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CHAPTER 10

EQUITY VALUATION: CONCEPTS AND BASIC TOOLS

John J.Nagorniak, CFA

Foxboro, MA, U.S.A.

Stephen E.Wilcox, CFA

Mankato, MN, U.S.A.

LEARNING OUTCOMES

After completing this chapter, you will be able to do the following:

• Evaluate whether a security, given its current market price and a value estimate, is overvalued, fairly valued, or undervalued by the market.
• Describe major categories of equity valuation models.
• Explain the rationale for using present value of cash flow models to value equity and describe the dividend discount and free cash flow to equity models.
• Calculate the intrinsic value of a noncallable, nonconvertible preferred stock.
• Calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate.
• Identify companies for which the constant growth or a multistage dividend discount model is appropriate.
• Explain the rationale for using price multiples to value equity and distinguish between multiples based on comparables versus multiples based on fundamentals.
• Calculate and interpret the following multiples: price-to-earnings, price to an estimate of operating cash flow, price-to-sales, and price-to-book value.
• Explain the use of enterprise value multiples in equity valuation and demonstrate the use of enterprise value multiples to estimate equity value.
• Explain asset-based valuation models and demonstrate the use of asset-based models to calculate equity value.
• Explain the advantages and disadvantages of each category of valuation model.

1. INTRODUCTION

Analysts gather and process information to make investment decisions, including buy and sell recommendations. What information is gathered and how it is processed depend on the analyst and the purpose of the analysis. Technical analysis uses such information as stock price and trading volume as the basis for investment decisions. Fundamental analysis uses information about the economy, industry, and company as the basis for investment decisions. Examples of fundamentals are unemployment rates, gross domestic product (GDP) growth, industry growth, and quality of and growth in company earnings. Whereas technical analysts use information to predict price movements and base investment decisions on the direction of predicted change in prices, fundamental analysts use information to estimate the value of a security and to compare the estimated value to the market price and then base investment decisions on that comparison.

This chapter introduces equity valuation models used to estimate the intrinsic value (synonym: fundamental value) of a security; intrinsic value is based on an analysis of investment fundamentals and characteristics. The fundamentals to be considered depend on the analyst’s approach to valuation. In a top-down approach, an analyst examines the economic environment, identifies sectors that are expected to prosper in that environment, and analyzes securities of companies from previously identified attractive sectors. In a bottom-up approach, an analyst typically follows an industry or industries and forecasts fundamentals for the companies in those industries in order to determine valuation. Whatever the approach, an analyst who estimates the intrinsic value of an equity security is implicitly questioning the accuracy of the market price as an estimate of value. Valuation is particularly important in active equity portfolio management, which aims to improve on the return–risk trade-off of a portfolio’s benchmark by identifying mispriced securities.

This chapter is organized as follows. Section 2 discusses the implications of differences between estimated value and market price. Section 3 introduces three major categories of valuation model. Section 4 presents an overview of present value models with a focus on the dividend discount model. Section 5 describes and examines the use of multiples in valuation. Section 6 explains asset-based valuation and demonstrates how these models can be used to estimate value. Section 7 states conclusions and summarizes the chapter.

2. ESTIMATED VALUE AND MARKET PRICE

By comparing estimates of value and market price, an analyst can arrive at one of three conclusions: The security is undervalued, overvalued, or fairly valued in the market place. For example, if the market price of an asset is $10 and the analyst estimates intrinsic value at $10, a logical conclusion is that the security is fairly valued. If the security is selling for $20, the security would be considered overvalued. If the security is selling for $5, the security would be considered undervalued. Basically, by estimating value, the analyst is assuming that the market price is not necessarily the best estimate of intrinsic value. If the estimated value exceeds the market price, the analyst infers the security is undervalued. If the estimated value equals the market price, the analyst infers the security is fairly valued. If the estimated value is less than the market price, the analyst infers the security is overvalued.

In practice, the conclusion is not so straightforward. Analysts must cope with uncertainties related to model appropriateness and the correct value of inputs. An analyst’s final conclusion depends not only on the comparison of the estimated value and the market price but also on the analyst’s confidence in the estimated value (i.e., in the model selected and the inputs used in it). One can envision a spectrum running from relatively high confidence in the valuation model and the inputs to relatively low confidence in the valuation model and/or the inputs. When confidence is relatively low, the analyst might demand a substantial divergence between his or her own value estimate and the market price before acting on an apparent mispricing. For instance, if the estimate of intrinsic value is $10 and the market price is $10.05, the analyst might reasonably conclude that the security is fairly valued and that the ½ of 1 percent market price difference from the estimated value is within the analyst’s confidence interval.

Confidence in the convergence of the market price to the intrinsic value over the investment time horizon relevant to the objectives of the portfolio must also be taken into account before an analyst acts on an apparent mispricing or makes a buy, sell, or hold recommendation: The ability to benefit from identifying a mispriced security depends on the market price converging to the estimated intrinsic value.

In seeking to identify mispricing and attractive investments, analysts are treating market prices with skepticism, but they are also treating market prices with respect. For example, an analyst who finds that many securities examined appear to be overvalued will typically recheck models and inputs before acting on a conclusion of overvaluation. Analysts also often recognize and factor into recommendations that different market segments—such as securities closely followed by analysts versus securities relatively neglected by analysts—may differ in how common or persistent mispricing is. Mispricing may be more likely in securities neglected by analysts.

Analysts often use a variety of models and inputs to achieve greater confidence in their estimates of intrinsic value. The use of more than one model and a range of inputs also helps the analyst understand the sensitivity of value estimates to different models and inputs.

