VALUATION: MARKET-BASED APPROACHES. Learning Objectives

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1 Chapter 13 VALUATION: MARKET-BASED APPROACHES Learning Objectives 1. Understand the practical advantages and disadvantages of using market multiples in valuation. 2. Apply a version of the residual income valuation model to estimate the value-to-book ratio (VB) as a theoretically correct valuation multiple. Understand how to compare the value-to-book ratio to the market-to-book ratio (MB). Also understand how to compare VB ratios and MB ratios to analyze values of firms over time and to compare values across firms. 3. Understand and estimate the firm s value-earnings ratio (VE) as a theoretically correct earnings-valuation multiple. Understand how to incorporate growth into the VE ratio to determine the value-earnings-growth ratio (VEG). Compare the VE and VEG ratios to the price-earnings ratio (PE) and the price-earningsgrowth ratio (PEG). Use VE and VEG ratios and PE and PEG ratios to evaluate firms over time and compare valuations across firms. 4. Understand the role of the following factors on market multiples: (a) risk and the cost of equity capital, (b) growth rates, (c) differences between current and expected future earnings, and (d) alternative accounting methods and principles. Use these factors to explain how VB, VE, and VEG ratios should differ across firms, and why MB, PE, and PEG ratios actually do differ across firms. 5. Estimate the price differential the difference between market price and risk-free value, which is computed using the residual income model and the risk-free discount rate. 912

2 Introduction and Overview 6. Reverse engineer the firm s stock price by using the residual income model to determine either the implicit expected return or the implicit expected long-run growth rate. 7. Understand the role of market efficiency in valuation, and the academic evidence on the degree to which the market efficiently impounds earnings information into share prices. INTRODUCTION AND OVERVIEW Chapters 1 to 12 have all focused on using the information in a firm s accounting numbers, financial statements, and related notes to analyze the firm s fundamental characteristics of profitability, risk, growth, and value. These prior chapters have established a coherent framework to attack a very difficult problem how to analyze and value a business. Using this framework to analyze and value a business, we must first understand the firm s industry and business strategy, and then we use that understanding to assess the quality of the firm s accounting, making adjustments as necessary. We then evaluate the firm s profitability, risk, growth, efficiency, liquidity, and leverage, using a set of financial ratios. On the foundation of these steps, we construct forecasts of future financial statements, from which we derive the expected future earnings, cash flows, and dividends that form the bases for valuation. We apply the free cash flows model, the residual income model, and the dividends model to value the firm, and we use these models to assess the sensitivity of firm value to key valuation parameters, such as costs of capital and expected growth rates. To culminate this process, we describe the realistic range of firm value estimates and compare this range of values to the firm s market share price for an intelligent investment decision. Exhibit 13.1 provides a summary representation of the fundamentals-driven valuation process. The bottom of the exhibit depicts the firm s value drivers, such as expected future earnings, cash flows, growth, and risk, which comprise the economic foundations of valuation. We capture these value drivers in forecasts of future pro forma financial statements, and then convert these forecasts into value estimates using valuation models, such as the residual income model, the free cash flows model, and the dividends model. In this chapter, we continue our focus on the firm s fundamental characteristics of profitability, risk, growth, and value, but now we augment that analytical approach with techniques that allow us to exploit the information in the firm s market value. We describe and apply a variety of techniques that compare the firm s market value (or share price) to firm fundamentals. The techniques we describe in this chapter include commonly used market multiples market-to-book ratios, price-earnings ratios, and price-earnings-growth ratios. Market multiples provide efficient shortcuts to the valuation process. As Exhibit 13.2 depicts, market multiples rest on the same foundation of value drivers in the valuation process as the valuation models discussed in Chapters 11 and 12 expected future earnings, cash flows, growth, and risk but market multiples collapse the valuation process in two important ways. 913

3 914 Chapter 13 Valuation: Market-based Approaches EXHIBIT 13.1 Fundamentals of Valuation Firm Value Estimate: Book Value of Common Equity plus Present Value of Expected Future Residual Income = Present Value of Expected Future Free Cash Flows to Common Equity Shareholders = Present Value of Expected Future Dividends Pro Forma Financial Statement Forecasts Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk (1) Instead of developing complete pro forma financial statement forecasts, multiples use just one or two summary accounting numbers to represent the value drivers. (2) Instead of using extensive present value model computations, market multiples summarize value using relatively simple ratios of market value of common equity to summary accounting numbers. EXHIBIT 13.2 Market Multiples Firm Value Market Multiples: Market-to-Book Ratios, Price-Earnings Ratios, Price-Earnings-Growth Ratios Summary Accounting Numbers: Earnings; Book Value of Common Shareholders Equity; Long-run Growth Fundamental Value Drivers over the Remaining Life of the Firm: Expected Future Earnings, Cash Flows, Growth, Risk

