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Relative Valuation

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					       Relative Valuation



                                             1




      Why relative valuation?
“If you think I’m crazy, you should see the
         h lives across th h ll”
   guy who li             the hall”
      Jerry Seinfeld talking about Kramer in a
   Seinfeld episode

“ A little inaccuracy sometimes saves tons of
  explanation”
                               H.H. Munro
                                             2
        What is relative valuation?
• In relative valuation, the value of an asset is compared to the values
  assessed by the market for similar or comparable assets.
• To do relative valuation then,
   – we need to identify comparable assets and obtain market values
      for these assets
   – convert these market values into standardized values, since the
      absolute prices cannot be compared This process of
      standardizing creates price multiples.
   – compare the standardized value or multiple for the asset being
      analyzed to the standardized values for comparable asset,
      controlling for any differences between the firms that might affect
      the multiple, to judge whether the asset is under or over valued


                                                                             3




               Standardizing Value
•   Prices can be standardized using a common variable such as earnings,
    cashflows, book value or revenues.
     – Earnings Multiples
          • Price/Earnings Ratio (PE) and variants (PEG and Relative PE)
          • Value/EBIT
          • Value/EBITDA
          • Value/Cash Flow
     – Book Value Multiples
          • Price/Book Value(of Equity) (PBV)
          • Value/ Book Value of Assets
          • Value/Replacement Cost (Tobin’s Q)
     – Revenues
          • Price/Sales per Share (PS)
          • Value/Sales
     – Industry Specific Variable (Price/kwh, Price per ton of steel ....)   4
             The Four Steps to
           Understanding Multiples
•   Define the multiple
     – In use, the same multiple can be defined in different ways by different
        users. When comparing and using multiples, estimated by someone
        else, it is critical that we understand how the multiples have been
        estimated
•   Describe the multiple
     – Too many people who use a multiple have no idea what its cross
        sectional distribution is. If you do not know what the cross sectional
        distribution of a multiple is, it is difficult to look at a number and pass
        judgment on whether it is too high or low.
•   Analyze the multiple
     – It is critical that we understand the fundamentals that drive each
        multiple, and the nature of the relationship between the multiple and
        each variable.
•   Apply the multiple
     – Defining the comparable universe and controlling for differences is far        5
        more difficult in practice than it is in theory.




                    Definitional Tests
• Is the multiple consistently defined?
   – Proposition 1: Both the value (the numerator) and the
          p                            (              )
      standardizing variable ( the denominator) should be to the
      same claimholders in the firm. In other words, the value of
      equity should be divided by equity earnings or equity book
      value, and firm value should be divided by firm earnings or
      book value.
• Is the multiple uniformally estimated?
   – The variables used in defining the multiple should be estimated
      uniformly across assets in the “comparable firm” list.
   – If earnings-based multiples are used, the accounting rules to
      measure earnings should be applied consistently across assets.
      The same rule applies with book-value based multiples.

                                                                                      6
                   Descriptive Tests
• What is the average and standard deviation for this multiple, across
  the universe (market)?
• What is the median for this multiple?
   – The median for this multiple is often a more reliable comparison
      point.
• How large are the outliers to the distribution, and how do we deal
  with the outliers?
   – Throwing out the outliers may seem like an obvious solution, but
      if the outliers all lie on one side of the distribution (they usually
      are large positive numbers), this can lead to a biased estimate.
• Are there cases where the multiple cannot be estimated? Will
  ignoring these cases lead to a biased estimate of the multiple?
• How has this multiple changed over time?

                                                                                  7




                     Analytical Tests
•   What are the fundamentals that determine and drive these multiples?
     – Proposition 2: Embedded in every multiple are all of the variables that
       drive every discounted cash flow valuation - growth, risk and cash flow
       patterns.
     – In fact, using a simple discounted cash flow model and basic algebra
       should yield the fundamentals that drive a multiple
•   How do changes in these fundamentals change the multiple?
     – The relationship between a fundamental (like growth) and a multiple
       (such as PE) is seldom linear. For example, if firm A has twice the
       g                     ,        g       y
       growth rate of firm B, it will generally not trade at twice its PE ratio
     – Proposition 3: It is impossible to properly compare firms on a
       multiple, if we do not know the nature of the relationship between
       fundamentals and the multiple.



                                                                                  8
                   Application Tests
•   Given the firm that we are valuing, what is a “comparable” firm?
     – While traditional analysis is built on the premise that firms in the same
       sector are comparable firms, valuation theory would suggest that a
       comparable firm is one which is similar to the one being analyzed in
       terms of fundamentals.
     – Proposition 4: There is no reason why a firm cannot be compared
       with another firm in a very different business, if the two firms have
       the same risk, growth and cash flow characteristics.
•   Given the comparable firms, how do we adjust for differences across firms
    on the fundamentals?
     – Proposition 5: It is impossible to find an exactly identical firm to
       the one you are valuing.




                                                                               9




    Price Earnings Ratio: Definition
             PE = Market Price per Share / Earnings per Share
•   There are a number of variants on the basic PE ratio in use. They are based
    upon how the price and the earnings are defined.
•   Price:        is usually the current price
                  is sometimes the average price for the year
•   EPS:          earnings per share in most recent financial year
                  earnings per share in trailing 12 months (Trailing PE)
                  forecasted earnings per share next year (Forward PE)
                  forecasted earnings per share in future year




                                                                              10
 PE Ratio: Descriptive Statistics
                                                   Distribution of PE Ratios - September 2001


       1200




       1000




        800




                                                                                                                                           Current PE
        600                                                                                                                                Trailing PE
                                                                                                                                           Forward PE




        400




        200




          0
              0-4   4-6   6-8   8 - 10   10 - 15   15-20    20-25   25-30      30-35   35-40    40 - 45   45- 50   50 -75   75 -   > 100
                                                                                                                            100

                                                                    PE ratio




                                                                                                                                                         11




PE: Deciphering the Distribution
               Current PE     Trailing PE     Forward PE
Mean                   30.93
                       30 93           30.33
                                       30 33         21 13
                                                     21.13
Standard Error           2.70            2.74          0.73
Median                 15.27           15.20         13.71
Mode                       10               0            14
Standard Devia       157.30           150.65         38.22
Kurtosis             795.82         1615.73         224.85
Skewness               26.28           36.04         12.97
Range               5370.00         7090.50         864.91
Maximum             5370.00         7090.50         865.00
Count                   3387            3021          2737
                                                                                                                                                         12
        PE Ratio: Understanding the
              Fundamentals
• To understand the fundamentals, start with a
                                    model.
  basic equity discounted cash flow model
• With the dividend discount model,
                                   DPS1
                            P0 
                                   r  gn




• Dividing both sides by the earnings per share,
                   P0          Payout Ratio * (1  g n )
                         PE =
                  EPS 0                r-gn



• If this had been a FCFE Model,
       FCFE 1       P0         (FCFE/Earnings) * (1  g n )
P0                      PE =
       r  gn      EPS0                 r-g n                 13




         PE Ratio and Fundamentals
• Proposition: Other things held equal, higher growth
  firms will have higher PE ratios than lower growth
  firms.
• Proposition: Other things held equal, higher risk
  firms will have lower PE ratios than lower risk firms
• Proposition: Other things held equal, firms with
  lower reinvestment needs will have higher PE ratios
  than firms with higher reinvestment rates.rates
• Of course, other things are difficult to hold equal since
  high growth firms, tend to have risk and high
  reinvestment rats.

                                                              14
     PE and Risk: Effects of Changing Betas on
                     PE Ratio:
                       Firm with x% growth for 5 years; 8% thereafter

                                  PE Ratios and Beta: Growth Scenarios

              50


              45


              40


              35


              30
                                                                                          g=25%
                                                                                          g=20%
              25
                                                                                          g=15%
                                                                                          g=8%
              20


              15


              10


               5


               0
                      0.75       1.00         1.25          1.50         1.75     2.00
                                                     Beta


                                                                                                         15




                                             PE: Emerging Markets

35



30



25



20



15



10



 5



 0
     Mexico        Malaysia   Singapore    Taiwan       Hong Kong    Venezuela   Brazil   Argentina   Chile
                                                                                                         16
  Comparisons across countries
• In July 2000, a market strategist is making
  the          t th t B il d Venezuela
  th argument that Brazil and V          l
  are cheap relative to Chile, because they
  have much lower PE ratios. Would you
  agree?
Yes
No
• What are some of the factors that may
  cause one market’s PE ratios to be lower
                                             17
  than another market’s PE?




