Chapter 8- Common Stock Valuation

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					Chapter 8: Common Stock Valuation

Placing a value on the equity of a company (Assets - Liabilities) is a "Holy Grail" of finance
           Knowing what the true price of a share should, versus what it trades at, is the key to riches.
           Why? You can test your wits against the market: if overvalued, sell; if undervalued, buy.
Valuation also lets you draw important conclusions from the observed price of assets.

Defining "Value"
          "Price" and true "Value" are different
          3 types of Value:
                      Book        Price of Asset minus Accumulated Depreciation
                                  Does not necessarily represent market value.

                       Market        Price determined by competitive marketplace (i.e. "the Stock Market")
                                     = Marginal PRICE an investor is willing to pay
                                     Changes constantly; difficult to nail down

                       Intrinsic     The Fundamental, Unique Value to any one particular investor
                                     Defined by DISCOUNTING FUTURE CASH FLOWS
                                     The DISCOUNT is at an investor's individual REQUIRED RATE OF RETURN
                                     Corporate finance deals with determining Intrinsic value

Fundamentals of Valuation
        Important factors:
                    The Larger the cash flows, and the More Quickly they are received, the greater the value.
                    The investor's required return-- "Opportunity Cost" or "Hurdle Rate"
                                 Stocks are riskier than bonds, so required return is higher for stocks.

                                                 N

                         Value of                                 Cash Flows in Period
                         Stock =
                                                 Ʃ               (1 + interest ) ^ Period
                                                t=1

           Hence need 3 things:
                     1. Expected Cash Flows
                     2. When Cash Flows Occur
                     3. Required Rate of Return for these Cash Flows

Required Rate of Return
         The hardest part of valuation

           Investors can be Risk Averse (prefers less risk), Risk Neutral (doesn't care about risk), or Risk Seeking (prefers r
                       We assume all investors are Risk Averse and hence require more return for more risk
         Simple Risk Premium Model
                    Expected Return = Base Rate + Risk Premium
                                  Base Rate = return of some benchmark security
                                  Risk Premium is subjectively determined
                    This is too subjective

         Capital Asset Pricing Model (CAPM)
                   Expected Return on a Particular Stock = Risk Free Rate + Beta * (Expected Market Return - Risk Free
                     E(Ri) = Rf + Bi * ( E(Rm) - Rf )
                                 E(Ri) = expected return of Security i
                                 Rf = risk-free rate (e.g. Treasury Bills)
                                 Bi = measure of riskiness of Security i
                                 E(Rm) = expected market return (e.g. S&P 500)
                     More objective-- commonly used in Finance.

                     The market return is a benchmark to which other portfolios are compared
                                Subtracting the Risk Free Rate from the market return gives the market premium for stock

                     Beta measures the risk of a particular security relative to the market return
                                Beta = 1 means a security is exactly as risky as the average stock (i.e. "the market")
                                Beta = 0 means a security has NO risk
                                Beta = 2 means a security has TWICE the riskiness of the average stock
                                Beta = (-1) means a security in INVERSELY proportional to the average stock (not comm
                     Research companies such as Value Line estimate betas based on a company's past performance

         The Security Market Line shows visually and mathematically how different stocks can be valued
                    Gives Required Rate of Return for any stock given its Beta

Tangible Value Models (a.k.a. "The Income Approach")

         First question: What is your strategy in buying a stock?
                     1. Dividend accumulation
                     2. Price appreciation as a result of earnings growth, with the intention of selling at a later period (i.e. "T

         The Constant-Growth Dividend Discount Model
                   With Dividends, we estimate a stock's value based on dividends accruing as we hold the stock indefinit

                       Value of        Period 1 Dividend
                       Stock =       (1 + Req. Return ) ^ 1               +

                     Since the Dividends never change, this can be restated in closed form as:
                       Value of          Period 1 Dividend
                       Stock =                  r-g

                     Where   r   is the "Required Return", aka the expected return
                     And where g is the growth rate of the dividend stream

         The Earnings Model
                   Whether they pay a dividend or not, most firms reinvest at least some of their earnings
                   Hence, a stock's value is equal to its current payout value plus its growth on reinvested earnings

                       Value of          Payout * Earnings
                       Stock =                 r-g
                                                                            =

                     Where   r   is the "Required Return", aka the expected return
                     And where g is the growth rate of future earnings (only those earnings that are reinvested as opposed t
                                    g   can be calculated as the % of reinvested earnings multiplied by the actual return (i.e. th
                                    Hence, g = Return on Equity * Retention Ratio

                     Note 1: The Reinvestment % + Payout % = 100% of Earnings
                     Note 2: Return on Equity is expressed as a %, where Total Earnings in the numerator is expressed in do
                     Note 3: The larger g , the smaller the demonimator, and hence, the greater the value of future projects

Relative Value Models (a.k.a. "The Market Approach")

         The above models depend on forecasting dividends and/or the future cash flows of tangible projects.
         In reality:
                     Companies don't always pay dividends
                     Future cash flows are uncertain, often extremely so

         As an alternative we can evaluate a stock by relating it to other, similar stocks using valuation ratios like the P/E (P
                     This takes the public markets' collective information into account, while applying it to a particular com
                     A company without positive Earnings can be valued using the P/S (Price-to-Sales) ratio, but this is VE

         The P/E ratio is defined as:

                                         Price per Share
                        P/E =           Earnings per Share

         Similar companies in the same industry should have similar P/E ratios
         Any differences in P/E ratios should be explained by differences in perceived risk or expected growth rates
         Hence, you can solve the Price question of Company A by comparing its Earnings to Company B
y Grail" of finance
rades at, is the key to riches.
 , sell; if undervalued, buy.




etplace (i.e. "the Stock Market")




 y one particular investor
E CASH FLOWS
dividual REQUIRED RATE OF RETURN
h determining Intrinsic value



hey are received, the greater the value.
 or "Hurdle Rate"
red return is higher for stocks.