3. MAJOR CATEGORIES OF EQUITY VALUATION MODELS

Three major categories of equity valuation models are as follows:

• Present value models (synonym: discounted cash flow models). These models estimate the intrinsic value of a security as the present value of the future benefits expected to be received from the security. In present value models, benefits are often defined in terms of cash expected to be distributed to shareholders (dividend discount models) or in terms of cash flows available to be distributed to shareholders after meeting capital expenditure and working capital needs (free-cash-flow-to-equity models). Many models fall within this category, ranging from the relatively simple to the very complex. In Section 4, we discuss in detail two of the simpler models, the Gordon (constant) growth model and the two-stage dividend discount models.
• Multiplier models (synonym: market multiple models). These models are based chiefly on share price multiples or enterprise value multiples. The former model estimates intrinsic value of a common share from a price multiple for some fundamental variable, such as revenues, earnings, cash flows, or book value. Examples of the multiples include price to earnings (P/E, share price divided by earnings per share) and price to sales (P/S, share price divided by sales per share). The fundamental variable may be stated on a forward basis (e.g., forecasted EPS for the next year) or a trailing basis (e.g., EPS for the past year), as long as the usage is consistent across companies being examined. Price multiples are also used to compare relative values. The use of the ratio of share price to EPS—that is, the P/E multiple—to judge relative value is an example of this approach to equity valuation.

• Asset-based valuation models. These models estimate intrinsic value of a common share from the estimated value of the assets of a corporation minus the estimated value of its liabilities and preferred shares. The estimated market value of the assets is often determined by making adjustments to the book value (synonym: carrying value) of assets and liabilities. The theory underlying the asset-based approach is that the value of a business is equal to the sum of the value of the business’s assets.

As already mentioned, many analysts use more than one type of model to estimate value. Analysts recognize that each model is a simplification of the real world and that there are uncertainties related to model appropriateness and the inputs to the models. The choice of model(s) will depend on the availability of information to input into the model(s) and the analyst’s confidence in the information and in the appropriateness of the model(s).

As you begin the study of specific equity valuation models in the next section, you must bear in mind that any model of value is, by necessity, a simplification of the real world. Never forget this simple fact! You may encounter models much more complicated than the ones discussed here, but even those models will be simplifications of reality.

4. PRESENT VALUE MODELS: THE DIVIDEND DISCOUNT MODEL

Present value models follow a fundamental tenet of economics stating that individuals defer consumption—that is, they invest—for the future benefits expected. Individuals and companies make an investment because they expect a rate of return over the investment period. Logically, the value of an investment should be equal to the present value of the expected future benefits. For common shares, an analyst can equate benefits to the cash flows to be generated by the investment. The simplest present value model of equity valuation is the dividend discount model (DDM), which specifies cash flows from a common stock investment to be dividends.1 If the issuing company is assumed to be a going concern, the intrinsic value of a share is the present value of expected future dividends. If a constant required rate of return is also assumed, then the DDM expression for the intrinsic value of a share is Equation 10.1:

where

At the shareholder level, cash received from a common stock investment includes any dividends received and the proceeds when shares are sold. If an investor intends to buy and hold a share for one year, the value of the share today is the present value of two cash flows—namely, the expected dividend plus the expected selling price in one year:

where P1 = the expected price per share at t = 1.

To estimate the expected selling price, P1, the analyst could estimate the price another investor with a one-year holding period would pay for the share in one year. If V0 is based on D1 and P1, it follows that P1 could be estimated from D2 and P2:

Substituting the right side of this equation for P1 in Equation 10.2 results in V0 estimated as

Repeating this process, we find the value for n holding periods is the present value of the expected dividends for the n periods plus the present value of the expected price in n periods:

Using summation notation to represent the present value of the n expected dividends, we arrive at the general expression for an n-period holding period or investment horizon:

The expected value of a share at the end of the investment horizon—in effect, the expected selling price—is often referred to as the terminal stock value (or terminal value).

Extending the holding period into the indefinite future, we can say that a stock’s estimated value is the present value of all expected future dividends as shown in Equation 10.1.

Consideration of an indefinite future is valid because businesses established as corporations are generally set up to operate indefinitely. This general form of the DDM applies even in the case in which the investor has a finite investment horizon. For that investor, stock value today depends directly on the dividends the investor expects to receive before the stock is sold and depends indirectly on the expected dividends for periods subsequent to that sale, because those expected future dividends determine the expected selling price. Thus, the general expression given by Equation 10.1 holds irrespective of the investor’s holding period.

In practice, many analysts prefer to use a free-cash-flow-to-equity (FCFE) valuation model. These analysts assume that dividend-paying capacity should be reflected in the cash flow estimates rather than expected dividends. FCFE is a measure of dividend-paying capacity. Analysts may also use FCFE valuation models for a non-dividend-paying stock. To use a DDM, the analyst needs to predict the timing and amount of the first dividend and all the dividends or dividend growth thereafter. Making these predictions for non-dividend-paying stock accurately is typically difficult, so in such cases, analysts often resort to FCFE models.

The calculation of FCFE starts with the calculation of cash flow from operations (CFO). CFO is simply defined as net income plus noncash expenses minus investment in working capital. FCFE is a measure of cash flow generated in a period that is available for distribution to common shareholders. What does “available for distribution” mean? The entire CFO is not available for distribution; the portion of the CFO needed for fixed capital investment (FCInv) during the period to maintain the value of the company as a going concern is not viewed as available for distribution to common shareholders. Net amounts borrowed (borrowings minus repayments) are considered to be available for distribution to common shareholders. Thus, FCFE can be expressed as

The information needed to calculate historical FCFE is available from a company’s statement of cash flows and financial disclosures. Frequently, under the assumption that management is acting in the interest of maintaining the value of the company as a going concern, reported capital expenditure is taken to represent FCInv. Analysts must make projections of financials to forecast future FCFE. Valuation obtained by using FCFE involves discounting expected future FCFE by the required rate of return on equity; the expression parallels Equation 10.1:

How is the required rate of return for use in present value models estimated? To estimate the required rate of return on a share, analysts frequently use the capital asset pricing model (CAPM):

Equation 10.5 states that the required rate of return on a share is the sum of the current expected risk-free rate plus a risk premium that equals the product of the stock’s beta (a measure of nondiversifiable risk) and the market risk premium (the expected return of the market in excess of the risk-free return, where in practice, the “market” is often represented by a broad stock market index). However, even if analysts agree that the CAPM is an appropriate model, their inputs into the CAPM may differ. Thus, there is no uniquely correct answer to the question: What is the required rate of return?