4 Market Multiples of Accounting Numbers In this chapter, we also introduce techniques to infer and exploit the information in share prices, including computing price differentials and reverse engineering share prices. In the last section of the chapter, we briefly summarize a few key insights from the last 40 years of accounting, finance, and economics research on how efficiently the market uses accounting earnings to price stocks. The research findings are very encouraging for those interested in using accounting numbers for fundamental analysis and valuation of stocks. MARKET MULTIPLES OF ACCOUNTING NUMBERS The market price for a share of common equity is a very special and important number: it reflects the aggregated expectations of all of the market participants following that particular stock. The market price reflects the result of the market s trading activity in that stock. It summarizes the aggregate information the market participants have about the firm, and the aggregate expectation for the firm s future profitability, growth, and risk. The market price of a share does not mean that all market participants agree that the price is the correct value for the share; indeed, the market price simply indicates the equilibrium point at which the forces of supply (participants potentially willing to sell the stock the ask side of trading) and the forces of demand (participants potentially willing to buy the stock the bid side of trading) are momentarily in balance. Stock prices are dynamic, constantly changing with the arrival of new information that changes investors expectations about share value and triggers trading in the firm s shares in the market. We can analyze share price for value-relevant information. Market participants commonly calibrate firm valuation using market value or share price expressed as a multiple of a fundamental summary accounting number, such as the market-to-book ratio or the price-earnings ratio. Thus, market multiples capture relative valuation per dollar of book value or per dollar of earnings. In this way, market multiples measure value relative to a key accounting number as a common denominator, thereby enabling analysts to draw inferences about a particular firm s relative market capitalization, to assess changes in relative valuation over time, to make comparisons of valuation across firms, and to make projections about comparable firms values. For example, price-earnings ratios allow an analyst to quickly gauge and compare the multiples at which the market is capitalizing different firms annual earnings. Market multiples can provide useful and efficient fundamental valuation ratios but they must be applied and interpreted carefully, after considering the firm s expected future profitability, growth, and risk. Multiples like market-to-book ratios and priceearnings ratios are relative value metrics and therefore are not meaningful by themselves. For example, whether a particular firm s price-earnings ratio should be 10, 20, 30, or some other number cannot be determined unless the analyst knows the firm s fundamental characteristics expected future profitability, growth, and risk. Analysts sometimes apply market multiples to estimate value in ad hoc ways. Valuation using market multiples may be efficient (the so-called quick and dirty approach) but may also be misleading. An analyst might be tempted to value a firm using that firm s historical average or the industry average market multiple. The 915

5 916 Chapter 13 Valuation: Market-based Approaches firm s historical average market-to-book ratio, for example, may be an appropriate fit for the firm today, but only if the firm s fundamental characteristics today match those of the firm s past. In the same vein, an industry average price-earnings multiple may be an appropriate yardstick for valuing a particular firm, but only if that firm matches the industry average fundamental characteristics. If the firm is different today than it was in the past, or if the firm does not match the industry average, then market multiples must be adjusted to reflect the firm s fundamental characteristics. This chapter continues to emphasize the distinction between value and price.the chapter focuses attention on how to compute value-based multiples that reflect the firm s fundamentals and that can be compared to market price-based multiples. This focus also directs our attention to the factors that drive multiples, so that the analyst can avoid being ad hoc and can correctly adjust historical or industry average multiples to reflect appropriately the firm s expected profitability, growth, and risk. MARKET-TO-BOOK AND VALUE-TO-BOOK RATIOS 1 The market-to-book ratio (MB) can be computed by dividing the firm s market value of common equity at a point in time by the book value of common shareholders equity from the firm s most recent balance sheet. For example, at the end of Year 11, PepsiCo s market value was $86,131.8 million (= $49.05 per share 1,756 million shares), and PepsiCo s Year 11 book value of common shareholders equity was $8,648.0 million (Appendix A). Thus, PepsiCo was trading at an MB ratio equal to 9.96 (=$86,131.8 million/$8,648.0 million). The MB ratio measures market value as a multiple of accounting book value at a point in time. The MB ratio reflects market value but it does not tell us what the ratio should be,given our estimate of value. A THEORETICAL MODEL OF THE VALUE-TO-BOOK RATIO To compute a ratio that reflects our expectation of the firm s intrinsic value to book value, we need to compute the value-to-book ratio (VB) the value of common shareholders equity divided by the book value of common shareholders equity. The VB ratio can be derived directly from the residual income model developed in Chapter 12. In fact, the VB ratio model is simply a version of the residual income model that is scaled by book value of common shareholders equity. The numerator of the VB ratio is the estimated value of common equity, which takes into account the book value of common shareholders equity, expected future profitability, growth, risk, and the time 1 As we noted in Chapter 12, credit for the rigorous development of the residual income model, and its extension to the value-to-book ratio model, goes to James Ohlson in: J. A. Ohlson, A Synthesis of Security Valuation Theory and the Role of Dividends, Cash Flows, and Earnings, Contemporary Accounting Research (Spring 1990), pp ; J. A. Ohlson, Earnings, Book Values, and Dividends in Equity Valuation, Contemporary Accounting Research (Spring 1995), pp ; G. A. Feltham and J. A. Ohlson, Valuation and Clean Surplus Accounting for Operating and Financial Activities, Contemporary Accounting Research (Spring 1995), pp The ideas underlying the value-to-book ratio also trace to early work by G.A.D. Preinreich, Annual Survey of Economic Theory: The Theory of Depreciation, Econometrica (1938), pp and E. Edwards and P. W. Bell, The Theory and Measurement of Business Income (Berkeley, CA: University of California Press), 1961.

