valuation_models by xiuliliaofz


									                   Valuation Models

                      Aswath Damodaran

Aswath Damodaran                         1
                   Misconceptions about Valuation

             Myth 1: A valuation is an objective search for “true” value
               • Truth 1.1: All valuations are biased. The only questions are how much
                 and in which direction.
               • Truth 1.2: The direction and magnitude of the bias in your valuation is
                 directly proportional to who pays you and how much you are paid.
             Myth 2.: A good valuation provides a precise estimate of value
               • Truth 2.1: There are no precise valuations
               • Truth 2.2: The payoff to valuation is greatest when valuation is least
             Myth 3: . The more quantitative a model, the better the valuation
               • Truth 3.1: One‟s understanding of a valuation model is inversely
                 proportional to the number of inputs required for the model.
               • Truth 3.2: Simpler valuation models do much better than complex ones.

Aswath Damodaran                                                                           2
                                    Approaches to Valuation

                                                                    Valuation Models

            Asset Based                       Discounted Cashflow                      Relative Valuation                Contingent Claim
            Valuation                         Models                                                                     Models

                 Liquidation                                                               Equity   Sector          Option to   Option to   Option to
                 Value                                                                                              delay       expand      liquidate
                                                      Stable            Current             Firm
                                                                                                                                   Young         Equity in
                 Replacement                          Two-stage                                                                    firms         troubled
                 Cost                                                   Normalized
                                                      or n-stage
                                                                         Earnings    Book Revenues       Sector                    Undeveloped
                                                                                     Value               specific                  land

                           Equity Valuation      Firm Valuation
                           Models                Models
                                                                                                         Patent            Undeveloped
              Dividends                                                                                                    Reserves

                                   Cost of capital       APV               Excess Return
           Free Cashflow           approach              approach          Models
           to Firm

Aswath Damodaran                                                                                                                                             3
                   Basis for all valuation approaches

             The use of valuation models in investment decisions (i.e., in decisions
              on which assets are under valued and which are over valued) are based
               •  a perception that markets are inefficient and make mistakes in assessing
               • an assumption about how and when these inefficiencies will get corrected
             In an efficient market, the market price is the best estimate of value.
              The purpose of any valuation model is then the justification of this

Aswath Damodaran                                                                             4
                   Discounted Cash Flow Valuation

             What is it: In discounted cash flow valuation, the value of an asset is
              the present value of the expected cash flows on the asset.
             Philosophical Basis: Every asset has an intrinsic value that can be
              estimated, based upon its characteristics in terms of cash flows, growth
              and risk.
             Information Needed: To use discounted cash flow valuation, you
               • to estimate the life of the asset
               • to estimate the cash flows during the life of the asset
               • to estimate the discount rate to apply to these cash flows to get present
             Market Inefficiency: Markets are assumed to make mistakes in
              pricing assets across time, and are assumed to correct themselves over
              time, as new information comes out about assets.
Aswath Damodaran                                                                             5
            Discounted Cashflow Valuation: Basis for

                                     t = n CF
                             Value =         t
                                     t =1 (1+ r)

          where CFt is the cash flow in period t, r is the discount rate appropriate
             given the riskiness of the cash flow and t is the life of the asset.
          Proposition 1: For an asset to have value, the expected cash flows
             have to be positive some time over the life of the asset.
          Proposition 2: Assets that generate cash flows early in their life will
             be worth more than assets that generate cash flows later; the latter
             may however have greater growth and higher cash flows to

Aswath Damodaran                                                                       6
              Equity Valuation versus Firm Valuation

             Value just the equity stake in the business
             Value the entire business, which includes, besides equity, the other
              claimholders in the firm

Aswath Damodaran                                                                     7
                                   I.Equity Valuation

             The value of equity is obtained by discounting expected cashflows to equity, i.e., the
              residual cashflows after meeting all expenses, tax obligations and interest and principal
              payments, at the cost of equity, i.e., the rate of return required by equity investors in the

                                                           CF to Equityt
                               Value of Equity =        (1+ k )t
                                                       t=1        e
                  CF to Equityt = Expected Cashflow to Equity in period t
                  ke = Cost of Equity
             Forms: The dividend discount model is a specialized case of equity valuation, and the
              value of a stock is the present value of expected future dividends. In the more general
              version, you can consider the cashflows left over after debt payments and reinvestment
              needs as the free cashflow to equity.