 Correlations and Regression of
            PE Ratios
• Correlations
                                             g
   – Correlation between PE ratio and long term interest rates = -
      0.733
   – Correlation between PE ratio and yield spread = 0.706
• Regression Results
   PE Ratio = 42.62 - 3.61 (10’yr rate) + 8.47 (10-yr - 2 yr rate) R2 =
      59%
   Input the interest rates as percent. For instance, the predicted PE
      ratio for Japan with this regression would be:
   PE: Japan = 42.62 - 3.61 (1.85) + 8.47 (1.27) = 46.70
   At an actual PE ratio of 52.25, Japanese stocks are slightly
      overvalued.


                                                                          18
        Predicted PE Ratios
Country             Actual PE      Predicted PE Under or Over V
UK                          22.02          20.83       5.71%
Germany                     26.33          25.62       2.76%
France                      29.04          25.98     11.80%
Switzerland                   19.6         30.58    -35.90%
Belgium                     14.74          26.71    -44.81%
Italy                       28.23          25.69       9.89%
Sweden                      32.39          28.63     13.12%
Netherlands                   21.1
                              21 1         26.01
                                           26 01     18 88%
                                                    -18.88%
Australia                   21.69          19.73       9.96%
Japan                       52.25          46.70     11.89%
United States               25.14          19.81     26.88%
Canada                      26.14          22.39     16.75%
                                                                  19




An Example with Emerging
   Markets: June 2000
        Country       PE Ratio   Interest   GDP Real   Country
                                  Rates      Growth     Risk
      Argentina          14       18.00%      2.50%      45
      Brazil             21       14.00%      4.80%      35
      Chile              25       9.50%       5.50%      15
      Hong Kong          20       8.00%       6.00%      15
      India              17       11.48%      4.20%      25
      Indonesia          15       21.00%      4.00%      50
      Malaysia           14       5.67%       3.00%      40
      Mexico             19       11.50%      5.50%      30
      Pakistan           14       19.00%      3.00%      45
      Peru               15       18.00%      4.90%      50
      Phillipines        15       17.00%      3.80%      45
      Singapore          24       6.50%       5.20%       5
      South Korea        21       10.00%      4.80%      25
      Thailand           21       12.75%      5.50%      25
      Turkey             12       25.00%      2.00%      35
      Venezuela          20       15.00%      3.50%      45

                                                                  20
               Regression Results
• The regression of PE ratios on these
     i bl       id the following
  variables provides th f ll i –
  PE = 16.16 - 7.94 Interest Rates
             + 154.40 Growth in GDP
             - 0.1116 Country Risk
  R Squared = 73%




                                                                            21




               Predicted PE Ratios
     Country     PE Ratio   Interest   GDP Real   Country   Predicted PE
                             Rates      Growth     Risk
   Argentina        14       18.00%      2.50%      45              13.57
   Brazil           21       14.00%      4.80%      35              18.55
   Chile            25       9.50%       5.50%      15              22.22
   Hong Kong        20       8.00%       6.00%      15              23.11
   India            17       11.48%      4.20%      25              18.94
   Indonesia        15       21.00%      4.00%      50              15.09
   Malaysia         14       5.67%       3.00%      40              15.87
   Mexico           19       11.50%      5.50%      30              20.39
   Pakistan         14       19.00%      3.00%      45              14.26
   Peru             15       18.00%      4.90%      50              16.71
   Phillipines      15       17.00%      3.80%      45              15.65
   Singapore        24       6.50%       5.20%       5              23.11
   South Korea      21       10.00%      4.80%      25              19.98
   Thailand         21       12.75%      5.50%      25              20.85
   Turkey           12       25.00%      2.00%      35              13.35
   Venezuela        20       15.00%      3.50%      45              15.35

                                                                            22
Comparisons of PE across time:
  PE Ratio for the S&P 500
                                                                PE Ratio: 1960-2000

     35.00




     30.00




     25.00




     20.00




     15.00




     10.00




      5.00




      0.00
          60


                 62


                        64


                               66


                                      68


                                             70


                                                    72


                                                           74


                                                                  76


                                                                         78


                                                                                80


                                                                                       82


                                                                                              84


                                                                                                     86


                                                                                                            88


                                                                                                                   90


                                                                                                                          92


                                                                                                                                 94


                                                                                                                                        96


                                                                                                                                               98


                                                                                                                                                      00
        19


               19


                      19


                             19


                                    19


                                           19


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                                                                                                                                                           23




             Is low (high) PE cheap
                  (expensive)?
• A market strategist argues that stocks are
         i d because th PE ratio t d i
  over priced b          the      ti today is
  too high relative to the average PE ratio
  across time. Do you agree?
  Yes
  No
• If you do not agree, what factors might
  explain the higer PE ratio today?

                                                                                                                                                           24
 E/P Ratios , T.Bond Rates and
        Term Structure
  16.00%



  14.00%
  14 00%




  12.00%



  10.00%



   8.00%
                                                                                                                                    Earnings Yield
                                                                                                                                    T.Bond Rate
                                                                                                                                    Bond-Bill
   6.00%



   4.00%
   4 00%



   2.00%



   0.00%
       60


             62


                   64


                         66


                               68


                                     70


                                           72


                                                 74


                                                       76


                                                             78


                                                                   80


                                                                         82


                                                                               84


                                                                                     86


                                                                                           88


                                                                                                 90


                                                                                                       92


                                                                                                             94


                                                                                                                   96


                                                                                                                         98


                                                                                                                               00
      19


            19


                  19


                        19


                              19


                                    19


                                          19


                                                19


                                                      19


                                                            19


                                                                  19


                                                                        19


                                                                              19


                                                                                    19


                                                                                          19


                                                                                                19


                                                                                                      19


                                                                                                            19


                                                                                                                  19


                                                                                                                        19


                                                                                                                              20
  -2.00%




                                                                                                                                                     25




 Comparing PE ratios across firms
Company Name                                    Trailing PE                         Expected Growth                     Standard Dev
Coca-Cola Bottling                              29.18                               9.50%                               20.58%
Molson Inc. Ltd. 'A'                            43.65                               15.50%                              21.88%
Anheuser Busch
Anheuser-Busch                                  24.31
                                                24 31                               11 00%
                                                                                    11.00%                              22 92%
                                                                                                                        22.92%
Corby Distilleries Ltd.                         16.24                               7.50%                               23.66%
Chalone Wine Group Ltd.                         21.76                               14.00%                              24.08%
Andres Wines Ltd. 'A'                           8.96                                3.50%                               24.70%
Todhunter Int'l                                 8.94                                3.00%                               25.74%
Brown-Forman 'B'                                10.07                               11.50%                              29.43%
Coors (Adolph) 'B'                              23.02                               10.00%                              29.52%
PepsiCo, Inc.                                   33.00                               10.50%                              31.35%
Coca-Cola                                       44.33                               19.00%                              35.51%
Boston Beer 'A'                                 10.59                               17.13%                              39.58%
Whitman Corp.                                   25.19                               11.50%                              44.26%
Mondavi (Robert) 'A'                            16.47                               14.00%                              45.84%
Coca-Cola Enterprises                           37.14                               27.00%                              51.34%
Hansen Natural Corp                             9.70                                17.00%                              62.45%
                                                                                                                                                     26
                         A Question
You are reading an equity research report
      this   t      d the  l t l i     that
  on thi sector, and th analyst claims th t
  Andres Wine and Hansen Natural are
  under valued because they have low PE
  ratios. Would you agree?
Yes
No
• Why or why not?
                                                                               27




 Comparing PE Ratios across a
           Sector
                             Company Name                  PE      Growth
        PT Indosat ADR                                       7.8       0.06
        Telebras ADR                                         8.9      0.075
        Telecom Corporation of New Zealand ADR
                      p                                     11.2       0.11
        Telecom Argentina Stet - France Telecom SA ADR B    12.5       0.08
        Hellenic Telecommunication Organization SA ADR      12.8       0.12
        Telecomunicaciones de Chile ADR                     16.6       0.08
        Swisscom AG ADR                                     18.3       0.11
        Asia Satellite Telecom Holdings ADR                 19.6       0.16
        Portugal Telecom SA ADR                             20.8       0.13
        Telefonos de Mexico ADR L                           21.1       0.14
        Matav RT ADR                                        21.5       0.22
        Telstra ADR                                         21.7       0.12
        Gilat Communications                                22.7       0.31
        Deutsche Telekom AG ADR                             24.6       0.11
        British Telecommunications PLC ADR                  25.7       0.07
        Tele Danmark AS ADR                                   27       0.09
        Telekomunikasi Indonesia ADR                        28.4       0.32
        Cable & Wireless PLC ADR                            29.8       0.14
        APT Satellite Holdings ADR                            31       0.33
        Telefonica SA ADR                                   32.5       0.18
        Royal KPN NV ADR                                    35.7       0.13
        Telecom Italia SPA ADR                              42.2       0.14
        Nippon Telegraph & Telephone ADR                    44.3         0.2
        France Telecom SA ADR                               45.2       0.19
        Korea Telecom ADR                                   71.3       0.44


                                                                               28
            PE, Growth and Risk
Dependent variable is: PE

R squared = 66.2%    R squared (adjusted) = 63.1%

Variable              Coefficient SE       t-ratio   prob
Constant              13.1151       3.471  3.78      0.0010
Growth rate           121.223       19.27  6.29      ≤ 0.0001
Emerging Market       -13.8531      3.606  -3.84     0.0009
Emerging Market is a dummy: 1 if emerging market
                           0 if not




                                                                29




      Is Telebras under valued?
• Predicted PE = 13.12 + 121.22 (.075) -
  13.85       8.35
  13 85 (1) = 8 35
• At an actual price to earnings ratio of 8.9,
  Telebras is slightly overvalued.