6 value of money. The VB ratio can be compared to the market-to-book ratio to identify whether the stock is correctly priced in the market. The VB ratio of one firm can also be used to estimate the value of a different but comparable firm, provided the analyst makes the appropriate and necessary adjustments to the VB ratio so that it matches the comparable firm s fundamental characteristics. This section explores the theoretical and empirical relation between estimated value, book value, and market value. Using the same notation from prior chapters, we can compute the VB ratio with the following model: V BV In short, the VB ratio should be equal to one, plus the present value of expected future abnormal return on common equity (the [ROCE t R E ] term above) times cumulative growth in book value (the BV t 1 /BV 0 term above). The growth in book value indicates the increase in net assets on which firms can earn abnormal earnings. The growth in book value depends on ROCE, dividend policy, and changes in common stock. To show how we derive this model, recall from Chapter 12 the following expression for the residual income valuation model: V 0 0 BVt ROCE R t E BV = 1+ [ ] t ( 1+ R ) = BV t= 1 Market-to-Book and Value-to-Book Ratios NI ( R BV ) t E t 1 t ( 1+ R ) t= 1 E Under the residual income valuation model, the value of common shareholders equity is equal to the book value of common equity plus the present value of all expected future residual income,which is the amount by which expected future earnings exceed required earnings, for the remaining life of the firm. 2 We compute the required earnings (or normal earnings) of the firm in year t as the product of the required rate of return on common equity capital times the book value of common equity at the beginning of year t (R E BV t 1 ). Required earnings captures the amount of net income the firm must generate in order to provide a return to common equity capital that is equal to the cost of common equity capital. We measure residual income (or abnormal earnings) by the subtraction term, NI t (R E BV t 1 ). Residual income is the difference between expected net income and required earnings of the firm in year t. Residual income measures the amount of wealth that the analyst expects the firm to create (or destroy) in year t for common equity shareholders above (or below) the cost of equity capital. 2 Chapter 12 describes that the residual income valuation model depends on clean surplus accounting for book value of common shareholders equity, which requires that expected future earnings forecasts are comprehensive measures of income for the firm s common equity shareholders, and that expected future dividends reflect all capital transactions between the firm and common equity shareholders. Throughout this chapter, when we refer to expected future earnings or net income in the context of residual income valuation, we mean expected future comprehensive income available for common shareholders. E

7 918 Chapter 13 Valuation: Market-based Approaches To convert the residual income model into a model for the VB ratio, we scale both sides of the equation by BV 0,which produces the following equation: We rewrite BV 0 divided by BV 0 as equal to one. We rewrite the NI t /BV 0 term as follows: To rewrite NI t /BV 0 this way, we state ROCE t = NI t /BV t 1.Note that this computation of ROCE t divides net income in period t by book value of common equity at the beginning of period t. This ROCE computation differs slightly from the approach in Chapter 4 in which we compute ROCE as net income divided by the average book value of equity during period t. 3 Also, note that BV t 1 /BV 0 is the cumulative growth factor in book value of common equity between year 0 (the date of the valuation) and period t 1. As indicated above, growth in book value is a function of the earnings generated each period plus additional capital contributions by shareholders, less equity capital paid out to shareholders through dividends and stock buybacks. The growth in book value indicates growth in net assets invested, on which a firm can earn abnormal returns. By decomposing the term NI t /BV 0 into these two parts, we can restate NI t /BV 0 as the product of ROCE in year t times the cumulative growth in book value from year 0 to the start of year t. Return on common equity is a function of profitability on beginning of year common equity; beginning of year common equity is a function of cumulative growth. We can substitute these two components of NI t /BV 0 into the VB equation, as follows: V0 BV 0 V0 BV NI t BV 0 NI BV t t R E BV BV BV 0 0 = + t BV ( + R ) NI BV BV t t 1 t = = ROCE t BV BV BV 0 t 1 BV BV t 1 t ROCE R t E BV BV 0 = 1+ t ( 1+ R ) t= t= 1 Now both terms in the numerator of the summation term are multiplied by the same cumulative book value growth factor. We rearrange that equation as follows: 0 3 Theoretical and empirical research on the VB ratio typically defines ROCE as net income to common shareholders for a year divided by common shareholders equity at the beginning of the year. In contrast, we have used average common shareholders equity in the denominator of ROCE throughout this book. The theoretical development and application of the VB model in this section uses shareholders equity at the beginning of the year, although the bias in using average shareholders equity should not be particularly significant. E E

8 V 0 BV 0 BVt ROCE R t E BV = 1+ [ ] t ( 1+ R ) t= 1 Market-to-Book and Value-to-Book Ratios We now have a useful model for the value-to-book ratio. Next we consider each term. First, as a starting point, the VB ratio will equal one, to reflect the book value of common equity invested in the firm. The summation term indicates how the VB ratio should differ from one as a function of the firm s expected future abnormal profitability (the ROCE t R E term) times the firm s cumulative growth in book value (the BV t 1 /BV 0 term), all of which is discounted to present value, reflecting the firm s cost of equity capital (R E ) and the time value of money. Thus, the residual income model specifies the firm s VB ratio as a function of the firm s value drivers: capital in place, profitability, cost of equity capital, growth, and time value of money. The VB model provides a valuation approach in which all of the inputs to valuation can be expressed as forecasts of rates expected future ROCE, R E, and growth. The only dollar amount the analyst needs in order to use the VB ratio to compute the dollar value of common shareholders equity is the book value of common shareholders equity, which is observable from the shareholders equity section of the balance sheet. The expression for the VB ratio provides some insights into valuation: Economics teaches that, in equilibrium, firms will earn a return equal to the cost of capital (that is, ROCE = R E ). The VB model indicates that a firm in steadystate equilibrium earning ROCE = R E will maintain (not create or destroy) shareholder wealth and will be valued at book value (that is, VB = 1). A firm s value should be greater than its book value of common equity insofar as the firm will generate wealth for common equity shareholders by earning a return (ROCE) that exceeds the cost of capital (R E ). That is, VB > 1 if ROCE > R E. Firms that earn a return that is less than the cost of equity capital (that is, ROCE < R E ) will destroy shareholder wealth and will be valued below book value (that is, VB < 1). Growth is not value-adding in itself. Growth adds value to shareholders only if the growth is abnormally profitable. If expected ROCE equals R E on new projects (that is, zero NPV projects), then these new projects will not create (or destroy) common shareholders equity value. New projects will be abnormally profitable only when their expected ROCE exceeds R E. The risk of the firm increases the equity cost of capital. Increasing the equity cost of capital reduces firm value in two ways: (1) by increasing the required ROCE the firm must earn to cover the increased cost of capital R E (that is, the hurdle rate goes up); and (2) by increasing the discount rate used to compute the present value of residual income. Ifa firm s VB ratio differs from the industry average VB ratio, it should be because the firm s expected future ROCE, R E,or book value growth differ from the industry averages. If a firm s VB ratio changes over time, it should be because current expectations for the firm s future ROCE, R E,or book value growth differ from the past expectations for the firm s future ROCE, R E,or book value growth. E

