EQ 4 – Market-Based Valuation_ Price and Enterprise Value Multiples

Graham and Dodd described valuation on price to earnings as the standard method of their era in the first edition of Security Analysis in 1934, and it remains the most familiar valuation measure today. Three arguments support its use.

• Earning power drives value. Earnings per share is probably the single number security analysts watch most closely. A 2007 survey of CFA Institute members ranked price to earnings first among price multiples used in market-based valuation, and the 2012 BofA Merrill Lynch Institutional Factor Survey found it the most popular valuation metric in investment decisions.
• It is universally understood. Investors recognise and use it without explanation.
• It has empirical support. Differences in price to earnings ratios appear to be related to differences in long-run average returns.

The drawbacks all trace back to the denominator rather than the numerator. Market price is unambiguous. Earnings per share is not.

• Earnings per share can be zero, negative, or so small relative to price that the ratio ceases to convey anything. A multiple with a zero denominator does not exist, and a negative one is misleading, as shown below.
• Separating the recurring part of earnings, which is what determines intrinsic value, from the transient part is difficult in practice.
• Accounting standards force managers to choose among permitted treatments and to make estimates. Those choices can distort earnings per share as a measure of economic performance and can damage comparability between companies.

Trailing and forward

Two definitions dominate. The trailing price to earnings ratio, sometimes called the current ratio, divides the current market price by earnings per share for the most recent four quarters, often labelled trailing twelve month earnings per share. Be careful with the label: the Value Line Investment Survey uses current price to earnings to mean a ratio built on the most recent six months of earnings plus the projected earnings for the coming six months, which blends history with forecast.

The forward ratio, also called leading or prospective, divides the current price by expected earnings for next year. Data vendors offer several variants. Thomson First Call, for instance, publishes ratios based on trailing twelve month earnings per share, on last reported annual earnings per share, and on earnings per share forecast one to three years ahead. Value Line reports a median price to earnings ratio, a rounded average of the four middle values in the range of annual average ratios over the past ten years.

The single rule that matters is consistency. Apply the same definition to every company and every period under examination, because the differences between definitions are systematic rather than random. For a company with rising earnings the forward ratio will be smaller than the trailing ratio, simply because the denominator is larger. Since valuation looks forward, analysts normally prefer the forward ratio when earnings forecasts are available. When earnings are not readily predictable a trailing ratio, or another metric altogether, may serve better. Logic sometimes rules out one definition entirely: after a major acquisition, a large divestiture, or a substantial change in financial leverage, the trailing ratio built on past earnings per share says nothing useful about the future, and the forward ratio is the only sensible measure.

Building the trailing ratio

Four issues arise when trailing earnings are used in the denominator: potential dilution of earnings per share, transitory items specific to the company, transitory items caused by the business or industry cycle, and differences in accounting methods across the companies being compared.

Dilution is the easiest, because companies report both figures themselves. Basic earnings per share takes total earnings over the share count that was genuinely in issue across the period, weighted by time. Diluted earnings per share instead assumes that every holder of an executive stock option, an equity warrant or a convertible bond takes up the right to common stock, and it corrects the numerator as well, because converting a bond removes an interest charge at the same time as it adds shares. Analysts generally prefer diluted earnings per share when comparing companies, so that businesses carrying different amounts of dilutive securities are placed on the same footing.

The forward ratio in practice

Analysts read the phrase next year expected earnings in three different ways: the next four quarters, the next twelve months, or the next fiscal year. The four-quarter reading sits closest to the way cash flows are dated in discounted cash flow work, so it is the default here. Suppose a stock trades at 15 dollars on 1 March 2020, and the quarterly forecasts of earnings per share run 0.15 through to 31 March 2020, then 0.18 through to 30 June, then 0.18 again through to 30 September, then 0.24 through to the 31 December year end. The sum is 0.75, and the forward ratio is 15 divided by 0.75, or 20.0.

A closely related figure is the next twelve month ratio, which is to the forward ratio what trailing twelve month is to the trailing ratio. It blends the annual estimates of two fiscal years, weighted by how close each one is. Consider an analyst looking at Microsoft Corporation in late August 2020. Microsoft has a 30 June fiscal year end, so ten months of fiscal 2021 remained, namely September 2020 through June 2021 inclusive. The estimated next twelve month earnings per share is ten twelfths of the fiscal 2021 estimate plus two twelfths of the fiscal 2022 estimate. The virtue of this construction is that it allows companies with different fiscal year ends to be compared without quarterly estimates, which for many companies are simply not available.

An analyst who understands discounted cash flow models can use them to build a justified price to earnings ratio directly, and can also use them to explain why two comparable companies trade at different multiples. The question being answered is precise: what should the market pay for one unit of earnings, given a particular set of expectations about profitability, growth and the cost of capital?

The simplest discounted cash flow model is the Gordon constant growth form of the dividend discount model. Dividing both sides by earnings gives the two standard expressions.

Both expressions state the multiple as a function of two fundamentals, the required rate of return which reflects risk, and the expected stable dividend growth rate. The dividend payout ratio, one minus the retention rate, enters as well. A particular set of forecasts therefore implies a particular value of the ratio, and that value is the justified multiple based on fundamentals.

