Application of the Model by alicejenny


									                      ANALYSIS OF COMMON STOCKS
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
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,

       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
        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
        Growth Industries
                industries with expected earnings growth significantly above the average of all
        Defensive Industries

                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.
                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
                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
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
       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.

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
        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
        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
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.
        Heavy trading volume, other things being equal, is generally regarded as a bullish sign.

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
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
         Upward trend
         Downward trend
         Neutral trend or “trading range”
                 Sequence of prices in which the trend is flat.
         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:
                 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

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
        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.
        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.

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.
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
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
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.
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

        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
        Growth rate = b x ROE
b     = Retention ratio
      = (Net Income – Dividends)/Net Income
ROE = Return on Equity = Net Income/Equity
      = Profit Margin x Total Assets Turnover x Equity Multiplier

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.
        The basic model for valuing equity is the dividend discount model – the value of a stock
is the present value of dividends through infinity:
         P0  
              t 1   r 
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.
         P0 
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.

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.

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.
                Dt            Pn
  P0                 
        t 1   r        1  r n
 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
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%

 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
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

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
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
    (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.

          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:
                 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 
                                                               r  g n 1  r n
            _________________            ___________         _______________
                  High Growth               Transition         Stable Growth
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:

            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
         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
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-

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.
        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.
         P0 
               r  gn
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

                FCFE / 1  r         Pn / 1  r 
                                 t                   n
        =                t
                t 1

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
Pn2 = terminal price at the end of the transition period.
         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:
                 P/E 
                           Payout Ratio 1  g n 
          EPS 0                      r  gn
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 Ratio1  g  1 
                                             1  g  n 
                                            1  r  n 
 P0                                                   
                             r  gn

           EPS0 Payout Ratio1  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 
         P/E                                                         
 EPS0                                       rg

                           Payout      Ratio1  g  n 1  g n 
                                     r  g n 1  r  n
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

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.


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