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ANALYSIS OF COMMON STOCKS APPROACHES FOR ANALYZING STOCK Fundamental Analysis A method of security analysis which seeks to determine the intrinsic value of securities based on underlying economic factors. Fundamental analysis focuses on the accounting and economic factors about a company. These include such information as data from financial statements (especially earnings and growth in earnings), quality of management, future prospects, economic and market conditions, forthcoming legislation that might affect the firm, new-product development and so on. For the fundamental analysts the valuation problem becomes one of forecasting future earnings and growth in earnings and multiplying the expected earnings by the appropriate multiplier. Technical Analysis A method of security analysis to forecast fluctuations in security prices based primarily on historical price and volume trends in those securities. Technical analysis is based on the premise that all information about a stock is reflected in the past sequence of its prices and trading volume. Technicians argue that anything that the fundamental analyst is trying to discover already is contained in its price chart, and the chart will tell you when it is time to buy, sell, or hold the security. Difference Between Fundamental and Technical Analysis 1. The fundamental analysts try to determine the economic worth of a security, while the technical analysts attempt to predict the future price of the security. For the technician, valuation is not really the objective; predicting the future price movements in the security is. 2. Whereas most fundamental analysts have an investment horizon of several months to three or more years, the investment horizon of the technical analysts is very short - the next hour or the next trading day. 3. Technical analysts focus on internal factors by analyzing movement in the market and/or a stock. In contrast, fundamental analysts focus on economic and political factors, which are external to the market itself. Why Technical Analysis is Supposed to Work? In their classic book on technical trading strategies, Technical Analysis of Stock Trends, R. D. Edwards and John Magee, Jr., listed five factors that are supposed to make technical analysis work: 1. The price of a security is determined solely by its supply and demand. 2. Prices tend to move in trends that persist for an appreciable time. 3. Changes in trends are caused by changes in supply and demand. 4. The patterns or trends tend to repeat themselves over time. 5. Supply and demand is governed by both rational and irrational factors. Framework for Fundamental Analysis Two General Approaches to Fundamental Analysis The Top-Down, Three-Step Approach The Bottom-Up, Stock Valuation, Stock picking Approach The Top-Down, Three-Step Approach Market Analysis Market analysis is important because: a) a substantial portion of the average stock's return is attributable to the market, 1 b) movements in the overall market are the dominant factor affecting the return of a diversified portfolio, c) market measures are useful to investors in quickly judging their overall portfolio performance, and d) as stocks tend to move together, the rising or falling of the market will generally indicate to the investor how he or she is likely to do. Complete market analysis would involve estimating and forecasting each of the following variables: a) Market interest rates (which serve as proxies for investors' required return) b) Money supply c) GNP d) Corporate sales e) Corporate earnings before and after taxes f) Government spending g) Price level and inflation Industry Analysis Identify those industries that will perform best in the future in terms of returns to shareholders. The significance of industry analysis can be established by considering the performance of various industries over time. This analysis will indicate the value to investors of selecting certain industries while avoiding others. Industries are analyzed through the study of a wide range of data, including sales, earnings, dividends, capital structure, product lines, regulations, innovations, and so on. Such analysis requires considerable expertise and is usually performed by industry analysts employed by brokerage firms and other institutional investors. Steps in Industry Analysis: a) Analyze industries in terms of their stage in the life cycle. b) Assess the position of the industry in relation to the business cycle and macroeconomic conditions. c) Quantitative analysis of industry characteristics to assess its future prospects. Industry Life Cycle Three stages of industry life cycle i) Pioneering stage Strong firms in the industry experience rapid growth in sales and earnings, possibly at an increasing rate, and the weaker ones failing and dropping out. ii) Expansion stage The survivors from the pioneering stage continue to grow and prosper, but at a rate more moderate than before. iii) Stabilization stage Growth begins to slow down and stabilize. Sales may be increasing but at a much slower rate than before. Business Cycle Analysis Industries are analyzed in terms of their ability to operate in different stages of business cycle. Growth Industries industries with expected earnings growth significantly above the average of all industries. Defensive Industries 2 industries least affected by recessions and economic adversity. Cyclical Industries industries most affected, both up and down, by the stages of business cycle. They do unusually well when the economy prospers and are likely to be hurt more when the economy falters. Interest-Sensitive Industries industries particularly sensitive to expectations about changes in interest rate. Quantitative Analysis of Industries Historical Performance Investors should consider track record of industry sales and earnings growth and price performance. Competition The nature of competition in an industry (such as entry restriction, excessive cost of building plants) determines an industry's ability to sustain above average returns. Regulations Impact of government regulations and actions on the firms in an industry. Structural Changes Impact of structural changes within the economy on the industry. Company Analysis The objective of fundamental analysis is to determine current and projected economic earnings for a company. Regardless of the accounting procedures used, the cash flow that the firm generates over the year will be same except for the amount of cash siphoned off to pay taxes. 