The comparative statics are the part worth committing to memory, because they carry over to models far more complex than the Gordon form. Using any discounted cash flow model, the justified ratio is inversely related to the required rate of return and positively related to the growth rate of expected future cash flows, however those cash flows are defined.

When the discounted cash flow model is complex, with varying growth rates and varying assumptions about dividends, the ratio cannot be written as a neat function of constant variables. That is not an obstacle. The analyst simply divides the value per share produced by the model by estimated earnings per share, and the result is a justified multiple in the ordinary sense. The same trick delivers justified values for any other multiple.

A predicted price to earnings ratio is conceptually a cousin of the justified ratio, but it is estimated statistically rather than derived from a valuation model. The analyst regresses observed multiples for a group of stocks on the fundamentals thought to determine them. Kisor and Whitbeck in 1963 and Malkiel and Cragg in 1970 pioneered the approach, measuring ratios for a group of stocks against the growth rate in earnings, the payout ratio and a measure of volatility such as the standard deviation of earnings changes or beta.

Any set of explanatory variables believed to determine investment value can be used. The warning attached is multicollinearity, meaning correlation among linear combinations of the independent variables, which distorts the individual coefficients even when the fitted values remain serviceable.

Three limitations

A cross-sectional regression compresses a great deal of data into one equation and can add a useful perspective, but it is rarely the main tool, for three reasons.

• It is local. The relationships captured belong to that sample of stocks over that period. What the regression predicts for a different stock in a different period is unknown.
• It is unstable. Coefficients and explanatory power change substantially over a run of years. Empirical work indicates that the relationships between the multiple and characteristics such as earnings growth, dividend payout and beta do not hold still. Because the distributions of multiples themselves change over time, the predictive power of any single estimation decays as time passes.
• The coefficients are hard to read. Multicollinearity among the independent variables makes the interpretation of any one coefficient unreliable, even when the equation as a whole fits.

It is worth noting where the weight of capital market research actually sits. Rather than regressing multiples on economic variables, most of it relates stock prices and returns to explanatory variables, one of which is often earnings or unexpected earnings. The Fama and French study of 1992 showed that used alone, earnings to price, size, leverage and book to market each explained cross-sectional stock returns over the 1963 to 1990 period; used together, size and book to market absorbed the explanatory role of the others. That work eventually produced the Fama–French three-factor model, with size, book to market and beta as the factors. Lakonishok, Shleifer and Vishny in 1994 found that value strategies, defined as purchasing shares that are cheap against earnings, against book value, against cash flow and against sales growth, delivered better returns on a five-year hold across the 1968 to 1990 window, and did so without taking on more fundamental risk than the growth alternative.

Rather than compare a stock with other stocks, an analyst can compare it with itself. The idea is that a multiple may regress toward its own historical average level. Value Line reports a median price to earnings ratio, a rounded average of the four middle values of the annual average ratio over the previous ten years. A five-year average trailing ratio is another reasonable metric, and trailing ratios are more commonly used than forward ratios in this exercise. Beyond simple higher and lower comparisons, the benchmark can be converted into a justified price.

Where own-history comparisons break down

Three things spoil the method. A substantial change in the business mix within the period examined makes the average meaningless. A shift in the use of financial leverage impairs comparability for the same reason, since the multiple reflects financial risk. And changes in the interest rate environment and in economic fundamentals across periods break the link between past and present.

Inflation deserves a paragraph of its own, because it distorts the economic meaning of reported earnings. If the inflationary environment reflected in the current multiple differs from the environment reflected in the historical average, a comparison between the two is misleading. So is a comparison across countries, and the mechanism is the ability of a company to pass cost inflation on to customers in the form of higher prices.

When comparing companies in different countries, two effects intrude. The first is the effect on earnings per share of differences in accounting standards, which distorts any unadjusted comparison when standards differ on the recognition of revenues, expenses or gains. The second is the effect on market-wide benchmarks of differences in macroeconomic context. Inflation and pass-through are a specific case of the second. For two companies with the same pass-through ability, the one operating in the environment with higher inflation has the lower justified multiple. For two companies facing equal inflation, the one with the lower pass-through rate has the lower justified multiple.

Multiples as terminal value

In any multistage dividend discount model, or in a spreadsheet that forecasts specific cash flows out to a horizon, the terminal value is a large part of the answer. One condition must hold: the growth embedded in that terminal value has to be growth the business can keep up indefinitely. Price multiples are a common way to set it, the earnings multiple and the book multiple above all, and a multiple used this way is a terminal price multiple. There are two ways to choose one.

A terminal multiple based on fundamentals restates the Gordon growth model as a multiple by dividing both sides by earnings. Dividing by earnings at time n, where n is the point at which the final stage begins, gives a trailing terminal multiple; dividing by earnings at time n plus one gives a leading terminal multiple. An analyst could of course use the Gordon growth model directly and skip the multiple, but multiples communicate an estimate of terminal value in a form the audience recognises.

A terminal multiple based on comparables uses a benchmark such as the median industry ratio, the average industry ratio, or the average of its own past ratios. Its strength is that it is grounded entirely in market data. The Gordon growth model, by contrast, requires specific estimates of the required rate of return, the payout ratio and the mature growth rate, and its output is highly sensitive to all three. The corresponding weakness of comparables is that if the benchmark reflects mispricing, so does the terminal value.