Aswath Damodaran                                                                                              8
                               II. Firm Valuation

             Cost of capital approach: The value of the firm is obtained by
              discounting expected cashflows to the firm, i.e., the residual cashflows
              after meeting all operating expenses and taxes, but prior to debt
              payments, at the weighted average cost of capital, which is the cost of
              the different components of financing used by the firm, weighted by
              their market value proportions.
                                              t= n
                                                     CF to Firm t
                            Value of Firm =    (1+ WACC)
                                              t =1

             APV approach: The value of the firm can also be written as the sum
              of the value of the unlevered firm and the effects (good and bad) of
               Firm Value = Unlevered Firm Value + PV of tax benefits of debt - Expected
                  Bankruptcy Cost

Aswath Damodaran                                                                           9
                          Generic DCF Valuation Model

                                                DISCOUNTED CASHFLOW VALUATION

                                                                               Expected Growth
                                   Cash flows                                  Firm: Growth in
                                   Firm: Pre-debt cash                         Operating Earnings
                                   flow                                        Equity: Growth in
                                                                               Net Income/EPS               Firm is in stable growth:
                                   Equity: After debt
                                                                                                            Grows at constant rate
                                   cash flows

                                                                                                                  Terminal Value
                                            CF1          CF2       CF3        CF4             CF5           CFn
             Value                                                                                  .........
             Firm: Value of Firm                                                                                                   Forever
             Equity: Value of Equity
                                                          Le ngth of Pe riod of High Growth

                                                                   Discount Rate
                                                                   Firm:Cost of Capital

                                                                   Equity: Cost of Equity

Aswath Damodaran                                                                                                                             10
                            VALUING ABN AMRO
                                                                                                          ROE = 16%
                                                                  Ratio =
                         Dividends                                41.56%         Expected Growth
                         EP S =        1.54 Eur                                  41.56% *                     g =4%: ROE = 8.95%(=Cost of equity)
                         * Payout Ratio 58.44%                                   16% = 6.65%                  Beta = 1.00
                         DPS = 0.90 Eur                                                                       Payout = (1- 4/8.95) = .553

                                                                                                  Terminal Value= EPS6*Payout/(r-g)
                                                                                                        = (2.21*.553)/(.0895-.04) = 24.69
                       EPS 1.64 Eur            1.75 Eur      1.87 Eur     1.99 Eur     2.12 Eur
Value of Equity per
share = 20.48 Eur      DPS 0.96 Eur            1.02 Eur      1.09 Eur     1.16 Eur     1.24 Eur
                                                          Discount at Cost of Equity

                                                                  Cost of Equity
                                                                  4.95% + 0.95 (4%) = 8.75%

                      Riskfree Rate :
                      Long term bond rate in                                               Risk Premium
                      Euros                                Beta                            4%
                      4.95%                         +      0.95                  X

                                                     Average beta for European banks =
                                                     0.95                                           Mature Market       Country Risk
                                                                                                    4%                  0%

 Aswath Damodaran                                                                                                                            11
Aswath Damodaran   12
      Avg Reinvestment                    Embraer: Status Quo ($)
      rate = 25.08%                                                                   Return on Capital
                                       Reinvestment Rate
                                       25.08%                                                             Stable Growth
 Curre nt Cashflow to Firm                                    Expected Growth                             g = 4.17%; Beta = 1.00;
 EBIT(1-t) :         $ 404                                    in EBIT (1-t)                               Country Premium= 5%
 - Nt CpX               23                                    .2185*.2508=.0548                           Cost of capital = 8.76%
 - Chg WC                 9                                   5.48 %                                      ROC= 8.76%; Tax rate=34%
 = FCFF              $ 372                                                                                Reinvestment Rate=g/ROC
 Reinvestment Rate = 32/404= 7.9%                                                                                =4.17/8.76= 47.62%

                                                                                       Terminal Value = 288/(.0876-.0417) = 6272
                                                      $ Cashflows
Op. Assets $ 5,272                                                                                                       Term Yr
+ Cash:         795      Year               1              2            3              4            5                       549
- Debt           717     EBIT(1-t)          426            449          474            500          527                   - 261
- Minor. Int.    12      - Reinvestment     107            113          119            126          132                  = 288
=Equity        5,349     = FCFF             319            336          355            374          395
-Options          28
Value/Share $7.47
       R$ 21.75          Discount at$ Cost of Capital (WACC) = 10.52% (.84) + 6.05% (0.16) = 9.81%

