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					Valuation
        Curriculum designed for
        use with the Iowa Electronic
        Markets

        by

        Roger Ignatius
        Thomas A. Rietz


                                   1
Valuation: Lecture Outline
   Principles of Valuation
   Discounted Dividend Models
     Constant Dividend Model
     Constant Growth Model
   Discounted Cash flow Model
   Market Multiple Models
     P/E versus Past and Peers
     P/S versus Past and Peers
     P/CF versus Past and Peers
   Summary                        2
Principles of Valuation
   Book Value
     Depreciated value of assets minus
      outstanding liabilities
   Liquidation Value
     Amount that would be raised if all assets
      were sold independently
   Market Value (P)
     Value according to market price of
      outstanding stock
   Intrinsic Value (V)
     NPV of future cash flows (discounted at
      investors’ required rate of return)         3
Intrinsic Valuation Procedure
Asset Characteristics                       Investor Characteristics
  • Size of Future Cash flows                 • Assessment of Cash
  • Time of Future Cash flows                   flow Riskiness
  • Risk of Future Cash flows                 • Risk Preferences



                        Investors’ Required Rate
                              of Return (k)



                                 n
                                   CFt
                         V 
                            t 1 1  k 
                                         t
Where Does the Discount
Rate (k) Come From?
   CAPM: k = rf + bxRP
   Beta (b) is estimated using historical data
    and is available from many sources
   The risk free rate (rf) is the current
    Treasury rate
     Typically the 3-mo rate, but other are
      sometimes used
   The risk premium (RP) is a historical
    average relative to the rf used

                                                  5
Example: Estimating k for
Wal-Mart (WMT) on 4/27/01
   Inputs
     Three month Treasury rate: 3.75%
     Historical average RP (1926-1996):
      8.74%
     Beta for Dell (from MoneyCentral): 0.9
   Computing k:
     CAPM: k = 0.0375 + 0.9x0.0874 =
     11.62%
                                               6
                     Sensitivity to CAPM Inputs
Required Return (k) from CAPM



                                                                                                                    Change in Risk Free
                                                                26%
                                                                                                                    Rate
                                                                24%
                                                                22%                                                 Change in Risk
                                                                20%                                                 Premium
                                                                18%
                                                                16%                                                 Change in Beta
                                                                14%                                                 (Scale Shows
                                                                                                                    Change / 10)
                                                                12%
                                                                10%                                               Initial values:
                                                                 8%
                                                                 6%
                                                                                                                  Rf = 3.75%
                                                                                                                  RP = 8.47%
                                -0.05
                                        -0.04
                                                -0.03
                                                        -0.02
                                                                -0.01
                                                                        0.00
                                                                               0.01
                                                                                      0.02
                                                                                             0.03
                                                                                                    0.04
                                                                                                           0.05
                                                                                                                  Beta = 1.5
                                                        Change in Input                                                                   7
Discounted Dividend Models
   Stock pricing relationship:
                    
                           Dt
              P0  
                   t 1 (1  k )t
   Dividends will be
     Forecast directly
     Assumed to be constant
     Assumed to grow at a constant rate or
     Some combination of the above

                                              8
Constant Dividend (Zero
Growth Model) Model
   Stock pricing relationship:
                     
                            Dt
               P0  
                    t 1 (1  k )t
   If Dt is constant, then it is an
    ordinary perpetuity:
                  
                         Dt        D1
            P0                 
                 t 1 (1  k )
                               t
                                   k
                                        9
Example: Wal-Mart (4/27/01)
   The current (annual) dividend is: $0.28
   According to the constant dividend (zero
    growth) model:
                      $0.28
            P0WMT
                             $2.41
                      0.1162
   The price of Wal-Mart was actually $52.83
   Can you explain the difference?


                                                10
    Sensitivity to Constant
    Dividend Model Inputs
                                                             $9
                                                                                                                Change in Dividend
Stock Price from Constan




                                                             $8                                                 (Scale shows
                                                             $7                                                 Change / 10)
     Growth Model




                                                             $6                                                 Change in Discount
                                                                                                                Rate
                                                             $5
                                                             $4
                                                             $3
                                                             $2
                                                                                                              Initial values:
                                                             $1
                                                                                                              D0 = $0.50
                                                             $0
                                                                                                              k = 12%
                           -0.05
                                   -0.04
                                           -0.03
                                                    -0.02
                                                            -0.01
                                                                    0.00
                                                                           0.01
                                                                                  0.02
                                                                                         0.03
                                                                                                0.04
                                                                                                       0.05