Valuing a business at some number of times its yearly revenue is an old habit among certain privately held firms, notably investment managers and the many businesses organised as partnerships. Over recent decades the same ratio has established itself as a recognised indicator for listed equity too. Working from US data, O’Shaughnessy in 2005 characterised it as the best ratio for selecting undervalued stocks. In the 2012 BofA Merrill Lynch Institutional Factor Survey, about 30 percent of respondents used it consistently.

Rationales

• Sales are harder to distort. Managers can shape earnings per share through discretionary accounting decisions about expenses. Total sales sit at the top of the income statement, before any expense.
• Sales are positive even when earnings are negative, so the ratio remains usable where price to earnings is not meaningful.
• Sales are more stable than earnings, which reflect operating and financial leverage, so the ratio is more stable and more meaningful when earnings are abnormally high or low.
• It has been regarded as appropriate for mature, cyclical and zero-income companies.
• Differences in the ratio appear to be related to differences in long-run average returns.

Drawbacks

• Rapid sales growth is entirely compatible with losses on both the earnings line and the operating cash flow line. A going concern has to produce both eventually or it has no value.
• The ratio contains a logical mismatch. What debt does to profitability and to risk is embedded in the share price, yet sales sits above financing altogether. Some practitioners use enterprise value to sales for exactly this reason, because enterprise value incorporates the value of debt.
• The ratio ignores differences in cost structure across companies.
• Although robust against manipulation compared with earnings, sales can still be distorted through revenue recognition practices.

One identity is worth carrying around. Because sales times net profit margin equals net income, the price to earnings ratio times the net profit margin equals the price to sales ratio. For two stocks with the same positive earnings multiple, the one with the higher sales multiple has the higher actual or forecast net profit margin, obtained as the ratio of the sales multiple to the earnings multiple.

Revenue recognition: the quality question

Determining sales is more straightforward than determining earnings, but that is not the same as being safe. An analyst using this ratio without assessing the quality of the accounting for sales, and in particular practices that accelerate recognition, may place far too high a value on the shares. Three episodes illustrate the range of the problem.

Barter advertising in the internet bubble. Analysts call markets bubbles when prices appear to lose contact with intrinsic values, and to many the run-up in US internet stocks from 1998 to 2000 was one. During that period many analysts adopted price to sales as the metric for internet companies with negative earnings and negative cash flow. Partly as a result, some of those companies used questionable revenue recognition to justify their valuations. Bartering website advertising with other internet companies was a favourite: one company might barter one million dollars of banner advertising with another, and each could then record one million dollars of revenue and one million dollars of expense. Neither had any net income or cash flow, yet the revenue growth and the market valuation of each was enhanced, at least for a time, and the value placed on the advertising was frequently questionable. The US SEC issued a stern warning and formalised revenue recognition for barter in Staff Accounting Bulletin No. 101; international standard setters issued Standing Interpretations Committee Interpretation 31 for barter transactions involving advertising services.

Bill and hold. Selling products but not delivering them until a later date accelerates recognition into an earlier period. In its Form 10-K filed on 30 September 2008, Diebold, a provider of bank security systems and automated teller machines, disclosed that its long-standing method of accounting for bill and hold transactions in its North America and International businesses was in error and represented a misapplication of GAAP. On 15 January 2008 the company announced the conclusion of discussions with the Office of the Chief Accountant, discontinued bill and hold as a revenue recognition method in both segments, and restated its financial statements. Under the corrected policy, where Diebold is contractually responsible for installation in North America, customer acceptance occurs on completion of installation of all items at a job site and demonstration that they are operable; where items are only delivered, recognition continues on shipment or delivery depending on the contract; and in the International segment acceptance is on either delivery or completion of installation depending on the contract. The company also adjusted other transactions in which revenue had been recognised in incorrect periods, generally where revenue had been recognised before title or risk of loss transferred to the customer. In 2010 Diebold agreed to pay 25 million dollars to settle SEC charges that it manipulated earnings from at least 2002 through 2007, misstating reported pre-tax earnings by at least 127 million dollars. According to the SEC, financial management received reports, sometimes daily, comparing actual earnings with analyst forecasts, and prepared opportunity lists of ways to close the gap. Many of the methods were fraudulent, and the SEC listed several: misusing bill and hold accounting, booking revenue on a lease that carried a side buy-back arrangement, manipulating reserves and accruals, deferring and capitalising expenses improperly, and marking up the carrying value of used inventory.

Gross versus net. Groupon is a deal-of-the-day website featuring discounted gift certificates usable at local or national companies. The registration statement was amended eight separate times ahead of the November 2011 listing. In one restatement demanded by the SEC, a revenue policy that its own auditors had accepted had to be abandoned, and reported sales fell by more than 50 percent as a result. What Groupon had been recording as revenue was the full amount members handed over for a coupon or certificate, with no deduction for the portion, usually half or more, that flows on to the merchant. A further SEC demand struck from the offering document a home-made non-GAAP measure called adjusted consolidated segment operating income, on the ground that leaving marketing spending out of a profitability measure is misleading when marketing spending is one of the principal risks the business runs.