                                                                                                                On October 6, 2003
                                                                                                                Embraer Price = R$15.51
       Cost of Equity               Cost of Debt
       10.52 %                      (4.17%+1%+4%)(1-.34)                   We ights
                                    = 6.05%                                E = 84% D = 16%

   Riskfree Rate:
   $ Riskfree Rate= 4.17%                 Beta                   Mature marke t                           Country Equity Risk
                               +          1.07         X         prem ium         +      Lambda     X     Premium
                                                                 4%                      0.27             7.67%

                                 Unlevered Beta for        Firm’s D/E                                                  Rel Equity
                                 Sectors: 0.95             Ratio: 19%                         Country Default          Mkt Vol
                                                                                              Spread               X
                                                                                              6.01%                     1.28

Aswath Damodaran                                                                                                                    13
           Current            Current
           Revenue            Margin:                                                                                                Stable Growth
           $ 3,804            -49.82%                        Cap ex growth slows                                                                       Stable
                                                             and net cap ex                                            Stable     Stable               ROC=7.36%
                                                             decreases                                                 Revenue    EBITDA/              Reinvest
                      EBIT                                                                                             Growth: 5% Sales                67.93%
                      -1895m                      Revenue                            EBITDA/Sales                                 30%
                                                  Growth:                            -> 30%
    NOL:                                          13.33%
    2,076m                                                                                                              Terminal Value= 677(.0736-.05)
                                                                                                                        =$ 28,683
                                                                                                                                                      Term. Year
                              Revenues          $3,804     $5,326     $6,923     $8,308     $9,139   $10,053 $11,058 $11,942 $12,659 $13,292          $13,902
                              EBITDA            ($95)      $0         $346       $831       $1,371   $1,809 $2,322 $2,508 $3,038 $3,589               $ 4,187
                              EBIT              ($1,675)   ($1,738)   ($1,565)   ($1,272)   $320     $1,074 $1,550 $1,697 $2,186 $2,694               $ 3,248
                              EBIT (1-t)        ($1,675)   ($1,738)   ($1,565)   ($1,272)   $320     $1,074 $1,550 $1,697 $2,186 $2,276               $ 2,111
                               + Depreciation   $1,580     $1,738     $1,911     $2,102     $1,051   $736     $773     $811    $852     $894          $ 939
                               - Cap Ex         $3,431     $1,716     $1,201     $1,261     $1,324   $1,390 $1,460 $1,533 $1,609 $1,690               $ 2,353
                               - Chg WC         $0         $46        $48        $42        $25      $27      $30      $27     $21      $19           $ 20
Value of Op Assets $ 5,530    FCFF              ($3,526)   ($1,761)   ($903)     ($472)     $22      $392     $832     $949    $1,407 $1,461          $ 677
+ Cash & Non-op $ 2,260                             1          2          3          4          5        6        7        8       9        10
= Value of Firm     $ 7,790                                                                                                                            Forever
- Value of Debt     $ 4,923   Beta              3.00       3.00       3.00       3.00       3.00     2.60     2.20     1.80     1.40     1.00
= Value of Equity   $ 2867    Cost of Equity    16.80%     16.80%     16.80%     16.80%     16.80%   15.20%   13.60%   12.00%   10.40%   8.80%
- Equity Options    $    14   Cost of Debt      12.80%     12.80%     12.80%     12.80%     12.80%   11.84%   10.88%   9.92%    8.96%    6.76%
Value per share     $ 3.22    Debt Ratio        74.91%     74.91%     74.91%     74.91%     74.91%   67.93%   60.95%   53.96%   46.98%   40.00%
                              Cost of Capital   13.80%     13.80%     13.80%     13.80%     13.80%   12.92%   11.94%   10.88%   9.72%    7.98%

                      Cost of Equity                             Cost of Debt                                          We ights
                      16.80%                                     4.8%+8.0%=12.8%                                       Debt= 74.91% -> 40%
                                                                 Tax rate = 0% -> 35%