                                                                30
   Using comparable firms- Pros
            and Cons
• The most common approach to estimating the PE ratio for a firm is
                  g p            p
   – to choose a group of comparable firms,   ,
   – to calculate the average PE ratio for this group and
   – to subjectively adjust this average for differences between the
     firm being valued and the comparable firms.
• Problems with this approach.
   – The definition of a 'comparable' firm is essentially a subjective
     one.
   – The use of other firms in the industry as the control group is
     often not a solution because firms within the same industry can
     have very different business mixes and risk and growth profiles.
   – There is also plenty of potential for bias.
   – Even when a legitimate group of comparable firms can be
     constructed, differences will continue to persist in fundamentals31
     between the firm being valued and this group.




Using the entire crosssection: A
     regression approach
• In contrast to the 'comparable firm'
           h the information i th entire
  approach, th i f       ti in the ti
  cross-section of firms can be used to
  predict PE ratios.
• The simplest way of summarizing this
  information is with a multiple regression,
  with the PE ratio as the dependent
  variable, and proxies for risk, growth and
  payout forming the independent variables.
                                                                      32
         PE versus Growth
            120


            100


               80


               60


               40


               20


                 0


               -20
                 -20                0          20             40                60           80         100


                                    Expected Growth in EPS: next 5 years

                                                                                                                        33




PE Ratio: Standard Regression
                                             Model Summary

                                                                    Adj t d R
                                                                    Adjusted                 Std. E     f
                                                                                             Std Error of
    Model                    R                R Square                Square                 the Estimate
    1                             .478   a         .229                    .227                 803.9541
     a. Predictors: (Constant), Expected Growth in EPS: next 5 y,
        PAYOUT1, Beta


                                                        Coefficients      a,b


                                                                             Standar
                                                Unstandardized                 dized
                                                 Coefficients
                                                 Coe c e ts                 Coe c e ts
                                                                            Coefficients
       Model                                    B          Std. Error           Beta           t              Sig.
       1             (Constant)                13.090            1.164                        11.242             .000
                     Beta                      -3.392            .908                -.089     -3.737           .000
                     PAYOUT1                    4.938           1.190                 .098      4.150           .000
                     Expected Growth
                                                 .880              .040              .527     22.115            .000
                     in EPS: next 5 y
        a. Dependent Variable: Current PE
        b. Weighted Least Squares Regression - Weighted by Market Cap



                                                                                                                        34
            Second Thoughts?
• Based on this regression, estimate the PE ratio for a firm
  with no growth, no payout and no risk.




• Is there a problem with your prediction?



                                                                                                                                 35




   PE Regression- No Intercept
                                                         Model Summary

                                                                                Adjusted R             Std. Error of
                                                                          a
                     Model               R                    q
                                                           R Square                q
                                                                                  Square               the Estimate
                     1                       .912   b           .832                   .832               833.0224
                      a. For regression through the origin (the no-intercept
                         model), R Square measures the proportion of the
                         variability in the dependent variable about the origin
                         explained by regression. This CANNOT be compared to R
                         Square for models which include an intercept.
                      b. Predictors: Expected Growth in EPS: next 5 y, PAYOUT1,
                         Beta

                                                                 Coefficients        a,b,c


                                                                                         Standar
                                                         Unstandardized                   dized
                                                          Coefficients                 Coefficients
             Model                                      B           Std. Error               Beta            t         Sig.
             1        Beta                              4.389              .609                 .188         7.212        .000
                      PAYOUT1                           13.299                .962              .189        13.823       .000
                      Expected Growth
                                                         1.014                .039              .608        25.786       .000
                      in EPS: next 5 y
              a. Dependent Variable: Current PE
              b. Linear Regression through the Origin
              c. Weighted Least Squares Regression - Weighted by Market Cap


                                                                                                                                 36
    Problems with the regression
           methodology
• The basic regression assumes a linear relationship
  between PE ratios and the financial proxies, and that
  might not be appropriate.
• The basic relationship between PE ratios and financial
  variables itself might not be stable, and if it shifts from
  year to year, the predictions from the model may not be
  reliable.
• The independent variables are correlated with each
  other. For example, high growth firms tend to have high
  risk. This multi-collinearity makes the coefficients of the
  regressions unreliable and may explain the large
  changes in these coefficients from period to period.
                                                                                                                      37




     The Multicollinearity Problem
                                                    Correlations

                                                                         Expected
                                                                       Growth in EPS:
                                                    Current PE            next 5 y          Beta       Payout Ratio
 Current PE              Pearson Correlation             1.000                    .342 **      .130 **         .009
                         Sig. (2-tailed)                           .              .000         .000            .594
                         N                                 3303                  2085         3027            3290
 Expected Growth         Pearson Correlation                .342 **             1.000          .397 **        -.078 **
 in EPS: next 5 y        Sig. (2-tailed)                    .000                        .      .000            .000
                         N                                 2085                  2675         2393            2143
 Beta                    Pearson Correlation                .130 **               .397 **     1.000           -.213 **
                         Sig (2-tailed)
                         Sig.                                000
                                                            .000                  .000
                                                                                   000                .         000
                                                                                                               .000
                         N                                 3027                  2393         4534            3114
 Payout Ratio            Pearson Correlation                .009                -.078 **      -.213 **       1.000
                         Sig. (2-tailed)                    .594                 .000          .000                   .
                         N                                 3290                 2143          3114            3388
   **. Correlation is significant at the 0.01 level (2-tailed).



                                                                                                                      38
    Using the PE ratio regression
• Assume that you were given the following information for Dell. The
  firm has an expected growth rate of 10%, a beta of 1.40 and pays no
  dividends. Based upon the regression, estimate the predicted PE
  ratio for Dell.
    Predicted PE =
    (Work with absolute values in regression - 10 for 10% etc.)

• Dell is actually trading at 18 times earnings. What does the
  predicted PE tell you?




                                                                   39




        Investment Strategies that
      compare PE to the expected
•
                    growth rate
    If we assume that all firms within a sector have similar
  growth rates and risk, a strategy of picking the lowest PE
  ratio stock in each sector will yield undervalued stocks.
• Portfolio managers and analysts sometimes compare PE
  ratios to the expected growth rate to identify under and
  overvalued stocks.
   – In the simplest form of this approach, firms with PE
      ratios less than their expected growth rate are viewed
      as undervalued.
   – In its more general form, the ratio of PE ratio to
      growth is used as a measure of relative value.

                                                                   40
   Problems with comparing PE
    ratios to expected growth
• In its simple form, there is no basis for believing that a
  firm is undervalued just because it has a PE ratio less
  than expected growth.
• This relationship may be consistent with a fairly valued
  or even an overvalued firm, if interest rates are high, or if
  a firm is high risk.
• As interest rate decrease (increase), fewer (more) stocks
                                            approach.
  will emerge as undervalued using this approach




                                                                             41




       PE Ratio versus Growth - The Effect of Interest rates:
    Average Risk firm with 25% growth for 5 years; 8% thereafter


                        Figure 14.2: PE Ratios and T.Bond Rates

              45

              40

              35

              30

              25

              20

              15

              10

               5

               0
                   5%      6%          7%           8%            9%   10%
                                         T.Bond Rate




                                                                             42
              PEG Ratio: Definition
•   The PEG ratio is the ratio of price earnings to expected growth in earnings
    per share.
                   PEG = PE / Expected Growth Rate in Earnings
•   Definitional tests:
     – Is the growth rate used to compute the PEG ratio
          • on the same base? (base year EPS)
          • over the same period?(2 years, 5 years)
          • from the same source? (analyst projections, consensus estimates..)
     – Is the earnings used to compute the PE ratio consistent with the growth
          t      ti t ?
        rate estimate?
          • No double counting: If the estimate of growth in earnings per share
             is from the current year, it would be a mistake to use forward EPS in
             computing PE
          • If looking at foreign stocks or ADRs, is the earnings used for the PE
             ratio consistent with the growth rate estimate? (US analysts use the
             ADR EPS)                                                           43




