current ex- div price (P0) using the constant dividend valuation model as follows:

Next year's dividend (Dt) and those thereafter are represented by the latest reported dividend (i.e. a constant). Rearranging terms, (Ke) the shareholders desired rate of return (equity capitalisation rate) is also a constant represented by the current yield, which is assumed to be maintainable indefinitely.

2.4. The Capitalisation of Earnings

For the purpose of exposition, so far we have focused on dividend income as a determinant of price and value, with only passing reference to earnings. But what about shareholders interested in their total periodic returns (dividends plus retentions) from corporate investment? They need to capitalize a post-tax earnings stream (Et) such as earnings per share (EPS) and analyse its yield (Ke). No problem: the structure of the valuation models summarized in Activity 2 remains the same but Et is substituted for Dt and Ke now represents an earnings yield, rather than a dividend yield. Thus, we can define a parallel series of equations using:

The single-period, earnings valuation model The finite-period, earnings valuation model The general earnings valuation model The constant earnings valuation model

Turning to stock exchange listings and the financial press, we also observe that for simplicity the publication of earnings data is still based on the capitalisation of a perpetual annuity.

Next year's earnings (Et) and those thereafter are represented by the latest reported profit (i.e. a constant). Rearranging terms, (Ke) the shareholders desired rate of return (equity capitalisation rate) is also a constant represented by the current earnings yield, which is assumed to be maintainable indefinitely.

Review Activity

Having downloaded this text and others in the bookboon series, it is reasonable to assume that you can already interpret a set of published financial accounts, if not share price data. To test your level of understanding for future reference, select a newspaper of your choice and a number of companies from its stock exchange listings. Then use the data to explain:

- The mathematical relationship between a company's dividend and earnings yields and why the two may differ.

- The definition of earnings yields published in the financial press.

Our discussion of efficient markets in Chapter One explained why a company's shares cannot sell for different prices at a particular point in time. So, it follows that:

And if a company adopts a policy of full distribution (whereby Dj = Et) then the equity capitalisation rates for dividends and earnings, using a current maintainable yield (Ke) must also be identical.

But what of the more usual situation, where a company retains a proportion of earnings for reinvestment? Given P0 (but Dj < Ej) the respective equity capitalisation rates (Ke) now differ.

Not only is the dividend yield lower than the earnings yield but as we shall explore in Chapter Three, there is a behavioral explanation for relationship between the two. For the moment, suffice it to say that there is also an underlying mathematical relationship. For example, if a company's current share price, latest reported dividend and earnings per share are $100, $10 and $20 respectively, then because earnings cover dividends twice (again, more of which later) the dividend yield is half the earnings yield (10 and 20 percent respectively).

This difference in yields is not a problem for investors who know what they are looking for. Some will prefer their return as current income (dividends and perhaps the sale of shares). Some will look to earnings that incorporate retentions (future dividends plus capital gains). Most will hedge their bets by combining the two in share portfolios that minimise risk. So, their respective returns will differ according to their risk-return profile. Which is why share price listings in newspapers worldwide focus on dividends and earnings, as well as the interrelationship between the two measured by dividend cover.

Moving on to the second question posed by our Review Activity, if you are at all familiar with share price listings published in the financial press, you will be aware of a convention that also enables investors to avoid any confusion between dividend and earnings yields when analysing a share's performance.

Given the current earnings yield:

The equation's terms can be rearranged to produce its reciprocal, the price-earnings (P/E) ratio.

Unlike the earnings yield, which is a percentage return, the P/E ratio is a real number that analyses price as a multiple of earnings. On the assumption that a firm's current post tax profits are maintainable indefinitely, the ratio therefore provides an alternative method whereby a company's distributable earnings can be capitalized to establish a share's value.

Because the two measures are reciprocals whose product always equals one, the interpretation of the P/E is that the lower the figure, the higher the earnings yield and vice versa. And because investors are dealing with an absolute P/E value and not a percentage yield, there is no possibility of confusing a share's dividend and earnings performance when reading share price listings, articles or commentaries from the press and media, analyst reports, or internet downloads.

Finally, having noted that low valuation multipliers correspond to high returns and that a number multiplied by its reciprocal equals one, use Table 2.1 to confirm a perfect inverse relationship between a share's P/E and its earnings yield. Not only will this exercise be useful for future reference throughout this text, but future reading of the financial press should also fall into place.

Table 2.1: The Relationship between the P/E Ratio and Earnings Yields

Summary and Conclusions

This Chapter has outlined the fundamental relationships between share valuation models and the derivation of the cost of equity capital for the purpose of analysing stock market returns.

We set the scene by explaining the derivation of basic share valuation models using discounted revenue theory, with particular reference to the capitalisation of a perpetual annuity. We noted that corresponding equity valuations based on current dividend and earnings should be financially equivalent.

The relationship between an ex-div dividend and earnings valuation revealed why a few select metrics (based on price, dividend yield and the P/E ratio) published in the financial press encapsulate a company's stock market performance and provide a guide to future investment.

As we shall discover in later chapters, a share's intrinsic value (price) is only meaningful if we consider other data about a company and then place it in context. For example, given a company's latest reported dividend and profit figures, investors can use existing dividend yields and P/E ratios to place a comparative value on that company's shares. These can then be compared with its actual value (current market price) to establish whether the company is either undervalued, equitable, or overvalued, relative to the market for similar shares of equivalent risk. Needless to say, undervalued, rational investors buy, equitable they hold, overvalued they sell.

Selected References

Hill, R.A., Strategic Financial Management: Chapters Two and Five (2008).

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