Common Stock Valuation

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					Common Stock Valuation

     Timothy R. Mayes, Ph.D.
      FIN 3600: Chapter 14
What is Value?

   In general, the value of an asset is the price that a
    willing and able buyer pays to a willing and able
   Note that if either the buyer or seller is not both
    willing and able, then an offer does not establish
    the value of the asset
Several Kinds of “Value”

   There are several types of value, of which we are
    concerned with four:
       Book Value – The carrying value on the balance sheet of the
        firm’s equity (Total Assets less Total Liabilities)
       Tangible Book Value – Book value minus intangible assets
        (goodwill, patents, etc)
       Market Value - The price of an asset as determined in a
        competitive marketplace
       Intrinsic Value - The present value of the expected future cash
        flows discounted at the decision maker’s required rate of return
Determinants of Intrinsic Value

   There are two primary determinants of the intrinsic value
    of an asset to an individual:
       The size and timing of the expected future cash flows.
       The individual’s required rate of return (this is determined by a
        number of other factors such as risk/return preferences, returns
        on competing investments, expected inflation, etc.).
   Note that the intrinsic value of an asset can be, and often
    is, different for each individual (that’s what makes
    markets work).
Common Stock

   A share of common stock represents an ownership
    position in the firm. Typically, the owners are entitled to
    vote on important matters regarding the firm, to vote on
    the membership of the board of directors, and (often) to
    receive dividends.
   In the event of liquidation of the firm, the common
    shareholders will receive a pro-rata share of the assets
    remaining after the creditors (including employees) and
    preferred stockholders have been paid off. If the
    liquidation is bankruptcy related, the common
    shareholders typically receive nothing, though it is
    possible that they may receive some small amount.
Common Stock Valuation

   As with any other security, the first step in valuing
    common stocks is to determine the expected future cash
   Finding the present values of these cash flows and adding
    them together will give us the value:
                       VCS  
                             t 1   k 
   For a stock, there are two cash flows:
       Future dividend payments
       The future selling price
Common Stock Valuation: An Example

   Assume that you are considering the purchase of a stock
    which will pay dividends of $2 (D1) next year, and $2.16
    (D2) the following year. After receiving the second
    dividend, you plan on selling the stock for $33.33. What
    is the intrinsic value of this stock if your required return
    is 15%?                                   33.33
               ?                      2.00                2.16

                       2.00           2.16  33.33
              VCS                                    28.57
                      1.15 1
                                        1.15   2
Some Notes About Common Stock

   In valuing the common stock, we have made two
       We know the dividends that will be paid in the future.
       We know how much you will be able to sell the stock
        for in the future.
   Both of these assumptions are unrealistic,
    especially knowledge of the future selling price.
   Furthermore, suppose that you intend on holding
    on to the stock for twenty years, the calculations
    would be very tedious!
Common Stock: Some Assumptions

   We cannot value common stock without making some
    simplifying assumptions. These assumptions will define
    the path of the future cash flows so that we can derive a
    present value formula to value the cash flows.
   If we make the following assumptions, we can derive a
    simple model for common stock valuation:
       Your holding period is infinite (i.e., you will never sell the stock
        so you don’t have to worry about forecasting a future selling
       The dividends will grow at a constant rate forever.
   Note that the second assumption allows us to predict
    every future dividend, as long as we know the most
    recent dividend and the growth rate.
The Dividend Discount Model (DDM)

   With these assumptions, we can derive a model
    that is variously known as the Dividend Discount
    Model, the Constant Growth Model, or the
    Gordon Model:
                     D0 1  g    D1
               VCS           
                     k CS  g   k CS  g
   This model gives us the present value of an
    infinite stream of dividends that are growing at a
    constant rate.
Estimating the DDM Inputs

   The DDM requires us to estimate the dividend growth
    rate and the required rate of return.
   The dividend growth rate can be estimated in three ways:
       Use the historical growth rate and assume it will continue
       Use the equation: g = br
       Generate your own forecast with whatever method seems
   The required return is often estimated by using the
    CAPM: ki = krf + bi(km – krf) or some other asset pricing
The DDM: An Example

