Choosing the Right Valuation Approach

Choosing the Right Valuation Approach Robert Parrino, CFA Director Hicks, Muse, Tate & Furst Center for Private Equity Finance McCombs School of Business, University of Texas at Austin Austin, Texas Before beginning any analysis, the analyst should define the claim and level of value, the valuation date, and the purpose/definition of value. In essence, those definitions help the analyst choose among the many valuation methodologies available. But even with the wide range of tools that are available, the quality of any value estimate ultimately depends on how well the analyst understands the firm and its strategy, its competitive position, and its future prospects. I n this presentation, I will focus on business valuation techniques. In the course of this discussion, I will present the concepts underlying a number of valuation methods. Although many people are familiar with these methods, it is still worthwhile to systematically examine and discuss the concepts that underlie these approaches, their proper applications, and the pros and cons associated with each. Ultimately, I hope to provide a better sense of how these different methods fit together and the circumstances under which one method might be preferable to another. Defining the Valuation Problem When trying to decide what valuation approach to use in a particular situation, it is important to begin by defining the objective of the analysis. In other words, it is important to accurately define the valuation problem. Three things are particularly important to consider in this context: the claim and level of value, the valuation date, and the purpose/definition of value. This process of defining the valuation problem often leads the analyst to the appropriate methodology. To understand the concept of defining the claim, consider the finance balance sheet. All analysts are familiar with the accounting balance sheet, where book value of assets equals the book value of liabilities plus shareholders equity. The finance balance sheet is similar except that it is forward looking and based on market values rather than book values. A graphical illustration is shown in Figure 1. On the left side is the value of the assets in the business. The value of the assets must equal the value of the claims on those assets; someone owns the assets, so the values have to be equal. Another way to think about this is that the present value of the cash flows from the business is on the left side and the values of the claims on those cash flows are on the right side. The first step the analyst should take is to ask precisely what is being valued. Is it the entire business or some claim on the business, such as the common equity, the preferred shares, or perhaps a layer of debt? If it is a claim, it is also important to specify precisely how much of that claim is being valued. Is it 5 percent, 20 percent, 70 percent, and so on? Identifying the claim is important because the specific claim that is being valued drives the choice of valuation method. It also has implications for the analysis, as will be seen later. Note that level of value refers to the distinctions between a liquid and an illiquid claim and between a controlling and a minority interest. For example, if you are valuing 100 shares of a publicly traded stock, more than likely you are valuing a marketable (liquid) minority interest. The second step is to define the valuation date. For most valuations that analysts do, the valuation date is as of today. Elsewhere in the valuation world, however, the valuation date is not always today. For example, the value as of some past date is often of interest in litigation and tax disputes. Defining the valuation date in advance is important because this date defines what information is appropriate for the analysis. Even if the analyst is valuing a share of stock 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 15

Analyzing, Researching, and Valuing Equity Investments Figure 1. Finance (Market Value) Balance Sheet Current Assets Non-Interest-Bearing Current Liabilities Firm Value Property, Plant, and Equipment Intangible Assets Debt Equity Value of Total Capital Going-Concern Value as of today, the value estimate should be dated because firm, industry, general economic, and capital market conditions can all change quickly and have an impact on the value of the asset. In other words, a recent value estimate may no longer be reasonable because conditions have changed. The third step in defining the valuation problem is to be very specific about the purpose of the valuation and the definition of value that will be used because there is no such thing as a single value of an asset. An asset may have many different values. For example, consider the fair market value concept (i.e., definition of value). The fair market value of any asset is defined as the cash price at which the asset would change hands between a willing buyer and a willing seller if the asset were offered for sale on the open market for a reasonable period of time with both the buyer and seller being apprised of the relevant facts and neither being under any compulsion to act. Basically, it is a freely traded value where cash is being exchanged and no one is being forced to act. When an analyst values a share of stock in a public company with a view toward making a buy, hold, or sell recommendation, the analyst is estimating the fair market value of that share. There is no specific buyer or seller in mind. What the analyst is looking for in this case is an estimate of the value of that share to a typical buyer. Contrast the fair market value concept with investment value. The investment value of an asset is the value of that asset to a specific buyer. If known, the identity of the prospective buyer affects the valuation. For example, the investment value of a share of stock to someone who already owns 49.9999 percent of the outstanding shares can be much different from the investment value of that share to a typical buyer. If an analyst is valuing an entire company, the same analogy applies. For example, suppose that XYZ Corporation announces that it is going to sell one of its divisions. One way to think about the price it might obtain for the sale of that division is to do a fair market value analysis on a controlling basis. In this situation, the analyst estimates what someone who is knowledgeable about that business and competent in managing that type of business would pay. What