Other common methods for estimating the required rate of return for the stock of a company include adding a risk premium that is based on economic judgments, rather than the CAPM, to an appropriate risk-free rate (usually a government bond) and adding a risk premium to the yield on the company’s bonds. Good business and economic judgment is paramount in estimating the required rate of return. In many investment firms, required rates of return are determined by firm policy.

4.1. Preferred Stock Valuation

General dividend discount models are relatively easy to apply to preferred shares. In its simplest form, preferred stock is a form of equity (generally, nonvoting) that has priority over common stock in the receipt of dividends and on the issuer’s assets in the event of a company’s liquidation. It may have a stated maturity date at which time payment of the stock’s par (face) value is made or it may be perpetual with no maturity date; additionally, it may be callable or convertible.

For a noncallable, nonconvertible perpetual preferred share paying a level dividend D and assuming a constant required rate of return over time, Equation 10.1 reduces to the formula for the present value of a perpetuity. Its value is:

For example, a $100 par value noncallable perpetual preferred stock offers an annual dividend of $5.50. If its required rate of return is 6 percent, the value estimate would be $5.50/0.06 = $91.67.

For a noncallable, nonconvertible preferred stock with maturity at time n, the estimated intrinsic value can be estimated by using Equation 10.3 but using the preferred stock’s par value, F, instead of Pn:

When Equation 10.7 is used, the most precise approach is to use values for n, r, and D that reflect the payment schedule of the dividends. This method is similar to the practice of fixed-income analysts in valuing a bond. For example, a nonconvertible preferred stock with a par value of £20.00, maturity in six years, a nominal required rate of return of 8.20 percent, and semiannual dividends of £2.00 would be valued by using an n of 12, an r of 4.10 percent, a D of £2.00, and an F of £20.00. The result would be an estimated value of £31.01. Assuming payments are annual rather than semiannual (i.e., assuming that n = 6, r = 8.20 percent, and D = £4.00) would result in an estimated value of £30.84.

Preferred stock issues are frequently callable (redeemable) by the issuer at some point prior to maturity, often at par value or at prices in excess of par value that decline to par value as the maturity date approaches. Such call options tend to reduce the value of a preferred issue to an investor because the option to redeem will be exercised by the issuer when it is in the issuer’s favor and ignored when it is not. For example, if an issuer can redeem shares at par value that would otherwise trade (on the basis of dividends, maturity, and required rate of return) above par value, the issuer has motivation to redeem the shares.

Preferred stock issues can also include a retraction option that enables the holder of the preferred stock to sell the shares back to the issuer prior to maturity on prespecified terms. Essentially, the holder of the shares has a put option. Such put options tend to increase the value of a preferred issue to an investor because the option to retract will be exercised by the investor when it is in the investor’s favor and ignored when it is not. Although the precise valuation of issues with such embedded options is beyond the scope of this chapter, Example 10-5 includes a case in which Equation 10.7 can be used to approximate the value of a callable, retractable preferred share.

4.2. The Gordon Growth Model

A rather obvious problem when one is trying to implement Equation 10.1 for common equity is that it requires the analyst to estimate an infinite series of expected dividends. To simplify this process, analysts frequently make assumptions about how dividends will grow or change over time. The Gordon (constant) growth model (Gordon, 1962) is a simple and well-recognized DDM. The model assumes dividends grow indefinitely at a constant rate.

Because of its assumption of a constant growth rate, the Gordon growth model is particularly appropriate for valuing the equity of dividend-paying companies that are relatively insensitive to the business cycle and in a mature growth phase. Examples might include an electric utility serving a slowly growing area or a producer of a staple food product (e.g., bread). A history of increasing the dividend at a stable growth rate is another practical criterion if the analyst believes that pattern will hold in the future.

With a constant growth assumption, Equation 10.1 can be written as Equation 10.8, where g is the constant growth rate:

If required return r is assumed to be strictly greater than growth rate g, then the square-bracketed term in Equation 10.8 is an infinite geometric series and sums to [(1 + g)/(r − g)]. Substituting into Equation 10.8 produces the Gordon growth model as presented in Equation 10.9:

For an illustration of the expression, suppose the current (most recent) annual dividend on a share is €5.00 and dividends are expected to grow at 4 percent per year. The required rate of return on equity is 8 percent. The Gordon growth model estimate of intrinsic value is, therefore, −5.00(1.04)/(0.08 − 0.04) = €5.20/0.04 = €130 per share. Note that the numerator is D1 not D0. (Using the wrong numerator is a common error.)

The Gordon growth model estimates intrinsic value as the present value of a growing perpetuity. If the growth rate, g, is assumed to be zero, Equation 10.8 reduces to the expression for the present value of a perpetuity, given earlier as Equation 10.6.

In estimating a long-term growth rate, analysts use a variety of methods, including assessing the growth in dividends or earnings over time, using the industry median growth rate, and using the relationship shown in Equation 10.10 to estimate the sustainable growth rate:

where

ROE = return on equity

Example 10-6 illustrates the application of the Gordon growth model to the shares of an integrated petroleum company. The analyst believes it will not continue to grow at the relatively fast growth rate of its past but will moderate to a lower and stable growth rate in the future. The example asks how much the dividend growth assumption adds to the intrinsic value estimate. The question is relevant to valuation because if the amount is high on a percentage basis, a large part of the value of the share depends on the realization of the growth estimate. One can answer the question by subtracting from the intrinsic value estimate determined by Equation 10.9 the value determined by Equation 10.6, which assumes no dividend growth.3

The assumptions of the Gordon model are as follows:

• Dividends are the correct metric to use for valuation purposes.
• The dividend growth rate is forever: It is perpetual and never changes.
• The required rate of return is also constant over time.
• The dividend growth rate is strictly less than the required rate of return.