1. The job is to try to make sense of the financial statements and produce an estimate of a company's economic income that is not biased by tax-driven manipulations or different accounting rules (relating to inventory valuation, depreciation expenses, merger and acquisition, expensing versus capitalizing expenditures, discontinued operations and extraordinary items that affect EPS) that can be used. 2. Fundamental analysis also examines the quality of reported earnings and the strength of the firm's earnings and financial statements. Quality refers to how the company generates its return on equity (ROE) and its ability to maintain and/or increase its rate of return in the future. The following tools are used in this analysis: a) Du Pont Analysis Decomposition of return on equity into component ratios derived from profitability of operations, utilization of assets, and use of debt financing: ROE = PM x TAT x EM The quality of earnings would be found in situations in which ROE is derived from the firm's net profit on sales and in an environment that is unlikely to change. b) Growth Analysis c) Financial Ratio Analysis Financial ratios are examined to find out more about the way the management controls the firm's liquidity, asset utilization, financial structure, and the relationship of book and market values. 3 A Framework for Technical Analysis Technical analysis can be applied to both the aggregate market and individual stocks. Either can be analyzed by graphs (charts) and, in some cases, by technical indicators that are applicable to both. Aggregate Market Analysis Dow Theory A technique for detecting long-term trends in the aggregate stock market. Three types of price movements 1) Primary moves; a movement lasting for several years. 2) Secondary (intermediate) moves; moves occurring within the primary moves, which represent interruptions lasting several weeks or months. 3) Day-to-day moves; moves occurring randomly around the primary and secondary moves. Bull market An upward primary move: a major upward move is said to occur when successive rallies penetrate previous highs, while declines remain above previous lows. Bear market A downward primary move: a major downward move is expected when successive rallies fail to penetrate previous highs, whereas declines penetrate previous lows. Technical corrections Corrections supposedly adjust for excesses that have occurred; secondary or intermediate moves give rise to technical corrections. Advance-Decline Line (Breadth of the market) Measures the net difference between the number of stocks advancing in price and those declining in price. The advance-decline line is compared to a stock index, in particular the DJIA, in order to determine whether movements in the market indicator have also occurred in the market as a whole. If both are rising (declining), the overall market is said to be technically strong (weak). Particular attention is given to the divergence between the two during a bull market. Moving Averages It is calculated by averaging prices over the most recent n days and as each day passes, the earliest day is dropped and the most recent one is included. The purpose is to "smooth" the data and eliminate the outliers. The moving average calculation is repeated daily or weekly and the resulting series of moving averages (called the moving average line) supposedly represents the basic trend of prices. It is specifically used to detect both the direction and the rate of change. A buy signal is given when daily price crosses upward through the moving average line, and a sell signal is occurs when the daily price falls below the moving average line. New Highs and Lows Technicians regard the market as bullish when a significant number of stocks each day hit 52-week highs. On the other hand, rising market indices and few stocks hitting new highs are considered a troublesome sign. Volume Heavy trading volume, other things being equal, is generally regarded as a bullish sign. 4 Mutual Fund Cash Positions When cash balances of mutual funds rise to abnormally high level, technicians become bullish on the market, and vice versa when cash balances become too low. When mutual fund managers are bearish, they transfer funds to cash because they believe stocks will become cheaper. Similarly, when they are bullish, they reduce cash balances as low as possible and become "fully invested." Thus the cash balances of mutual funds are used as a contrary indicator. Large cash balances provide liquidity for buying stock and low cash balances mean that new positions can be taken only by selling currently held stocks. Mutual fund cash positions are reported each week in Barron's. Historically, cash balances above 12 percent are considered too high and thus signal buying opportunities, and balances below 7 percent are too low and indicate time to sell. Short Interest Ratio Total shares sold short divided by average daily trading volume. High short interest ratio is taken as a bullish sign, because the large number of shares short sold represents a large number of shares that must be repurchased to cover short sale increasing the potential demand for the stock. Contrarian Investment Strategy To do the opposite of what most other investors are doing in the belief that investors tend to overreact to news. That is, buying “losers” or “fallen angels” and selling “winners.” In