is the present value of the cash flows to someone like that? Answering that question involves valuing the firm under the assumptions that operating and financial policies are typical of those in that industry. That situation is much different from the sale by XYZ Corporation of a division to a private investment firm that will likely roll the business up with some other businesses. In this case, a lot of leverage will probably be applied to the transaction and the operating policies of the business will be different. This will have different implications for the value of the business and the sale price that will ultimately be agreed upon. The bottom line is that defining the valuation problem up-front is important because it has implications for the choice of valuation method as well as for the information that is used, the assumptions that are made, and the way the selected valuation methods are applied. Although a wide range of valuation methodologies exists, the majority fall within three categories: asset/cost approaches, market approaches, and income approaches. To see how these categories differ, think of commercial real estate. The asset/cost approach might be used for insurance purposes, such as determining what it would cost to replace a structure. The market approach, in contrast, is the evaluation of what comparable buildings sold for on a square footage basis, with adjustments for specific features of the asset being valued. The income approach involves discounting the present value of the rental stream net of any expenses and investment requirements. 16 CFA Institute Conference Proceedings 2005, CFA Institute cfapubs.org

Choosing the Right Valuation Approach The same three categories of approaches are used in business valuation. They are generic to the valuation of any asset. So, what I will do is frame this discussion in the context of asset/cost, market, and income approaches. I will describe methodologies that use each of the three approaches, the cases in which each approach is useful, the ways in which each approach is used, and the pros and cons of each approach. Although it is not one of the three major categories I just mentioned asset/cost, market, and income a fourth approach I will briefly discuss is the contingent claims approach. Contingent claims methods are used to value claims on underlying assets. In that sense, I will distinguish these methods from the other approaches, which value the underlying assets themselves. Option-pricing methodologies are examples of the contingent claims approach. The contingent claims approach is useful in business valuation for cases in which someone does not have a 100 percent claim on the cash flows of an asset. In those instances, those claims look a lot like derivatives. In fact, as will be seen, they can look a lot like options. I will thus discuss how to value equity using contingent claims methods because these methods can be very useful. How many analysts have ever done a discounted cash flow (DCF) analysis of a financially distressed company and arrived at a negative equity value? This, of course, means the equity is worth zero because equity cannot have a negative value. If the shares in this example are trading with a positive price, then they are effectively trading on their option value. Asset/Cost Approaches This section reviews two basic asset/cost methods: the adjusted book value approach and the replacement cost approach. Adjusted Book Value Approach. The adjusted book value approach is conceptually simple. The adjusted book value of a firm equals the sum of the market value of each of the firm s identifiable assets. The value of the equity equals this value less the market value of all liability claims on the business. This method is commonly used for valuing mutual funds. If an analyst is valuing an operating company with separate autonomous units, he or she can value each of the business units separately and then add those values together to estimate the value of the total enterprise. Although straightforward, this method is not very useful for valuing a typical operating business because the value of a typical operating business is greater than the sum of the values of the individual identifiable assets. The reason for this is that a typical operating business has something called goingconcern value. The going-concern value is value that is attributable to the way a business is organized and managed. For example, suppose you are starting a decorative brick manufacturing business and you have a national franchise to sell your bricks. Would you locate in California or Kansas? Given that transportation costs would presumably be significant for transporting bricks around the country, you would opt for a location in Kansas over California. If you located on the West Coast, you might kill your opportunities in the eastern half of the country. The choice of location thus has value implications because it affects the number of potential customers (sales); costs; and to the extent that regional economies differ, risks. But when using the adjusted book value approach, you might come up with the same value for both locations even though the going-concern value is quite different. Operating policies, the quality of management, the organizational structure, and a lot of other factors contribute to going-concern value. These factors are not all properly accounted for with the adjusted book value method. The situations where this approach can be very useful are ones where the analyst is valuing a business with separate autonomous assets and where there are no synergies between those assets. It can also be very useful in estimating the liquidation value of a business, which, incidentally, is often done when the going-concern value is negative. Finally, this approach can be useful as a sanity check for other valuation methods, such as the DCF methods discussed later. The reason adjusted book value can be useful as a sanity check is that it provides an estimate of the floor value for a business. So, if a DCF analysis yields a value estimate that is lower than adjusted book value, a problem more than likely exists with the DCF analysis. Perhaps the analyst misestimated revenue growth, margins, or the appropriate discount rate. If there is no problem with the DCF analysis and the DCF value is less than the adjusted book value, then the business should be shut down because it is destroying, rather than creating, value. Replacement Cost Approach. The second asset/cost approach is the replacement cost approach. The replacement cost simply reflects the cost of duplicating assets in their present form at a particular point in time. It thus reflects the asset type and condition. Although this approach is generally more useful for insurance than for any other purpose, in business valuation, a replacement cost analysis can be helpful in conducting a buy-versus-build analysis. Think about some of the prices people were paying for domain names in 1999 and 2000. It was not unusual 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 17