            PEG Ratio: Distribution
                      400




                      300




                      200




                      100

                                                           Std Dev = 1 05
                                                           Std. D    1.05
                                                           Mean = 1.55

                        0                                  N = 2084.00




                             Price/ Expected Growth RAte
                                                                               44
       PEG Ratios: The Beverage Sector
 Company Name              Trailing PE   Growth   Std Dev   PEG
 Coca-Cola Bottling        29.18         9.50%    20.58%    3.07
 Molson Inc. Ltd. 'A'      43.65         15.50%   21.88%    2.82
 Anheuser-Busch            24.31         11.00%   22.92%    2.21
 Corby Distilleries Ltd.
     y                     16.24         7.50%    23.66%    2.16
 Chalone Wine Group Ltd.     21.76       14.00%   24.08%    1.55
 Andres Wines Ltd. 'A'     8.96          3.50%    24.70%    2.56
 Todhunter Int'l           8.94          3.00%    25.74%    2.98
 Brown-Forman 'B'          10.07         11.50%   29.43%    0.88
 Coors (Adolph) 'B'        23.02         10.00%   29.52%    2.30
 PepsiCo, Inc.             33.00         10.50%   31.35%    3.14
 Coca-Cola                 44.33         19.00%   35.51%    2.33
               A
 Boston Beer 'A'           10.59         17.13%   39.58%    0.62
 Whitman Corp.             25.19         11.50%   44.26%    2.19
 Mondavi (Robert) 'A'      16.47         14.00%   45.84%    1.18
 Coca-Cola Enterprises        37.14      27.00%   51.34%    1.38
 Hansen Natural Corp          9.70       17.00%   62.45%    0.57

 Average                   22.66         0.13     0.33      2.00
                                                                   45




        PEG Ratio: Reading the
             Numbers
• The average PEG ratio for the beverage
     t i 2.00. The lowest PEG ratio i th
  sector is 2 00 Th l      t        ti in the
  group belongs to Hansen Natural, which
  has a PEG ratio of 0.57. Using this
  measure of value, Hansen Natural is
the most under valued stock in the group
the most over valued stock in the group
• What other explanation could there be for
  Hansen’s low PEG ratio?
                                                                   46
PEG Ratios and Fundamentals
• Risk and payout, which affect PE ratios,
     ti    to ff t        ti         ll
  continue t affect PEG ratios as well.
  – Implication: When comparing PEG ratios
    across companies, we are making implicit or
    explicit assumptions about these variables.
• Dividing PE by expected growth does not
  neutralize the effects of expected growth,
  since the relationship between growth and
  value is not linear and fairly complex (even
  in a 2-stage model)                        47




               PEG Ratios and Risk
                   PEG Ratios and Beta: Different Growth Rates

       3




     2.5




       2


                                                                               g =25%
                                                                               g=20%
     1.5
                                                                               g=15%
                                                                               g=8%


       1




     0.5




       0
        0.75     1.00            1.25           1.50             1.75   2.00
                                        Beta




                                                                                        48
  PEG Ratios and Quality of
          Growth
                                        PEG Ratios and Retention Ratios

   1.4




   1.2



     1



   0.8

                                                                                                                PEG

   0.6




   0.4



   0.2



     0
               1                  0.8                0.6                 0.4               0.2          0
                                                       Retention Ratio




                                                                                                                      49




PE Ratios and Expected Growth
                         PEG Ratios, Expected Growth and Interest Rates

   2.50




   2.00




   1.50
                                                                                                             r=6%
                                                                                                             r=8%
                                                                                                             r=10%

   1.00




   0.50




   0.00
          5%       10%      15%           20%       25%        30%             35%   40%         45%   50%
                                                Expected Growth Rate




                                                                                                                      50
PEG Ratios and Fundamentals:
        Propositions
• Proposition 1: High risk companies will trade at much lower PEG
  ratios than low risk companies with the same expected growth rate.
   – Corollary 1: The company that looks most under valued on a
       PEG ratio basis in a sector may be the riskiest firm in the sector
• Proposition 2: Companies that can attain growth more efficiently by
  investing less in better return projects will have higher PEG ratios
  than companies that grow at the same rate less efficiently.
   – Corollary 2: Companies that look cheap on a PEG ratio basis
       may be companies with high reinvestment rates and poor project
       returns.
• Proposition 3: Companies with very low or very high growth rates
  will tend to have higher PEG ratios than firms with average growth
  rates. This bias is worse for low growth stocks.
   – Corollary 3: PEG ratios do not neutralize the growth effect.
                                                                         51




       PE, PEG Ratios and Risk
         45                                            2.5


         40

                                                       2
         35


         30

                                                       1.5
         25
                                                             PE
                                                             PEG Ratio
         20
                                                       1

         15


         10
                                                       0.5

          5


          0                                            0
              Lowest   2       3       4     Highest



                                                                         52
     PEG Ratio: Returning to the Beverage Sector
  Company Name                   Trailing PE   Growth   Std Dev   PEG
  Coca-Cola Bottling             29.18         9.50%    20.58%    3.07
  Molson Inc. Ltd. 'A'           43.65         15.50%   21.88%    2.82
  Anheuser-Busch                 24.31         11.00%   22.92%    2.21
  Corby Distilleries Ltd.        16.24         7.50%    23.66%    2.16
  Chalone Wine Group Ltd  Ltd.    21.76
                                  21 76        14 00%
                                               14.00%   24 08%
                                                        24.08%    1 55
                                                                  1.55
  Andres Wines Ltd. 'A'          8.96          3.50%    24.70%    2.56
  Todhunter Int'l                8.94          3.00%    25.74%    2.98
  Brown-Forman 'B'               10.07         11.50%   29.43%    0.88
  Coors (Adolph) 'B'             23.02         10.00%   29.52%    2.30
  PepsiCo, Inc.                  33.00         10.50%   31.35%    3.14
  Coca-Cola                      44.33         19.00%   35.51%    2.33
  Boston Beer 'A'                10.59         17.13%   39.58%    0.62
           Corp.
  Whitman Corp                   25.19
                                 25 19         11.50%
                                               11 50%   44.26%
                                                        44 26%    2 19
                                                                  2.19
  Mondavi (Robert) 'A'           16.47         14.00%   45.84%    1.18
  Coca-Cola Enterprises          37.14         27.00%   51.34%    1.38
  Hansen Natural Corp            9.70          17.00%   62.45%    0.57

  Average                        22.66         0.13     0.33      2.00
                                                                         53




               Analyzing PE/Growth
• Given that the PEG ratio is still determined by the expected growth
  rates, risk and cash flow patterns, it is necessary that we control for
  differences in these variables.
• Regressing PEG against risk and a measure of the growth
  dispersion, we get:
PEG = 3.61 - 2.86 (Expected Growth) - 3.75 (Std Deviation in Prices)
                                           R Squared = 44.75%
• In other words,
   – PEG ratios will be lower for high growth companies
   – PEG ratios will be lower for high risk companies
• We also ran the regression using the deviation of the actual growth
  rate from the industry-average growth rate as the independent
  variable, with mixed results.
                                                                         54
   Estimating the PEG Ratio for
             Hansen
• Applying this regression to Hansen, the predicted PEG ratio for the
  firm can be estimated using Hansen’s measures for the independent
  variables:
    – Expected Growth Rate = 17.00%
    – Standard Deviation in Stock Prices = 62.45%
• Plugging in,
Expected PEG Ratio for Hansen = 3.61 - 2.86 (.17) - 3.75 (.6245)
                                 = 0.78
                               0 57               undervalued,
• With its actual PEG ratio of 0.57, Hansen looks undervalued
  notwithstanding its high risk.




                                                                   55




    Extending the Comparables
• This analysis, which is restricted to firms in
  the ft             t        b        d dt
  th software sector, can be expanded to
  include all firms in the firm, as long as we
  control for differences in risk, growth and
  payout.
• To look at the cross sectional relationship,
  we first plotted PEG ratios against
  expected growth rates.

                                                                   56
      A Variant on PEG Ratio: The PEGY ratio

• The PEG ratio is biased against low growth firms
  because the relationship between value and growth is
  non-linear. One variant that has been devised to
  consolidate the growth rate and the expected dividend
  yield:
  PEGY = PE / (Expected Growth Rate + Dividend Yield)
• As an example, Con Ed has a PE ratio of 16, an
  expected growth rate of 5% in earnings and a dividend
  yield of 4.5%.
   – PEG = 16/ 5 = 3.2
   – PEGY = 16/(5+4.5) = 1.7
                                                             57




         Relative PE: Definition
• The relative PE ratio of a firm is the ratio of the PE of the
  firm to the PE of the market.
             Relative PE = PE of Firm / PE of Market
• While the PE can be defined in terms of current
  earnings, trailing earnings or forward earnings,
  consistency requires that it be estimated using the same
  measure of earnings for both the firm and the market.
                                                    time. Thus,
• Relative PE ratios are usually compared over time Thus
  a firm or sector which has historically traded at half the
  market PE (Relative PE = 0.5) is considered over valued
  if it is trading at a relative PE of 0.7.