other words, going against the crowd. Individual Stock Analysis Technical analysts use a number of basic patterns and indicators to analyze stock price movement. These are Trends Upward trend Downward trend Neutral trend or “trading range” Sequence of prices in which the trend is flat. Divergence The relationship between one high (low) and the subsequent high (low). Bearish divergence A subsequent high is lower than the previous high and signals selling your position and going short. Bullish divergence A subsequent low is higher than the previous low and signals going long. Moving Averages Relative Strength Index Attempts to determine the security's strength depending on the pattern of closing prices. For a given period, relative strength index is calculated as the ratio of the number of “up” closes (that is, a day's closing price exceeded that of the previous trading day), Uc , and the sum of “up” closes and “down” closes, Dc , times 100: UC Relative Strength Index = x 100 UC U D Number of days is usually set between 10 and 20 days. If the ratio is 50, then the closes are evenly divided between ups and downs. As the ratio goes above (below) 50, more (less) closes 5 are up than down, so the market is trending up (down). The technicians would state that when the ratio passes (falls below) 70 (30) the market has reached a top (bottom) and would issue a sell (buy) recommendation because the market will reverse itself. Relative strength is also used to describe the price performance of a stock compared to the general market, an industry, or another stock in its industry. The technicians relate the price behavior of the security to an industry or market index, buying (selling) those that show positive (negative) relative strengths. Momentum Investing One of the most popular technical analysis techniques is that of momentum investing, which a relative strength approach is basically. The basic premise of momentum investing is that if a stock has outperformed the market over some recent period, it is likely to continue to do so for a while. In fact, this approach is of following the trend. Support and Resistance Levels A support level is a narrow price range at which an increase is expected in the demand for a stock, thus providing a floor on the price. A resistance level is a narrow price range at which the technician expects additional supply of the stock, thus providing a ceiling for price increase. The technician would expect a stock to trade between the support and resistance levels until new, significant information causes it to move beyond one of these two prices. Overbought and Oversold A stock that is overbought is too high relative to where it will be in the near future and thus is predicted to fall in price. A stock that is oversold has been driven too low and should recover in the near future. Filter Rules Buy a stock if the price rises from a base price (previous low price) by the filter percentage (say 1 percent), or more, and sell if it falls from a subsequent peak by the same filter percentage, at the same time selling short. Super Bowl Indicator If a team from NFC wins the Super Bowl, the market is destined to advance, and if an AFC team wins, the market will decline. 20 out of 22 years the predictor has correctly indicated the direction of the market over the year. Because individual indicators can give spurious signals and thus are not completely reliable, most technicians look at a number of them and form their recommendation on their interpretation of all of the indicators they use. Common Stock Valuation APPROACHES TO VALUATION In general terms, there are three approaches to valuation. The first, discounted cash flow valuation, relates the value of an asset to the present value of expected futures cash flows on that asset. The second, relative valuation, estimates the value of an asset by looking at the pricing of “comparable assets.” The third, contingent claim valuation uses option pricing models to measure the value of assets that share option characteristics. ESTIMATION OF GROWTH RATES The value of a firm is ultimately determined not by current cash flows but by expected future cash flows. The estimation of growth rates in earnings and cash flows is therefore central to doing a reasonable valuation. Growth rates can be obtained in many ways – they can be based upon past growth, drawn from estimates made by other analysts who follow the firm or related to the firm’s fundamentals. 6 Using Average Growth Rates from the Past This approach uses the average growth rate from the past as the predicted growth rate for the future. The average growth rate can be very different depending upon whether it is an arithmetic average or a geometric average. The arithmetic average is the arithmetic mean of past growth rates, while the geometric average takes into account the compounding effect. The latter is clearly a much more accurate measure of true growth in the past earnings, especially when year-to-year growth has been erratic. Example The following are the EPS at Glaxo Pharmaceuticals, starting in 1989 and ending in 1994: Year EPS Growth Rate 1989 $0.66 1990 0.90 36.36% 1991 0.91 1.11 1992 1.27 39.56 1993 1.13 -11.02 1994 1.27 12.39 Arithmetic average = (36.36 + 1.11 + 39.56 - 11.02 + 12.39%)/5 = 15.68% Geometric average = (1.27/.66)1/5 – 1 = 13.99% The arithmetic average will be higher than geometric average and the difference will increase with the variability in earnings. An alternative to the standard calculation of the arithmetic average is a weighted average, with growth rates in more recent years being weighted more heavily than growth rates in earlier years. This would lead to a much lower estimate of the average for Glaxo. Regression Models for Growth The linear version of the model is: EPSt = a + bt where EPSt = earnings per share in period t t = time period t The slope coefficient on the time variable is a measure of earnings change per time period. The log-linear