An analyst might be dissatisfied with these assumptions for many reasons. The equities being examined might not currently pay a dividend. The Gordon assumptions might be too simplistic to reflect the characteristics of the companies being evaluated. Some alternatives to using the Gordon model are as follows:

• Use a more robust DDM that allows for varying patterns of growth.
• Use a cash flow measure other than dividends for valuation purposes.
• Use some other approach (such as a multiplier method) to valuation.

Applying a DDM is difficult if the company being analyzed is not currently paying a dividend. A company may not be paying a dividend if (1) the investment opportunities the company has are all so attractive that the retention and reinvestment of funds is preferable, from a return perspective, to the distribution of a dividend to shareholders or (2) the company is in such shaky financial condition that it cannot afford to pay a dividend. An analyst might still use a DDM to value such companies by assuming that dividends will begin at some future point in time. The analyst might further assume that constant growth occurs after that date and use the Gordon growth model for valuation. Extrapolating from no current dividend, however, generally yields highly uncertain forecasts. Analysts typically choose to use one or more of the alternatives instead of or as a supplement to the Gordon growth model.

The next section addresses the application of the DDM with more flexible assumptions as to the dividend growth rate.

4.3. Multistage Dividend Discount Models

Multistage growth models are often used to model rapidly growing companies. The two-stage DDM assumes that at some point the company will begin to pay dividends that grow at a constant rate, but prior to that time the company will pay dividends that are growing at a higher rate than can be sustained in the long run. That is, the company is assumed to experience an initial, finite period of high growth, perhaps prior to the entry of competitors, followed by an infinite period of sustainable growth. The two-stage DDM thus makes use of two growth rates: a high growth rate for an initial, finite period followed by a lower, sustainable growth rate into perpetuity. The Gordon growth model is used to estimate a terminal value at time n that reflects the present value at time n of the dividends received during the sustainable growth period.

Equation 10.11 will be used here as the starting point for a two-stage valuation model. The two-stage valuation model is similar to Example 10-7 except that instead of assuming zero dividends for the initial period, the analyst assumes that dividends will exhibit a high rate of growth during the initial period. Equation 10.11 values the dividends over the short-term period of high growth and the terminal value at the end of the period of high growth. The short-term growth rate, gS, lasts for n years. The intrinsic value per share in year n, Vn, represents the year n value of the dividends received during the sustainable growth period or the terminal value at time n. Vn can be estimated by using the Gordon growth model as shown in Equation 10.12, where gL is the long-term or sustainable growth rate. The dividend in year n + 1, Dn + 1, can be determined by using Equation 10.13:

The DDM can be extended to as many stages as deemed appropriate. For most publicly traded companies (that is, companies beyond the start-up stage), practitioners assume growth will ultimately fall into three stages:4 (1) growth, (2) transition, and (3) maturity. This assumption supports the use of a three-stage DDM, which makes use of three growth rates: a high growth rate for an initial finite period, followed by a lower growth rate for a finite second period, followed by a lower, sustainable growth rate into perpetuity.

One can make the case that a three-stage DDM would be most appropriate for a fairly young company, one that is just entering the growth phase. The two-stage DDM would be appropriate to estimate the value of an older company that has already moved through its growth phase and is currently in the transition phase (a period with a higher growth rate than the sustainable growth rate) prior to moving to the maturity phase (the period with a lower, sustainable growth rate).

However, the choice of a two-stage DDM need not rely solely on the age of a company. Long-established companies sometimes manage to restart above-average growth through, for example, innovation, expansion to new markets, or acquisitions. Or a company’s long-run growth rate may be interrupted by a period of subnormal performance. If growth is expected to moderate (in the first case) or improve (in the second case) toward some long-term growth rate, a two-stage DDM may be appropriate. Thus, we chose a two-stage DDM to value Brown-Forman in Example 10-9.

5. MULTIPLIER MODELS

The term price multiple refers to a ratio that compares the share price with some sort of monetary flow or value to allow evaluation of the relative worth of a company’s stock. Some practitioners use price ratios as a screening mechanism. If the ratio falls below a specified value, the shares are identified as candidates for purchase, and if the ratio exceeds a specified value, the shares are identified as candidates for sale. Many practitioners use ratios when examining a group or sector of stocks and consider the shares for which the ratio is relatively low to be attractively valued securities.

Price multiples that are used by security analysts include the following:

• Price-to-earnings ratio (P/E). This measure is the ratio of the stock price to earnings per share. P/E is arguably the price multiple most frequently cited by the media and used by analysts and investors (Block 1999). The seminal works of McWilliams (1966), Miller and Widmann (1966), Nicholson (1968), Dreman (1977), and Basu (1977) presented evidence of a return advantage to low-P/E stocks.
• Price-to-book ratio (P/B). The ratio of the stock price to book value per share. Considerable evidence suggests that P/B multiples are inversely related to future rates of return (Fama and French 1995).
• Price-to-sales ratio (P/S). This measure is the ratio of stock price to sales per share. O’Shaughnessy (2005) provided evidence that a low P/S multiple is the most useful multiple for predicting future returns.
• Price-to-cash-flow ratio (P/CF). This measure is the ratio of stock price to some per-share measure of cash flow. The measures of cash flow include free cash flow (FCF) and operating cash flow (OCF).

A common criticism of all of these multiples is that they do not consider the future. This criticism is true if the multiple is calculated from trailing or current values of the divisor. Practitioners seek to counter this criticism by a variety of techniques, including forecasting fundamental values (the divisors) one or more years into the future. The resulting forward (leading or prospective) price multiples may differ markedly from the trailing price multiples. In the absence of an explicit forecast of fundamental values, the analyst is making an implicit forecast of the future when implementing such models. The choice of price multiple—trailing or forward—should be used consistently for companies being compared.