The practical rule that follows is uncomfortable but correct. Even where a company discloses its revenue recognition practices, the analyst often cannot determine by how much sales may be overstated. If practices are questionable and the amount is unknowable, the analyst might reasonably suggest avoiding the securities altogether. At the very least, scepticism argues for a higher risk premium, which lowers the justified price to sales ratio.

The justified price to sales ratio

The ratio links to a discounted cash flow model in the usual way. On forward sales:

On trailing sales the equivalent expression carries the growth factor in the numerator:

Both say the justified ratio is an increasing function of the profit margin and of the earnings growth rate, and the intuition survives in more complex discounted cash flow models. The profit margin actually works twice, directly and through growth, which becomes visible when the sustainable growth expression is decomposed:

An increase in the profit margin produces a higher sustainable growth rate as long as sales do not fall proportionately, and a decrease works the other way. So a margin improvement raises the justified ratio through the numerator and again through the growth term in the denominator.

Price to cash flow is widely reported. In the 2012 BofA Merrill Lynch Institutional Factor Survey, only seven factors were more popular than price to free cash flow: the earnings multiple, beta, the enterprise value multiple on earnings before interest, taxes, depreciation and amortization, return on equity, size, and the book multiple. Roughly half of the institutions surveyed used it.

A terminology warning first. The phrase price to cash flow is used loosely for the ratio of share price to any cash flow concept. P/CF is used here in a narrower sense, for price divided by the earnings-plus-noncash-charges figure alone. Because so many cash flow concepts circulate, always establish, and always communicate, exactly which definition is in use.

Rationales and drawbacks

• Cash flow is less subject to manipulation by management than earnings.
• Cash flow is generally more stable than earnings, so the ratio is more stable than price to earnings.
• Using cash flow rather than earnings addresses differences in accounting conservatism between companies, which is to say differences in the quality of earnings.
• Differences in the ratio appear to be related to differences in long-run average returns.

Against that:

• Approximating operating cash flow as earnings per share with noncash charges added back leaves out things that genuinely move operating cash flow, among them revenue that never arrives in cash and the net swing in working capital. Aggressive front-end loading of revenue would therefore not be captured, because the measure does not reflect the divergence between reported revenues and the cash actually collected.
• Theory points to free cash flow to equity, not cash flow, as the right variable for a price-based multiple. Free cash flow to equity, however, is more volatile than cash flow for many businesses and turns negative more often.
• As analysts have leaned more on cash flow, some companies have adopted accounting methods that flatter it. Operating cash flow can be improved by securitising accounts receivable to accelerate inflows, or by outsourcing the payment of accounts payable to slow outflows while the outsourcing company continues to pay on time and finances the timing difference.
• Operating cash flow under IFRS may not be comparable with operating cash flow under US GAAP, because IFRS allows more flexibility in classifying interest paid, interest received and dividends received. US GAAP classifies all three as operating; IFRS permits interest and dividends received to be classified as operating or investing, and interest paid as operating or financing.

Which cash flow

In practice analysts and data vendors use simple approximations of cash flow from operations. For many companies depreciation and amortization are the major noncash charges added back to net income under the add-back method, so the approximation concentrates on them. The representative version specifies cash flow per share as earnings per share plus per-share depreciation, amortization and depletion, and that is the earnings-plus-noncash-charges definition abbreviated as CF. It is a convention, not an accounting definition. The trailing form is reported most often. It divides today market price by four quarters of cash flow per share added together, and as with earnings per share a fiscal year version is equally available.

Three more technically accurate concepts stand behind the approximation. Cash flow from operations comes straight from the statement of cash flows; as with earnings, adjustments may be needed for components not expected to persist, and further adjustments may be needed when comparing companies reporting under different standards, given the IFRS flexibility over interest and dividend classification noted above. Free cash flow to equity has the strongest link to valuation theory. Because the ratio of capital expenditure to cash flow from operations generally differs among companies, rankings by price to cash flow from operations and by price to cash flow will differ from rankings by price to free cash flow to equity. Period-by-period free cash flow to equity is also more volatile, so a trailing ratio built on it is not automatically more informative: two similar businesses with the same total cash flow from operations and capital expenditure over two years will show sharply different ratios if one front-loads its capital expenditure and the other back-loads it, with no economic difference whatever. The proper remedy is to use the free cash flow to equity discounted cash flow model, which incorporates all expected future free cash flows, or at least to use price to average free cash flow.

The third concept is earnings before interest, taxes, depreciation and amortization. Analysts usually forecast it by forecasting earnings before interest and taxes and adding depreciation and amortization. From historical figures, start with earnings from continuing operations excluding nonrecurring items and add back interest, taxes, depreciation and amortization. Both enterprise value to that measure and price to that measure are used in practice, but the enterprise value form is preferred, because the numerator includes the value of debt and the denominator is a pre-interest flow to debt and equity alike.

The justified ratio and comparables

The relationship to fundamentals follows from present value mathematics without any new machinery. All else equal, the justified price to cash flow ratio is inversely related to the required rate of return and positively related to the growth rate of expected future cash flows, however defined. It is found by valuing the stock with the most suitable discounted cash flow model and dividing by cash flow on the chosen definition.