9 920 Chapter 13 Valuation: Market-based Approaches Example 1. Suppose an analyst is evaluating a firm with $1,000 of book value of common equity and a cost of equity capital equal to 10 percent. Assume that the analyst forecasts that the firm will earn ROCE of 15 percent until Year +3, but then after Year +3 the firm will earn ROCE equal to 10 percent. The analyst also expects the firm will reinvest all net income (that is, pay zero dividends), and it will not issue or buy back stock. Using the VB ratio approach, the analyst should assign the firm a VB ratio equal to one plus the present value of future residual ROCE times growth. The present value of future residual ROCE times growth is determined as follows: PV of Residual Residual Cumulative ROCE ROCE Residual Book Value times times Expected ROCE Growth Factor Cumulative Cumulative Year ROCE = ROCE R E to Year t 1 Growth PV Factor Growth = (1.15) = (1.15) = (1.15) = (1.15) The sum of the present values of residual ROCE times cumulative growth through Year +3 equals , and the sum in all years after Year +3 is zero. The VB ratio of this firm is therefore We can multiply the VB ratio by book value of equity to determine that firm value is $1, (= VB ratio $1,000 book value equity). Note that we have determined this VB ratio with all of the inputs expressed in rates. We can confirm this value using dollar amounts and the residual income model approach from Chapter 12, as follows: Cumulative Book Value at the end Required PV of Expected Expected of Year t 1 Income Residual PV Residual Year ROCE Earnings (BV t 1 ) = BV t 1 R E Income Factor Income $ $100 $ = ,000 $1,000 = 1, = $45.45 $ $1,150 $115 $ = ,150 = 1, = 1, = $47.52 $ $1,322.5 $ $ = ,322.5 = 1, = 1, = $49.68 $ $1, $ $ = , = 1, = 1, = $ 0.00 The sum of the present values of residual income through Year +3 equals $142.65, the sum in all years after Year +3 is zero, and book value of equity is $1,000, so the residual income model confirms that firm value is $1,

10 Market-to-Book and Value-to-Book Ratios REASONS WHY VB RATIOS AND MB RATIOS MAY DIFFER FROM ONE We described above a number of economic reasons why VB and MB ratios may differ from one. For example, the firm may have competitive advantages that enable it to earn an ROCE that is greater than R E.To the extent that the firm can create and sustain these competitive advantages, the firm will increase the magnitude and persistence over time of the degree to which ROCE exceeds R E, thereby increasing the VB and MB ratios. In addition, to the extent the firm will generate future growth by investing in abnormally profitable projects, the VB and MB ratios will differ from one. A firm s VB and MB ratio may differ from one for accounting reasons in addition to economic reasons. 4 The firm may have investments in projects for which accounting methods and principles cause ROCE to differ from R E.For example, firms may make substantial investments in successful research and development projects, brand equity, or human capital. If these investments were internally generated through research and development activities, marketing and advertising activities, or human capital recruiting and training activities, and if the investments in these activities were expensed according to conservative accounting principles (as is common under GAAP in the United States and most countries), then the firm will have substantial off-balance sheet assets and off-balance sheet common shareholders equity. These off-balance sheet assets generate net income, but common shareholders equity is understated, so ROCE will be relatively high. These effects can be observed among certain firms in many different industries, such as pharmaceuticals, biotechnology, software, and consumer goods. In the case of PepsiCo and Coca-Cola, for example, these firms have created substantial off-balance sheet brand equity over many years of successful product development, advertising, and brand-building activities, and the investments in these activities have been expensed. Thus, for these firms, the book value of common shareholders equity does not recognize the off-balance sheet value of brand equity. Relative to R E,ROCE for PepsiCo and Coca-Cola is very high and likely will continue to be very high for many years in the future. Over a sufficiently long period of time, however, the impact of accounting principles on the VB and MB ratio will diminish because economics teaches us to expect that competitive equilibrium forces will drive ROCE to converge to R E in the long run. Also, the self-correcting nature of accounting will eventually eliminate biases in ROCE and book value of equity. For example, consider a biotechnology company that invests for several years in research and development to develop a particular drug. During the initial years of research, the firm incurs research costs that GAAP 4 Stephen Ryan found that book value changes lag market value changes in part because of GAAP s use of historical cost valuations for assets. The lag varies in part based on the degree of capital intensity of firms. See Stephen Ryan, A Model of Accrual Measurement and Implications for the Evolution of the Book-to- Market Ratio, Journal of Accounting Research (Spring 1995), pp