Besides the traditional price multiples used in valuation, just presented, analysts need to know how to calculate and interpret other ratios. Such ratios include those used to analyze business performance and financial condition based on data reported in financial statements. In addition, many industries have specialized measures of business performance that analysts covering those industries should be familiar with. In analyzing cable television companies, for example, the ratio of total market value of the company to the total number of subscribers is commonly used. Another common measure is revenue per subscriber. In the oil industry, a commonly cited ratio is proved reserves per common share. Industry-specific or sector-specific ratios such as these can be used to understand the key business variables in an industry or sector as well as to highlight attractively valued securities.

5.1. Relationships among Price Multiples, Present Value Models, and Fundamentals

Price multiples are frequently used independently of present value models. One price multiple valuation approach, the method of comparables, does not involve cash flow forecasts or discounting to present value. A price multiple is often related to fundamentals through a discounted cash flow model, however, such as the Gordon growth model. Understanding such connections can deepen the analyst’s appreciation of the factors that affect the value of a multiple and often can help explain reasons for differences in multiples that do not involve mispricing. The expressions that are developed can be interpreted as the justified value of a multiple—that is, the value justified by (based on) fundamentals or a set of cash flow predictions. These expressions are an alternative way of presenting intrinsic-value estimates.

As an example, using the Gordon growth model identified previously in Equation 10.9 and assuming that price equals intrinsic value (P0 = V0), we can restate Equation 10.9 as follows:

To arrive at the model for the justified forward P/E given in Equation 10.14, we divide both sides of Equation (10.9′) by a forecast for next year’s earnings, E1. In Equation 10.14, the dividend payout ratio, p, is the ratio of dividends to earnings:

Equation 10.14 indicates that the P/E is inversely related to the required rate of return and positively related to the growth rate; that is, as the required rate of return increases, the P/E declines, and as the growth rate increases, the P/E increases. The P/E and the payout ratio appear to be positively related. This relationship may not be true, however, because a higher payout ratio may imply a slower growth rate as a result of the company retaining a lower proportion of earnings for reinvestment. This phenomenon is referred to as the dividend displacement of earnings.

Justified forward P/E estimates can be sensitive to small changes in assumptions. Therefore, analysts can benefit from carrying out a sensitivity analysis, as shown in Exhibit 10-4, which is based on Example 10-11. Exhibit 10-4 shows how the justified forward P/E varies with changes in the estimates for the dividend payout ratio (columns) and return on equity. The dividend growth rate (rows) changes because of changes in the retention rate (1 − Payout rate) and ROE. Recall g = ROE times retention rate.

EXHIBIT 10-4 Estimates for Nestlé’s Justified Forward P/E (required rate of return = 12 percent)

5.2. The Method of Comparables

The method of comparables is the most widely used approach for analysts reporting valuation judgments on the basis of price multiples. This method essentially compares relative values estimated using multiples or the relative values of multiples. The economic rationale underlying the method of comparables is the law of one price: Identical assets should sell for the same price. The methodology involves using a price multiple to evaluate whether an asset is fairly valued, undervalued, or overvalued in relation to a benchmark value of the multiple. Choices for the benchmark multiple include the multiple of a closely matched individual stock or the average or median value of the multiple for the stock’s industry. Some analysts perform trend or time-series analyses and use past or average values of a price multiple as a benchmark.

Identifying individual companies or even an industry as the “comparable” may present a challenge. Many large corporations operate in several lines of business, so the scale and scope of their operations can vary significantly. When identifying comparables (sometimes referred to as “comps”), the analyst should be careful to identify companies that are most similar according to a number of dimensions. These dimensions include (but are not limited to) overall size, product lines, and growth rate. The type of analysis shown in Section 5.1 relating multiples to fundamentals is a productive way to identify the fundamental variables that should be taken into account in identifying comparables.

5.3. Illustration of a Valuation Based on Price Multiples

Telefónica S.A. (LSE: TDE), a world leader in the telecommunication sector, provides communication, information, and entertainment products and services in Europe, Africa, and Latin America. It has operated in its home country of Spain since 1924, but as of 2008, more than 60 percent of its business was outside its home market.

Deutsche Telekom AG (FWB: DTE) provides network access, communication services, and value-added services via fixed and mobile networks. It generates more than half of its revenues outside its home country, Germany.

Exhibit 10-6 provides comparable data for these two communication giants for 2006–2008.

EXHIBIT 10-6 Data for Telefónica and Deutsche Telekom

Sources: Company web sites: www.telefonica.es and www.deutschetelekom.com.

Time-series analysis of all price multiples in Exhibit 10-6 suggests that both companies are currently attractively valued. For example, the 2008 price-to-revenue ratio (P/R) of 1.3 for Telefónica is below the 2006–2008 average for this ratio of approximately 1.6. The 2008 P/CF of 3.0 for Deutsche Telekom is below the 2006–2008 average for this ratio of approximately 4.0.

A comparative analysis produces somewhat mixed results. The 2008 values for Deutsche Telekom for the P/R, P/CF, P/B multiples are lower than those for Telefónica. This result suggests that Deutsche Telekom is attractively valued when compared with Telefónica. The 2008 P/E for Telefónica, however, is much lower than for Deutsche Telekom.

An analyst investigating these contradictory results would look for information not reported in Exhibit 10-6. For example, the earnings before interest, taxes, depreciation, and amortization (EBITDA) for Telefónica was €22.9 billion in 2008. The EBITDA value for Deutsche Telekom was €18.0 billion in 2008. The 2008 price-to-EBITDA ratio for Telefónica is [(15.85×4,646)/22,900] or [15.85/(22,900/4,646)] = 3.2, whereas the 2008 price-to-EBITDA ratio for Deutsche Telekom is 2.6. Thus, the higher P/E for Deutsche Telekom may be explained by higher depreciation charges, higher interest costs, and/or a greater tax burden.