Total return on an equity investment splits into capital appreciation and dividend yield, and dividend yield data are frequently published to give investors an estimate of the second component. It is also used as a valuation indicator in its own right. The 2012 BofA Merrill Lynch Institutional Factor Survey did not cover the metric, but across the surveys from 1989 to 2006 slightly more than a quarter of respondents on average reported using it as a factor in the investment process.

Rationales and drawbacks

Two arguments are offered in favour. The yield forms part of total return, and it is the part that carries less risk than capital appreciation does. Three arguments run the other way.

• Dividend yield is only one component of total return, and using less than all the information relevant to expected return is suboptimal.
• Investors may be trading future earnings growth for current income. With return on equity held fixed, every unit paid out today is a unit not reinvested, so it removes earnings from every subsequent period, an idea known as the dividend displacement of earnings. Empirical work by Arnott and Asness in 2003 and by Zhou and Ruland in 2006 shows that caution is required before assuming displacement holds in practice, because payout may be correlated with future profitability.
• The argument that dividends are safer presupposes that market prices reflect the relative risk of the components of return in a biased way. If prices already price that difference correctly, there is nothing to exploit.

Computing the yield

Every multiple so far has carried market price in the numerator. Price to dividends has appeared in valuation, particularly for indexes, but many stocks pay no dividend at all and the ratio is undefined with zero in the denominator. For a non-paying stock the dividend yield is defined, and it is zero. For practical purposes, therefore, dividend yield is the preferred presentation.

Trailing dividend yield divides the dividend rate by the current market price per share. The dividend rate is the annualised amount of the most recent dividend: for a company paying quarterly, four times the most recent quarterly per-share dividend. Some data sources instead use the dividends of the last four quarters. For a company paying semiannually with an interim dividend that differs in size from the final dividend, the dividend rate is usually taken as the most recent annual per-share dividend. The dividend rate states the annual amount under the assumption of no change over the year; a forecast of leading dividends may be higher or lower, and it is the basis of the leading dividend yield, which divides forecast dividends per share over the next year by the current market price.

Fundamentals and comparables

The Gordon growth model supplies the link to fundamentals directly:

Dividend yield is therefore negatively related to the expected growth rate of dividends and positively related to the required rate of return. The first of those implies something about investment style: selecting stocks on high dividend yield is consistent with a value orientation rather than a growth orientation, because the same expression that makes the yield high makes the growth low.

Using the yield with comparables is the familiar exercise. Compare a company with its peers, taking account of yield and risk, and ask whether differences in expected growth explain differences in yield. Many investors add a second question about the security of the dividend, meaning the probability that it will be cut or eliminated. The payout ratio is the standard metric: a high payout relative to companies in the same industry may signal a less secure dividend, because the payment is less well covered by earnings. Balance sheet metrics matter just as much, and the interest coverage ratio and the ratio of net debt to earnings before interest, taxes, depreciation and amortization both belong in the assessment.

Enterprise value multiples relate the enterprise value of a company to a measure of value, typically a pre-interest income measure. The argument most often made for them over price multiples is that they are relatively less sensitive to the effects of financial leverage when the companies being compared use different amounts of debt. There is a second argument. By defining the numerator as the value of the whole capital structure, these multiples take a control perspective, the perspective of a buyer of the entire business rather than of a minority shareholder. So even where leverage differences are not an issue, they complement price multiples. Some analysts favour one family strictly; many report both.

Building enterprise value

Enterprise value is total company value, meaning the market value of debt, common equity and preferred equity, less the value of cash and short-term investments. The standard build is:

• Market value of common equity, computed as the number of shares outstanding times price per share;
• plus preferred stock at market value where there is any, together with minority interest where that has not already been picked up;
• plus debt at market value;
• less the cash pile, meaning cash itself, cash equivalents and investments of short maturity;
• equals enterprise value.

Why EBITDA

Enterprise value to earnings before interest, taxes, depreciation and amortization is by far the most widely used enterprise value multiple. That measure is an estimate of pre-interest, pretax operating cash flow, and because it is a flow to both debt and equity, pairing it with a numerator that measures total company value is the internally consistent choice. Strictly the ratio is a valuation indicator for the whole company rather than for the common stock alone, but if the analyst can assume that the debt and any preferred stock are efficiently priced, an inference about the valuation of the common equity follows, and that assumption is often reasonable.

Three rationales support the ratio.

• It is usually more appropriate than price to earnings alone for comparing companies with different financial leverage, because the denominator is a pre-interest earnings figure whereas earnings per share is post-interest.
• By adding back depreciation and amortization it controls for differences in depreciation and amortization policy, in contrast to net income which is after both. That is why it is used so heavily for capital-intensive businesses such as cable companies and steel companies, which carry substantial charges of this kind.
• It is frequently positive when earnings per share is negative.

Two drawbacks matter.

• When working capital is expanding it overstates operating cash flow, and it takes no notice of how differing revenue recognition policies feed through to that cash flow.
• Free cash flow to the firm, which directly reflects required capital expenditure, has a stronger link to valuation theory. Only where depreciation expense matches capital expenditure should the measure be expected to reflect differences in capital programmes, and that qualification bites hardest for exactly the capital-intensive businesses to which the ratio is most often applied.