   Recall our previous example in which the
    dividends were growing at 8% per year, and your
    required return was 15%.
   The value of the stock must be (D0 = 1.85):
                  .                2.00
         VCS                           28.57
                  .15.08       015.08
   Note that this is exactly the same value that we
    got earlier, but we didn’t have to use an assumed
    future selling price.
The DDM Extended

   There is no reason that we can’t use the DDM at
    any point in time.
   For example, we might want to calculate the
    price that a stock should sell for in two years.
   To do this, we can simply generalize the DDM:
                  D N 1  g D N 1
             VN           
                  k CS  g   k CS  g
   For example, to value a stock at year 2, we
    simply use the dividend for year 3 (D3).
The DDM Example (cont.)

   In the earlier example, how did we know that the
    stock would be selling for $33.33 in two years?
   Note that the period 3 dividend must be 8%
    larger than the period 2 dividend, so:
               2.161.08        2.33
        V2                            33.33
                .15.08        015.08
   Remember, the value at period 2 is simply the
    present value of D3, D4, D5, …, D∞
What if Growth Isn’t Constant?

   The DDM assumes that dividends will grow at a constant
    rate forever, but what if they don’t?
   If we assume that growth will eventually be constant,
    then we can modify the DDM.
   Recall that the intrinsic value of the stock is the present
    value of its future cash flows. Further, we can use the
    DDM to determine the value of the stock at some future
    period when growth is constant. If we calculate the
    present value of that price and the present value of the
    dividends up to that point, we will have the present value
    of all of the future cash flows.
What if Growth Isn’t Constant? (cont.)

   Let’s take our previous example, but assume that
    the dividend will grow at a rate of 15% per year
    for the next three years before settling down to a
    constant 8% per year. What’s the value of the
    stock now? (Recall that D0 = 1.85)

                2.1275   2.4466   2.8136    3.0387 …

          0       1        2        3            4
                      g = 15%           g = 8%
What if Growth Isn’t Constant? (cont.)

   First, note that we can calculate the value of the stock at
    the end of period 3 (using D4):
                          V3               43.41
                                 .15  .08
   Now, find the present values of the future selling price
    and D1, D2, and D3:
                    2.1275 2.4466 2.8136  43.41
             V0                2
                                         3
                                                  34.09
                     1.15   1.15      1.15
   So, the value of the stock is $34.09 and we didn’t even
    have to assume a constant growth rate. Note also that the
    value is higher than the original value because the
    average growth rate is higher.
Two-Stage DDM Valuation Model

   The previous example showed one way to value
    a stock with two (or more) growth rates.
    Typically, such a company can be expected to
    have a period of supra-normal growth followed
    by a slower growth rate that we can expect to last
    for a long time.
   In these cases we can use the two-stage DDM:
                                        D0 1  g1  1  g 2 

            D 1  g1    1  g n         kCS  g 2
       VCS  0          1     1
                                    
             kCS  g1   1  kCS          1  kCS n
                                  
Two-Stage DDM Valuation Model (cont.)

   The two-stage growth model is not a complex as it seems:
       The first term is simply the present value of the first N dividends (those
        before the constant growth period)
       The second term is the present value of the future stock price.
                                            D0   g1    g 2 
                                               1         1
                D0   g1    1  g1  
                   1                              kCS  g 2
        VCS                1        
                kCS  g1   1  kCS           1  kCS n
                                      

                 PV of the first N dividends + PV of stock price at period N
       So, the model is just a mathematical formulation of the methodology
        that was presented earlier. It is nothing more than an equation to
        calculate the present value of a set of cash flows that are expected to
        follow a particular growth pattern in the future.
Three-Stage DDM Valuation Model

   One improvement that we can make to the two-
    stage DDM is to allow the growth rate to change
    slowly rather than instantaneously.
   The three-stage DDM is given by:

                                    n1  n2       
                        1  g 2   2 g1  g 2 
    VCS   
            kCS  g 2                             
Other Valuation Methods

   Some companies do not pay dividends, or the
    dividends are unpredictable.
   In these cases we have several other possible
    valuation models:
       Earnings Model
       Free Cash Flow Model
       P/E approach
       Price to Sales (P/S)
The Earnings Model

   The earnings model separates a company’s
    earnings (EPS) into two components:
       Current earnings, which are assumed to be repeated
        forever with no growth and 100% payout.
       Growth of earnings which derives from future
   If the current earnings are a perpetuity with
    100% payout, then they are worth:
                        VCE   
The Earnings Model (cont.)