Analyzing, Researching, and Valuing Equity Investments to hear of prices in the billions of dollars. Hopefully, they paid that much only after asking themselves the obvious question: Can we create the consumer awareness that is associated with that particular domain name in a reasonable period for less money? Or, put another way, what is the opportunity cost for not making the investment? Likewise, if a company announces that it is going to acquire another business at a specified price, the first thing an analyst should do is think about whether the company is overpaying. Is this something the company could do on its own for less? Certainly, getting to the market more quickly has some value, and it may be risky to try to play catchup with a competitor at this particular point in time. Those factors will serve to complicate the analysis. Nevertheless, analysts should be conducting this type of analysis whenever they hear a company say it is considering purchasing a business. Market Approaches In this section, I will two discuss two market approaches: guideline multiples analysis and guideline transactions analysis. In both of these approaches, the term guideline is simply another way to say comparable. Guideline Multiples. Multiples analysis is commonly used by investment analysts. It involves identifying publicly traded companies engaged in similar business activities and that have risk return characteristics that are similar to those of the company being analyzed. The analyst then uses the prices at which shares of those publicly traded companies are trading to infer something about the company of interest, such as whether the company s shares are over- or undervalued. Similarly, if an analyst is valuing a closely held business, guideline multiples analysis might help the analyst estimate the fair market value of its securities. Commonly used multiples for assessing equity value are price/earnings, price/dividends, price/ revenue, and market value/book value. Other ratios divide enterprise value by a proxy for cash flow, such as enterprise value/revenue or enterprise value/free cash flow. 1 These enterprise multiples are used to derive a value estimate for the total business. Applying the guideline multiples approach is conceptually straightforward, but in practice, applying the approach correctly can be very difficult. For instance, often a business has no true comparables, or 1 Enterprise value is typically defined as being equal to market value of common stock plus market value of preferred stock plus market value of debt minus excess cash and cash equivalents. what are often called pure plays. This can be very frustrating because in such cases a guideline multiples analysis can yield a wide range of value estimates that are difficult to reconcile. The ideal comparable has to match on many dimensions. For example, the ideal comparable is a company that sells the same products, competes in the same markets, is of similar size, has similar revenue growth prospects, has similar profit margins, and has similar management quality. In addition, if the analyst is using an equity ratio (such as price/earnings or price/dividends) the comparable should have a similar capital structure because, all else being equal, capital structure can have a dramatic impact on those ratios. The importance of identifying guideline companies that are similar to the company being analyzed can be illustrated by considering the characteristics that determine a company s P/E: DIV P 1 EPS 1 b 0 ------------- --------------- ------------ b = = = g g EPS ------------- 1 g, where DIV 1 = dividends in Period 1 EPS 1 = earnings per share in Period 1 b = payout ratio = cost of equity g = dividends/earnings growth rate This equation is a simple constant growth model. I will talk about this model in more detail later, but for now, it is useful to recognize the fact that it can be rearranged to represent the P/E multiple as essentially the payout ratio over minus g. It can be further simplified by setting b to 1 if some assumptions are made about the net present value of projects that the company invests its retained earnings in. By focusing on the variables that drive the P/E multiple, even in this admittedly simple context, one can see the importance of identifying a good comparable. What drives, the cost of equity? In a capital asset pricing model (CAPM) world, the cost of equity is the risk-free rate plus beta times the market risk premium. What drives beta? Beta is the riskiness of the overall business plus the financial risk (i.e., asset risk plus financial risk). The financial risk is a function of leverage. So, if the leverage of the comparable company is different from the leverage of the company being analyzed, the two betas will be different even if the underlying businesses are identical. Think about what drives the business risk of a company: products, markets, margins, growth rates, and so on. They will affect the underlying asset risk of the company, which will affect the asset beta, which, in turn, will affect the cost of equity. What drives the growth rate? The same things I just described. So, if the analyst is not matching the comparable company and P 0 18 CFA Institute Conference Proceedings 2005, CFA Institute cfapubs.org