 (doesn't care about risk), or Risk Seeking (prefers risk)
e require more return for more risk
Rate + Beta * (Expected Market Return - Risk Free Rate)




 portfolios are compared
he market return gives the market premium for stocks

 ive to the market return
s risky as the average stock (i.e. "the market")

 the riskiness of the average stock
RSELY proportional to the average stock (not commonly used)
etas based on a company's past performance

 how different stocks can be valued




 with the intention of selling at a later period (i.e. "Terminal Value")


on dividends accruing as we hold the stock indefinitely

                           Period 2 Dividend                                     Period infinity Dividend
                         (1 + Req. Return ) ^ 2             +          …   +   (1 + Req. Return ) ^ infinity

ted in closed form as:
 nvest at least some of their earnings
  value plus its growth on reinvested earnings

                   Payout % * Total Earnings in dollars
                  Required Return - (ROE * Reinvestment %)



 (only those earnings that are reinvested as opposed to paid out in a dividend)
 ested earnings multiplied by the actual return (i.e. the Return on Equity) as opposed to the required return r




 e Total Earnings in the numerator is expressed in dollars. They are referencing the same Earnings number
 , and hence, the greater the value of future projects




 future cash flows of tangible projects.




 , similar stocks using valuation ratios like the P/E (Price-to-Earnings) ratio
 n into account, while applying it to a particular company's fundamentals
 d using the P/S (Price-to-Sales) ratio, but this is VERY risky and not recommended (see: dotcom crash)




 es in perceived risk or expected growth rates
mparing its Earnings to Company B
Capital Asset Pricing Model


E(Ri) = Rf + Bi * ( E(Rm) - Rf )
Expected Return                       =      Risk-free         +            Stock    *
  on a Stock                                   Rate                         Beta

Objective: Determine the Security Market Line so any stock can be valued according to our Required Rate o



                                      The Security Market Line
                                   Risk-free   Market      Stock X     Stock Y
Beta                                  0.0        1.0         0.5          1.5
Expected Return                     5.00%     11.00%         ???         ???
                                                           Use CAPM to calculate

                                      The Security Market Line
                                   Risk-free   Market         X               Y
Beta                                  0.0        1.0         0.5             1.5
Expected Return                      5.0%      11.0%        8.0%            14.0%


                                                  The Security Market Line
                     16.0%

                     14.0%                                     Stock X
                     12.0%
                                      Risk
   Expected Return




                     10.0%

                     8.0%                                                             Stock Y

                     6.0%
                                                                   Market
                     4.0%

                     2.0%

                     0.0%
                             0.0      0.2       0.4      0.6         0.8       1.0   1.2
                                                                     Beta
             ( Expected Market     -     Risk-free
                  Return                  Rate)

be valued according to our Required Rate of Return




       Stock Y




                 1.4    1.6
                                                            Period
Cash Received                0                       1                    2
Dividends                   $0                     $2.40                $2.40
Sale of Stock               $0                      $0                   $0
Total                      $0.00                   $2.40                $2.40

Recall that…

                             N
                                            Cash Flows in Period
  Value of Stock =
                             Ʃ             (1 + interest ) ^ Period
                            t=1


Suppose Required Rate of Return = 12% from CAPM
                                                           Period
Value                        0                       1                    2
Numerator:                 0.00                    2.40                 2.40
Denominator:               1.00                    1.12               (1.12) 2
Value:                     0.00                    2.14                1.91

If the current share price is $25, you would Sell the stock if you had any
If the current share price is $18, you would Buy more shares and wait for the true value to equalize.
                      3
                    $2.40
                   $20.00
                   $22.40




                    3
                  22.40
                  (1.12) 3
                   15.94



or the true value to equalize.   = $20.00
                              Period Dividend
 Value of Stock =
                     Req. Return - Dividend Growth Rate



From Previous Example, dividends do not grow, so…



Value
Numerator:                        2.40
Denominator:                     0.12 - 0
Value:                           20.00




Period                                                    1      2      3      4      5
FCF                                                     2.4    2.4    2.4    2.4    2.4
Rate                                                  0.12   0.12   0.12   0.12   0.12
PVCF                                                $2.143 $1.913 $1.708 $1.525 $1.362
NPV                               20.00
      6      7      8      9     10     11     12     13     14     15     16     17     18
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$1.216 $1.086 $0.969 $0.865 $0.773 $0.690 $0.616 $0.550 $0.491 $0.438 $0.391 $0.350 $0.312
     19     20     21     22     23     24     25     26     27     28     29     30     31
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$0.279 $0.249 $0.222 $0.198 $0.177 $0.158 $0.141 $0.126 $0.113 $0.100 $0.090 $0.080 $0.072
     32     33     34     35     36     37     38     39     40     41     42     43     44
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$0.064 $0.057 $0.051 $0.045 $0.041 $0.036 $0.032 $0.029 $0.026 $0.023 $0.021 $0.018 $0.016
     45     46     47     48     49     50     51     52     53     54     55     56     57
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$0.015 $0.013 $0.012 $0.010 $0.009 $0.008 $0.007 $0.007 $0.006 $0.005 $0.005 $0.004 $0.004
     58     59     60     61     62     63     64     65     66     67     68     69     70
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$0.003 $0.003 $0.003 $0.002 $0.002 $0.002 $0.002 $0.002 $0.001 $0.001 $0.001 $0.001 $0.001
     71     72     73     74     75     76     77     78     79     80
    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4    2.4
  0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12   0.12
$0.001 $0.001 $0.001 $0.001 $0.000 $0.000 $0.000 $0.000 $0.000 $0.000

				
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