   VCE is the value of the stock if the company does not
    grow, but if it does grow in the future its value must be
    higher than VCE so this represents the minimum value
    (assuming profitable growth).
   If the company grows beyond their current EPS by
    reinvesting a portion of their earnings, then the value of
    these growth opportunities is the present value of the
    additional earnings in future years.
   The growth in earnings will be equal to the ROE times
    the retention ratio (1 – payout ratio):
                       g  br
   Where b = retention ratio and r = ROE (return on equity).
The Earnings Model (cont.)

   If the company can maintain this growth rate
    forever, then the present value of their growth
    opportunities is:       
                    PVGO  
                             t 1   1  k t
   Which, since NPV is growing at a constant rate
    can be rewritten as:
                              r            r 
                         RE1   RE1   RE1   1
           PVGO 
                             k           k 
                  kg        kg         kg
The Earnings Model (cont.)

   The value of the company today must be the sum
    of the value of the company if it doesn’t grow
    and the value of the future growth:
                                    r 
                                RE1   1
       VCS   
               EPS1 NPV1 EPS1
                                 k 
                k    kg   k      kg

   Where RE1 is the retained earnings in period 1, r
    is the return on equity, k is the required return,
    and g is the growth rate
The Free Cash Flow Model

   Free cash flow is the cash flow that’s left over
    after making all required investments in
    operating assets:
               FCF  NOPAT  Op Cap
   Where NOPAT is net operating profit after tax
   Note that the total value of the firm equals the
    value of its debt plus preferred plus common:

                  V  VD  VP  VCS
The Free Cash Flow Model (cont.)

   We can find the total value of the firm’s
    operations (not including non-operating assets),
    by calculating the present value of its future free
    cash flows:
                            FCF0 1  g 
                     VOps 
   Now, add in the value of its non-operating assets
    to get the total value of the firm:
                                    FCF0 1  g 
             V  VOps  VNonOps                   VNonOps
The Free Cash Flow Model (cont.)

   Now, to calculate the value of its equity, we
    subtract the value of the firm’s debt and the
    value of its preferred stock:
                     FCF0 1  g 
             VCS                   VNonOps  VD  VP

   Since this is the total value of its equity, we
    divide by the number of shares outstanding to get
    the per share value of the stock.
Relative Value Models

   Professional analysts often value stocks relative to one another.
   For example, an analyst might say that XYZ is undervalued relative
    to ABC (which is in the same industry) because it has a lower P/E
    ratio, but a higher earnings growth rate.
   These models are popular, but they do have problems:
       Even within an industry, companies are rarely perfectly comparable.
       There is no way to know for sure what the “correct” price multiple is.
       There is no easy, linear relationship between earnings growth and price
        multiples (i.e., we can’t say that because XYZ is growing 2% faster that
        it’s P/E should be 3 points higher than ABC’s – there are just too many
        additional factors).
       A company’s (or industry’s) historical multiples may not be relevant
        today due to changes in earnings growth over time.
The P/E Approach

   As a rule of thumb, or simplified model, analysts often
    assume that a stock is worth some “justified” P/E ratio
    times the firm’s expected earnings.
   This justified P/E may be based on the industry average
    P/E, the company’s own historical P/E, or some other
    P/E that the analyst feels is justified.
   To calculate the value of the stock, we merely multiply
    its next years’ earnings by this justified P/E:

                  VCS  P  EPS1
The P/S Approach

   In some cases, companies aren’t currently earning any
    money and this makes the P/E approach impossible to
    use (because there are no earnings).
   In these cases, analysts often estimate the value of the
    stock as some multiple of sales (Price/Sales ratio).
   The justified P/S ratio may be based on historical P/S for
    the company, P/S for the industry, or some other
                    VCS  P  Sales1

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