In summary, the major advantage of using price multiples is that they allow for relative comparisons, both cross-sectional (versus the market or another comparable) and in time series. The approach can be especially beneficial for analysts who are assigned to a particular industry or sector and need to identify the expected best performing stocks within that sector. Price multiples are popular with investors because the multiples can be calculated easily and many multiples are readily available from financial web sites and newspapers.

Caution is necessary. A stock may be relatively undervalued when compared with its benchmarks but overvalued when compared with an estimate of intrinsic value as determined by one of the discounted cash flow methodologies. Furthermore, differences in reporting rules among different markets and in chosen accounting methods can result in revenues, earnings, book values, and cash flows that are not easily comparable. These differences can, in turn, result in multiples that are not easily comparable. Finally, the multiples for cyclical companies may be highly influenced by current economic conditions.

5.4. Enterprise Value

An alternative to estimating the value of equity is to estimate the value of the enterprise. Enterprise value is most frequently determined as market capitalization plus market value of preferred stock plus market value of debt minus cash and investments (cash equivalents and short-term investments). Enterprise value is often viewed as the cost of a takeover: In the event of a buyout, the acquiring company assumes the acquired company’s debt but also receives its cash. Enterprise value is most useful when comparing companies with significant differences in capital structure.

Enterprise value (EV) multiples are widely used in Europe, with EV/EBITDA arguably the most common. EBITDA is a proxy for operating cash flow because it excludes depreciation and amortization. EBITDA may include other noncash expenses, however, and noncash revenues. EBITDA can be viewed as a source of funds to pay interest, dividends, and taxes. Because EBITDA is calculated prior to payment to any of the company’s financial stakeholders, using it to estimate enterprise value is logically appropriate.

Using enterprise value instead of market capitalization to determine a multiple can be useful to analysts. Even where the P/E is problematic because of negative earnings, the EV/EBITDA multiple can generally be computed because EBITDA is usually positive. An alternative to using EBITDA in EV multiples is to use operating income.

In practice, analysts may have difficulty accurately assessing enterprise value if they do not have access to market quotations for the company’s debt. When current market quotations are not available, bond values may be estimated from current quotations for bonds with similar maturity, sector, and credit characteristics. Substituting the book value of debt for the market value of debt provides only a rough estimate of the debt’s market value. This is because market interest rates change and investors’ perception of the issuer’s credit risk may have changed since the debt was issued.

6. ASSET-BASED VALUATION

An asset-based valuation of a company uses estimates of the market or fair value of the company’s assets and liabilities. Thus, asset-based valuations work well for companies that do not have a high proportion of intangible or “off the books” assets and that do have a high proportion of current assets and current liabilities. The analyst may be able to value these companies’ assets and liabilities in a reasonable fashion by starting with balance sheet items. For most companies, however, balance sheet values are different from market (fair) values, and the market (fair) values can be difficult to determine.

Asset-based valuation models are frequently used together with multiplier models to value private companies. As public companies increase reporting or disclosure of fair values, asset-based valuation may be increasingly used to supplement present value and multiplier models of valuation. Important facts that the practitioner should realize are as follows:

• Companies with assets that do not have easily determinable market (fair) values—such as those with significant property, plant, and equipment—are very difficult to analyze using asset valuation methods.
• Asset and liability fair values can be very different from the values at which they are carried on the balance sheet of a company.
• Some assets that are “intangible” are shown on the books of the company. Other intangible assets, such as the value from synergies or the value of a good business reputation, may not be shown on the books. Because asset-based valuation may not consider some intangibles, it can give a “floor” value for a situation involving a significant amount of intangibles. When a company has significant intangibles, the analyst should prefer a forward-looking cash flow valuation.
• Asset values may be more difficult to estimate in a hyperinflationary environment.

We begin by discussing asset-based valuation for hypothetical nonpublic companies and then move on to a public company example. Analysts should consider the difficulties and rewards of using asset-based valuation for companies that are suited to this measure. Owners of small privately held businesses are familiar with valuations arrived at by valuing the assets of the company and then subtracting any relevant liabilities.

Example 10-17 shows some of the subtleties present in applying asset-based valuation to determine company value. It also shows how asset-based valuation does not deal with intangibles. Example 10-18 emphasizes this point.

For public companies, the assets will typically be so extensive that a piece-by-piece analysis will be impossible, and the transition from book value to market value is a nontrivial task. The asset-based valuation approach is most applicable when the market value of the corporate assets is readily determinable and the intangible assets, which are typically difficult to value, are a relatively small proportion of corporate assets. Asset-based valuation has also been applied to financial companies, natural resource companies, and formerly going concerns that are being liquidated. Even for other types of companies, however, asset-based valuation of tangible assets may provide a baseline for a minimal valuation.

Analysts recognizing the uncertainties related to model appropriateness and the inputs to the models frequently use more than one model or type of model in valuation to increase their confidence in their estimates of intrinsic value. The choice of models will depend on the availability of information to put into the models. Example 10-20 illustrates the use of three valuation methods.

7. SUMMARY

The equity valuation models used to estimate intrinsic value—present value models, multiplier models, and asset-based valuation—are widely used and serve an important purpose. The valuation models presented here are a foundation on which to base analysis and research but must be applied wisely. Valuation is not simply a numerical analysis. The choice of model and the derivation of inputs require skill and judgment.

When valuing a company or group of companies, the analyst wants to choose a valuation model that is appropriate for the information available to be used as inputs. The available data will, in most instances, restrict the choice of model and influence the way it is used. Complex models exist that may improve on the simple valuation models described in this chapter; but before using those models and assuming that complexity increases accuracy, the analyst would do well to consider the “law of parsimony”: A model should be kept as simple as possible in light of the available inputs. Valuation is a fallible discipline, and any method will result in an inaccurate forecast at some time. The goal is to minimize the inaccuracy of the forecast.