version of this model converts the coefficient into a percentage change: Ln(EPSt) = a + bt where Ln(EPSt) = natural logarithm of earnings per share in period t The coefficient b on the time variable becomes a measure of the percentage change in earnings per unit time. Example The following are the EPS at Glaxo Pharmaceuticals, starting in 1988 and ending in 1994: Time (t) Year EPS Ln(EPSt) 1 1988 $0.65 -0.43 2 1989 0.66 -0.42 3 1990 0.90 -0.11 4 1991 0.91 -0.09 5 1992 1.27 0.24 6 1993 1.13 0.12 7 1994 1.27 0.24 7 Linear Regression: EPS = .5171 + .1132t Log-linear regression: Ln(EPS) = -.55536 + 1225t The slope from the log-linear regression (0.1225) provides an estimate of growth rate of 12.25% in earnings. The slope from the linear regression is in dollar terms. The Use of Analyst’s Forecasts of Earnings The information in the growth rates estimated by analysts can and should be incorporated into estimation of expected future growth. Analysts who follow a firm, in addition to using historical data for growth estimation, can avail themselves of other information that may be useful in predicting future growth. This makes analysts’ forecasts of growth better than mechanical models. (a) Firm-specific information that has been made public since the last earnings report. Analysts can use information that has come out about the firm since the last earnings report to make predictions about future growth. The information can sometimes lead to significant reevaluation of the firm’s expected cash flows. (b) Macroeconomic information that may impact future growth. The expected growth rates of all firms are affected by economic news on GNP growth, interest rates, and inflation. Analysts can update their projections of future growth as new information comes out about the overall economy and about changes in fiscal and monetary policy. Information, for instance, that shows the economy growing at a faster rate than forecast will result in analysts increasing their estimates of expected growth for cyclical firms. (c) Information reveled by competitors on future prospects. Analysts can also condition their growth estimates for a firm on information revealed by competitors on pricing policy and future growth. (d) Private Information about the firm. Analysts sometimes have access to private information about the firms they follow that may be relevant in forecasting future growth. This avoids answering the delicate question of when private information becomes illegal inside information. There is no doubt, however, that good private information can lead to significantly better estimates of future growth. (e) Public information other than earnings. Models for forecasting earnings that depend entirely upon past earnings data may ignore other publicly available information that is useful in forecasting future earnings. It has been shown, for instance, that other financial variables such as earnings retention, profit margins, and asset turnover are useful in predicting future growth. Analysts can incorporate information from these variables into their forecasts. Growth Rates Based on Firm’s Fundamentals While growth in a firm may be measured by using history or analyst forecasts, it is determined by fundamental decisions that a firm makes on product line, profit margins, leverage, and dividend policy. The simplest relationship determining growth is one based upon the retention ratio (percentage of earnings retained in the firm and the return on equity on its projects): Growth rate = b x ROE where b = Retention ratio = (Net Income – Dividends)/Net Income ROE = Return on Equity = Net Income/Equity = Profit Margin x Total Assets Turnover x Equity Multiplier 8 Weighting Different Estimates of Growth There are three possible ways of estimating growth: use historical data in either naïve or time series models, use the consensus forecasts made by the analysts, or use growth rates estimated from the firm’s fundamentals. From a practical standpoint, the three approaches often overlap. Analysts use historical data in forecasting earnings, and analyst estimates of fundamentals (such as profit margins) as well as historical data drive many fundamental models of growth. On the contrary, they often provide very different estimates of growth, leaving the analyst with the difficult decisions of which growth rate or what combination of growth rates to use in valuation. If only one of these three growth rates is to be used, the appropriate one will depend upon the firm being analyzed. If the firm is going through a complex restructuring, the growth rate from fundamentals is the best choice because it can be conditioned on the planned changes in the asset and liability mix. If the firm is relatively stable in terms of its fundamentals and is heavily followed by analysts, their long-term forecasts are likely to dominate forecasts from other approaches. If a firm has established a stable pattern of historical growth and the fundamentals of the business have not changes, the time series models based upon historical data will provide accurate forecasts of future growth. There is no reason, however, to use only one of these growth rates. Each approach provides a forecast of future growth and is informative. A weighted average of these growth rates, with the weight based upon the informativeness of each growth rate, may provide an estimate of future growth superior to any one of the three. DIVIDEND DISCOUNT MODELS The basic model for valuing equity is the dividend discount model – the value of a stock is the present value of dividends through infinity: Dt P0 t 1 r t 1 where P0 = value of a stock Dt = expected dividends per share in period t r = required rate of return on stock The Gordon Growth Model The Gordon model relates the value of a stock to its expected dividends in the next time period, the required rate of return on the stock, and the expected growth rate in dividends. D1 P0 rg where D1 = expected dividends one period from now = Do (1 + g) Do = Current dividends g = growth rate in dividends forever Suitability of the Model The Gordon model is best suited for firms growing at a rate comparable to or lower than the normal growth rate in the economy and that have well-established dividend payout policies that they intend to continue into the future. The dividend payout of the firm has to be consistent with the assumption of stability, since stable firms generally pay substantial dividends. 