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II: Share Valuation TheoriesHow to Value a ShareIntroductionThe key to understanding how markets work and the basic measures used by investors to analyse their performance (price, dividend yield, cover, and the P/E ratio) requires a theoretical appreciation of the relationship between a share's price, its return (dividend or earnings) and growth prospects using various models based on discounted revenue theory. Chapter Two of CVT set the scene, by outlining the determinants of exdiv share price using discounted techniques to define current price in a variety of ways. Each depends on a definition of future periodic income (either a dividend or earnings stream) under growth or nongrowth conditions discounted at an appropriate cost of equity (either a dividend or earnings yield) also termed the equity capitalisation rate, within a time continuum. For example, given a forecast of periodic future dividends (Dt) and a shareholder's desired rate of return (Ke) based on current dividend yields for similar companies of equivalent risk, we defined the finiteperiod dividend valuation model. The present exdiv value (P0) of a share held for a given number of years (n) should equal the discounted sum of future dividends (Dt) plus its eventual exdiv sale price (Pn) using the current dividend yield (Ke) as a capitalisation rate. Expressed algebraically, using the Equation numbering from the CVT text, which we shall adhere to wherever possible throughout the remainder of this study: Likewise, given a forecast for periodic future earnings (Et) and a desired return (Ke) based on current earnings yields of equivalent risk, we defined the finiteperiod earnings valuation model as follows: The present exdiv value (P0) of a share held for a given number of years (n) should equal the discounted sum of future earnings (Et) plus its eventual exdiv sale price (Pn) using the current earnings yield (Ke) as a capitalisation rate. We eventually focused on a far simpler model using the capitalisation of a perpetual annuity favored by stock exchanges worldwide, which enables the daily publication of price data, the current dividend yield and earnings yield, in the form of a priceearnings (P/E) ratio, by newspapers across the globe. This assumes that if shares are held indefinitely and the latest reported dividend or profit per share remains constant, current ex div price can be expressed using the constant dividend valuation model as follows: Next year's dividend (Dj) and those thereafter are represented by the latest reported dividend (i.e. a constant). Rearranging terms, (Ke) the shareholders' prospective rate of return (equity capitalisation rate) is also a constant represented by the current yield, which is assumed to be maintainable indefinitely. Turning to published earnings data we observed that: Next year's earnings (Ej) and those thereafter are represented by the latest reported profit (i.e. a constant). Rearranging terms, (Ke) the shareholders prospective rate of return (equity capitalisation rate) is also a constant represented by the current earnings yield, which is assumed to be maintainable indefinitely. Because a company's shares cannot sell for different prices at a particular point in time we then noted that: If management pursue a policy of full distribution (whereby D = Ej) then the current dividend and earnings yields must also be identical. But if a company retains a proportion of earnings for reinvestment (Dj< E1) the dividend yield will be lower than the earnings yield: For example, if a company's, latest reported dividend and earnings per share are £1.00 and £1.60 respectively, trading at a current price of £8.00 then because earnings cover dividends 1.6 times, the dividend yield is only 62.5 per cent of the earnings yield (12.5 per cent and 20 percent respectively). This difference in yields is not a problem for investors who know what they are looking for. Some prefer their return as current income (dividends and perhaps the sale of shares). Some look to earnings that incorporate retentions (future dividends plus capital gains). So, their respective returns will differ according to their consumption preferences and the riskreturn profile of their portfolio of investments. This is why share price listings in the newspapers focus on dividends and earnings, as well as the interrelationship between the two measured by dividend cover. However, you will recall that to avoid any confusion between dividend and earnings yields when analysing a company's performance, published listings adopt a universal convention. The righthand terms of the current earnings yield defined by Equation (11) are inverted to produce the return's reciprocal, namely a valuation multiplier: the priceearnings (P/E) ratio. Exercise 2: The Dividend Yield, Cover and the P/E RatioUnlike the dividend yield and the earnings yield, which are percentage returns, the P/E ratio is a real number that analyses price as a multiple of earnings. On the assumption that a firm's current posttax profits are maintainable indefinitely, the ratio therefore provides an alternative method whereby a company's distributable earnings can be capitalised to establish a share's value. However, it does not stand alone when we analyse a company's performance. With information on dividend yield, or dividend cover it is possible to construct a comprehensive investment profile for the basis of analysis. Consider the following data relating to four companies whose dividends are covered twice by earnings. Required: 1. Tabulate the earnings yield and corresponding P/E ratio for each company. 2. Comment on the mathematical relationship between these two measures and its utility. An Indicative Outline Solution 1. The corresponding earnings yields and P/E ratios for each company can be tabulated as follows: 2. The Mathematical Relationship Because the two measures are reciprocals of one another, whose product always equals one, there is always a perfect inverse relationship between a share's earnings yield and its P/E ratio. The interpretation of the P/E is that the lower the figure, the higher the earnings yield and vice versa. 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, media, analyst reports, or internet downloads. Summary and ConclusionsNot only is the previous exercise useful for future reference throughout this text once we begin to interpret the interrelationships between price, dividend yield and the P/E ratio in Part Three. But in the interim your regular reading of the financial press as a guide to further study outlined in Chapter One should also fall into place. However, before we analyse this practical methodology for analysing corporate, stock market performance, we need to consider its theoretical limitations with answers to the following questions. What happens to current share prices listed in the financial press if the latest reported dividends, or earnings, are not constant in perpetuity? For the purpose of equity valuation, are dividends (yields) more important than earnings (P/E ratios) or vice versa within the investment community? To understand the debate, I suggest that you do some preparation by reading the remainder of CVT Part Two (Chapters' Three and Four) which evaluates the theoretical and realworld implications of dividend policy, rather than earnings, as a determinant of equity prices and shareholder wealth maximisation. Selected ReferenceHill, R.A., Corporate Valuation and Takeover: Parts One and Two (2011). 
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