                                                   Change in Input                                                                   11
Why do a firm’s dividends
grow?
   Because earnings grow. Why?
   Because of reinvested funds
     Used to expand or to undertake new projects
     Used in positive NPV projects
   Leads to
     Earnings growth
     Investments growth and
     Dividend growth
Constant Growth Model
   Stock pricing relationship:
                     
                            Dt
               P0  
                    t 1 (1  k )t
   If Dt grows at a constant rate, g,
    then it is a growth perpetuity:
            
                   D1         D1    D0 (1  g )
      P0                       
           t 1 (1  k )     k g    k g
                         t


                                                  13
How do You Estimate Growth
(g)?
   Historical average
   Average analyst forecast
   Sustainable growth
     g = (1-Payout Ratio)xROE
   Required return versus dividend yield:
                                         D0
                                    k
       D1      D0 (1  g )             P0
    k    g              gg 
       P0          P0               D
                                  1 0
                                       P0
   NOTE: Must have g<k in the long run!
                                              14
Estimating g for Wal-Mart
(4/27/01)
       5 year historical average: 19.72%
       Average 5-year analyst forecast: 14.4%
       Sustainable growth
          g = (1-0.17)x0.22 = 18.26%
       Required return versus dividend yield:
                0.1162  $0.28
           g                    $52.83  11.03%
                  1  $0.28
                              $52.83
       What should it be?
         1st 3 are too high b/c long run must have g<k
         Guess: 11%?                                     15
Example: Wal-Mart (4/27/01)
   Current (annual) dividend is: $0.28
   If we use estimated growth of 11%:
                $0.28  1.11
          P0                 $50.13
               0.1162  0.11
   The price of Wal-Mart was actually $52.83
   Notes:
     Must have g<k in long run
     As gk, the price increases without bound

                                                  16
    Sensitivity to Constant Growth
    Model Inputs
                                                                                                                Change in Dividend
                                                            $60
                                                                                                                (Scale shows
Stock Price from Constan




                                                                                                                Change / 10)
                                                            $50
                                                                                                                Change in Discount
     Growth Model




                                                            $40                                                 Rate

                                                            $30                                                 Growth Rate

                                                            $20

                                                            $10                                               Initial values:
                                                                                                              D0 = $0.50
                                                             $0
                                                                                                              k = 12%
                                                                    0.00
                                                                           0.01
                                                                                  0.02
                                                                                         0.03
                                                                                                0.04
                                                                                                       0.05
                           -0.05
                                   -0.04
                                           -0.03
                                                    -0.02
                                                            -0.01




                                                                                                              g = 6%
                                                   Change in Input                                                                   17
Summary of Dividend
Discount Models
   Represents the value of dividends
    received by shareholders
   Requires
     A discount rate (k)
     Dividends (D)
     Steady or zero growth (g, with g<k)
   Trouble valuing
     Companies with D=0
     Fast growing companies with g>k       18
Discounted Cash Flow Model
   Shareholders receive or “own”:
    1. Dividends
    2. Re-invested earnings
     The effects of re-invested earnings
       are captured in dividend growth if a
       firm pays dividends and growth can
       be estimated
   An alternative valuation comes
    from valuing cash flows available
    to stockholders directly
     Useful for companies that pay no
       dividends                              19
What Constitutes Cash flows?
   There is some debate over exactly
    what constitutes cash flows
   The GAAP cash flow statement:
     CF = NI + depreciation – preferred
      stock dividends
     This should represent CFs that are
      either
      1. Paid out in common stock dividends or
      2. Re-invested
                                                 20
What Discount Rate Should
be used?
   It depends on the definition of CFs
     If CFs are defined as those available to
      all investors, WACC should be used
     If CFs are defined as those available to
      common stockholders, k from CAPM
      should be used
   We will use the latter


                                                 21
Example: Estimating k for K-
Mart (K) on 4/27/01
   Inputs
     Three month Treasury rate: 3.75%
     Historical average RP (1926-1996):
      8.74%
     Beta for K-Mart (from MoneyCentral): 1
   Computing k:
     CAPM: k = 0.0375 + 1x0.0874 = 12.49%


                                               22
How do You Estimate Growth
(g)?
   CFs will also grow
   Use methods similar to dividend growth,
    but
     Analysts forecasts are typically unavailable
     For many companies, dividend yield cannot be
      used b/c there is no dividend
   Often, earnings or sales growth are used
     Expenses and re-investment need to be
      relatively constant percentages of sales
   NOTE: Must have g<k in the long run!
                                                     23
Estimating g for K-Mart
(4/27/01)
   From the historical income statement:
                     Dec-00     Dec-99     Dec-98    Dec-97     Dec-96
    Net Income  $ (244.00) $ 403.00 $ 518.00 $ 249.00 $ (220.00)
    Dep & Amort $1,460.00 $2,070.00 $1,762.00 $1,555.00 $1,427.00
    Pref Div    $      -   $      -   $      -   $      -   $      -
    Cashflow    $ 1,216.00 $ 2,473.00 $ 2,280.00 $ 1,804.00 $ 1,207.00
    Growth         -50.83%      8.46%     26.39%     49.46%
    Avg Growth:      8.37%

