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									Ertuna – Stock Valuation                                                                   1/7

                           STOCKS and their VALUATION
Stocks can be divided into two categories: Common Stock and Preferred Stocks.
Preferred stock is a hybrid security, sharing features of both bonds and common stock.
Firms usually issue preferred stock with a stated par value and promise to periodically
pay a percentage of the par value as dividend.
                 kp                                                                ∞

       where,                                           P
       D = Dividend of Preferred Stock
       kp = Required rate of return on the Preferred Stock
       P = Price of the Preferred Stock

The cash flow pattern of preferred stock is like perpetuity. It starts from period one, has
no gaps, all payments are equal, and payments continue forever.

Common stock represents an ownership position in the firm. Common Stock is a long-
term financial asset that provides to the common stockholders (owners of the firm) legal
rights and privileges such as:
a. Residual claim on the income and assets of the firm
    The claim is residual because stockholders can claim on the firm’s income and assets
    only after all claims of all stakeholders (bondholders, employees, suppliers, and the
    government) are satisfied. Although stockholders are last in line to enforce their
    claim, they can claim everything that remains in the firm and they have a limited
    liability, meaning that the stockholders’ liability to the stakeholders are limited to the
    equity they contributed.
b. Voting power
    Voting power is the power to elect directors (who in turn elect managers and officers
    to the company). Usually in annual meetings stockholders elect 1/3 of the directors
    for 3 years. Voting mechanism could be either “majority voting” or “cumulative
    voting.” Stockholders could vote either in person or by means of a proxy.
c. Preemptive right
    Preemptive right is a provision in the corporate charter or bylaws that gives common
    stockholders the right to purchase on a pro rata basis new issues of common stock or
    convertible securities. It serves for two purposes. First it enables current stockholders
    to maintain control. If this safeguard were not in place, the management of the
    corporation could issue large numbers of additional shares and purchase these shares
    itself and thereby seize control of the firm. Second, it protects stockholders against a
    dilution of value. If this safeguard were not in place, selling common stock at a price
    lower than the market value would transfer wealth from the present stockholders to
    those who were allowed to purchase the new shares.
Ertuna – Stock Valuation                                                                  2/7

Terminology used in Stock Valuation
1. Intrinsic Value
    Intrinsic value is the value of an asset that in the mind of a particular investor is
    justified by the facts. Intrinsic value may be different form current market price or its
    book value or both.
2. Proxy
    Proxy is a document giving one person the authority to act for another, typically the
    power to vote shares of common stock.
3. Proxy Fight
    Proxy fight is an attempt by a person or group to gain control of a firm by getting its
    stockholders to grant that person or group the authority to vote their shares to place a
    new management into office.
4. Takeover
    Takeover is an action by a person or group to take control of the company and oust
    the firm’s management. That could be done either through proxy fight or by
    purchasing majority of outstanding stock.
5. Founder’s Shares
    Founder’s shares are Stocks owned by the firm’s founders that have sole voting rights
    but restricted dividends for a specified number of years.
6. Classified Stock
    Classified stock is common stock that is given a special designation such as Class A,
    Class B, and so forth. One class may have no voting right but may have rights to
    dividends, another may have no rights to dividends but may have voting rights.
7. Closely Held Corporation
    Closely held corporation (also called privately owned corporation) is a corporation
    that is owned by a few individuals who are typically associated with the firm’s
    management. The shares of the firm are not traded actively.
8. Publicly Owned Corporation
    Publicly owned corporation is a corporation that is owned by a relatively large
    number of individuals who are not actively involved in its management. Institutional
    investors own more than 60% of common shares and account for 75% of transactions
    of larger publicly held corporations.
9. Going Public
    The act of selling stock to the public at large by closely held corporation or its
    principal stockholders.
10. Initial Public Offering (IPO)
    The first time stock issue offered to the public to raise money.
Ertuna – Stock Valuation                                                                 3/7

Market Mechanism that determines the Stock Value
The price of a firm’s stock represents the value of the firm per share of stock. Since the
value of firm change continuously, so do stock prices. Institutional and individual
investors constantly value stocks so that they can capitalize on expected changes in stock
New information about economic conditions or other factors, including firm-specific
conditions, causes investors to revalue stocks. When new information suggest that a firm
will experience more favorable cash flows or lower risk (and therefore lower required
rate of return = lower cost to obtain funds), investors will revalue the corresponding stock
upward. As these investors attempt to purchase the stock, there is an immediate upward
adjustment in the stock’s market price.

1. Common Stock Valuation Methods
    There are several methods (models) to assess the value of a stock
    A. Price-Earning (PE) Model
       A relatively simple method of valuing a stock.
       Stock Price of a firm = (Expected earnings of the firm per share for the current
                               year) x (Mean value of expected PE ratio of the
                               competitors of the firm)
    B. Divided Discount Model
       This approach assumes that the investors are interested in the dividend payments
       of the company. To compute the value of the stock, all expected future dividend
       payments are discounted at an appropriate rate to the Present Value.
                  D1             D2                  D
        S0                              ... 
               (1  k s ) (1  k s )   2
                                                 (1  k s ) 
       S0 = current Stock Price
       D1 = Dividend Payment in Period-1 (one period from now)
       ks = Required rate of return on the Stock

        The above formula could be presented in a much compact form as the following:

                  S0  
                           t 1   (1  k s ) t

        t = index for period

        Since it is impossible to forecast all the expected future dividend payments (up to
        infinity), there are several practical adjustments to this approach.
Ertuna – Stock Valuation                                                                      4/7

        i.    Zero Growth Model: If we assume that the dividend payments will remain
              constant then the formula could be written as:

                           D           D                    D
                S0                             ... 
                        (1  k s ) (1  k s ) 2
                                                        (1  k s ) 

                S0 

              Cash flow pattern of zero growth stock is (like preferred stock) perpetuity.

        ii.   Constant Growth Model: This model assumes that the dividend payments
              are growing each year at a constant rate of “g”.