      Riskfree Rate:
      T. Bond rate = 4.8%
                                                                                       Risk Prem ium
                                                                                                                                                  Global Crossing
                                         Beta                                          4%                                                         November 2001
                                  +      3.00> 1.10                              X                                                                Stock price = $1.86

                                    Internet/       Operating               Current                  Base Equity          Country Risk
                                    Retail          Leverage                D/E: 441%                Premium              Premium

  Aswath Damodaran                                                                                                                                                      14
              Valuing Global Crossing with Distress

             Probability of distress
               • Price of 8 year, 12% bond issued by Global Crossing = $ 653
                                      120(1  Distress) t 1000(1  Distress) 8
                                  t 8
                             653                        
                                          (1.05) t              (1.05) 8

               • Probability of distress = 13.53% a year
               • Cumulative probability of survival over 10 years = (1- .1353)10 = 23.37%
             Distress sale value of equity
               •   Book value of capital = $14,531 million
               •   Distress sale value = 15% of book value = .15*14531 = $2,180 million
               •   Book value of debt = $7,647 million
               •   Distress sale value of equity = $ 0
             Distress adjusted value of equity
               • Value of Global Crossing = $3.22 (.2337) + $0.00 (.7663) = $0.75

Aswath Damodaran                                                                            15
                    Adjusted Present Value Model

             In the adjusted present value approach, the value of the firm is written
              as the sum of the value of the firm without debt (the unlevered firm)
              and the effect of debt on firm value
             Firm Value = Unlevered Firm Value + (Tax Benefits of Debt -
              Expected Bankruptcy Cost from the Debt)
               • The unlevered firm value can be estimated by discounting the free
                 cashflows to the firm at the unlevered cost of equity
               • The tax benefit of debt reflects the present value of the expected tax
                 benefits. In its simplest form,
                                       Tax Benefit = Tax rate * Debt
               • The expected bankruptcy cost is a function of the probability of
                 bankruptcy and the cost of bankruptcy (direct as well as indirect) as a
                 percent of firm value.

Aswath Damodaran                                                                           16
                           Excess Return Models

             You can present any discounted cashflow model in terms of excess
              returns, with the value being written as:
               • Value = Capital Invested + Present value of excess returns on current
                 investments + Present value of excess returns on future investments
             This model can be stated in terms of firm value (EVA) or equity value.

Aswath Damodaran                                                                         17
                                       EQUITY VALUATION W ITH EQUITY EVA
                                                                                                  Firm is in stable growth:
                     Curre nt EVA                                         Expected Growth         Growth rate = 5%
                     Net Income =        $ 3104                           .60 * 20% =12%          Return on Equity = 15%
                     - Equity cost =     $ 1645                                                   Cost of equity =9.40%
                     Equity EVA =        $ 1459

                                                                                        Terminal Value= $2220/(.094-.05)=50,459
                           Net Income                $3,599          $4,031        $4,515      $5,057       $5,664
                           - Equity Cost (see below) $1,908          $2,137        $2,393      $2,680       $3,002
                           Excess Equity Return      $1,692          $1,895        $2,122      $2,377       $2,662
Book Equity= 17997
+ PV of EVA= 38334
= Equity EVA=56331                                                                                                     Forever
Value/sh = $50.26                                   Discount atCost of Equity

                                                         Cost of Equity

                                                                                  Risk Pre mium
                                                  Beta                            4.00%
                Riskfree Rate:             +      1.40                        X

                                                                                       Base Equity        Country Risk
                                                                                       Premium = 4%       Premium=0%

Aswath Damodaran                                                                                                                 18
                                       Choosing the right Discounted Cashflow Model

            Can you estimate cash flows?           Are the current earnings                          What rate is the firm growing
                                                   positive & normal?                                at currently?
      Yes                         No             Yes                  No                   < Growth rate                 > Growth rate of
                                                                                           of economy                    economy

                                                Use current          Is the cause
   Is leverage stable or     Use dividend       earnings as          temporary?                Stable growth             Are the firm’s
   likely to change over     discount model     base                                           model                     competitive
   time?                                                                                                                 advantges time
                                                               Yes                   No