9 Application of the Model Consolidated Edison is the utility that supplies power to homes and businesses in New York and its environs. It is a monopoly whose prices and profits are regulated by the State of New York. Rationale for using the model: The firm is in stable growth, based upon size and the area that it serves. Its rates are regulated; it is unlikely that regulators will allow profits to grow at extraordinary rates. The beta is .75 and has been stable over time. The firm is in stable leverage. The firm pays out dividends that are roughly equal to its free cash flows to equity. Background Information: Dividends per share in 1994 = $2.00 Expected growth rate = 5% Long-term bond rate = 7.5% S&P 500 Index return = 13% Discount rate = 7.5% + (.75 x 5.5%) = 11.63% Value of equity = $2.00 x 1.05 / (.1163 - .05) = $31.67. Con Ed was trading at $26.75 on the day of this analysis (March 1995) What growth rate would Con Ed have to have to justify the current stock price? Solving for the expected growth rate that provides the current price, $26.75 = $2.00(1 + g)/(.1163 – g) Solving for g, g = (.1163x $26.75 - $2.00)/($26.75 + $2.00) = 3.86% The growth rate would have to be 3.86% to justify the stock price of $26.75. Chemical Bank is one of the largest commercial banks in the United States, and it also derives considerable revenues from providing other financial services and from trading. Rational for using the model: As a large financial service firm in a competitive environment, it is unlikely that Chemical’s earnings are going to grow much faster than the economy over the long term. Allowing for international expansion, the expected growth rate used is 7%. As a financial service firm, free cash flows to equity are difficult to estimate; hence the dependence on dividends. The leverage of financial service firms is high and unlikely to change over time. Background information: Dividends per share = $1.76 Expected growth rate = 7% Long-term bond rate = 7.5% S&P 500 Index return = 13% Discount rate = 7.5% + (1.25 x 5.5%) = 14. 38% Value of equity = $1.76 x 1.07 / (.1438 - .07) = $25.52 Limitations of the Model The Gordon model is a simple and convenient way of valuing stocks, but it is extremely sensitive to the inputs for the growth rate. As the growth rate converges on the discount rate, the value goes to infinity. 10 Two-Stage Dividend Discount Model The two-stage growth model allows for two stages of growth: an initial phase that lasts for n years where the growth rate is high and a subsequent steady state that lasts forever where the growth rate is stable. Value of the stock is the present value of dividends during high-growth phase plus the present value of stock price at the end of the high-growth phase. n Dt Pn P0 t 1 r 1 r n t 1 where Dn1 Pn = price at the end of year n rn g n g = extraordinary-growth rate for the first n years gn = growth rate forever after n years rn = required return in steady-state Suitability of the Model Since the two-stage model is based upon two clearly delineated growth rates – high growth and stable growth – it is best suited for firms that are in high growth and expect to maintain that growth for a specific time period, after which the sources of the high growth are expected to disappear. One scenario, for instance, in which this may apply is when a company is in an industry that is enjoying super-normal growth, because there are significant barriers to entry (either legal or as a consequence of infrastructure requirements), which can be expected to keep new entrants out for several years. Application of the Model In February 1995, Warren Buffett announced that he was increasing his stake in American Express from 5% to 9.8%, leading to a surge in the stock price. As a large financial service firm, American Express would be a good candidate for a two-stage dividend discount model. Rationale for using the model: Why two-stage? While American Express is a large financial service firm in a competitive market place, normally not a candidate for above-stable growth, it has gone through an extended period of depressed earnings (EPS in 1994 was $2.70 while earnings five years earlier was $3.52). It is expected that the recovery in earnings will create higher growth over the next five years. Why dividends? As a financial service firm, free cash flows to equity are difficult to estimate. The financial leverage is stable. Background information: EPS in 1994 = $2.70 Dividends per share in 1994 = $.90 Length of the high-growth period = 5 years High-growth payout ratio = 33.33% Long-term bond rate = 7.50% S&P 500 Index return = 13% Beta during the high-growth period = 1.45 Discount rate during the high-growth period = 15.48% Expected growth rate during the high-growth period = 13.04% Expected growth rate in stable-growth period = 6% 11 Beta during the stable-growth period = 1.10 Stable payout ratio = 69.33% Discount rate during the stable-growth period = 13.55% Estimating the value: Based upon the current EPS of $2.70, the expected growth rate of 13.04%, and the expected dividend payout ratio of 33.33%, the expected dividends can be computed for each year in the high-growth period: Year EPS Div PV 1 $3.05 $1.02 $0.88 2 3.45 1.15 .86 3 3.90 1.30 .84 4 4.41 1.47 .83 5 4.98 1.66 .81 PV of dividends during years 1-5 = $4.22 The price at the end of high-growth phase (end of year 5) is $4.98 x 1.06 x .6933 / (.1355 -.06) = $48.47 PV of this terminal price is $48.47/(1.1548)5 = $23.60 The