   5 year sales growth: 2.35%
   Analysts’ 5 year earnings forecast: 10.3%
   Suppose, you believe K-Mart will not grow
    at all!                                                              24
Example: K-Mart (4/27/01)
   According to the last statements:
     CF = $1,216 million
     Shares = 486.5 million
     CF/Share = $2.50
   If we use estimated growth of 0.0%:
                $2.50  1.00
          P0                 $20.01
               0.1249  0.00
   The price of K-Mart was actually $9.82
   What must the market be expecting for K-
    Mart’s growth in the future?
                                               25
    Sensitivity to Constant Growth
    Cash flow Model Inputs
                                                                                                                Change in Cashflow
                                                            $60
                                                                                                                (Scale shows
Stock Price from Constan




                                                                                                                Change / 10)
                                                            $50
                                                                                                                Change in Discount
     Growth Model




                                                            $40                                                 Rate

                                                            $30                                                 Growth Rate

                                                            $20

                                                            $10                                               Initial values:
                                                                                                              CF0 = $0.50
                                                             $0
                                                                                                              k = 12%
                                                                    0.00
                                                                           0.01
                                                                                  0.02
                                                                                         0.03
                                                                                                0.04
                                                                                                       0.05
                           -0.05
                                   -0.04
                                           -0.03
                                                    -0.02
                                                            -0.01




                                                                                                              g = 6%
                                                   Change in Input                                                                   26
Summary of Discounted Cash
flow Models
   Represents the value of cash flows
    available to shareholders
   Requires
     A discount rate (k)
     A reasonable measure of cash flows
       o   IMPORTANT: How much depreciation MUST be
           replaced ? Model assumes zero.
     Steady or zero growth (g, with g<k)
   Trouble valuing
     Companies with CF<0
     Fast growing companies with g>k
     Companies with necessary replacement of
      depreciated assets                              27
Market Multiples
   Valuations are derived by:
    1. Forecasting earnings, sales or cash
       flows
    2. Applying the company’s historical
       P/E, P/S or P/CF to forecast
    3. Applying industry average P/E, P/S or
       P/CF to current inputs
Why do P/E Ratios Make
Sense?
   A company with a payout ratio of 1 will
    not grow and be valued at:
                  D   E
              P   1  1  P0  1
               0  r    r   E1 r

   A company with a payout less than 1 will
    grow and be valued at:
            E
         P  1  PVGO  P  1  PVGO
            r           E   r    E
                         1        1
                                               29
Logic of Market Multiple
Models
   Sales, earnings and cash flow drive
    profits, growth and value
   P/S, P/E & P/CF ratios show the
    relationship between price and these
    value drivers
   Firms within an industry have similar
    sales, profit and cash flow patterns and
    similar required returns
   Therefore, a reasonable value for a firm is
    its sales, earnings or cash flows times
    the respective industry ratio                 30
P/E Ratio Valuation
   If company “j” is “valued at historical
    ratios” relative to earnings:
                              P0j   
                 P1j  E1j   j
                             E      
                                     
                              0     

   If company “j” is “valued at industry
    ratios” relative to earnings:
                                  P0i 
              P0j  E0j  Avg  i 
                                  
                         Industry E 0 
                                              31
Example: Wal-Mart (4/27/01)
   Valued at historical P/E ratio:
     Analysts forecast next year’s earnings for
      WMT at $1.58
     WMT’s recent P/E was 37.7
     Then: P = $1.58x37.7 = $59.57
   Valued at industry average P/E ratio:
     This year, earnings for WMT were $1.40
     The industry average P/E was 36.0
     Then: P = $1.40x36.0 = $50.40
   The price of Wal-Mart was actually $52.83
                                                   32
    Sensitivity to P/E Multiple
    Model Inputs
                                                            $70                                                 Change in Earnings
Stock Price from Constan