11 922 Chapter 13 Valuation: Market-based Approaches requires the firm to expense. Its ROCE and book value of equity will be low during these years. After developing and then marketing the final drug, ROCE will be high because the firm generates revenues without offsetting research costs. The high ROCE will increase retained earnings, and, over time, the initial conservative biases in ROCE and book value will be corrected. EMPIRICAL DATA ON MB RATIOS Exhibit 13.3 presents descriptive statistics for MB ratios across 36 industries during the decade from 1991 to The descriptive statistics include the 25th percentile, median, and 75th percentile MB ratios for the sample as a whole and for each industry, listed in ascending order of the median MB ratio. The median MB ratio for the 64,297 firm-years in this sample is These data reveal substantial variation in MB ratios across industries and within industries during this period. The differences in industry median MB ratios in Exhibit 13.3 likely relate in part to differences in competitive conditions driving differences in growth and ROCE relative to R E, as well as differences in alternative accounting principles. Economically, in an industry that can be characterized as mature and competitive, the median firm will likely generate ROCE that is close to R E and will not likely generate unusually high rates of growth. Such firms tend to have median MB ratios closer to one. For example, firms in mature competitive industries such as textiles, real estate, insurance, banking, metals, and metal products tend to have MB ratios that are lower than the sample average. With respect to accounting, the assets of firms in some of these industries particularly banks and insurers are primarily investments in financial assets, some of which appear on the balance sheet at fair value, and thus MB ratios are closer to one. In contrast, some of the industries with relatively high MB ratios are more likely to have off-balance sheet assets and shareholders equity. For example, the chemical industry includes pharmaceutical firms, which expense research and development expenditures in the year incurred. The health services, personal services, and business services industries expense compensation costs in the year incurred and do not capitalize the value of their employees on the balance sheet. The balance sheet understates the economic value of key resources in each of these industries. These industries have MB ratios considerably in excess of one. EMPIRICAL RESEARCH RESULTS ON THE PREDICTIVE POWER OF MB RATIOS Several empirical studies have found that MB ratios are fairly stable, mean reverting slowly over time, and that MB ratios are reliable predictors of future growth in book value and expected future ROCE (implying that ROCE also mean reverts 5 To compute these descriptive statistics on market-to-book value ratios, we deleted firm-years with negative book value of equity. We also deleted firm-year observations in the top 1 percent of the distribution as potential outliers with undue influence on the descriptive statistics.

12 Market-to-Book and Value-to-Book Ratios EXHIBIT 13.3 Descriptive Statistics on Market-to-Book Ratios, th Percentile Median 75th Percentile Full Sample* on Compustat (N = 64,297 firm-years) Industry: Textiles Real Estate Insurance Depository Institutions Metals Metal Products Hotels Retailers General Merchandise Wholesale Durables Lumber Utilities Paper Motion Pictures Security Brokers Metal Mining Oil and Gas Extraction Grocery Stores Restaurants Transportation by Air Petroleum and Coal Wholesale Nondurables Transportation Equipment Amusements Retailing Apparel Forestry Industrial Machinery and Equipment Food Processors Electronic and Electric Equipment Health Services Personal Services Instruments and Related Products Printing and Publishing Communication Business Services Chemicals Tobacco *To compute these descriptive statistics on market-to-book value ratios, we deleted firm-years with negative book value of equity.we also deleted firmyear observations in the top 1 percent of the distribution as potential outliers with undue influence on the descriptive statistics. 923

13 924 Chapter 13 Valuation: Market-based Approaches slowly). 6 For example, Victor Bernard grouped roughly 1,900 firms into 10 portfolios each year between 1972 and 1981 based on their MB ratios. He then computed the mean ROCE for each portfolio in the formation year and for each of the ten subsequent years. Exhibit 13.4 summarizes a portion of Bernard s results, grouping firms in the lowest 3 MB portfolios, middle 4 MB portfolios, and highest 3 MB portfolios. 7 The data in Exhibit 13.4 indicate that firms with the highest MB ratios tend to have the highest ROCEs through Year +10, and firms with the lowest MB ratios tend to have the lowest ROCEs through Year +10. The results from the Bernard study also indicate that firms with the highest MB ratios have the highest growth rates in book value of equity through Year +10, and firms with the lowest MB ratios have the lowest growth rates through Year +10. The results in the Bernard study also indicate (although it is not apparent from the summary of results in Exhibit 13.4) that the predictive power of MB ratios for future ROCEs does tend to diminish as the horizon lengthens. In Year +10, for example, there is relatively little difference in ROCEs across firms in the 3rd through 9th MB portfolios, as these firms experience ROCEs that tend to converge to 14 percent. These results are consistent with the steady mean EXHIBIT 13.4 The Relation between MB Ratios and Future ROCE and Future Book Value Growth Median ROCE for Year: MB Portfolio Mean MB Ratio Low Medium High Cumulative Percent Increase in Book Value through Year: Low % 15% 54% 190% Medium % 15% 69% 204% High % 21% 139% 394% 6 Victor L. Bernard, Accounting-Based Valuation Methods, Determinants of Market-to-Book Ratios and Implications for Financial Statement Analysis, Working Paper,University of Michigan, 1993; Jane A. Ou and Stephen H. Penman, Financial Statement Analysis and the Evaluation of Market-to-Book Ratios, Working Paper, Columbia University, 1995; Stephen H. Penman, The Articulation of Price-Earnings Ratios and Market-to-Book Ratios and the Evaluation of Growth, Journal of Accounting Research,Vol. 34, No.2 Autumn 1996, pp ; William H. Beaver and Stephen G. Ryan, Biases and Lags in Book Value and Their Effects on the Ability of the Book-to-Market Ratio to Predict Book Return on Equity, Journal of Accounting Research,Vol. 38, No. 1 (Spring 2000), pp To reduce the effects of survivorship bias, Bernard included firms that did not survive the entire 10-year future horizon, and included any gain or loss on the cessation of the firm (from bankruptcy, takeover, or liquidation) in the final year ROCE.