value of the stock today is $4.22 + $23.60 = $27.82 Limitations of the Model There are three problems with the two-stage dividend discount model. The first practical problem is in defining the length of the extraordinary-growth period. Since the growth rate is expected to decline to a stable level after this period, the value of an investment will increase as this period is made longer. While, in theory, the duration of the growth phase can be linked to product life cycles and project opportunities, it is difficult in practice to convert these qualitative considerations into a specific time period. The second problem with this model lies in the assumption that the growth rate is high during the initial period and is transformed overnight to a lower stable rate at the end of the period. While these sudden transformations in growth can happen, it is much more realistic to assume that the shift from high to stable growth happens gradually over time. Third, since a significant component of the present value in the two-stage model comes from the terminal price (Pn), which is calculated using the Gordon model, the value is sensitive to assumptions about the stable growth. Overestimating or underestimating this growth can lead to significant errors in value. The H Model The H model is a two-stage model for growth, but unlike the classical two-stage model, the growth rate in the initial-growth phase (which is assumed to last 2H periods) is not constant but declines linearly over time to reach the stable-growth rate in steady state. The model is based upon the assumption that the earnings growth rate starts at a high initial rate (ga) and declines linearly over the extraordinary-growth period to a stable growth rate (gn). It also assumed that the payout ratio and the required rate of return are constant over time and are not affected by the shifting growth rates. The value of stock in the H model can be estimated as follows: Do 1 g n D0 x H g a g n P0 r gn r gn ___________ __________________ Stable Growth Extraordinary Growth 12 Suitability of the Model The allowance for a gradual decrease in growth rates over time may make this a useful model for firms that are growing rapidly right now but whose growth is expected to decline gradually over time as the firms get larger and the differential advantage they have over their competitors declines. The assumption that the payout ratio is constant, however, makes this an inappropriate model to use for any firm that has low or no dividends currently. Thus, the model, by requiring a combination of high growth and high payout, may be quite limited in its applicability. Application of the Model Syntex Corporation was expected to have earnings per share of $2.15 in 1993 and to payout dividends of $1.08 in the same year. The earnings had grown 18% a year for the previous five years, but this growth was expected to decline linearly (2% a year) over the next six years to a stable growth rate of 6%. The decline in growth can be attributed to three factors: (a) Declining profitability on two of the company’s flagship products, Naprosyn and Anaprox (which generated almost half of all revenues in 1992), due to increased competition. (b) Lower profitability in the health care sector overall. (c) The fact that the firm has grown in size substantially, and maintaining high growth is getting progressively more difficult. The beta for Syntex was 1.25, while the Treasury bond rate was 7%. Current EPS = $2.15 Current dividends = $1.08 Current growth rate (ga) = 18% Length of transition period = 6 years Stable growth rate (gn) = 6% Discount rate = 7% + 1.25 x 5.5% = 13.88% Value of stable growth = ($1.08 x 1.06)/(.1388 - .06) = $14.53 Value of high growth = ($1.08 x 6/2 x (.18 - .06)/(.1388 - .06) = $4.91 Value of stock = $14.53 + $4.91 = $19.44 The stock was trading at $19.00 in May 1993. Limitations of the H Model This model avoids the problems associated with the growth rate dropping precipitously from the high-growth to the stable growth phase, but does so at a cost. First, the decline in the growth rate is expected to follow the strict structure laid out in the model – it drops in linear increments each year based upon the initial-growth rate, the stable-growth rate, and the length of the extraordinary-growth period. While small deviations from this assumption do not affect the value significantly, large deviations can cause problems. Second, the assumption that the payout ratio is constant through both phases of growth exposes the analyst to an inconsistency – as growth rate decline, the payout ratio remains unchanged (when it should be increasing). Three-Stage Dividend Discount Model The three-stage dividend discount model combines the features of the two-stage model and the H model. It allows for an initial period of high growth, a transitional period of declining growth, and a final stable-growth phase that lasts forever. It is the most general of the models because it does not impose any restrictions on the payout ratio. The payout ratio will generally be low in the high-growth period, increase during the transition period, and be high in the stable- growth period. 