Fundamentals and comparables

The drivers follow the pattern set by every other multiple, adapted to the fact that the flow belongs to all providers of capital. All else equal, three drivers move it. Faster expected growth in free cash flow to the firm raises the justified ratio. Higher expected profitability, measured here by return on invested capital, also raises it. A higher weighted average cost of capital lowers it. Return on invested capital is operating profit after tax divided by invested capital, and it is the relevant profitability measure here precisely because the denominator of the multiple flows to every capital provider.

In a comparables exercise a lower ratio relative to peers indicates relative undervaluation, all else equal. A recommendation is rarely determined by the ratio alone; it is one piece of information among several.

Enterprise value to EBITDA is the best known member of the family but not the only one. Some alternatives are used broadly, such as enterprise value to free cash flow to the firm. Others are industry specific, such as enterprise value to EBITDAR, where the R stands for rent expense, which airline analysts favour because operating lease commitments dominate their capital structures. Any of these metrics could equally be formulated using total invested capital in place of enterprise value.

The major alternatives to EBITDA in the denominator are free cash flow to the firm, EBITA, meaning earnings before interest, taxes and amortization, and EBIT, meaning earnings before interest and taxes.

Analysts typically forecast EBITDA by forecasting EBIT and adding depreciation and amortization.

Every one of these measures adds interest back to net income, which records the fact that they are flows relevant to all providers of debt and equity capital alike. Reading down the four rows, each successive measure carries less precise information about the tax position of the company and about its capital investment, yet each has a rationale. EBITA may be the right choice where amortization, which relates to intangibles, is a major expense for the companies being compared but depreciation, which relates to tangibles, is not. EBIT may be the right choice where neither is a major item.

Denominators need not be financial at all. In some industries a nonfinancial measure specific to that sector is more informative: enterprise value to subscribers for satellite and cable television broadcasters, or a multiple based on reserves for a resource company. The concept survives whatever goes underneath: set the market value of the whole business against some fundamental measure of what the business owns or turns out.

Enterprise value to sales

Enterprise value to sales is the major alternative to price to sales, and it exists to repair a specific conceptual weakness. Price to sales fails to recognise that for a debt-financed company not all sales belong to the equity investors: some of the proceeds go to paying interest and principal to the providers of debt capital. A price to sales ratio for a company with little or no debt is therefore not comparable with the ratio for a company financed largely with debt. Enterprise value to sales is the valid basis for comparison in that situation, and more generally whenever the companies being compared carry diverse capital structures.

Where multiples sit across the market

An analyst using multiples with a benchmark drawn from closely similar companies should know the range of values that peer companies exhibit, and should track the fundamentals that might explain the differences. The table below shows median values of various multiples by economic sector under the Global Industry Classification System, together with the median dividend payout ratio and median values of selected fundamentals: return on equity and its determinants, namely net profit margin, asset turnover and financial leverage, and, in the final column, how fast the operating margin compounded across the three years to fiscal 2007. The underlying universe is the S&P 1500 Composite Index for US equities, which pools three constituent indexes: the S&P 500 at the large end, the S&P MidCap 400 in the middle and the S&P SmallCap 600 below it.

Source: Standard and Poor’s Research Insight. At this level of aggregation the data are arguably most relevant to relative sector valuation; for valuing individual companies, analysts would use a more narrowly defined industry or sector classification.

Read across a few rows and the internal logic of the whole lesson becomes visible. Financials show the lowest median price to book, at 1.559, alongside the highest financial leverage, at 5.848, and the lowest asset turnover, at 0.113. Health care carries the highest trailing price to earnings, at 23.027, and a dividend payout ratio of zero at the median. Utilities and financials carry the two highest dividend yields, both 3.1 percent, and utilities the highest payout ratio at 52.738 percent. None of these are anomalies to be arbitraged; they are the fundamentals of each sector showing through in the multiples, exactly as the justified expressions predict.

Relative valuation requires comparable companies and underlying financial data prepared by comparable methods. Both conditions become difficult in an international setting. A cross-border comparison drags in accounting methods that differ, cultures that differ and economies that differ, and out of all three come differences in risk and in the opportunities to grow. Price to earnings ratios for individual companies in the same industry but different countries have been found to vary widely, and the ratios of different national markets often differ substantially at any single point in time.

Accounting differences persist even after convergence

International accounting standards are converging, but significant differences remain and sometimes make comparison hard. Even complete harmonisation of principles would not remove the need to adjust accounting data, because even within one country accounting standards permit choices, such as first in, first out against average cost for inventory valuation, that produce different reported numbers for identical economics.

Analysts once had a valuable resource here. Before 2008 the US SEC required non-US companies whose securities traded in US markets to reconcile earnings from home-country accounting principles to US GAAP. That requirement not only helped with the reconciling company itself but also gave insight into the adjustments appropriate for other companies that did not have to file it. In December 2007 the SEC eliminated the reconciliation requirement for non-US companies using IFRS. Studies of the reconciliations filed by European Union companies carrying US listings found that for most of them the IFRS net income figure came in above the US GAAP figure while the IFRS equity figure came in below it. Both effects push the same way, so a majority of the sample showed a higher return on equity under IFRS.