                                                             58
  Relative PE and Relative Risk
                     Relative PE and Relative Risk: Stable Beta Scenarios

       4.5



         4



       3.5



         3



       2.5
                                                                                Beta stays at current level
                                                                                Beta drops to 1 in stable phase
         2



       15
       1.5



         1



       0.5



         0
             0.25   0.5     0.75      1      1.25      1.5     1.75         2




                                                                                                                  59




             Relative PE: Summary of
                   Determinants
• The relative PE ratio of a firm is determined by two variables. In
  particular, it will
   – increase as the firm’s growth rate relative to the market
     increases. The rate of change in the relative PE will itself be a
     function of the market growth rate, with much greater changes
     when the market growth rate is higher. In other words, a firm or
     sector with a growth rate twice that of the market will have a
     much higher relative PE when the market growth rate is 10%
     than when it is 5%.
   – decrease as the f firm’s risk relative to the market increases. The
     extent of the decrease depends upon how long the firm is
     expected to stay at this level of relative risk. If the different is
     permanent, the effect is much greater.
• Relative PE ratios seem to be unaffected by the level of rates,
  which might give them a decided advantage over PE ratios.               60
  Relative PE Ratios: The Auto
             Sector
                                 Relative PE Ratios: Auto Stocks

     1.20




     1.00




     0.80



                                                                                    Ford
     0.60                                                                           Chrysler
                                                                                    GM



     0.40
     0 40




     0.20




     0.00
            1993   1994   1995         1996        1997        1998   1999   2000




                                                                                               61




    Relative PEs: Why do they
             change?
• Historically, GM has traded at the highest
    l ti         ti f the three auto
  relative PE ratio of th th       t
  companies, and Chrysler has traded at the
  lowest. In the last two or three years, this
  historical relationship has been upended
  with Ford and Chrysler now trading at the
  higher ratios than GM. Analyst projections
  for earnings growth at the three
  companies are about the same. How
  would you explain the shift?                 62
             Value/Earnings and
            Value/Cashflow Ratios
•  While Price earnings ratios look at the market value of equity relative to
   earnings to equity investors, Value earnings ratios look at the market value
    f th fi      l ti to         ti
   of the firm relative t operating earnings. V l t cash fl
                                         i     Value to              ti     dif
                                                            h flow ratios modify
   the earnings number to make it a cash flow number.
• The form of value to cash flow ratios that has the closest parallels in DCF
   valuation is the value to Free Cash Flow to the Firm, which is defined as:
Value/FCFF =         (Market Value of Equity + Market Value of Debt-Cash)
                   EBIT (1-t) - (Cap Ex - Deprecn) - Chg in WC
• Consistency Tests:
                                                         used
    – If the numerator is net of cash (or if net debt is used, then the interest
        income from the cash should not be in denominator
    – The interest expenses added back to get to EBIT should correspond to
        the debt in the numerator. If only long term debt is considered, only long
        term interest should be added back.


                                                                                63




          Value/FCFF Distribution
                   800




                   600




                   400




                   200

                                                     Std.      21.77
                                                     Std Dev = 21 77
                                                     Mean = 20.6
                     0                               N = 3063.00




                            Enterprise Value/FCFF

                                                                                64
Alternatives to FCFF - EBIT and
            EBITDA
• Most analysts find FCFF to complex or messy to use in multiples
  (partly because capital expenditures and working capital have to be
  estimated). They use modified versions of the multiple with the
  following alternative denominator:
   – after-tax operating income or EBIT(1-t)
   – pre-tax operating income or EBIT
   – net operating income (NOI), a slightly modified version of
       operating income, where any non-operating expenses and
       income is removed from the EBIT
   – EBITDA, which is earnings before interest, taxes, depreciation
       and amortization.




                                                                                65




   Reasons for Increased Use of
         Value/EBITDA
1. The multiple can be computed even for firms that are reporting net losses,
    since earnings before interest, taxes and depreciation are usually positive.
2. For firms in certain industries, such as cellular, which require a substantial
    investment in infrastructure and long gestation periods, this multiple seems
    to be more appropriate than the price/earnings ratio.
3. In leveraged buyouts, where the key factor is cash generated by the firm
    prior to all discretionary expenditures, the EBITDA is the measure of cash
    flows from operations that can be used to support debt payment at least in
    the short term.
4. By looking at cashflows prior to capital expenditures, it may provide a better
    estimate of “optimal value”, especially if the capital expenditures are unwise
    or earn substandard returns.
5. By looking at the value of the firm and cashflows to the firm it allows for
    comparisons across firms with different financial leverage.


                                                                                66
            Value/EBITDA Multiple
•   The Classic Definition

            Value   Market Value of Equity + Market Value of Debt
                  
           EBITDA   Earnings before Interest, Taxes and Depreciation
•   The No-Cash Version

         Enterprise Value Market Value of Equity + Market Value of Debt - Cash
                         
             EBITDA          Earnings before Interest, Taxes and Depreciation

•   When cash and marketable securities are netted out of value, none of the
    income from the cash and securities should be reflected in the denominator.




                                                                             67




    The Determinants of Value/EBITDA
    Multiples: Linkage to DCF Valuation
• Firm value can be written as:
                                          FCFF1
                                 V0 =
                                         WACC - g
• The numerator can be written as follows:
     FCFF    = EBIT (1-t) - (Cex - Depr) -  Working Capital
             = (EBITDA - Depr) (1-t) - (Cex - Depr) -  Working
     Capital
             = EBITDA ( ) + Depr ( ) - C -  Working C
                        (1-t)         (t) Cex            Capital




                                                                             68
   From Firm Value to EBITDA
            Multiples
• Now the Value of the firm can be rewritten
  as,

                EBITDA (1 - t) + Depr (t) - Cex -  Working Capital
      Value =
                                     WACC - g




                       f
• Dividing both sides of the equation by
  EBITDA,
   Value    (1- t)    Depr (t)/EBITDA   CEx/EBITDA    Working Capital/EBITDA
         =          +                 -            -
  EBITDA   WACC - g      WACC -g         WACC - g            WACC - g
                                                                          69




                A Simple Example
• Consider a firm with the following
   h    t i ti
  characteristics:
  – Tax Rate = 36%
  – Capital Expenditures/EBITDA = 30%
  – Depreciation/EBITDA = 20%
  – Cost of Capital = 10%
  – The firm has no working capital requirements
  – The firm is in stable growth and is expected to
    grow 5% a year forever.
                                                                          70
    Calculating Value/EBITDA
             Multiple
• In this case, the Value/EBITDA multiple for
  this fi       b    ti t d    follows:
  thi firm can be estimated as f ll

    Value       (1 - .36)               (0.2)(.36)                          0.3          0
            =                     +                                 -              -           = 8.24
   EBITDA       .10 - .05                .10 - .05                       .10 - .05   .10 - .05




                                                                                                        71




       Value/EBITDA Multiple:
        Trucking Companies
                                    Company Name             Value         EBITDA       Value/EBITDA
                            KLLM Trans. Svcs.           $      114.32    $     48.81         2.34
                            Ryder System                $   5,158.04     $ 1,838.26          2.81
                            Rollins Truck Leasing       $   1,368.35     $    447.67         3.06
                            Cannon Express Inc.         $       83.57    $     27.05         3.09
                            Hunt (J.B.)                 $      982.67    $    310.22         3.17
                            Yellow Corp.                $      931.47    $    292.82         3.18
                            Roadway Express             $      554.96    $    169.38         3.28
                            Marten Transport Ltd.       $      116.93    $     35.62         3.28
                            Kenan Transport Co.         $       67.66    $     19.44         3.48
                            M.S. Carriers               $      344.93    $     97.85         3.53
                            Old Dominion Freight        $      170.42    $     45.13         3.78
                            Trimac Ltd                  $      661.18    $    174.28         3.79
                            Matlack Systems             $      112.42    $     28.94         3.88
                            XTRA Corp.                  $   1,708.57     $    427.30         4.00
                            Covenant Transport Inc      $      259.16    $     64.35         4.03
                            Builders Transport          $      221.09    $     51.44         4.30
                            Werner Enterprises          $      844.39    $    196.15         4.30
                            Landstar Sys.               $      422.79    $     95.20         4.44
                            AMERCO                      $   1,632.30     $    345.78         4.72
                            USA Truck                   $      141.77    $     29.93         4.74
                            Frozen Food Express         $      164.17    $     34.10         4.81
                            Arnold Inds.                $      472.27    $     96.88         4.87
                            Greyhound Lines Inc.        $      437.71    $     89.61         4.88
                            USFreightways               $      983.86    $    198.91         4.95
                            Golden Eagle Group Inc.     $       12.50    $       2.33        5.37
                            Arkansas Best               $      578.78    $    107.15         5.40
                            Airlease Ltd.               $       73.64    $     13.48         5.46
                            Celadon Group               $      182.30    $     32.72         5.57
                            Amer. Freightways           $      716.15    $    120.94         5.92
                            Transfinancial Holdings     $       56 92
                                                                56.92    $       8 79
                                                                                 8.79        6 47
                                                                                             6.47
                            Vitran Corp. 'A'            $      140.68    $     21.51         6.54
                            Interpool Inc.              $   1,002.20     $    151.18         6.63
                            Intrenet Inc.               $       70.23    $     10.38         6.77
                            Swift Transportation        $      835.58    $    121.34         6.89
                            Landair Services            $      212.95    $     30.38         7.01
                            CNF Transportation          $   2,700.69     $    366.99         7.36
                            Budget Group Inc            $   1,247.30     $    166.71         7.48
                            Caliber System              $   2,514.99     $    333.13         7.55
                            Knight Transportation Inc   $      269.01    $     28.20         9.54
                            Heartland Express           $      727.50    $     64.62        11.26
                            Greyhound CDA Transn Corp   $       83.25    $       6.99       11.91
                            Mark VII                    $      160.45    $     12.96        12.38
                            Coach USA Inc               $      678.38    $     51.76        13.11
                            US 1 Inds Inc.              $         5.60   $     (0.17)         NA
                            Average                                                         5.61