Stable            Unstable
leverage          leverage                                    Replace current    Is the firm                Yes                  No
                                                              earnings with      likely to
                                                              normalized         survive?
                                                              earnings                                                         3-stage or
 FCFE               FCFF                                                                                   2-stage             n-stage
                                                                                                           model               model
                                                                           Yes                 No

                                                                      Adjust               Does the firm
                                                                      margins over         have a lot of
                                                                      time to nurse        debt?
                                                                      firm to financial


                                                                                 Value Equity              Estimate
                                                                                 as an option              liquidation
                                                                                 to liquidate              value

 Aswath Damodaran                                                                                                                     19
                               Relative Valuation

             What is it?: The value of any asset can be estimated by looking at
              how the market prices “similar” or „comparable” assets.
             Philosophical Basis: The intrinsic value of an asset is impossible (or
              close to impossible) to estimate. The value of an asset is whatever the
              market is willing to pay for it (based upon its characteristics)
             Information Needed: To do a relative valuation, you need
               • an identical asset, or a group of comparable or similar assets
               • a standardized measure of value (in equity, this is obtained by dividing the
                 price by a common variable, such as earnings or book value)
               • and if the assets are not perfectly comparable, variables to control for the
             Market Inefficiency: Pricing errors made across similar or
              comparable assets are easier to spot, easier to exploit and are much
              more quickly corrected.
Aswath Damodaran                                                                            20
                             Variations on Multiples

             Equity versus Firm Value
               •   Equity multiples (Price per share or Market value of equity)
               •   Firm value multiplies (Firm value or Enterprise value)
             Scaling variable
               •   Earnings (EPS, Net Income, EBIT, EBITDA)
               •   Book value (Book value of equity, Book value of assets, Book value of capital)
               •   Revenues
               •   Sector specific variables
             Base year
               •   Most recent financial year (Current)
               •   Last four quarters (Trailing)
               •   Average over last few years (Normalized)
               •   Expected future year (Forward)
             Comparables
               •   Sector
               •   Market

Aswath Damodaran                                                                                    21
                               Definitional Tests

             Is the multiple consistently defined?
               • Proposition 1: Both the value (the numerator) and the 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.

Aswath Damodaran                                                                             22
         An Example: 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

Aswath Damodaran                                                                      23
                               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?

Aswath Damodaran                                                                            24
                   PE Ratio: Descriptive Statistics

Aswath Damodaran                                      25
                   PE: Deciphering the Distribution

                                 Current PE   Trailing PE   Forward PE
          Mean                     36.04        34.14         30.79
          Standard Error            1.94         2.93          1.15
          Median                   18.25        17.25         18.52
          Standard Deviation      123.36        176.34        57.56
          Skewness                 23.13        28.40         13.66
          Minimum                   0.65         1.35          3.30
          Maximum                 5103.50      6914.50       1414.00
          Count                    4024          3627          2491
          Largest(500)             48.00        39.60         34.49
          Smallest(500)             9.38         9.62         12.94

Aswath Damodaran                                                         26
                   8 Times EBITDA is not cheap…

Aswath Damodaran                                  27
                                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
               • 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 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.

Aswath Damodaran                                                                           28
                           Relative Value and Fundamentals

                                     Value of Stock = DPS 1/(ke - g)

   PE=Payout Ratio             PEG=Payout ratio              PBV=ROE (Payout ratio)            PS= Net Margin (Payout ratio)
   (1+g)/(r-g)                 (1+g)/g(r-g)                  (1+g)/(r-g)                       (1+g)/(r-g)

   PE=f(g, payout, risk)     PEG=f(g, payout, risk)         PBV=f(ROE,payout, g, risk)        PS=f(Net Mgn, payout, g, risk)

                                                         Equity Multiples

                                                         Firm Multiple s

  V/FCFF=f(g, WACC)         V/EBIT(1-t)=f(g, RIR, WACC)           V/EBIT=f(g, RIR, WACC, t)      VS=f(Oper Mgn, RIR, g, WACC)

   Value/FCFF=(1+g)/           Value/EBIT(1-t) = (1+g)              Value/EBIT=(1+g)(1-                 VS= Oper Margin (1-
   (WACC-g)                    (1- RIR)/(WACC-g)                    RiR)/(1-t)(WACC-g)                  RIR) (1+g)/(WACC-g)

                                          Value of Firm = FCFF 1/(WACC -g)

Aswath Damodaran                                                                                                               29
                       What to control for...