Harris and Muller in 1999 classified common differences into these seven categories from companies filing reconciliations to US GAAP. Note that four of the seven categories push earnings and equity in opposite directions, which means an adjustment that flatters one multiple will often penalise another.

A later study by Henry, Lin and Yang in 2009 examined reconciliation data across 20 categories and found that the most frequent adjustments occurred in the pension category, including post-retirement benefits, while the largest in value occurred in the goodwill category. Removing the reconciliation requirement removed an important resource, but accounting research still indicates where differences between IFRS and US GAAP commonly arise, and the analyst must be aware of those differences and adjust wherever disclosures allow.

Which multiples suffer most

International accounting differences affect the comparability of every price multiple, but not equally. Ratios built on cash flow from operations and on free cash flow to equity are generally least affected, because cash movements are less shaped by accounting policy. Price to book, price to earnings and multiples built on concepts such as EBITDA, all of which start from accounting earnings or accounting balances, are generally the most affected. When a cross-border comparison has to be made and time is short, that ordering tells you which multiple to trust.

A momentum indicator takes price, or takes some fundamental such as earnings, and measures it against the history of that same series, or occasionally against what the series is expected to become. Certain growth investors screen on positive momentum in one sense or another, and the resulting strategies are sometimes labelled growth or momentum strategies. Where the indicator is built from price alone, as the relative-strength measure described below is, the label technical indicator is also applied. The BofA Merrill Lynch Institutional Factor Survey reported that indicators of this kind were in use across a large part of the institutional investor base. Three representative indicators are covered here: earnings surprise, standardized unexpected earnings and relative strength.

Earnings surprise

Unexpected earnings, also called earnings surprise, is the difference between reported earnings and expected earnings for the quarter.

A stock reporting quarterly earnings of 1.05 dollars against expected earnings of 1.00 dollars has a positive earnings surprise of 0.05 dollars. Data providers often report the percentage surprise, meaning the surprise divided by expected earnings per share, which here is 0.05 divided by 1.00, or 5 percent.

Before it is used as a valuation indicator in its own right, the surprise is normally rescaled by something that captures how far apart the analyst estimates were. The principle is that the less disagreement there is among forecasts, the more meaningful a forecast error of any given size becomes relative to the mean. Dividing unexpected earnings by the standard deviation of analyst forecasts gives the scaled earnings surprise.

Standardized unexpected earnings

Why look at earnings surprise at all? The claim behind it is that a positive surprise tends to be followed by abnormal returns that persist rather than reverse, which is to say by alpha. The same thesis lies behind a closely related but far more heavily researched indicator, standardized unexpected earnings.

The distinction from the scaled earnings surprise is precisely which standard deviation is used. In the scaled surprise the denominator is the dispersion of analyst forecasts today. In standardized unexpected earnings it is the dispersion of past forecast errors, for example over the 20 quarters before t, as in the article by Latané and Jones in 1979 that introduced the concept. The principle is that the smaller the historical size of forecast errors, the more meaningful an error of a given size becomes, and the larger the historical size, the less meaningful.

The arithmetic makes the point quickly. For a stock with a 0.05 dollar earnings surprise, if the standard deviation of past surprises is 0.20 dollars the score is 0.05 divided by 0.20, or 0.25, and the surprise is small against history. If the standard deviation of past surprises were 0.07 dollars the score would be 0.05 divided by 0.07, or 0.71, and the same surprise would be a substantial event.

Relative strength

A relative-strength indicator sets what a stock did over some interval against one of two yardsticks: what the same stock did previously, or what a chosen collection of stocks did over the same interval.

The simplest indicator of the first type is the compound rate of return of the stock over a specified horizon such as six months or one year, an indicator also known in the academic literature as price momentum. Despite its simplicity it has been used in numerous studies. The rationale is that patterns of persistence or reversal exist in stock returns and may be shown empirically to depend on the time horizon of the investor.

Variants of the first type set the recent return of a stock against its return across a longer window in which the recent one is nested. A classic study of technical momentum indicators by Brock, Lakonishok and LeBaron in 1992 examined trading strategies based on two technical rules, a moving-average oscillator and a trading-range break, meaning resistance and support levels, in which buy and sell signals depend on the relationship between a short-period moving average and a longer-period moving average and on bands around those averages. Two cautions attach to this whole literature. Studies that hunt for patterns in past stock returns are famously exposed to data snooping and to hindsight bias. And strategies built purely on technical momentum indicators are viewed as inherently self-destructing, on the argument that once a useful technical rule or price pattern is discovered, the mass of traders attempting to exploit it ought to invalidate it. The possibility of finding a profitable rule and exploiting it before it becomes crowded is what keeps the research going.

The simplest indicator of the second type divides the performance of the stock by the performance of an equity index. If the ratio rises, the stock is gaining on the index and displays positive relative strength. The indicator is usually scaled to 1.0 at the start of the study period, so that a value above 1.0 means the stock has grown at a higher rate than the index and a value below 1.0 means the opposite. Relative strength in this sense is often computed for industries as well as for individual stocks.

Momentum indicators have a substantial following among professional investors. Some regard them as signals that should prompt an analyst to ask whether a stock price is moving successively further from, or successively closer to, the fundamental valuations produced by models and multiples. Put another way, an analyst may be right about the intrinsic value of a business, and a momentum indicator may offer a clue about when the market price will converge on it. The use of such indicators remains an active research subject in industry and in business schools.