                                                                                                        72
               A Test on EBITDA
• Ryder System looks very cheap on a
  Value/EBITDA        lti l basis, l ti to
  V l /EBITDA multiple b i relative t
  the rest of the sector. What explanation
  (other than misvaluation) might there be
  for this difference?




                                                                       73




    Analyzing the Value/EBITDA
              Multiple
• While low value/EBITDA multiples may be a symptom of
  undervaluation, a few questions need to be answered:
   – Is the operating income next year expected to be significantly
     lower than the EBITDA for the most recent period? (Price may
     have dropped)
   – Does the firm have significant capital expenditures coming up?
     (In the trucking business, the life of the trucking fleet would be a
     good indicator)
   – Does the firm have a much higher cost of capital than other firms
     in the sector?
   – Does the firm face a much higher tax rate than other firms in the
     sector?


                                                                       74
Value/EBITDA Multiples: Market
• The multiple of value to EBITDA varies widely across firms in the
  market, depending upon:
   – how capital intensive the firm is (high capital intensity firms will
     tend to have lower value/EBITDA ratios), and how much
     reinvestment is needed to keep the business going and create
     growth
   – how high or low the cost of capital is (higher costs of capital will
     lead to lower Value/EBITDA multiples)
   – how high or low expected growth is in the sector (high growth
     sectors will tend to have higher Value/EBITDA multiples)




                                                                            75




         Price-Book Value Ratio:
                Definition
• The price/book value ratio is the ratio of the market value of equity to
  the book value of equity, i.e., the measure of shareholders’ equity in
  the balance sheet.
• Price/Book Value = Market Value of Equity
                         Book Value of Equity
• Consistency Tests:
   – If the market value of equity refers to the market value of equity
      of common stock outstanding, the book value of common equity
      should be used in the denominator.
   – If there is more that one class of common stock outstanding, the
      market values of all classes (even the non-traded classes) needs
      to be factored in.


                                                                            76
Price to Book Value: Distribution
             1000




              800




              600




              400




              200
                                                                       Std. Dev = 2.36
                                                                       Mean = 2.39
                0                                                      N = 4866.00




                    PBV Ratio

                                                                                         77




 Price Book Value Ratio: Stable
          Growth Firm
• Going back to a simple dividend discount model,

                                                 DPS1
                                         P0 
                                                 r  gn
• Defining the return on equity (ROE) = EPS0 / Book Value of Equity,
  the value of equity can be written as:

                                    BV 0 * ROE * Payout Ratio * (1  gn )
                            P0 
                                                    r-gn

                             P0          ROE * Payout Ratio * (1  g n )
                                  PBV =
                            BV 0                    r-g        n


• If the return on equity is based upon expected earnings in the next
  time period, this can be simplified to,
                                 P0          ROE * Payout Ratio
                                      PBV =
                                BV 0                r-g    n

                                                                                         78
    Price Book Value Ratio: Stable
             Growth Firm
         Another Presentation
•  This formulation can be simplified even further by relating growth to
  the return on equity:
                        g = (1 - Payout ratio) * ROE
• Substituting back into the P/BV equation,
                        P0             ROE - gn
                              PBV =
                      BV 0                 r-g      n


•         price-book
     The price book value ratio of a stable firm is determined by the
    differential between the return on equity and the required rate of
    return on its projects.




                                                                         79




                         PBV/ROE: Oil Companies
    Company Name              Ticker Symbol      PBV      ROE
    Crown Cent. Petr.'A'                  CNPA   0.29     -14.60%
    Giant Industries          GI          0.54   7.47%
    Harken Energy Corp.                   HEC    0.64     -5.83%
    Getty Petroleum Mktg.                 GPM    0.95     6.26%
    Pennzoil-Quaker State                 PZL    0.95     3.99%
    Ashland Inc.              ASH         1.13   10.27%
    Shell Transport           SC          1.45
                                          1 45   13.41%
                                                 13 41%
    USX-Marathon Group                    MRO    1.59     13.42%
    Lakehead Pipe Line                    LHP    1.72     13.28%
    Amerada Hess                          AHC    1.77     16.69%
    Tosco Corp.               TOS         1.95   15.44%
    Occidental Petroleum                  OXY    2.15     16.68%
    Royal Dutch Petr.         RD          2.33   13.41%
    Murphy Oil Corp.          MUR         2.40   14.49%
    Texaco Inc.               TX          2.44   13.77%
    Phillips Petroleum        P           2.64
                                          2 64   17 92%
                                                 17.92%
    Chevron Corp.             CHV         3.03   15.69%
    Repsol-YPF ADR                        REP    3.24     13.43%
    Unocal Corp.              UCL         3.53   10.67%
    Kerr-McGee Corp.                      KMG    3.59     28.88%
    Exxon Mobil Corp.                     XOM    4.22     11.20%
    BP Amoco ADR                          BPA    4.66     14.34%
    Clayton Williams Energy               CWEI   5.57     31.02%         80
    Average                               2.30   12.23%
  PBV versus ROE regression
• Regressing PBV ratios against ROE for oil
           i    i ld the following
  companies yields th f ll i regression:  i
   PBV = 1.04 + 10.24 (ROE)        R2 = 49%
• For every 1% increase in ROE, the PBV
  ratio should increase by 0.1024.




                                            81




            Valuing Pemex
• Assume that you have been asked to
    l             f th M i
  value a PEMEX for the Mexican
  Government; All you know is that it has
  earned a return on equity of 10% last year.
  The appropriate P/BV ratio can be
  estimated
 P/BV Ratio (based upon regression) = 1.04
             + 10.24 * 0.1 = 2.06

                                            82
        Looking for undervalued
      securities - PBV Ratios and
•
                           ROE
    Given the relationship between price-book value ratios
  and returns on equity, it is not surprising to see firms
  which have high returns on equity selling for well above
  book value and firms which have low returns on equity
  selling at or below book value.
• The firms which should draw attention from investors are
  those which provide mismatches of price-book value
  ratios and returns on equity - low P/BV ratios and high
  ROE or high P/BV ratios and low ROE.



                                                               83




            The Valuation Matrix
                               MV/BV




                  Overvalued
                  Low ROE              High ROE
                  High MV/BV           High MV/BV




                                                       ROE-r



                                         Undervalued
                  Low ROE                High ROE
                  Low MV/BV              Low MV/BV




                                                               84
          Value/Book Value Ratio:
                 Definition
•   While the price to book ratio is a equity multiple, both the market value and
    the book value can be stated in terms of the firm.
•   Value/Book Value = Market Value of Equity + Market Value of Debt
                         Book Value of Equity + Book Value of Debt




                                                                                85




      Price Sales Ratio: Definition
• The price/sales ratio is the ratio of the market value of
  equity to the sales.
• Price/ Sales=      Market Value of Equity
                     Total Revenues
• Consistency Tests
   – The price/sales ratio is internally inconsistent, since
     the market value of equity is divided by the total
     revenues of the firm.