Choosing the Right Valuation Approach the company being analyzed on a lot of these dimensions, the analyst has to be somewhat careful using a ratio such as P/E. Another important point is that analysts should use contemporaneous data with the multiples approach. Remember that earlier I said analysts should define the valuation date in advance because any value estimate is specific to a particular date. That thought certainly applies here. For multiples analysis, analysts have to be sure that the multiples they are using are obtained for the point in time for which they are doing the valuation. Finally, analysts have to make sure that they are being consistent with the numerator and the denominator in all these ratios. In other words, they have to be sure that the value in the numerator is consistent with the flow measure in the denominator. If equity price is in the numerator, some proxy for cash flow to equity must be in the denominator. If enterprise value is in the numerator, a proxy for total cash flows from the entire business must be in the denominator. The exception to this rule is the price-to-revenue ratio. I would not normally recommend using this ratio, but it can be helpful in certain situations, such as cases where the analyst is evaluating a relatively young company that is not yet generating profits. For example, companies in high-tech industries often trade based on multiples of their revenue. Implicit in those multiples are expectations about future margins, as well as growth in revenue. By using price to revenue, the analyst is effectively assuming that the company being analyzed has profit margins similar to those that are anticipated by the market in pricing the publicly traded comparable(s). Guideline Transactions. The guideline transactions approach is another useful valuation tool. In transactions analysis, the analyst looks at what was paid for similar companies in mergers and acquisitions. Several databases report transactions data. The problem is that transactions data are not typically as reliable as the data available for multiples analysis, especially when the guideline transactions involve private companies. The databases may report revenues of the private company but not data on profitability. They might report the net income but not enough information to estimate cash flows. Consequently, it can be difficult to compute some of the key ratios. Additionally, the terms of the transactions can be difficult to assess. The P/E multiple for a publicly traded company is an indicator of fair market value; for all intents and purposes, it is an indicator of what might be obtained in a cash transaction. Frequently, however, guideline transactions involve some combination of cash, debt, or equity payments. A whole package of such securities and promises, which are difficult to value, could be included in the reported transaction price, and this may not be apparent to the analyst. The value estimates for those securities and claims can be distorted for various reasons, and analysts have to be very sensitive to these problems when using this approach. A guideline transactions analysis yields a value estimate on a controlling basis, whereas a multiples analysis provides an estimate on a minority basis. With a transactions analysis, the analyst knows how much someone paid for a business. It was worth at least that much to the buyer, and this provides at least some idea of the value of control. Of course, it also includes synergies to that specific buyer, which may or may not be relevant in this valuation case. Summary. Market approaches reflect prices that have actually been paid. Thus, the analyst sees what people are actually willing to pay for a similar asset. It may not be obvious what drove these people to pay that price, but that information is helpful and is a big benefit from using this approach. Guideline multiples and transactions analyses can provide useful valuation benchmarks for valuations based on other methodologies, such as the income approaches that I will discuss next. Income Approaches Under the category of income approaches, I will discuss free cash flow to the firm (FCFF), free cash flow to equity (FCFE), and dividend discount model (DDM) approaches. FCFF Approaches. In the FCFF approaches, the analyst values the free cash flows that the firm is expected to generate. This is the free cash flows from the left-hand side of the finance balance sheet (shown in Figure 1), which includes a measure of net working capital (current assets less non-interest-bearing current liabilities), PP&E (property, plant, and equipment), intangible assets, and going-concern value. The FCFF is independent of the financing used by the firm. The most common FCFF approach involves using the weighted-average cost of capital (WACC) to discount the FCFF, or the WACC method. Specifically, the total value of the firm, V F, is computed as the present value of the FCFF discounted by the firm s WACC: V F = t=0 FCFF ---------------------------------- t ( 1+ WACC) t, where t equals the period when the cash flow is received. In estimating FCFF, the analyst begins with net revenue and makes several adjustments, as shown in Exhibit 1. Analysts typically forecast the future FCFF 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 19

Analyzing, Researching, and Valuing Equity Investments Exhibit 1. FCFF: WACC Method Net revenue Operating expenses Earnings before interest, taxes, depreciation, and amortization Depreciation and amortization Operating profit (1 Average tax rate) Operating profit after tax + Depreciation and amortization Capital expenditures Additions to working capital FCFF by forecasting each of the individual components and then performing the calculation shown in Exhibit 1. The resulting FCFF values are discounted back to the present using the WACC, which is estimated with the following formula: WACC = V E V D + V E V D V D V E --------------------- + k D ( 1 t C )---------------------, + where = cost of equity (often estimated using the CAPM) k D = cost of debt (should be consistent with the firm s financial policy) t C = corporate tax rate V E /(V D +V E ) = market value of equity to market value of total capital (i.e., proportion of the firm s capital represented by equity) V D /(V D +V E ) = market value of debt to market value of total capital (i.e., proportion of the firm s capital represented by debt) The WACC is simply a weighted average of the various layers of financing used by the business. The first term represents the proportionate cost of equity (in practice, there is actually a separate term like this for each class of equity), and the second term represents the proportionate cost of debt. When analysts use this method, the key assumption concerns how the firm s operations will be financed in the future. For example, the financing might be 80 percent equity and 20 percent debt. Or it might be 30 percent equity and 70 percent debt. The WACC method is typically used to value a mature firm under the assumption that over the long run, the firm will manage its capital structure toward some target level of debt. With that