13 The value of the stock is then the PV of expected dividends during the high-growth and the transitional periods, and of the terminal price at the start of the final stable-growth phase: n1 EPS0 1 g a x a t n2 Dt EPSn2 1 g n x n P0 t 1 1 r t t n1 1 r 1 t r g n 1 r n _________________ ___________ _______________ High Growth Transition Stable Growth where ga = growth rate in high-growth phase (lasts n1 years) gn = growth rate in stable-growth phase a = payout ratio in high-growth phase n = payout ratio in stable-growth phase r = discount rate in high-growth phase rn = discount rate in stable-growth phase Suitability of the Model The model’s flexibility makes it a useful model for any firm, which in addition to changing growth over time is expected to change on other dimensions as well – in particular, payout policies and risk. It is best suited for firms that are growing at an extraordinary rate now and are expected to maintain this rate for an initial period, after which the differential advantage of the firm is expected to deplete leading to gradual declines in the growth rate to a stable-growth rate. Practically speaking, this may be the more appropriate model to use for a firm whose earnings are growing at very high rates, are expected to continue growing at those rates for an initial period, but are expected to start declining gradually toward a stable rate as the firm becomes larger and loses its competitive advantages. Application of the Model The Home Depot is one of the great retailing success stories of the 1980s and early 1990s. It posted extraordinary growth both in revenues and profits and reaped its stockholders immense returns. Rationale for using the model: Why three-stage? The Home Depot is still in very high growth phase. Analysts project that its EPS will grow at 36% a year for the next 5 years. Why dividends? The firm has had a track record of paying out dividends those roughly approximate free cash flows to equity. The financial leverage is stable. Background information: Current earnings/dividends: EPS in 1994 = $1.33 Dividends in 1994 = $0.16 Inputs for the high-growth period: Length of the high-growth period = 5 years Expected growth rate = 36% Beta = 1.60 Discount rate = 7.5% + 1.60(5.5) = 16.30% Long-Term bond rate = 7.5% Payout ratio = 12.03% Inputs for the transition period: 14 Length of the transition period = 5 years Growth rate in earnings will decline from 36% in year 5 to 6% in year 10 in linear increments. Beta will drop from 1.60 to 1.00 over the same period in linear increments. Inputs for the stable-growth period: Expected growth rate = 6% Beta = 1.00 Discount rate = 7.5% + (1.0 x 5.5%) = 13.00% Payout ratio = 60% Estimating the value: These inputs are used to estimate expected EPS, payout ratios, dividends, and discount rates for the high-growth, transition, and stable-growth periods. The PVs are as follows: Year EPS Payout Div r PV 1 $1.81 12.03% $0.22 16.30% $0.19 2 2.46 12.03 .30 16.30 .22 3 3.35 12.03 .40 16.30 .26 4 4.55 12.03 .55 16.30 .30 5 6.19 12.03 .74 16.30 .35 6 8.04 40.81 3.28 15.64 1.33 7 9.97 45.64 4.55 14.98 1.61 8 11.77 50.38 5.93 14.32 1.83 9 13.18 55.24 7.28 13.66 1.98 10 13.97 60.00 8.38 13.00 2.02 Since the discount rate changes each year, the PV has to be calculated using the cumulated discount rate. Thus, in year 7, the PV of dividends is $4.55/(1.16305 x 1.1564 x 1.1498) = $1.61 The terminal price at the end of year 10 can be calculated based upon the EPS in year 11, the stable-growth rate of 6%, a discount rate of 13%, and the payout ratio of 60%. Terminal price = $13.97 x 1.06 x .60/(.13 -.06) = $126.96 The components of value are as follows: PV of dividends in high-growth phase = $1.31 PV of dividends in transition phase = $8.77 PV of terminal price = $30.57 Value of Home Depot stock = $40.65 Home Depot stock was trading at $45 in February 1995. Limitations of the Model The model removes many of the constraints imposed by other versions of the dividend discount model. In return, however, it requires a much larger number of inputs – year-specific payout ratios, growth rates, and betas. For firms where there is substantial noise in the estimation process, the errors in these inputs can overwhelm any benefits that accrue from the additional flexibility in the model. Valuing Non-Dividend-Paying or Low-Dividend-Paying Stocks The conventional wisdom is that the dividend discount model cannot be used to value a stock that pays low or no dividends. This is incorrect. If the dividend payout ratio is adjusted to reflect changes in the expected growth rate, a reasonable value can be obtained even for non- 15 dividend-paying firms. Thus, a high-growth firm, paying no dividends currently, can still be valued based upon dividends that it is expected to pay out when the growth rate declines. FREE CASH FLOWS TO EQUITY DISCOUNT MODELS The FCFE discount model values stock as the PV of future expected free cash flows to equity (FCFE). Estimation of Free Cash Flows to Equity FCFE for an unlevered firm can be estimated as follows: FCFE = NI + Dep – Net Capital Spending – Change in NWC. FCFE for a levered firm can be estimated as follows: NI + Dep – Preferred Dividends – Net Capital Spending - Change in NWC – Principal Repayments + Proceeds from New Debt Issue. If a levered firm is at its desired leverage, that is, it has a debt ratio that it views as acceptable for future financing, the calculation of FCFE is simplified. For a firm with a desired debt ratio, FCFE equals NI – (Net Capital Spending – Dep)(1 – Debt Ratio) – Change in NWC (1 – Debt Ratio). FCFE Valuation Models The three versions of the FCFE models are simple variants on the dividend discount model, with one significant change – FCFE replaces dividends in the model. The Stable-Growth FCFE Model The value of equity, under the stable-growth model, is a function of the expected FCFE in the next period, the stable-growth rate, and the required rate of return. FCFE1 P0 r gn where FCFE1 = expected FCFE next year Example: AT&T Rationale for using the model: Given its size, it is unlikely that AT&T will be able to grow much faster than the economy in the long term. AT&T pays out much less in dividends than it generates in FCFE. The financial leverage is stable. Background Information: EPS = $3.15 Capital Expenditure per share = $3.15 Dep per share = $2.78 Change in NWC per share = $0.50 Debt ratio = 25% Expected growth rate = 6% Discount rate = 12.45% Estimating the value: FCFE = $3.15 – ($3.15 - $2.78)(1 - .25) - $0.50(1 - .25) = $2.49 Stock Value = $2.49 x 1.06 / (.1245 - .06) = $41.00 The Two-Stage FCFE Model Value = PV of FCFE + PV of Terminal Price n FCFE / 1 r Pn / 1 r t n = t t 1 where 16 Pn = Stock price at the end of high-growth phase The E Model – A