Every indicator described so far is a quantitative aid rather than a solution to the problem of security selection. This closing section covers three practical issues: how to average a group of multiples correctly, how multiple indicators are combined in practice, and the traps that lie in screening.

The harmonic mean

Averaging a set of price multiples is very often done with a harmonic mean, weighted or otherwise, and the reason is arithmetic rather than aesthetic. Consider a hypothetical portfolio holding 100 percent of the shares of two companies. One has a market capitalisation of 715 million euros and earnings of 71.5 million euros, a multiple of 10. The other has a market capitalisation of 585 million euros and earnings of 29.25 million euros, a multiple of 20. The portfolio multiple can be computed directly by aggregating the capitalisations and the earnings: 1,300 divided by 100.75, or 12.90. The question is which average of the two individual multiples reproduces that figure.

Using the median rather than the arithmetic mean also mitigates the effect of outliers. The harmonic mean is sometimes used for the same purpose, but the two behave differently at the two ends of the distribution. The harmonic mean tends to mitigate the impact of large outliers, which are typically what worries an analyst using an arithmetic mean multiple. It may aggravate the impact of small outliers, those close to zero, although such outliers are bounded below by zero.

Using several indicators together

Because each carefully selected multiple, momentum indicator or fundamental supplies one piece of the puzzle, many investors and analysts use more than one indicator in valuation and selection. Two short excerpts adapted from past equity analyst reports show how this reads in practice. In a report on Aussie Beverage Ltd., the analyst uses a discounted cash flow valuation as the preferred methodology but notes the stock is also attractive on other metrics: a discounted cash flow value of A dollars 0.82 per share representing a 44 percent premium to the current price; a mid-cycle earnings multiple of 10.5 times, a 30 percent discount to the market, applied to fiscal 2008 earnings per share of 7.6 cents to derive a valuation of A dollars 0.80; a note that were the stock to reach the target of A dollars 0.75 per share within twelve months it would trade on a forward multiple of 9.1 times, which the analyst does not view as demanding; and a fully franked dividend yield of 5.7 percent at current levels. In a report on Südliche Logistik, trading at 42.80, the analyst evaluates the price on two multiples against revised forecasts: on slightly increased estimates the shares are valued at a 2012 price to earnings ratio of 12.4 times and enterprise value to EBITDA of 9 times, slightly below the valuation of peer companies, and given stronger profit growth the company could command a premium, so the target price is raised from EUR 52 to EUR 53, implying 24 percent upside, with a buy recommendation.

How many indicators is normal? In the BofA Merrill Lynch Institutional Factor Surveys from 1989 to 2012, excluding 2008 to 2010 for lack of sufficient responses, institutional investors used an average of 9.3 factors in selecting stocks. The factors surveyed included price multiples, momentum indicators and the dividend discount model, but also return on equity, debt to equity, projected five-year earnings growth, earnings variability, earnings estimate dispersion, size, beta, foreign exposure, low price and analyst neglect. Of 137 responders in 2012, six factors were used by more than 50 percent: price to earnings, beta, enterprise value to EBITDA, return on equity, size and price to book. A large middle band, used by between 30 and 50 percent, included price to free cash flow, share repurchase, earnings estimate revision, margins, relative strength, earnings momentum, debt to equity, earnings variability, discounted models, the PEG ratio, long-term price trend, price to cash flow, analyst neglect, dividend growth, projected five-year earnings growth, mean reversion, normalized price to earnings and price to sales. Fewer than 30 percent used net debt to EBITDA, earnings surprise, return on capital, return on assets, earnings estimate dispersion, analyst rating revisions, foreign exposure, long-term price trend with short-term reversal, trading volume, price target, ownership, short-term price trend, enterprise value to sales, low price, the Altman Z-score and equity duration.

Look-ahead bias

Look-ahead bias is the use of information that was not contemporaneously available when a quantity is computed. It matters most in back testing, because time lags in the reporting of financial results create the opportunity for it. As of early January 2019 most companies had not yet reported earnings per share for the last quarter of 2018, so a trailing multiple computed at that moment would rest on the first three quarters of 2018 and the last quarter of 2017. Any strategy that used actual fourth-quarter 2018 earnings could only have been implemented later, once the data existed. An analysis assuming an investment made in early January 2019 on full-year 2018 data therefore contains look-ahead bias. The remedy is to build the trailing multiple from the most recent four quarters of earnings then being reported, and the same principle applies to every multiple computed on a trailing basis.

Screening

Screening means imposing a list of conditions on an investment universe so that only a much smaller set survives. Doing it by computer is an efficient way to narrow a search and it forms part of many stock selection disciplines. Screens usually combine criteria based on valuation measures with fundamental criteria that may explain differences in those measures. The limitations of commercial databases and screening tools generally include a lack of user control over the calculation of important inputs such as earnings per share, and the absence of qualitative factors from most databases.

Finally, every metric illustrated here for individual stocks applies equally to industries and economic sectors. Averaged multiples and momentum readings feed sector rotation work, where the aim is to spot which sectors look cheap and which look dear. A rotation strategy of that kind simply overweights the sectors expected to lead the wider market.