14 Application of the Value-to-Book Model to PepsiCo reversion in ROCEs over time, consistent with movement toward competitive equilibrium. APPLICATION OF THE VALUE-TO-BOOK MODEL TO PEPSICO In Chapter 12, we estimated PepsiCo s share value at the end of Year 11 to be roughly $69, based on the pro forma financial statement forecasts developed in Chapter 10 and the residual income model valuation. We next illustrate the valuation of PepsiCo shares using the value-to-book model, implementing the same forecasts developed in Chapter 10, the same equity cost of capital (8.0 percent), and the same long-run growth rate (5.0 percent). We also demonstrate the forecasts and valuation estimates in the FSAP Forecasts and Valuation spreadsheets in Appendix D. To proceed with the VB model, we will follow seven steps: (1) estimate the expected ROCE each period, computed as NI t /BV t 1 ; (2) compute expected residual ROCE each period by subtracting the equity cost of capital from expected ROCE; (3) determine the cumulative growth factor in book value of common shareholders equity to the beginning of each period (computed as BV t 1 /BV 0 ); (4) multiply the expected residual ROCE by the cumulative growth factor; (5) discount the expected residual ROCE with growth to present value, including continuing value; (6) compute the implied VB ratio by adding one (the ratio of book value over book value) to the sum of the present value of the expected residual ROCE with growth; (7) compare the implied VB ratio to the MB ratio to determine whether market price is greater than, equal to, or less than our estimate of value. Equivalently, we can multiply the implied VB ratio by book value of equity to determine the value of common shareholders equity, and then divide by the number of shares outstanding to convert this total to a per-share estimate of value for PepsiCo, which we then compare to market price. We next illustrate each of these seven steps with PepsiCo. The Year +1 projected ROCE is 38.9 percent, computed as net income available for common shareholders in Year +1 divided by book value of common equity at the start of Year +1 (= $3,367.3 million/$8,648.0 million). The residual ROCE is 30.9 percent after subtracting 8.0 percent for the cost of equity capital. The cumulative growth in book value (BV t 1 /BV 0 ) in Year +1 is 1.0, because Year +1 is the first year of the valuation horizon. 8 The product of Year +1 residual ROCE and cumulative growth is 30.9 percent, which we discount to present value using an 8.0 percent cost of equity capital. Exhibit 13.5 presents these 8 We project PepsiCo s book value of common equity will grow to $9,466.2 million during Year +1. Therefore the cumulative growth factor in book value of common equity as of the start of Year +2 will be (= $9,466.2 million/$8,648.0 million). 925

15 926 Chapter 13 Valuation: Market-based Approaches EXHIBIT 13.5 Valuation of PepsiCo: Present Value of Residual ROCE in Year +1 through Year +10 Year +1 Year +2 Year +3 COMPREHENSIVE INCOME AVAILABLE FOR COMMON SHAREHOLDERS $3,367.3 $3,656.4 $ 3,975.8 Common Shareholders Equity (at beginning of year) $8,648.0 $9,466.2 $10,364.7 Implied ROCE (Comp Inc./Begin. Common Equity) Residual ROCE (assuming R E = 0.08) Cumulative Book Value Growth Factor as of the Beginning of Year Residual ROCE times Cumulative Book Value Growth Factor Present Value Factors PV Residual ROCE times Growth Sum of PV Residual ROCE in Year +1 through Year computations for PepsiCo for Year +1 through Year +10. The sum of the present value of residual ROCE times growth in Year +1 through Year +10 is We use the same steps to compute the Year +11 residual ROCE for purposes of computing continuing value. As described in the previous chapter, we project net income in Year +11 to grow by the 5.0 percent long-run growth rate. We compute book value as of the start of Year +11 (the end of Year +10), compute implied residual ROCE, and multiply by the cumulative growth factor in book value up to the beginning of Year +11. The projected ROCE 11 is 36.3 percent (= NI 11 /BV 10 = $6,920.0 million/$19,073.7 million). The projected residual ROCE 11 is therefore 28.3 percent. Cumulative growth in book value from Year 0 to the beginning of Year +11 (the end of Year +10) is (= BV 10 /BV 0 = $19,073.7 million/$8,648.0 million). We therefore project in Year +11 the product of residual ROCE times cumulative growth is 62.4 percent (= 28.3 percent 2.206). We use the Year +11 residual ROCE with growth (62.4 percent) in the continuing value computation, as follows (allowing for rounding): 10 ContinuingValue = [( NI ( 1+ g )/ BV ) R ] [ BV / BV ] [ 1/ ( R g )] [ 1/ ( 1+ R ) ] E 10 0 E E = + 10 [($ 6, / $ 19, ) 0. 08] [$ 19, / $ 8, ] [ 1/ ( )] [ 1/ ( ) ] = = This value should be interpreted as a component of the VB ratio, because all of the computations in the model are scaled by BV 0.Thus, the amount can be interpreted as an estimate that PepsiCo will create residual income in Years +1 through +10 that, in present value, is equal to times the current book value of common equity. To reconcile this computation with the residual income model computations in Chapter 12, recognize that times book value of $8,648.0 million equals $24,613.0 (allow for rounding), which is the present value of residual income through Year +10 computed in Exhibit 12.2.