Three-Stage FCFE Model The E model is designed to value firms that are expected to go through three stages of growth: initial phase of high growth rates, a transition period where the growth rate declines, and a steady-state period where growth is stable. n1 n2 FCFEt FCFEt Pn2 P0 t 1 r t n1 1 r 1 r n2 t t 1 1 where Pn2 = terminal price at the end of the transition period. RELATIVE VALUATION MODELS Relative valuation models estimate the value of an entity by comparing it to similar entities on the basis of several relative ratios that compare its stock price to relevant variables that affect a stock’s value, such as earnings, cash flow, book value, and sales. Price/Earnings Multiples The price/earnings (P/E) multiple or ratio is most widely used because of its simplicity. There are a number of reasons the P/E ratio is used so widely. First, it is an intuitively appealing statistic that relates the price paid to current earnings. Second, it is simple to compute for most stocks and is widely available. Third, it can be a proxy for a number of other characteristics of the firm including risk and growth. The P/E ratio can be related to the same fundamentals that determine value in discounted cash flow models – expected growth rates, payout ratios, and risk. P/E Ratio for a Stable Firm The value of equity for a stable firm can be written as EPS 0 Payout Ratio 1 g n P0 r gn since D1 = EPS1 (Payout Ratio). Rearranging to yield the P/E ratio: P0 P/E Payout Ratio 1 g n EPS 0 r gn Example Estimating the P/E ratio for a stable firm using FCFE: Siemens Siemens AG had EPS of 32.76 DM and paid dividends of 13 DM in 1994. The beta for the stock was 0.93. The ten-year bond rate in Germany was 7.5%, and the risk premium for stocks over bonds is assumed to be 4.5%. The company had FCFE in 1994 of 20 DM per share. FCFE Payout Ratio = 20 DM/32.76 DM = 61.05% Dividend Payout Ratio = 39.68% Expected Growth Rate = 6% Discount Rate = 7.5% + (.93 x 4.5%) = 11.69% P/E Ratio = .6105 x 1.06 / (.1169 - .06) = 11.37 Siemens was selling at a P/E multiple of 16.68. P/E Ratio for a High-Growth Firm The P/E ratio for a high-growth firm can be estimated using the dividend discount model for high-growth firm: EPS0 Payout Ratio1 g 1 1 g n 1 r n P0 r gn 17 EPS0 Payout Ratio1 g n 1 g n r g n 1 r n Rearranging to yield the P/E ratio: Payout Ratio 1 g 1 1 g n 1 r n P0 P/E EPS0 rg Payout Ratio1 g n 1 g n r g n 1 r n Example Estimating the P/E Ratio: Nike The following is an estimation of the appropriate P/E for Nike in March 1995. High-growth period: Discount rate = 15.48% Expected payout ratio = 20% Growth rate = 14.4% Stable-growth period: Expected growth rate = 6% Discount rate = 13.55% Expected payout ratio = 60% 1.1445 1.15485 .20 x 1.144 x 1 + .60 x 1.445 x 1.06 P/E = 9.01 .1548 .144 1.15485 .1355 .06 Nike was trading at a P/E ratio of 14 in March 1995. Variant of the P/E Ratio – Price/FCFE Multiple There are some analysts who prefer to use price/FCFE ratios to value firms because of well-documented problems with accounting measures of earnings. The determinants of price/FCFE ratios are similar to those of P/E ratios – they include the expected growth rate in the initial high-growth period, the expected growth rate during the stable-growth period, and the relationship between capital expenditure and depreciation. Price/Book Value Multiples Book value provides a relatively stable, intuitive measure of value that can be compared to the market price. Price/book value (PBV) ratio can be used as an indication of under- or over- valuation of a stock. Stocks selling for well below (more than) book value are considered undervalued (overvalued). For investors who instinctively mistrust discounted cash flow estimates of value, it is a much simpler benchmark for comparison. Moreover, given reasonably consistent accounting standards across firms, PBV can be compared across similar firms for signs of under- or over-valuation. Finally, even firms with negative earnings, which cannot be valued using P/E ratios, can be evaluated using PBV ratios. However, one disadvantage associated with measuring and using PBV ratios, is that book values, like earnings, are affected by accounting decisions. When accounting standards vary widely across firms, the PBV ratios 18 may not be comparable across firms. Moreover, book value may not carry much meaning for service firms that do not have significant fixed assets. Price/Sales Multiples In recent years, analysts have increasingly turned to value as a multiple of sales. The price/sales (PS) multiple is widely used to value privately held firms and to compare value across publicly traded firms. The PS ratio has proved attractive to analysts for a number of reasons. First, unlike P/E and PBV ratios, which can become negative and not meaningful, PS multiple is available even for the most troubled firms. Second, unlike earnings and book value, which are heavily influenced by accounting standards, revenue is relatively difficult to manipulate. Third, PS multiples are not as volatile as P/E multiples and hence more reliable for use in valuation. For instance, the P/E ratio of a cyclical firm changes more than its PS ratio, because earnings are much more sensitive to economic changes than revenue. Fourth, the PS multiple provides a convenient handle for examining the effects of changes in pricing policy and other corporate strategic decisions. One of the advantages of using revenue instead of earnings and book value is its stability. This stability can also become a disadvantage, when the firm’s problems lie in cost control. In such cases, revenues may not decline even though the earnings and value drop precipitously. Thus, while it is tempting to use PS multiples to value troubled firms with negative earnings and book value, the failure to control for differences across firms in costs and profit margins can lead to very misleading valuations. 19

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