                   D0 (1  g )1 D0 (1  g ) 2        D0 (1  g )
              S0                             ...
                    (1  ks )1   (1  ks ) 2          (1 ks )
              The cash flow pattern of Constant Growth Stock looks like the following:

                                                   D0(1+g)      It starts from period-1, has no
                                                   ∞            gaps, cash flows grow at a
                            D1                                  constant rate, and forever.



                         D1                       D1
                S0                        kS       g
                       ks  g                     S0

             g = expected growth rate in dividends = (ROE)*(p)
             D1 = Expected Dividend Payments in the next period = D0(1+g)
             D0 = Most recent Dividend Payment
             D1/S0 = Dividend yield
             ROE = Return on Equity = (Net income) / (Common Stock Book Value)
             q = dividend pay out ratio
             Dt = q*(Earnings)t
        iii. Variable Growth Model: This model assumes that the company and its
             dividend payments grow much faster then the economy for a certain period at
             the beginning and then settles to a constant growth rate.
Ertuna – Stock Valuation                                                                    5/7

    C. Capital Asset Pricing Model (CAPM)
       CAPM determines appropriate required rate of return on a stock.

           k i  k rf   i ( k m  k rf )

        ki = Required rate of return on Stock “i”
        krf = Risk free rate
        km = Return on market
        (km - krf) is also called market risk premium. That is required rate of return to bear
                   market’s risk.
        βi = Beta of stock “i". Beta of a stock reflects how risky a stock is compared to
              market. Market’s beta is one (βm =1). If firm-i’s beta is more than one (βi >1)
              that means that firm-i is more riskier than the market and that in turn results
              in higher risk premium, thus, higher required return for the firm-i.

        The key to the Capital Asset Pricing Model is the market risk. This model
        recognizes only one risk, market risk, and calls it also systematic risk or non-
        diversifyable risk. In this model risk of a financial asset is expressed as a fraction
        of the market risk.

    D. Arbitrage Pricing Model (APT)
       Like CAPM this model tries to determine the required rate of return on a
       particular stock. However, Arbitrage Pricing Model recognizes more than one
       fundamental factor as source of risk. There are many factors (such as economic
       growth, level of inflation, etc.) that could be source for risk. However, there is no
       single set of factors that everyone agrees upon. Sensitivity of a stock to each of
       these factors should be determined first in order to calculate the required rate of
       return on that particular stock.
Ertuna – Stock Valuation                                                                6/7

2. Factors Affecting Stock Prices
    There are three types of factors, firm specific, economic, and market related, that can
    affect a stock’s value.
    a. Expectations
        Investors do not necessarily wait for a firm to announce a new policy before they
        revalue the firm’s stock. They make their decision on the basis of some (most of
        the time incomplete) information in order to act before other investors.
        Expectations on the future cash flows of a company affect the stock’s value.
    b. Earnings Surprises
        Recent earnings are used to forecast future earnings and therefore earning
        surprises affect future cash flow estimates and consequently the stock’s price.
    c. Acquisitions & Divestiture
        An expected acquisition of a firm typically results in an increase demand for the
        target’s stock and therefore raises the stock prices. Divestitures tend to be
        regarded as a favorable signal and are interpreted as an attempt of the firm to
        focus on the core business.
    d. Stock Offerings & Repurchase
        Some investors believe that firms attempt to issue stock when they feel that their
        stock is overpriced and repurchase the stock when underpriced.
    e. Dividend Policy Changes
        An increase in dividends may reflect the firm’s expectations that it can more
        easily afford to pay higher dividends.
    f. Interest Rates
        Risk-free rate affects required return on stocks and therefore the market value of
    g. Economic growth
        Economic growth affects projections for corporate earnings and therefore stock
    h. Exchange Rates
        Foreign investors tend to purchase domestic stocks when the domestic currency is
        weak and sell them when it is near its peak.
    i. January Effect
        Because many portfolio managers are evaluated over the calendar year, they tend
        to invest in riskier small stocks at the beginning of the year and shift to larger
        companies near the end of year. This tendency puts upward pressure on small
        stocks in January every year.
    j. Noise Trading
        Many uninformed traders (noise traders) may buy or sell positions that push a
        stock’s price away from its fundamental value. Given the uncertainty about the
        stock’s fundamental value, informed investors may be unwilling to capitalize on
        the discrepancy.
Ertuna – Stock Valuation                                                                7/7

3. Measure of Risk for Stocks
    There are two measures of risk, stock volatility and beta.
    a. Volatility of a Stock
       It is measured by the standard deviation of stock’s return (or price) over a period
       of time. It captures total volatility of the stock and is appropriate if there is no
       trend in volatility.
    b. Beta of a Stock
       Beta is a measure that reflects the tendency of a stock to move up or down with
       the market. It measures the systematic risk of the stock.
       Beta of a stock = (covariance between stock and the market returns) x (variance of
                           market returns)

4. Stock Performance Measure
    The performance of a stock (or stock portfolio) can be measured by its excess return
    (return over risk free rate → r-rf ) over that period divided by its risk. Two common
    methods of measuring stock (or stock portfolio) performance are the Sharpe index
    and Treynor Index.

    a. Sharpe Index
       It assumes that the total variability is the appropriate measure of risk
                              _       _
                              r  rf
             Sharpe Index 

        r = Average return on stock
        r f = Average risk-free rate
         = Standard deviation of stock’s return

    b. Treynor Index
       It assumes that the beta is the most appropriate measure of risk

                                  _       _
                                  r  rf
             Treynor Index 

        β = Stock’s beta

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