assumption, the analyst can just plug in the percentages and does not have to actually estimate V D or V E. If it is not reasonable to assume that the firm s capital structure will be stable in the future (for example, if the firm is currently highly leveraged and its leverage is expected to decline), then the WACC method is problematic. Assuming a constant capital structure when valuing such a business can yield misleading results. Some of the other methods I will discuss can be used to work around that problem, but the WACC method is the most common and simplest income approach that uses FCFF. It is adequate for most analyses of large, publicly traded firms that are relatively stable. These types of firms manage their capital structure within an admittedly broad range sometimes, but they typically target a particular structure if for no other reason than to maintain a specific debt credit rating. In cases where it is not reasonable to assume that the firm is managing its financial policy toward some specific capital structure, an analyst can use another approach called the adjusted present value (APV) method. This method involves first valuing the business under the assumption that it is financed entirely with equity and then adding the present value of the effects of the firm s financing decisions to this unlevered firm value. The APV method is a lot easier to use than the WACC method when the debt-to-total-capital ratio for a firm is changing over time. The APV method also uses the FCFF exactly the same cash flow definition used with the WACC method. With the APV method, however, FCFF is discounted using the unlevered WACC to obtain the unlevered value of the firm, V UF. V UF = n t=0 FCFF --------------------------------------------------------------- t ( 1 + Unlevered WACC) t. The unlevered WACC is literally the cost of equity when the firm has no debt. If the CAPM is used to estimate the cost of equity, the unlevered WACC is simply the risk-free rate plus the asset beta (or unlevered beta) times the market risk premium. Thus, Unlevered WACC = k F + β A Market risk premium, where k F = risk-free rate β A = asset beta Market risk premium = expected market return less the risk-free rate Once the analyst has estimated the unlevered value of the firm, the effects of the firm s financing decisions on the value of the firm are computed and added to the unlevered value to obtain the APV. The APV method is usually applied in this way: n Tax rate t Interest t APV = V UF + -------------------------------------------------- ( 1 + k D ) t. t=0 The second term in this equation is the present value of the interest tax shields that the firm is expected to 20 CFA Institute Conference Proceedings 2005, CFA Institute cfapubs.org

Choosing the Right Valuation Approach realize from its debt financing. This is simply the present value of the tax rate times the interest payment in each year discounted using the cost of debt, k D. The cost of debt is often used in this calculation under the assumption that the tax shields will be realized when the firm is able to make its debt payments; therefore, the tax shields are about as risky as the debt. By that reasoning, the cost of debt is an appropriate discount rate for the tax shields. When using the APV method, analysts should be aware of one issue in particular: With the way this method is typically applied, something is missing. If the APV were plotted as a function of debt (i.e., APV on the vertical axis and debt level on the horizontal axis), the result would be an upward-sloping line that never turns downward. Of course, this implies that more debt is always better. The problem is that bankruptcy costs are missing from the calculation. Typically, as a firm levers up, the probability that it will get into financial difficulty increases. There is thus an increase in the expected costs associated with financial distress, which should cause the line in my example to start curving down at some point. Consequently, when the APV method is applied, analysts should be sure to include not only the benefits of debt (such as the value of the tax shield) but also the costs (such as bankruptcy costs and possibly debt issuance costs). The APV method is easier to use in instances when a firm has a changing capital structure because it involves forecasting the dollar interest payments rather than the debt-to-value ratio, which is inherently difficult to estimate in an exercise where the goal is to estimate the value of the firm or its securities in the first place. For example, the APV method would be particularly useful for a leveraged buyout analysis. Suppose a company is acquiring another business and levering it up to 65 percent debt. Furthermore, suppose that over the next five or six years, the company is going to pay down the debt to some normal level and then maintain a more typical capital structure thereafter. In such a case, the financing is set up-front and the analyst has a good idea of what the interest payments will be. The cost of each of the layers of debt and the repayment schedules are known, so the analyst can estimate the cost of debt and the present value of the tax shields year by year. In a case like this, the APV method is easier to apply than the WACC method. The bottom line with the FCFF approaches is that the WACC method is relatively straightforward to use with a mature firm where the analyst can assume that the firm will target a constant capital structure going forward. In cases where the capital structure may change substantially over time, the APV method can be much easier to use. FCFE Approach. The free cash flow to equity approach is very similar to the FCFF approaches except that instead of valuing the left-hand side of the balance sheet, meaning the assets of the business, the analyst is valuing only the equity claims on the righthand side of the balance sheet. To see how the FCFF and FCFE approaches are related, ask yourself the following question. If you wanted to value only the equity claims, how would you adjust the cash flows that are used in the FCFF approach? The answer is that you would simply want to strip out the cash flows to or from the creditors (debtholders). Recall from the discussion of the finance balance sheet (shown in Figure 1) that the value of the firm equals the value of the debt plus the value of the equity. Stripping out the cash flows to or from the creditors leaves the cash flows available to equityholders. So, the calculation in Exhibit 