                                                                                86
  PS Ratios: The Inconsistency
              Test
• Assume that you are comparing
    i / l       ti          firms i a sector,
  price/sales ratios across fi    in      t
  and that there are differences in financial
  leverage across firms. What type of firms
  will emerge with the lowest price/sales
  ratios?
Low Leverage Firms
Average Leverage Firms
High Leverage Firms
                                                87




     Price/Sales Ratio: Cross
       Sectional Distribution
        1400


        1200


        1000


         800


         600


         400


                              Std. Dev = 2.55
         200
                              Mean = 1.87
           0                  N = 4634.00




               PS RATIO

                                                88
   Price Sales Ratios and Profit
             Margins
• The key determinant of price-sales ratios is the profit
  margin.
• A decline in profit margins has a two-fold effect.
   – First, the reduction in profit margins reduces the price-
     sales ratio directly.
   – Second, the lower profit margin can lead to lower
     growth and hence lower price-sales ratios.
   E     t d     th t      Retention ti
   Expected growth rate = R t ti ratio * R t             Equity
                                             Return on E it
       = Retention Ratio *(Net Profit / Sales) * ( Sales / BV of Equity)
       = Retention Ratio * Profit Margin * Sales/BV of Equity



                                                                                      89




       Effect of Margin Changes
                          Price/Sales Ratios and Net Margins

       1.8


       1.6


       1.4


       1.2


         1


       0.8


       0.6


       0.4


       0.2


         0
             2%      4%         6%          8%                10%   12%   14%   16%
                                                 Net Margin




                                                                                      90
   PS/Margins: Greek Retailers
      Company           PS           Net Margin
      SPAKIANAKIS SA          0.25         2.88%
      KOTSOVOLOS SA           0.48         1.91%
      SANYO HELLAS            1.12         5.07%
      IMAGE-SOV2VD SA         1.31         2.86%
      GERMAN0S                1.49         6.94%
      ELEKTRONIKI             1.61         6.29%
      JUMBO                   1.68         6.08%
      PHiLIPPOS NAKAS         1 71
                              1.71         5 04%
                                           5.04%
      GOODY'S                 2.24         6.77%
      HELLENIC DUTY           5.60        19.49%
      AS COMPANY              7.02         8.23%
      FOLLI-FOLLIE           10.82        29.08%
                                                    91




 Regression Results: PS Ratios
         and Margins
• Regressing PS ratios against net margins,
    PS = -.10 + 36 29 (N t M i )
           10 36.29 (Net Margin)        R2 = 78%
• Thus, a 1% increase in the margin results in an
  increase of 0.36 in the price sales ratios.
• The regression also allows us to get predicted
  PS ratios for these firms




                                                    92
             Predicted PS Ratios
Symbol        Company     PS                Predicted PS Under or Over V
SFA           SPAKIANAKIS            0.25            0.94    73.28%
                                                            -73.28%
KOTSV         KOTSOVOLOS             0.48            0.59   -18.47%
SANYO         SANYO HELLA            1.12            1.74   -35.37%
IKONA         IMAGE-SOV2V            1.31            0.94     39.82%
GERM          GERMAN0S               1.49            2.42   -38.41%
ELATH         ELEKTRONIKI            1.61            2.18   -26.47%
BABY          JUMBO                  1.68            2.11   -20.39%
NAKAS         PHXLXPPOS N            1 71
                                     1.71            1.73
                                                     1 73     -1 38%
                                                              -1.38%
GOODY         GOODY'S                2.24            2.36     -5.01%
HDF           HELLENIC DUT           5.60            6.97   -19.72%
ASCO          AS COMPANY             7.02            2.89   143.07%
FOLLI         FOLLX-FOLLXE          10.82           10.45      3.51%

                                                                      93




         Current versus Predicted
                 Margins
• One of the limitations of the analysis we did in these last few pages
  is the focus on current margins. Stocks are priced based upon
  expected margins rather than current margins.
• For most firms, current margins and predicted margins are highly
  correlated, making the analysis still relevant.
• For firms where current margins have little or no correlation with
  expected margins, regressions of price to sales ratios against
  current margins (or price to book against current return on equity)
  will not provide much explanatory power.
• In these cases, it makes more sense to run the regression using
  either predicted margins or some proxy for predicted margins.




                                                                      94
     A Case Study: The Internet
              Stocks
           30




                                                                       PKSI

                                                                                 LCOS                                 SPYG
           20
                         INTM                                                           MMXI
                                                              SCNT


                                                                MQST                                         FFIV     ATHM
       A
                                                                CNET                                                DCLK
       d
       j                                        RAMP
                                      INTW
       P   10                                                                 CSGP                    CBIS           NTPA
       S          NETO                                                                                    SONE
                                             APNT                                          CLKS               PCLN
                                      PSIX
                                   EDGR                                           ATHY         AMZN
                         SPLN                  BIDS
                                                                       ALOY                                ACOM EGRP
                                                       BIZZ                             IIXL
                                                                                               ITRA              ANET
                ONEM      FATB                             ABTL           INFO                         TMNT GEEK
                            RMII
           -0                                              TURF                  PPOD                 BUYX        ELTX
                                                                                 GSVI                            ROWE




                            -0.8                    -0.6                  -0.4                   -0.2
                                                       AdjMargin


                                                                                                                             95




 PS Ratios and Margins are not
       highly correlated
• Regressing PS ratios against current margins yields the following
   PS = 81.36        - 7.54(Net Margin)
                           (        g )            R2 = 0.04
                     (0.49)
• This is not surprising. These firms are priced based upon expected
  margins, rather than current margins.




                                                                                                                             96
Solution 1: Use proxies for survival and
    growth: Amazon in early 2000
• Hypothesizing that firms with higher revenue growth and higher cash
   balances should have a greater chance of surviving and becoming
   profitable, we ran the following regression: (The level of revenues
   was used to control for size)
PS = 30.61 - 2.77 ln(Rev) + 6.42 (Rev Growth) + 5.11 (Cash/Rev)
         (0.66) (2.63) (3.49)
R squared = 31.8%
Predicted PS = 30.61 - 2.77(7.1039) + 6.42(1.9946) + 5.11 (.3069) =
   30.42
Actual PS = 25.63
Stock is undervalued, relative to other internet stocks.



                                                                         97




          Solution 2: Use forward
                 multiples
• You can always estimate price (or value) as a multiple of revenues,
  earnings or book value in a future year. These multiples are called
            multiples.
  forward multiples
• For young and evolving firms, the values of fundamentals in future
  years may provide a much better picture of the true value potential
  of the firm. There are two ways in which you can use forward
  multiples:
   – Look at value today as a multiple of revenues or earnings in the
      future (say 5 years from now) for all firms in the comparable firm
      list. Use the average of this multiple in conjunction with your
      firm’s      i                  to ti t the l           f
      fi ’ earnings or revenues t estimate th value of your firm    fi
      today.
   – Estimate value as a multiple of current revenues or earnings for
      more mature firms in the group and apply this multiple to the
      forward earnings or revenues to the forward earnings for your
      firm. This will yield the expected value for your firm in the forward
      year and will have to be discounted back to the present to get 98
      current value.
    An Example of Forward
Multiples: Amazon in early 2000
•   Amazon.com lost $0.63 per share in 2000 but is expected to earn $ 1.50 per
    share in 2005. At its current price of $ 49 per share, this would translate into
                                          32.67.
    a price/future earnings per share of 32 67
•   In the first approach, this multiple of earnings can be compared to the
    price/future earnings ratios of comparable firms. If you define comparable
    firms to be e-tailers, Amazon looks reasonably attractive since the average
    price/future earnings per share of e-tailers is 65. If, on the other hand, you
    compared Amazon’s price to future earnings per share to the average price
    to future earnings per share (in 2004) of specialty retailers, the picture is
    bleaker. The average price to future earnings for these firms is 12, which
    would lead to a conclusion that Amazon is over valued.
•                    approach,
    In the second approach the current price to earnings ratio for specialty
    retailers, which is estimated to be 20.31 to the earnings per share of
    Amazon in 2004 (which is estimated to be $1.50). This would yield a target
    price of $30.46. Discounting this price back to the present using Amazon’s
    cost of equity of 12.94% results in a value per share:
      Value per share = Target price in five years/ (1 + Cost of equity)5
           = $30.46/1.12945 = $16.58.
                                                                                                                            99




                             PS Regression
                                                                    Model Summary

                                                                                   Adjusted R    Std. Error of
                                  Model              R               R Square        Square      the Estimate
                                  1                      .851   a         .723            .723        88.1869
                                    a. Predictors: (Constant), Beta, MARGIN, PAYOUT, Expected
                                       Growth in EPS: next 5 y
                                                  Coefficients a,b,c

                                                                                  Standar
                                          Unstandardized                            dized
                                           Coefficients                          Coefficients
    Model                                 B                Std. Error                Beta                 t       Sig.
    1       Expected Growth
                                   4.392E-02                          .005               .199             9.210      .000
            in EPS: next 5 y
            PAYOUT                            .807                    .115               .087             7.007      .000
            MARGIN                     23.747                         .466               .876           50.955       .000
            Beta                         -.607                        .085              -.187           -7.110       .000
     a. Dependent Variable: PS RATIO
     b. Linear Regression through the Origin
     c. Weighted Least Squares Regression - Weighted by Market Cap




                                                                                                                            100
     Value/Sales Ratio: Definition
•   The value/sales ratio is the ratio of the market value of the firm to the sales.
•   Value/ Sales= Market Value of Equity + Market Value of Debt-Cas
                             Total Revenues




                                                                                 101




          Value/Sales Ratio: Cross
           Sectional Distribution
                    1400


                    1200


                    1000


                     800


                     600


                     400

                                                       Std.      2.48
                                                       Std Dev = 2 48
                     200
                                                       Mean = 2.01
                       0                               N = 4644.00




                                   EV/SALES

                                                                                 102
       Brand Name Premiums in
              Valuation
• You have been hired to value Coca Cola for an analyst
  reports and you have valued the firm at 6.10 times
  revenues, using the model described in the last few
  pages. Another analyst is arguing that there should be a
  premium added on to reflect the value of the brand
  name. Do you agree?
 Yes
 No
• Explain.