                                                            $60
     Growth Model




                                                            $50                                                 Change Benchmark
                                                                                                                P/E Ratio (Scale
                                                            $40                                                 shows Change / 10)
                                                            $30
                                                            $20
                                                                                                              Initial values:
                                                            $10
                                                                                                              E1 = $1.50
                                                             $0
                                                                                                              P/E = 35
                                                                    0.00
                                                                           0.10
                                                                                  0.20
                                                                                         0.30
                                                                                                0.40
                                                                                                       0.50
                           -0.50
                                   -0.40
                                           -0.30
                                                    -0.20
                                                            -0.10




                                                   Change in Input                                                                   33
P/S Ratio Valuation
   For companies w/o earnings, P/S is
    sometimes used
   If you have a sales forecast, company “j” is
    “valued at historical ratios” relative to
    sales:                    j       P0   
                    P1j      S1j    j    
                                     S     
                                      0    
   Using current sales, a company “j” is
    “valued at industry ratios” relative to sales:
                                   P0i 
               P0j  S0j  Avg  i 
                                   
                          Industry S0              34
Example: Amazon (4/27/01)
   For the year ending 12/00
     Sales = 2,762 million (income statement)
     Shares = 357.1 million (balance sheet)
    Sales/Share = 2762/357.1 = 7.73
   Industry average P/S = 3.46
   So, using industry P/S Amazon should be
    priced at: 3.46x7.73 = $26.76
   The price of Amazon was actually $15.27

                                                 35
    Sensitivity to P/S Multiple
    Model Inputs
                                                            $70                                                 Change in Sales
Stock Price from Constan




                                                            $60
     Growth Model




                                                            $50                                                 Change Benchmark
                                                                                                                P/S Ratio (Scale
                                                            $40                                                 shows Change / 10)
                                                            $30
                                                            $20
                                                                                                              Initial values:
                                                            $10
                                                                                                              S1 = $3.00
                                                             $0
                                                                                                              P/S = 15
                                                                    0.00
                                                                           0.10
                                                                                  0.20
                                                                                         0.30
                                                                                                0.40
                                                                                                       0.50
                           -0.50
                                   -0.40
                                           -0.30
                                                    -0.20
                                                            -0.10




                                                   Change in Input                                                                   36
P/CF Ratio Valuation
• For companies w/o dividends, P/CF is
  sometimes used
• If you have a cash flow forecast, company “j” is
  “valued at historical ratios” relative to cash
  flows:
                                   P0j      
                     P1j  CF1j            
                                   CF j     
                                   0        
• Using current cash flow, company “j” is “valued
  at industry ratios” relative to cash flows:
                                          P0i     
               P0j      CF0j    Avg             
                                         
                                 Industry CF0
                                               i   
                                                   
                                                       37
Example: K-Mart (4/27/01)
   For the year ending 12/00
     CF = 1,216 million (discussed previously)
     Shares = 486.5 million (balance sheet)
    CF/Share = 1216/486.51 = 2.50
   Industry average P/CF = 21.3
   Using industry P/CF K-Mart should be
    priced at: 21.3x2.50 = $53.24
   The price of K-Mart was actually $9.82
   Is K-Mart undervalued or in serious
    trouble?
                                                  38
                 Sensitivity to P/CF Multiple
                 Model Inputs
                                                            $70                                                 Change in Cashflow
Stock Price from Constan




                                                            $60
     Growth Model




                                                            $50                                                 Change Benchmark
                                                                                                                P/CF Ratio (Scale
                                                            $40                                                 shows Change / 10)
                                                            $30
                                                            $20
                                                                                                              Initial values:
                                                            $10
                                                                                                              CF = $1.00
                                                             $0
                                                                                                              P/S = 30
                                                                    0.00
                                                                           0.10
                                                                                  0.20
                                                                                         0.30
                                                                                                0.40
                                                                                                       0.50
                           -0.50
                                   -0.40
                                           -0.30
                                                    -0.20
                                                            -0.10




                                                   Change in Input                                                                   39
Summary of Market Multiples
Models
   Valuations using historical and industry
    ratios
     Provide useful benchmarks
     Useful when dividends and cash flows cannot
      be discounted directly
     Can be compared to current ratios as a
      measure of market sentiment
   Weaknesses
     Misleading for firms that are changing rapidly
      or do not resemble the industry
                                                       40
Summary
• Discounted Dividend       • Why several
  w/ dividends and           methods?
   constant expected           Each has strengths
   (possibly zero) growth       and weaknesses
   in dividends                Different methods
• Discounted Cash flow          useful in different
  w/o dividends and            situations
   constant expected           Each gives a different
   (possibly zero) growth       “take” on the value of
   in cash flows                the company’s stock
• P/E, P/S and P/CF            Provides a range of
  ratios                        valuations instead of
                                point estimates
  Comparison with past
   or industry

                                                         41

				
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