Among the points made in this chapter are the following:

• An analyst estimating intrinsic value is implicitly questioning the market’s estimate of value.
• If the estimated value exceeds the market price, the analyst infers the security is undervalued. If the estimated value equals the market price, the analyst infers the security is fairly valued. If the estimated value is less than the market price, the analyst infers the security is overvalued. Because of the uncertainties involved in valuation, an analyst may require that value estimates differ markedly from market price before concluding that a misvaluation exists.
• Analysts often use more than one valuation model because of concerns about the applicability of any particular model and the variability in estimates that result from changes in inputs.
• Three major categories of equity valuation models are present value, multiplier, and asset-based valuation models.
• Present value models estimate value as the present value of expected future benefits.
• Multiplier models estimate intrinsic value based on a multiple of some fundamental variable.
• Asset-based valuation models estimate value based on the estimated value of assets and liabilities.
• The choice of model will depend upon the availability of information to input into the model and the analyst’s confidence in both the information and the appropriateness of the model.
• In the dividend discount model, value is estimated as the present value of expected future dividends.
• In the free-cash-flow-to-equity model, value is estimated as the present value of expected future free cash flow to equity.
• The Gordon growth model, a simple DDM, estimates value as D1/(r – g).
• The two-stage dividend discount model estimates value as the sum of the present values of dividends over a short-term period of high growth and the present value of the terminal value at the end of the period of high growth. The terminal value is estimated using the Gordon growth model.
• The choice of dividend model is based upon the patterns assumed with respect to future dividends.
• Multiplier models typically use multiples of the form: P/measure of fundamental variable or EV/measure of fundamental variable.
• Multiples can be based upon fundamentals or comparables.
• Asset-based valuation models estimate value of equity as the value of the assets less the value of liabilities.

PROBLEMS

1. An analyst estimates the intrinsic value of a stock to be in the range of €17.85 to €21.45. The current market price of the stock is €24.35. This stock is most likely:

A. Overvalued.

B. Undervalued.

C. Fairly valued.

2. An analyst determines the intrinsic value of an equity security to be equal to $55. If the current price is $47, the equity is most likely:

A. Undervalued.

B. Fairly valued.

C. Overvalued.

3. In asset-based valuation models, the intrinsic value of a common share of stock is based on the:

A. Estimated market value of the company’s assets.

B. Estimated market value of the company’s assets plus liabilities.

C. Estimated market value of the company’s assets minus liabilities.

4. Which of the following is most likely used in a present value model?

A. Enterprise value.

B. Price to free cash flow.

C. Free cash flow to equity.

5. Book value is least likely to be considered when using:

A. A multiplier model.

B. An asset-based valuation model.

C. A present value model.

6. An analyst is attempting to calculate the intrinsic value of a company and has gathered the following company data: EBITDA, total market value, and market value of cash and short-term investments, liabilities, and preferred shares. The analyst is least likely to use:

A. A multiplier model.

B. A discounted cash flow model.

C. An asset-based valuation model.

7. An analyst who bases the calculation of intrinsic value on dividend-paying capacity rather than expected dividends will most likely use the:

A. Dividend discount model.

B. Free cash flow to equity model.

C. Cash flow from operations model.

8. An investor expects to purchase shares of common stock today and sell them after two years. The investor has estimated dividends for the next two years, D1 and D2, and the selling price of the stock two years from now, P2. According to the dividend discount model, the intrinsic value of the stock today is the present value of:

A. Next year’s dividend, D1.

B. Future expected dividends, D1 and D2.

C. Future expected dividends and price—D1, D2, and P2.

9. In the free-cash-flow-to-equity (FCFE) model, the intrinsic value of a share of stock is calculated as:

A. The present value of future expected FCFE.

B. The present value of future expected FCFE plus net borrowing.

C. The present value of future expected FCFE minus fixed capital investment.

10. With respect to present value models, which of the following statements is most accurate?

A. Present value models can be used only if a stock pays a dividend.

B. Present value models can be used only if a stock pays a dividend or is expected to pay a dividend.

C. Present value models can be used for stocks that currently pay a dividend, are expected to pay a dividend, or are not expected to pay a dividend.

11. A Canadian life insurance company has an issue of 4.80 percent, $25 par value, perpetual, nonconvertible, noncallable preferred shares outstanding. The required rate of return on similar issues is 4.49 percent. The intrinsic value of a preferred share is closest to:

A. $25.00.

B. $26.75.

C. $28.50.

12. Two analysts estimating the value of a nonconvertible, noncallable, perpetual preferred stock with a constant dividend arrive at different estimated values. The most likely reason for the difference is that the analysts used different:

A. Time horizons.

B. Required rates of return.

C. Estimated dividend growth rates.

13. The Beasley Corporation has just paid a dividend of $1.75 per share. If the required rate of return is 12.3 percent per year and dividends are expected to grow indefinitely at a constant rate of 9.2 percent per year, the intrinsic value of Beasley Corporation stock is closest to:

A. $15.54.

B. $56.45.

C. $61.65.

14. An investor is considering the purchase of a common stock with a $2.00 annual dividend. The dividend is expected to grow at a rate of 4 percent annually. If the investor’s required rate of return is 7 percent, the intrinsic value of the stock is closest to:

A. $50.00.

B. $66.67.

C. $69.33.

15. An analyst gathers or estimates the following information about a stock:

Current price per share	€22.56
Current annual dividend per share	€1.60
Annual dividend growth rate for Years 1–4	9.00%
Annual dividend growth rate for Years 5 +	4.00%
Required rate of return	12%

Based on a dividend discount model, the stock is most likely:

A. Undervalued.

B. Fairly valued.

C. Overvalued.

16. An analyst is attempting to value shares of the Dominion Company. The company has just paid a dividend of $0.58 per share. Dividends are expected to grow by 20 percent next year and 15 percent the year after that. From the third year onward, dividends are expected to grow at 5.6 percent per year indefinitely. If the required rate of return is 8.3 percent, the intrinsic value of the stock is closest to:

A. $26.00.

B. $27.00.

C. $28.00.

17. Hideki Corporation has just paid a dividend of ¥450 per share. Annual dividends are expected to grow at the rate of 4 percent per year over the next four years. At the end of four years, shares of Hideki Corporation are expected to sell for ¥9,000. If the required rate of return is 12 percent, the intrinsic value of a share of Hideki Corporation is closest to:

A. ¥5,850.

B. ¥7,220.

C. ¥7,670.

18. The Gordon growth model can be used to value dividend-paying companies that are:

A. Expected to grow very fast.

B. In a mature phase of growth.

C. Very sensitive to the business cycle.

19. The best model to use when valuing a young dividend-paying company that is just entering the growth phase is most likely the:

A. Gordon growth model.

B. Two-stage dividend discount model.

C. Three-stage dividend discount model.

20. An equity analyst has been asked to estimate the intrinsic value of the common stock of Omega Corporation, a leading manufacturer of automobile seats. Omega is in a mature industry, and both its earnings and dividends are expected to grow at a rate of 3 percent annually. Which of the following is most likely to be the best model for determining the intrinsic value of an Omega share?

A. Gordon growth model.

B. Free-cash-flow-to-equity model.

C. Multistage dividend discount model.

21. A price-to-earnings ratio that is derived from the Gordon growth model is inversely related to the:

A. Growth rate.

B. Dividend payout ratio.

C. Required rate of return.

22. The primary difference between P/E multiples based on comparables and P/E multiples based on fundamentals is that fundamentals-based P/Es take into account:

A. Future expectations.

B. The law of one price.

C. Historical information.

23. An analyst makes the following statement: “Use of P/E and other multiples for analysis is not effective because the multiples are based on historical data and because not all companies have positive accounting earnings.” The analyst’s statement is most likely:

A. Inaccurate with respect to both historical data and earnings.

B. Accurate with respect to historical data and inaccurate with respect to earnings.

C. Inaccurate with respect to historical data and accurate with respect to earnings.

24. An analyst has prepared a table of the average trailing 12-month price-to-earning (P/E), price-to-cash flow (P/CF), and price-to-sales (P/S) for the Tanaka Corporation for the years 2005 to 2008.

As of the date of the valuation in 2009, the trailing 12-month P/E, P/CF, and P/S are, respectively, 9.2, 8.0, and 2.5. Based on the information provided, the analyst may reasonably conclude that Tanaka shares are most likely:

A. Overvalued.

B. Undervalued.

C. Fairly valued.

25. An analyst has gathered the following information for the Oudin Corporation:

Expected earnings per share = €5.70

Expected dividends per share = €2.70

Dividends are expected to grow at 2.75 percent per year indefinitely

The required rate of return is 8.35 percent

Based on the information provided, the price/earnings multiple for Oudin is closest to:

A. 5.7.

B. 8.5.

C. 9.4.

26. An analyst gathers the following information about two companies:

	Alpha Corp.	Delta Co.
Current price per share	$57.32	$18.93
Last year’s EPS	$3.82	$1.35
Current year’s estimated EPS	$4.75	$1.40

Which of the following statements is most accurate?

A. Delta has the higher trailing P/E multiple and lower current estimated P/E multiple.

B. Alpha has the higher trailing P/E multiple and lower current estimated P/E multiple.

C. Alpha has the higher trailing P/E multiple and higher current estimated P/E multiple.

27. An analyst gathers the following information about similar companies in the banking sector:

Which of the companies is most likely to be undervalued?

A. First Bank.

B. Prime Bank.

C. Pioneer Trust.

28. The market value of equity for a company can be calculated as enterprise value:

A. Minus market value of debt, preferred stock, and short-term investments.

B. Plus market value of debt and preferred stock minus short-term investments.

C. Minus market value of debt and preferred stock plus short-term investments.

29. Which of the following statements regarding the calculation of the enterprise value multiple is most likely correct?

A. Operating income may be used instead of EBITDA.

B. EBITDA may not be used if company earnings are negative.

C. Book value of debt may be used instead of market value of debt.

30. An analyst has determined that the appropriate EV/EBITDA for Rainbow Company is 10.2.

The analyst has also collected the following forecasted information for Rainbow Company:

EBITDA = $22,000,000

Market value of debt = $56,000,000

Cash = $1,500,000

The value of equity for Rainbow Company is closest to:

A. $169 million.

B. $224 million.

C. $281 million.

31. Enterprise value is most often determined as market capitalization of common equity and preferred stock minus the value of cash equivalents plus the:

A. Book value of debt.

B. Market value of debt.

C. Market value of long-term debt.

32. Asset-based valuation models are best suited to companies where the capital structure does not have a high proportion of:

A. Debt.

B. Intangible assets.

C. Current assets and liabilities.

33. Which of the following is most likely a reason for using asset-based valuation?

A. The analyst is valuing a privately held company.

B. The company has a relatively high level of intangible assets.

C. The market values of assets and liabilities are different from the balance sheet values.

34. A disadvantage of the EV method for valuing equity is that the following information may be difficult to obtain:

A. Operating income.

B. Market value of debt.

C. Market value of equity.

35. Which type of equity valuation model is most likely to be preferable when one is comparing similar companies?

A. A multiplier model.

B. A present value model.

C. An asset-based valuation model.

36. Which of the following is most likely considered a weakness of present value models?

A. Present value models cannot be used for companies that do not pay dividends.

B. Small changes in model assumptions and inputs can result in large changes in the computed intrinsic value of the security.

C. The value of the security depends on the investor’s holding period; thus, comparing valuations of different companies for different investors is difficult.

1Companies may also distribute cash to common shareholders by means of share repurchases.

2“Retraction” refers to this option, which is a put option. The terminology is not completely settled: The type of share being called “retractable term preferred” is also known as “hard retractable preferred,” with “hard” referring to payment in cash rather than common shares at the retraction date. See the 2009 ScotiaMcLeod report, www.ritceyteam.com/pdf/guide_to_preferred_shares.pdf.

3A related concept, the present value of growth opportunities (PVGO), is discussed in more advanced readings.

4Sharpe, Alexander, and Bailey (1999).