          Multiple      Variables that determine it…
          PE Ratio      Expected Growth, Risk, Payout Ratio
          PBV Ratio     Return on Equity, Expected Growth, Risk, Payout
          PS Ratio      Net Margin, Expected Growth, Risk, Payout Ratio
          EVV/EBITDA    Expected Growth, Reinvestment rate, Cost of capital
          EV/ Sales     Operating Margin, Expected Growth, Risk, Reinvestment

Aswath Damodaran                                                                30
                               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.

Aswath Damodaran                                                                            31
              Comparing PE Ratios across a Sector

                                          Comp any Name                       PE       Gr owth
                    PT In dosat ADR                                             7.8         0.06
                    Tele bra s ADR                                              8.9        0.07 5
                    Tele co m Cor por ation of Ne w Ze aland ADR               11 .2        0.11
                    Tele co m Argen tin a Ste t - Fra nce Te lecom SA ADR B    12 .5        0.08
                    Hellen ic Telecommun ica tio n Org anization SA ADR        12 .8        0.12
                    Tele co municacion es d e Ch ile ADR                       16 .6        0.08
                    Swisscom AG ADR                                            18 .3        0.11
                    Asia Satellite Te lecom Holdin gs ADR                      19 .6        0.16
                    Por tu gal Telecom SA ADR                                  20 .8        0.13
                    Tele fo nos de Mexico ADR L                                21 .1        0.14
                    Matav RT ADR                                               21 .5        0.22
                    Telstra ADR                                                21 .7        0.12
                    Gila t Commu nications                                     22 .7        0.31
                    Deutsch e Te leko m AG ADR                                 24 .6        0.11
                    British Telecommunication s PLC ADR                        25 .7        0.07
                    Tele Dan mark AS ADR                                         27         0.09
                    Tele komunika si Indo nesia ADR                            28 .4        0.32
                    Cable & Wire less PLC ADR                                  29 .8        0.14
                    APT Satellite Hold ings ADR                                  31         0.33
                    Tele fo nica SA ADR                                        32 .5        0.18
                    Royal KPN NV ADR                                           35 .7        0.13
                    Tele co m Italia SPA ADR                                   42 .2        0.14
                    Nippo n Telegr aph & Tele pho ne ADR                       44 .3          0.2
                    Fra nce Telecom SA ADR                                     45 .2        0.19
                    Kor ea Telecom ADR                                         71 .3        0.44

Aswath Damodaran                                                                                    32
                          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

Aswath Damodaran                                                             33
                        Is Telebras under valued?

             Predicted PE = 13.12 + 121.22 (.075) - 13.85 (1) = 8.35
             At an actual price to earnings ratio of 8.9, Telebras is slightly

Aswath Damodaran                                                                  34
              PE Ratio without a constant - US Stocks
                                                                         Mo d e l Su mm a ry

                                                                                        Adjus t e d R           St d. Er ro r o f th e
                                        Mo de l          R        R Sq ua r e            Sq ua r e                   Es tim a te
                                        1                .8 5 6 b     .73 3                      .73 2         13 5 0.6 77 6 1 93 1 3
                                           a . Fo r r e g re ss io n t hr ou gh th e or igin (th e n o - int e rc e pt
                                               m od e l), R Squ a r e m e a su r e s t he pr o po rt ion of t he
                                               va r ia b ility in th e de p e n de n t va ria ble a b ou t th e o rig in
                                               ex pla ine d b y r e gr e s sion . T his CANNOT b e c o m p ar ed to R
                                               Sq ua r e fo r m od e ls whic h inc lu d e a n int er c e p t.
                                           b . Pr e d ic tor s: Valu e Line Bet a , P a you t Ra tio , Ex pe c te d
                                               Gr owt h in EPS: ne x t 5 ye a rs
                                                                                        Co e f fici e n ts a,b ,c