2 includes three lines that are not in the FCFF calculation. One is the interest expense, which is a cash flow to the creditors. The others are the cash flows associated with proceeds of new debt issues and the repayment of debt. This approach takes the total cash flows from the business and nets out any cash flows to the creditors, leaving cash flows available to the equityholders. Exhibit 2. FCFE Sales Operating expenses Earnings before interest, taxes, depreciation, and amortization Depreciation and amortization Operating profit Interest expense (1 Average tax rate) Net income + Depreciation and amortization Capital expenditures Additions to working capital + Proceeds from new debt issues Principal repayments FCFE Because cash flows available to equityholders are residual cash flows, they are riskier than the total cash flows from the firm if the firm has any leverage. Consequently, in using the FCFE valuation approach, if the firm has debt, the analyst must use a different discount rate from the one in the FCFF approach the standard cost of equity: FCFE t V E = -------------------- ( 1 + ) t. t=0 Unfortunately, this approach can be very difficult to apply in practice, especially for a mature firm, because it is has the worst of both worlds from the 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 21

Analyzing, Researching, and Valuing Equity Investments examples I have discussed. In order to forecast these cash flows, an analyst must forecast the actual dollar interest expense incurred to finance the firm in each year. In order to estimate the discount rate, the analyst also has to forecast the debt-to-total-capital ratio, on a market value basis, for each year. Remember that the cost of equity is a function of the levered beta. Going forward, as the dollar value of outstanding debt changes (or even if it does not change), the debtto-total-capital ratio is likely to be moving around as the value of the firm also changes. For the discount rate to be consistent with the cash flow forecasts (which include forecasts of the dollar interest expense), the analyst must estimate future debt-toequity ratios that are consistent with the dollar interest numbers he or she is putting in the cash flow forecasts. So, this approach can be very difficult and may require several iterations through the computations to obtain a reasonable result. It is a lot easier to use the WACC or the APV method to value the entire firm and then to just subtract the value of the debt if the analyst wants to estimate the value of the equity. DDM Approach. The dividend discount model approach is the third income approach I will discuss in this presentation. In the purest form, the DDM approach values the stream of cash flows that shareholders expect to receive. In contrast, the FCFF and FCFE approaches use cash flows available for distribution to shareholders. The firm may or may not be expected to distribute all available cash flows. DDMs are easy to use because they are simple models. But I will argue that they are likewise easy to abuse. They can be used to develop ballpark estimates for some shares, but in many cases, they are not very useful if the objective is to determine the intrinsic value of a business. Another thing to keep in mind is that the application of DDMs became more difficult as dividend payments declined from the late 1980s through the end of the 1990s. Market valuations and the values implied by traditional DDMs diverged during this period. Although dividend payments have risen somewhat since 2000, dividend yields remain low by historical standards. That said, the modeling technologies used by DDMs are still quite useful because they can be used elsewhere, such as with the FCFF or FCFE approaches. In the FCFF or FCFE approaches, analysts typically forecast cash flows year by year for several years and then estimate a terminal value as of the last year that is forecasted individually. Instead, they could simply compute the present values of all future cash flows using one of the DDM models. When analysts use the constant growth DDM, which I will discuss in detail shortly, they are simply assuming that the growth rate in dividends will be constant in perpetuity. With a two-stage model, an analyst assumes one rate over some period of time and then a different growth rate thereafter. These are really just modeling techniques that can be applied to any cash flow stream, including FCFF and FCFE, depending on how the analyst sees the cash flows evolving over time. So, DDMs can be useful in some circumstances as a distinct valuation method, but even where analysts do not feel comfortable forecasting the dividends, or if they believe the dividends do not reflect the intrinsic value of the business, DDM methods can be applied in other cash flow valuation approaches. Constant growth model. The constant growth DDM is familiar to most analysts: DIV P 0 ( 1 + g) DIV 0 = ------------------------------- = ------------- 1 g g where P 0 = current price of stock DIV 0 = dividend payment today DIV 1 = dividend payment next period g = dividend growth rate = cost of equity Keep in mind that a lot of assumptions are implicit in this model; for example, one assumption is that the cost of equity is greater than the growth rate of dividends. If the dividend growth rate is greater than the cost of equity, the model yields a negative share price. Of course, this cannot happen because equity is an option on the underlying assets of the firm and options cannot have negative values. So, this model cannot work if the dividend growth rate is greater than the cost of equity, which is one reason why it makes sense to use this model only when the growth rate has slowed to some long-run sustainable rate. (Another reason is that if one assumes a growth rate that is greater than the expected rate of inflation plus the real growth rate in the economy, then one is essentially assuming that the firm will become larger than the economy. Remember that this model assumes a growth rate in perpetuity.) In addition to assuming an infinite time horizon, the model assumes a constant return on reinvested equity. Many do not realize they are making this assumption when they use this model. The model assumes that every year, as the business grows and the firm reinvests a constant percentage of its earnings (the dividend payout rate is assumed to be constant), the firm will earn the same rate of return on reinvested capital. The dollar amount is increasing annually while the rate of return is remaining constant. Thus, some fairly strict assumptions underlie the constant growth model. 22 CFA Institute Conference Proceedings 2005, CFA Institute cfapubs.org