                                                                           103




      The value of a brand name
• One of the critiques of traditional valuation is that it fails to consider
  the value of brand names and other intangibles.
• The approaches used by analysts to value brand names are often
  ad-hoc and may significantly overstate or understate their value.
• One of the benefits of having a well-known and respected brand
  name is that firms can charge higher prices for the same products,
  leading to higher profit margins and hence to higher price-sales
  ratios and firm value. The larger the price premium that a firm can
  charge, the greater is the value of the brand name.
• In general, the value of a brand name can be written as:
   Value of brand name ={(V/S)b-(V/S)g }* Sales
   (V/S)b = Value of Firm/Sales ratio with the benefit of the brand
      name
   (V/S)g = Value of Firm/Sales ratio of the firm with the generic
      product                                                              104
     Illustration: Valuing a brand
           name: Coca Cola
                        Coca Cola         Generic Cola Company
   O      ti    M
AT Operating Margin i   18.56%
                        18 56%            7.50%
                                          7 50%
Sales/BV of Capital     1.67              1.67
ROC                     31.02%            12.53%
Reinvestment Rate       65.00% (19.35%)   65.00% (47.90%)
Expected Growth         20.16%            8.15%
Length                  10 years          10 yea
Cost of Equity          12.33%            12.33%
E/(D E)
E/(D+E)                 97.65%
                        97 65%            97.65%
                                          97 65%
AT Cost of Debt         4.16%             4.16%
D/(D+E)                 2.35%             2.35%
Cost of Capital         12.13%            12.13%
Value/Sales Ratio       6.10              0.69
                                                                 105




     Value of Coca Cola’s Brand
               Name
• Value of Coke’s Brand Name = ( 6.10 - 0.69)
  ($18 868 million) = $102 billion
  ($18,868
• Value of Coke as a company = 6.10 ($18,868)
  million) = $ 115 Billion
• Approximately 88.69% of the value of the
  company can be traced to brand name value




                                                                 106
Choosing Between the Multiples
• As presented in this section, there are dozens of multiples that can
  be potentially used to value an individual firm.
• In addition, relative valuation can be relative to a sector (or
  comparable firms) or to the entire market (using the regressions, for
  instance)
• Since there can be only one final estimate of value, there are three
  choices at this stage:
   – Use a simple average of the valuations obtained using a number
      of different multiples
   – Use a weighted average of the valuations obtained using a
      number of different multiples
   – Choose one of the multiples and base your valuation on that
      multiple

                                                                    107




     Averaging Across Multiples
• This procedure involves valuing a firm using five or six or
  more multiples and then taking an average of the
  valuations across these multiples.
• This is completely inappropriate since it averages good
  estimates with poor ones equally.
• If some of the multiples are “sector based” and some are
  “market based”, this will also average across two
                                            valuation.
  different ways of thinking about relative valuation




                                                                    108
     Weighted Averaging Across
             Multiples
• In this approach, the estimates obtained from using different
  multiples are averaged, with weights on each based upon the
  precision of each estimate. The more precise estimates are
  weighted more and the less precise ones weighted less.
• The precision of each estimate can be estimated fairly simply for
  those estimated based upon regressions as follows:
         Precision of Estimate = 1 / Standard Error of Estimate
  where the standard error of the predicted value is used in the
  denominator.
• This approach is more difficult to use when some of the estimates
  are subjective and some are based upon more quantitative
  techniques.


                                                                      109




             Picking one Multiple
• This is usually the best way to approach this issue. While a range of
  values can be obtained from a number of multiples, the “best
  estimate” value is obtained using one multiple.
• The multiple that is used can be chosen in one of two ways:
   – Use the multiple that best fits your objective. Thus, if you want
      the company to be undervalued, you pick the multiple that yields
      the highest value.
   – Use the multiple that has the highest R-squared in the sector
      when regressed against fundamentals. Thus, if you have tried
      PE, PBV, PS, etc. and run regressions of these multiples against
      fundamentals, use the multiple that works best at explaining
      differences across firms in that sector.
   – Use the multiple that seems to make the most sense for that
      sector, given how value is measured and created.
                                                                      110
    Self Serving Multiple Choice
• When a firm is valued using several multiples, some will yield really
  high values and some really low ones.
• If there is a significant bias in the valuation towards high or low
  values, it is tempting to pick the multiple that best reflects this bias.
  Once the multiple that works best is picked, the other multiples can
  be abandoned and never brought up.
• This approach, while yielding very biased and often absurd
  valuations, may serve other purposes very well.
• As a user of valuations, it is always important to look at the biases of
  the entity doing the valuation, and asking some questions:
    – Why was this multiple chosen?
    – What would the value be if a different multiple were used? (You
       pick the specific multiple that you want to see tried.)

                                                                        111




         The Statistical Approach
• One of the advantages of running regressions of multiples against
  fundamentals across firms in a sector is that you get R-squared
  values on the regression (that provide information on how well
  fundamentals explain differences across multiples in that sector).
• As a rule, it is dangerous to use multiples where valuation
  fundamentals (cash flows, risk and growth) do not explain a
  significant portion of the differences across firms in the sector.
• As a caveat, however, it is not necessarily true that the multiple that
  has the highest R-squared provides the best estimate of value for
  firms in a sector.




                                                                        112
           A More Intuitive Approach
•    As a general rule of thumb, the following table provides a way of picking a multiple for
     a sector
Sector                        Multiple Used                Rationale
Cyclical Manufacturing        PE, Relative PE              Often with normalized earnings
High Tech, High Growth        PEG                          Big differences in growth across
                                                           firms
High Growth/No Earnings       PS, VS                       Assume future margins will be good
Heavy Infrastructure          VEBITDA                      Firms in sector have losses in early
                              years and reported earnings can vary
                                                           depending on depreciation method
REITa                         P/CF                         Generally no cap ex investments
                                                           from equity earnings
Financial Services            PBV                          Book value often marked to market
Retailing
R t ili                       PS                              l        i i il            firms
                                                           If leverage is similar across fi
                              VS                           If leverage is different




                                                                                                  113




           Sector or Market Multiples
•    The conventional approach to using multiples is to look at the sector or
     comparable firms.
•    Whether sector or market based multiples make the most sense depends
     upon how you think the market makes mistakes in valuation
       – If you think that markets make mistakes on individual firm valuations but
           that valuations tend to be right, on average, at the sector level, you will
           use sector-based valuation only,
       – If you think that markets make mistakes on entire sectors, but is
           generally right on the overall market level, you will use only market-
           based valuation
•    It is usually a good idea to approach the valuation at two levels:
       – At the sector level, use multiples to see if the firm is under or over
           valued at the sector level
       – At the market level, check to see if the under or over valuation persists
           once you correct for sector under or over valuation.
                                                                                                  114
                            A Test
• You have valued Earthlink Networks, an internet service provider,
  relative to other internet companies using Price/Sales ratios and find
  it to be under valued almost 50% .When you value it relative to the
  market, using the market regression, you find it to be overvalued by
  almost 50%. How would you reconcile the two findings?
 One of the two valuations must be wrong. A stock cannot be under
  and over valued at the same time.
 It is possible that both valuations are right.
What has to be true about valuations in the sector for the second
  statement to be true?




                                                                     115




   Reviewing: The Four Steps to
     Understanding Multiples
• Define the multiple
   – Check for consistency  y
   – Make sure that they are estimated uniformally
• Describe the multiple
   – Multiples have skewed distributions: The averages are seldom
     good indicators of typical multiples
   – Check for bias, if the multiple cannot be estimated
• Analyze the multiple
           f
   – Identify the companion variable that drives the multiple
   – Examine the nature of the relationship
• Apply the multiple


                                                                     116

				
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