                                                         Uns t an d ar d iz ed             St a nd a r diz e d                                    9 5% Co nf ide n ce Int e rva l f or
                                                           Coe f fic ie nt s                C oe ffic ie n ts                                                     B
         Mo de l                                              B         Std . Er r or             Be t a                t           Sig .         Lo wer Bo un d     Up pe r Bo un d
         1          Exp e ct e d Gro wth in
                                                              1 .2 28         .05 5                        .51 4    22 .1 87             .0 0 0           1 .1 19              1.3 3 6
                    EPS: n e xt 5 ye ar s
                    Pa yo ut Ra tio                   - 1 .1 E- 0 2           .01 4                    - .01 3        - .7 68            .4 4 3           - .03 9               .0 1 7
                    Va lu e Lin e B ta                   1 1. 70 5            .82 5                        .38 4    14 .1 84             .0 0 0         1 0. 08 7            13 .3 24
           a . De p e nd e n t Va r ia b le : Cu r re nt PE
           b . Line a r Re g r e ss ion t hr ou gh th e Orig in
           c . We igh te d Le a st Sq u ar e s Re g re ss ion - We ig h te d by Ma r ke t Ca p

Aswath Damodaran                                                                                                                                                                         35
        Relative Valuation: Choosing the Right Model

Aswath Damodaran                                       36
                   Contingent Claim (Option) Valuation

             Options have several features
               • They derive their value from an underlying asset, which has value
               • The payoff on a call (put) option occurs only if the value of the underlying
                 asset is greater (lesser) than an exercise price that is specified at the time
                 the option is created. If this contingency does not occur, the option is
               • They have a fixed life
             Any security that shares these features can be valued as an option.

Aswath Damodaran                                                                              37
                         Option Payoff Diagrams

                                 Strike P rice                Value of Asset

                                                 Put Option
                   Call Option

Aswath Damodaran                                                               38
         Underlying Theme: Searching for an Elusive

             Traditional discounted cashflow models under estimate the value of
              investments, where there are options embedded in the investments to
               • Delay or defer making the investment (delay)
               • Adjust or alter production schedules as price changes (flexibility)
               • Expand into new markets or products at later stages in the process, based
                 upon observing favorable outcomes at the early stages (expansion)
               • Stop production or abandon investments if the outcomes are unfavorable
                 at early stages (abandonment)
             Put another way, real option advocates believe that you should be
              paying a premium on discounted cashflow value estimates.

Aswath Damodaran                                                                             39
                             Three Basic Questions

             When is there a real option embedded in a decision or an asset?
               •   There has to be a clearly defined underlying asset whose value changes over time
                   in unpredictable ways.
               •   The payoffs on this asset (real option) have to be contingent on an specified event
                   occurring within a finite period.
             When does that real option have significant economic value?
               •   For an option to have significant economic value, there has to be a restriction on
                   competition in the event of the contingency.
               •   At the limit, real options are most valuable when you have exclusivity - you and
                   only you can take advantage of the contingency. They become less valuable as the
                   barriers to competition become less steep.
             Can that value be estimated using an option pricing model?
               •   The underlying asset is traded - this yield not only observable prices and volatility
                   as inputs to option pricing models but allows for the possibility of creating
                   replicating portfolios
               •   An active marketplace exists for the option itself.
               •   The cost of exercising the option is known with some degree of certaint

Aswath Damodaran                                                                                           40
         Putting Natural Resource Options to the Test

             The Option Test:
               •   Underlying Asset: Oil or gold in reserve
               •   Contingency: If value > Cost of development: Value - Dev Cost
                                 If value < Cost of development: 0
             The Exclusivity Test:
               •   Natural resource reserves are limited (at least for the short term)
               •   It takes time and resources to develop new reserves
             The Option Pricing Test
               •   Underlying Asset: While the reserve or mine may not be traded, the commodity is. If we
                   assume that we know the quantity with a fair degree of certainty, you can trade the underlying
               •   Option: Oil companies buy and sell reserves from each other regularly.
               •   Cost of Exercising the Option: This is the cost of developing a reserve. Given the experience
                   that commodity companies have with this, they can estimate this cost with a fair degree of
             Bottom Line: Real option pricing models work well with natural resource options.