Choosing the Right Valuation Approach Alternative form of constant growth DDM. An alternative form of the constant growth model is a little more complicated but provides some interesting insights: P 0 EPS 1 b EPS 1 ( 1 b) ( ROE/ ) = --------------- + --------------------------------------------------------, where EPS 1 = earnings per share in the next period b = the dividend payout ratio (dividend per share/earnings per share) ROE = return on equity This model is just like the traditional constant growth model except it makes a different assumption regarding reinvestment: Instead of assuming that a constant proportion of earnings is reinvested, this model assumes the firm reinvests a constant dollar amount of earnings, on which it earns the same rate of return. An interesting feature of this model is that it separates the value of the firm into two components. The first term is the present value of the stream of dividends if one assumes earnings and the payout ratio remain constant. This can be viewed as the value of the existing dividend stream. The second term is the value of all the earnings that will be reinvested in the firm in the future (retained earnings) and that, presumably, will generate additional dividends at some point in the future. The second term of the formula includes the ratio of ROE to, the required rate of return on the firm s equity. If ROE exactly equals, then $1.00 reinvested is worth $1.00. If ROE is greater than, then $1.00 reinvested is worth more than $1.00. In other words, the $1.00 has been invested in a positive net present value project if ROE is greater than. So, this model explicitly recognizes or focuses on how value is created with reinvested earnings. It also provides a useful way to think about what drives the value of a business: The value of the business is a function of the cash flow stream from the projects that are in place plus the value that will be created by future investments. Application of the constant growth DDM. A potentially useful application of the constant growth model is in computing the cost of equity. Note that the constant growth model can be rearranged as follows: P ------------- DIV 1 0 g k DIV 1 EPS ------------ + g 1 b = = = --------------- + g. E P 0 One can plug in today s stock price (P 0 ), an estimate of the dividend next period (DIV 1 or EPS 1 b), and an estimate of the growth rate (g) to obtain an estimate of the cost of equity that is implied by today s stock price. 2 Just keep in mind that the reliability of the estimate depends on how appropriate this model is for the firm under consideration and on how efficiently the market is pricing its stock. If an analyst thinks the market is efficiently pricing the stock and the constant growth model is applicable, this analysis can be useful in deriving the cost of equity for a DCF analysis. 3 Another useful application of the cost of equity derived in this way arises when the analyst is not sure the current stock price is reasonable and wants a sanity check. In this case, the analyst can compare the cost of equity implied by the model with what he or she believes the cost of equity should be for the stock being analyzed. Figure 2 shows a security market line (SML) extending from the risk-free rate, k F. The CAPM says that the expected return is a linear function of beta. If I took some publicly traded stocks, backed out the cost of equity using a DDM, and plotted the implied expected return against the stocks betas, most of the points would not fall on the SML. 2 To estimate the growth rate for an exercise such as this, one might use I/B/E/S or consensus forecasts. 3 Other, more complicated models can be used to accomplish this same task, but the math is somewhat more complex. P 0 Figure 2. Application of Estimated Using the DDM Expected Return Security Market Line k F Beta 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 23

Analyzing, Researching, and Valuing Equity Investments If an implied expected return plots below the SML, the implication is that the stock is overvalued because the expected return is too low. In contrast, a stock that plots above the SML would be undervalued. Of course, this analysis assumes that the analyst believes his or her estimate of the appropriate required rate of return is reasonable given the risk of the business. Two-stage model. For some firms, dividends are expected to grow at a high rate in the short term and then to decline to some sustainable level in the long run. In using a DDM to value the stock of these firms, one can discount the dividends during the high-growth phase individually and use the constant growth model to value subsequent dividends. For instance, if a constant growth rate is assumed for a high-growth phase lasting n years, g stage1, and a lower constant growth rate is assumed for the terminal period, g terminal, a common two-stage DDM can be used: n DIV 0 ( 1 + g stage1 ) t P 0 = ---------------------------------------------- ( 1 + ) t t=1 DIV 0 ( 1 + g stage1 ) n ( 1 + g terminal ) ------------------------------------------------------------------------------------ g terminal + ----------------------------------------------------------------------------------------- ( 1 + ) n. Aside from the added complexity of the initial stage, the two-stage model is not conceptually much different from the constant growth model. In fact, the value of the dividends following the high-growth period is typically computed by using the constant growth model. As was the case with the constant growth model, the two-stage model is flexible enough to help answer a variety of questions. As an example, I used data from Bloomberg to calculate the growth rate in ebay s cash flows that was implied by its stock price on 16 November 2004. 