16 Application of the Value-to-Book Model to PepsiCo EXHIBIT 13.5 Exhibit 13.5 continued Year +4 Year +5 Year +6 Year +7 Year +8 Year +9 Year +10 $ 4,312.3 $ 4,649.6 $ 4,991.0 $ 5,350.0 $ 5,734.9 $ 6,147.5 $ 6,590.4 $11,572.9 $12,149.2 $13,380.8 $14,366.6 $15,423.7 $16,556.8 $17, The total present value of PepsiCo s expected residual ROCE with growth, expressed as components of the VB ratio, is the sum of these two parts: Present Value of Residual ROCE in Year +1 through Year Present Value of Continuing Value of ROCE in Year +11 and beyond Present Value of Residual ROCE Necessary Adjustments to Compute the Value-to-Book Ratio To compute the VB ratio for common equity, we need to add PepsiCo s beginning book value of common equity expressed as a ratio of beginning book value of equity, which is, of course, equal to one. As described in Chapters 11 and 12, our present value calculations overdiscount because they discount each year s residual ROCE for full periods when, in fact, the firm generates residual ROCE throughout each period and we should discount from the midpoint of each year to the present. Therefore, to make the correction, we multiply the present value sum by the mid-year adjustment factor [1 + (R E /2) = 1 + (0.080/2) = 1.040]. Making these two adjustments produces the implied VB ratio as follows: Present Value of Residual ROCE Add: Beginning Book Value Total Multiply by the Mid-Year Correction Factor Implied VB Ratio

17 928 Chapter 13 Valuation: Market-based Approaches These computations suggest that PepsiCo common equity should be valued at times the book value of equity at the start of the valuation horizon, which is the end of Year 11. At that time, PepsiCo s market value was $86,131.8 million (= $49.05 per share 1,756 million shares). Thus, PepsiCo was trading at an MB ratio equal to 9.96 (= $86,131.8 million/$8,648.0 million). The VB ratio is 41 percent greater than the MB ratio, implying PepsiCo shares were underpriced by 41 percent at that time. Equivalently, we can convert the VB ratio into a share value estimate for purposes of comparing to price. If we multiply book value equity by the VB ratio, we obtain the value estimate of PepsiCo common equity of $121,205.9 million (= $8,648.0 million VB ratio; allow for rounding). Dividing by 1,756 million shares outstanding indicates that PepsiCo s common equity shares have a value of $69.02 per share, a value estimate that is identical to the value estimates we obtained from the residual income and dividend models in Chapter 12 and the free cash flows to common equity shareholders model in Chapter 11. The computations to arrive at PepsiCo s common equity share value are summarized in Exhibit We can conduct a sensitivity analysis for the estimate of PepsiCo s VB ratio to assess a reasonable range of VB ratios for PepsiCo. We will find that the sensitivity of the VB ratio estimate is identical to the sensitivity of the residual income model value estimates demonstrated in Chapter 12. This is to be expected because both models use the same forecasts and valuation assumptions. The VB model is simply a scaled version of the residual income model. EXHIBIT 13.6 Valuation of PepsiCo using the Residual ROCE Valuation Model Valuation Steps Computations Amounts Sum of PV Residual ROCE in Year +1 See Exhibit through Year +10 Add Continuing Value in Present Value Year +11 residual ROCE assumed to grow at 5.0%; discounted at 8.0%. Computations in FSAP. Total PV Residual ROCE = Add: Beginning Book Value of Equity Ratio Beginning Book Value of Equity from Year 11 Balance Sheet. = Adjust to Midyear Multiply by 1 + (R E /2) Value-to-Book Ratio of Common Equity = Book Value of Common Equity $ 8,648.0 Value of Common Equity =$121,205.9 Shares Outstanding 1,756.0 Estimated Value per Share =$ Current Price per Share $ Percent Difference (Positive number indicates 41% underpricing.)

18 Price-Earnings and Value-Earnings Ratios PRICE-EARNINGS AND VALUE-EARNINGS RATIOS As we noted in Chapter 12, the capital markets devote enormous amounts of time and energy to forecasting and analyzing firms earnings numbers. It is, therefore, no surprise that the market multiple that receives most frequent use and attention is the price-earnings (PE) ratio. Analysts reports and the financial press make frequent references to PE ratios. The Wall Street Journal reports PE ratios as part of the daily coverage of stock prices and trading. The capital markets increasingly evaluate ratios that integrate the PE ratio with expected future earnings growth, to capture explicitly the links between price, earnings, and growth. This section first describes the theoretical model for computing value-earnings ratios. The section then describes computing and using PE ratios from a practical perspective because of the widespread use of PE ratios in practice. We then discuss the strict assumptions implied by PE ratios, and describe the conditions in which PE ratios may not capture appropriately the theoretical relation between value and earnings for most firms and the difficulties one encounters in reconciling actual PE ratios with those indicated by the theoretical value-earnings model. In this section, we also incorporate the role of earnings growth and examine price-earnings-growth (PEG) ratios. We conclude the section by describing empirical data on PE ratios, the predictive power of PE ratios, and the empirical evidence on the articulation between PE ratios and MB ratios. A THEORETICAL MODEL FOR THE VALUE-EARNINGS RATIO The VE ratio is the ratio of the value of common shareholders equity divided by earnings for a single period. The previous chapter described how to determine common equity value as a function of present value of expected future earnings and the residual income model. In the residual income model, we use clean surplus accounting and measure future earnings as expected future comprehensive income (that is, income that includes all of the income to common shareholders). Thus, in theory, the analyst should measure the VE ratio as the value of common equity divided by next period s expected comprehensive income. This way, the VE ratio achieves consistent alignment of perspective (numerator and denominator both forward-looking) and measurement (numerator and denominator both based on income measurement that is comprehensive). If one has already computed firm value using the forecasting and valuation models developed in the last three chapters, then computing the VE ratio is a simple matter of division. For example, in prior chapters we estimated PepsiCo s common shareholders equity value to be $121,205.9 million at the end of Year 11. We also projected Year +1 comprehensive income will equal net income available for common shareholders, which will equal $3,367.3 million. Thus, we can compute the VE ratio for PepsiCo at the end of Year 11 as: V 0 /E 1 = $121,205.9 million/$3,367.3 million =