Aswath Damodaran                                                                                                    41
                   The Real Options Test: Patents and

             The Option Test:
               •    Underlying Asset: Product that would be generated by the patent
               •    Contingency:
                      If PV of CFs from development > Cost of development: PV - Cost
                      If PV of CFs from development < Cost of development: 0
             The Exclusivity Test:
               •    Patents restrict competitors from developing similar products
               •    Patents do not restrict competitors from developing other products to treat the same disease.
             The Pricing Test
               •    Underlying Asset: Patents are not traded. Not only do you therefore have to estimate the
                    present values and volatilities yourself, you cannot construct replicating positions or do
               •    Option: Patents are bought and sold, though not as frequently as oil reserves or mines.
               •    Cost of Exercising the Option: This is the cost of converting the patent for commercial
                    production. Here, experience does help and drug firms can make fairly precise estimates of the
             Bottom Line: Use real option pricing arguments with caution.

Aswath Damodaran                                                                                                     42
       The Real Options Test for Growth (Expansion)

             The Options Test
               • Underlying Asset: Expansion Project
               • Contingency
               If PV of CF from expansion > Expansion Cost: PV - Expansion Cost
               If PV of CF from expansion < Expansion Cost: 0
             The Exclusivity Test
               •   Barriers may range from strong (exclusive licenses granted by the government) to weaker
                   (brand name, knowledge of the market) to weakest (first mover).
             The Pricing Test
               •   Underlying Asset: As with patents, there is no trading in the underlying asset and you have to
                   estimate value and volatility.
               •   Option: Licenses are sometimes bought and sold, but more diffuse expansion options are not.
               •   Cost of Exercising the Option: Not known with any precision and may itself evolve over time
                   as the market evolves.
             Bottom Line: Using option pricing models to value expansion options will not only
              yield extremely noisy estimates, but may attach inappropriate premiums to discounted
              cashflow estimates.

Aswath Damodaran                                                                                                    43
            Summarizing the Real Options Argument

             There are real options everywhere.
             Most of them have no significant economic value because there is no
              exclusivity associated with using them.
             When options have significant economic value, the inputs needed to
              value them in a binomial model can be used in more traditional
              approaches (decision trees) to yield equivalent value.
             The real value from real options lies in
               • Recognizing that building in flexibility and escape hatches into large
                 decisions has value
               • Insights we get on understanding how and why companies behave the way
                 they do in investment analysis and capital structure choices.

Aswath Damodaran                                                                      44
                                                         Valuation Models

 Asset Based                       Discounted Cashflow                      Relative Valuation                Contingent Claim
 Valuation                         Models                                                                     Models

      Liquidation                                                               Equity   Sector          Option to   Option to   Option to
      Value                                                                                              delay       expand      liquidate
                                           Stable            Current             Firm
                                                                                                                        Young         Equity in
      Replacement                          Two-stage                                                                    firms         troubled
      Cost                                                   Normalized
                                           or n-stage
                                                              Earnings    Book Revenues       Sector                    Undeveloped
                                                                          Value               specific                  land

                Equity Valuation      Firm Valuation
                Models                Models
                                                                                              Patent            Undeveloped
   Dividends                                                                                                    Reserves

                        Cost of capital       APV               Excess Return
Free Cashflow           approach              approach          Models
to Firm

Aswath Damodaran                                                                                                                          45
          Which approach should you use? Depends
                upon the asset being valued..
                                           Asset Marketabili ty and Val uation Approaches

                    Mature businesses                                              Growth businesses
                    Separable & marketable assets                                  Linked and non-marketable assets

                    Liquidation &                                                       Other valuation models
                    Replacement cost
                                           Cash Flows and Val uati on Approaches

                   Cashflows currently or            Cashflows if a contingency      Assets that will never
                   expected in near future           occurs                          generate cashflows

                   Discounted cashflow                 Option pricing models           Relative valuation models
                   or relative valuation
                                           Uni queness of Asset and Valuati on Approaches

                                                                                       Large number of similar
                    Unique asset or business                                           assets that are priced

                    Discounted cashflow                                                 Relative valuation models
                    or option pricing

Aswath Damodaran                                                                                                      46
              And the analyst doing the valuation….

                              Investor Time Hori zon and Val uati on Approaches

         Very short time horizon
                                                                           Long Time Horizon

         Liquidation value         Relative valuation   Option pricing     Discounted Cashflow value
                              Views on market and Val uati on Approaches

           Markets are correct on          Asset markets and financial        Markets make mistakes but
           average but make mistakes       markets may diverge                correct them over time
           on individual assets

         Relative valuation                Liquidation value               Discounted Cashflow value

                                                                           Option pricing models

Aswath Damodaran                                                                                       47

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