4 In this instance, I plugged FCF/share from Bloomberg into the formula instead of dividends under the assumption that FCF/share is a reasonable estimate for FCFE/share. The fiveyear I/B/E/S forecast for EPS was about 34.4 percent (reported in Bloomberg as LT Growth ). For the cost of equity, I began with an estimate of the CAPM market risk premium, 6 percent; multiplied that by ebay s beta of 1.07; and added the risk-free rate, which was 4.89 percent, to arrive at an estimate of 11.31 percent. (I assumed it is reasonable to use a constant cost of equity in this analysis, which may not be a good assumption because ebay s risk will change as the company matures.) I assumed the abnormal growth period at ebay would continue for five years and would be followed by a terminal growth rate of 4 All data were as of 16 November 2004. about 4.5 percent, a number that is sustainable over a very long period. I arrived at 4.5 percent by adding an average 2 percent real economic growth rate for the economy to inflation expectations of about 2.5 percent. Now, the question is: What growth rate in Stage 1 is necessary to justify ebay s stock price of $108.08 as of 16 November 2004? The answer is an ambitious 66.66 percent. If ebay s cash flow per share is expected to grow at 66.66 percent a year for the next five years and then grow at 4.5 percent thereafter, and if one believes the constant 11.31 percent discount rate is reasonable, then the $108 price is justified. Notice again that the I/B/E/S forecast is just over 34 percent, which is far short of 66.66 percent. So, another question might be: How long does FCF/share have to grow at 34.4 percent annually to justify the $108 price? The answer is 10 years. The model indicates that if ebay s cash flows grow at a 34.56 percent annual rate for 10 years and then grow at 4.5 percent a year thereafter, this price is justified. This and other DDM models are thus useful in helping analysts think about what assumptions are implicit in the price observed in the market. In other words, these models can be used as a sanity check in support of other valuation approaches as well as an independent approach for estimating the intrinsic value of a stock directly. Contingent Claims Approach: Option Valuation Method The last of the valuation approaches I will discuss are those that use option valuation methods. To see why option valuation concepts are relevant to the valuation of equity, consider a firm with a single $5 million face value, zero-coupon debt issue outstanding that matures in one year. Furthermore, assume that V F * is the value of the assets of the firm when the debt matures a year from now. Figure 3 shows the payoffs to the debtholders and to the equityholders when the debt in this example matures. If the firm is worth more than $5 million, the debtholders will be paid off in full and the shareholders will get any residual value above the $5 million face value of the debt, F. If the value of the firm is below $5 million, the debtholders, at least in theory, get the firm. In other words, the shareholders have an option to default. The shareholders downside is limited to what they have already invested in the firm, and the debtholders receive the residual value of the firm if that option is exercised. 24 CFA Institute Conference Proceedings 2005, CFA Institute cfapubs.org

Choosing the Right Valuation Approach Figure 3. Option Characteristics of Debt and Equity Claims A. Payoff to Debtholders at Maturity B. Payoff to Shareholders at Maturity V D * V E * F V F * F F = $5 million V F * F = $5 million V F * Another way of thinking about this idea is to realize that the shareholders essentially have a call option on the underlying assets of the firm. When the debt matures, the shareholders have the option to pay off the debt or walk away. If, on the one hand, the value of the firm is greater than $5 million, the shareholders can pay the $5 million and realize the difference in value even if they do not want to continue to hold the firm; they can always sell it and pocket the difference. If, on the other hand, the firm s assets are worth less than $5 million, the shareholders will let their option expire and will walk away, leaving the debtholders to receive whatever is left. The debtholders, in turn, have a payoff function similar to that of someone who is short a put option. The debtholders have effectively sold the shareholders a put option on the firm. The shareholders have the right to put the firm back to the debtholders, forcing the debtholders to bear the loss if the value of the firm is less than the $5 million the debtholders are owed. Therefore, debt and equity are essentially options on the underlying assets of the firm. Whenever there are multiple claims on an underlying asset that have different priorities, analysts should be aware that they may be dealing with option claims. Recognizing this, one can see the rationale, under certain circumstances, of valuing equity by using option-pricing methods. For example, the following is a variation of the Black Scholes model that includes dividends: C V F e δt N ln ( V F /F) + ( r f δ + σ 2 /2)T = ------------------------------------------------------------------------ σ T Fe r f T N ln ( V F /F) + ( r f δ σ 2 /2)T ------------------------------------------------------------------------, σ T where V F = value of the firm F = face value of the debt in this corporate valuation context T = length of time until the debt matures r f = risk-free rate σ = volatility of the rate of return on the underlying asset, the firm δ = dividend yield Note that the above six variables drive the value of this option. It is quite possible to find real-world companies for which a DCF valuation analysis yields a negative equity value, which I already pointed out is unreasonable. It is also common to see stocks in this situation trading at a positive, albeit relatively small, price. Just because a DCF analysis yields a negative number, implying a value of zero, does not mean the equity is worthless. Things change. For example, general economic conditions change, industry conditions change, firm conditions change, quotas and tariffs change, and capital market conditions change. Some possibility virtually always exists with an operating company that between now and the time when the firm s debt matures, the value of the firm will exceed the face value of the debt, the firm will pay off the debt, and the shareholders will receive some residual value. Valuing those possibilities is very difficult in the context of a DCF analysis because the firm s risk, and therefore its discount rate, is changing over time as the underlying characteristics of the business change. One way to get around this problem is to use an option-pricing approach. The option I have just discussed is the option to liquidate the firm where the shareholders have the option to absolve themselves of the firm s obligations by filing for bankruptcy. Option-pricing models can 2005, CFA Institute cfapubs.org CFA Institute Conference Proceedings 25