19 930 Chapter 13 Valuation: Market-based Approaches Or equivalently, on a per-share basis as: PRICE-EARNINGS RATIOS Vps 0 /Eps 1 = ($121,205.9 million/1,756 million shares)/($3,367.3 million/ 1,756 million shares) = $69.02/$1.92 = 36.0 We can also derive the VE ratio from the VB ratio determined using the residual income model in the previous section. We can employ an algebraic step to derive the firm s VE ratio from the firm s VB ratio, as follows: V 0 /E 1 = V 0 /BV 0 BV 0 /E 1 = V 0 /BV 0 (1/ROCE 1 ) Using this approach, we can derive PepsiCo s VE ratio from the VB ratio we computed in the previous section, as follows: V 0 /E 1 = V 0 /BV 0 BV 0 /E 1 = V 0 /BV 0 (1/ROCE 1 ) = ($121,205.9 million/$8,648.0 million) ($8,648.0 million/$3,367.3 million) = = (1/0.389) = 36.0 Thus, we compute that PepsiCo s VE ratio should equal We convert PepsiCo s VB ratio of into the VE ratio by multiplying by 1/ROCE 1,which we project will be the inverse of 38.9 percent. Notice that we simply derived the VE ratio from the computation that PepsiCo s value is equal to $121,205.9 million, which is based on specific forecasts of PepsiCo s future earnings. Obviously, using value to compute a VE ratio will not provide any new information about PepsiCo s value. So what is the point of computing a VE ratio? The VE ratio provides the theoretically correct benchmark to evaluate the firm s PE ratio. We can compare PepsiCo s VE ratio of 36.0 to PepsiCo s PE ratio to assess the market value of PepsiCo shares. This comparison is equivalent to comparing V to P (that is, value to price). With the theoretically correct VE ratio, we can also project VE ratios for other firms, including making adjustments as necessary to capture the other firms fundamental characteristics of profitability, growth, and risk. In addition, with the theoretically correct VE ratio, we have a benchmark to gauge other firms PE ratios in order to assess whether the market is under- or overpricing their shares. In the next section, we discuss the practical advantages and disadvantages in using PE ratios as shortcut valuation metrics. As a practical matter, analysts, the financial press, and financial databases commonly measure PE ratios as current period share price divided by reported earnings per share for either the most recent prior fiscal year or the most recent four quarters

20 Price-Earnings and Value-Earnings Ratios (sometimes referred to as the trailing-twelve-months earnings). 10 The Wall Street Journal and financial data web sites such as Yahoo! Finance commonly compute PE ratios this way. With this approach, we compute the PE ratio for PepsiCo as of the end of Year 11 as follows: Price per share 11 /Earnings per share 11 = $49.05/$1.51 = Thus, at the end of Year 11, PepsiCo shares traded at a multiple of 32.5 times Year 11 earnings per share. 11 The common approach to compute the PE ratio by dividing market price by earnings per share for the most recent year is practical because analysts can readily observe price per share and historical earnings per share for most firms. However, this common approach creates a logical misalignment for valuation purposes because it divides share price which reflects the present value of future earnings by historical earnings. If historical earnings contain unusual or nonrecurring gains or losses that are not expected to persist in future earnings, then the analyst should cleanse the reported historical earnings of these effects in order to compute a PE ratio that reflects earnings that are likely to persist in the future. Chapter 6 describes techniques to identify elements of income that are unusual and nonrecurring, adjust reported earnings to eliminate their effects, and thereby measure recurring, persistent earnings. As an alternative approach to create a more logical alignment of price and earnings, the analyst can compute the PE ratio by dividing share price by the analyst s forecast of future earnings per share for example, expected earnings per share one year ahead. A PE ratio based on expected future earnings, however, requires the analyst to forecast future earnings (or have access to another analyst s forecast). The reliability of a forward-looking PE ratio then depends on the reliability of the earnings forecast. Earnings forecast errors will distort forward-looking PE ratios. We compute the forward-looking PE ratio for PepsiCo as of the end of Year 11 using our forecast that Year +1 earnings will be $3,367.3 million as follows: Price per share 0 /Earnings per share +1 = $49.05 per share/($3,367.3 million/1,756 million shares) = Thus, at the end of Year 11, PepsiCo shares traded at a multiple of 25.6 times the Year +1 earnings forecast. PepsiCo s VE ratio of 36.0 is 41 percent greater than PepsiCo s PE ratio of 25.6 at the end of Year 11, consistent with our prior estimates of PepsiCo s value In theory, to be consistent with clean surplus accounting and residual income valuation, the denominator should be based on comprehensive income per share. However, analysts, the financial press, and financial databases rarely, if ever, compute PE ratios based on comprehensive income per share, in part because (a) U.S. GAAP does not yet require reporting comprehensive income on a per-share basis, and (b) the other comprehensive income items are usually unrealized gains and losses that are not likely to be a permanent component of income each period. We follow traditional practice in this chapter and compute PE ratios using reported earnings figures. 11 If we compute PepsiCo s PE ratio using amounts in millions rather than per-share amounts, we obtain a PE ratio of 32.4 (= $86,131.8 million/(net Income of $2,662 million $4 million preferred dividends)). This PE ratio is slightly lower than the PE ratio of 32.5 based on per-share amounts because PepsiCo reports earnings per share based on the weighted average number of common shares outstanding during the year (which is consistent with U.S. GAAP) rather than the number of shares outstanding at year-end. 12 In this case, our forecasts of net income and comprehensive income for PepsiCo in Year +1 are the same, so the PE ratio using earnings per share is equal to that using comprehensive income per share. 931