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					Valuation of Stocks and
 Company Valuation


      Econ 181
  Corporate Finance
        Wadia Haddaji
    Department of Economics
        Duke University

                              RK-CH



                                      1
                        Overview


   Introduction
    » Stocks and stock markets
    » Transactions & Orders
   Valuation:
    » Present Value
    » Dividend growth models
   Financial ratios
    » Dividend yields
    » P/E multiples

                                   2
                        Common Stock

   What does it mean to own common stock?
    »   ownership
    »   residual claimants.
   What rights do common shareholders have?
    »   vote at company meetings
    »   dividends
    »   sell their shares
   What are the benefits of stock ownership?
    »   dividends
    »   capital gains
   Why do firms issue stock?
    »   to finance investments
    »   to acquire other companies
    »   to repurchase debt
                                                3
        Preferred Stock: Debt or Equity?

   What does it mean to own preferred stock?
    »   ownership
    »   senior to equity, junior to debt securities in case of default
   What rights do preferred shareholders have?
    »   usually no voting rights, except in case of default on dividend
    »   dividends and other distributions
   What are the benefits of preferred stock ownership?
    »   periodic dividend rate, typically cumulative
    »   capital gains
   Why do firms issue preferred stock?
    »   often because of the favorable tax treatment when held by other
        firms
                                                                          4
           Transactions Involving Stocks

   Buy (Long Position)
     Savings motive
     Speculative
   Sell
     Liquidity needs
     Expect stock to decline in value
   Short Sell
     Sell stock without first owning it.
     Borrow stock from your broker with the promise to return it at some
      later date.
     Sell the borrowed stock.
     Repurchase it at a later date to return it to your broker.
     Responsible for all dividends and other distributions while short the
      stock.
                                                                              5
            Short selling (in detail)
Why Short Sell?
 Short Selling is one way of benefiting from a stock that is expected to decline
  in price.
    » Instead of buying today and selling later, the short seller sells today and
       buys later.
How to Short Sell?
 The short-seller (A) finds an existing owner of the shares (B) who is willing
  and able to lend the shares to A. Once A has negotiated a loan, A can then sell
  the borrowed shares to any willing buyer (C).
 A posts collateral with B. In the US, the standard collateral is cash amounting
  to 102 per cent of the value of the shares, to be adjusted daily as their value
  fluctuates.
    » Note though that under Federal Reserve Regulation T, in case where B is a
       U.S. broker/dealer A has to post an additional 50% margin (any long
       securities can be pledged to satisfy this requirement). Further, broker-
       dealers may institute higher short sale margin requirements than those
       imposed by self-regulatory organization rules. e.g., the NASD Rule
       2520(d) and NYSE Rule 431(d).                                                6
              Short selling (in detail)
   A pays B a fee. The fee can be determined by the “rebate” rate, which is the
    interest that B pays A for use of the cash collateral. For example, if the market
    rate for cash funds were 5% and the stock loan fee were 1.5% then B would
    rebate A only 3.5%. (Note that is it possible to have fees that exceed the cash
    rate, which would result in negative rebate rates).
   A pays B any dividends/distributions made to the owners of the shares during
    the loan.
   B has the right to recall the shares from A at any time. Loans are “open” and
    effectively rolled over each night until either B wants the shares returned or A
    voluntarily returns them. Given notice of recall, A has three days to return the
    shares. After this, A can try borrowing the shares from another lender or can
    “cover” the short position by purchasing the shares.




                                                                                        7
             Short selling (in detail)
Who are the Participants?
 The role of B (the lenders) is largely assumed by the big custody banks in the U.S. who act
  as intermediaries for large institutional owners like pension funds, mutual funds etc.

   Loans of shares can also be made by a broker from his own inventory, from the margin
    account of another customer, or shares borrowed from another broker. These shares are used
    to make settlement with the buying broker within three days of the short sale transaction, and
    the proceeds are used to secure the loan.

   Another group that assume the role of B (lenders) consists of the broker-dealers (e.g.
    Goldman Sachs, Morgan Stanley). These broker-dealers lend from their internal supply of
    securities held by their market makers and proprietary trading desks, the accounts of
    institutional customers, and the margin accounts of individual investors.
      »   Note that Section 8 of the Exchange Act of 1934 prohibits brokers from lending shares
          held in retail cash or non-margin accounts.

   The role of A (the short-sellers) is assumed by a broader group. More obvious examples
    include:
      »  Specialists and market makers (for balancing buy orders with sell orders)
      »  Traders of equity options, index futures, equity return swaps and convertible bonds (for
         hedging their positions)
      »  Hedge Funds (to execute “arbitrage” strategies)
      »  Speculators                                                                                 8
             Short selling (in detail)
   The NYSE, NASD and AMEX reported short interest (the number of shares that
    have already been sold short) with a market value in excess of $260 billion (just
    over 1.7% of total market capitalization) at June 2001.
   Shorting is subject to many restrictions on the size, price, and types of stocks
    able to be shorted. For example, you cannot short sell penny stocks (they are
    non-marginable due to Regulation T) and most short sales need to be done in
    round lots.
   Additionally, the SEC, NYSE and NASD have rules preventing short selling
    unless the last trade is at the same or higher price (known as an uptick or zero
    plus tick), the purpose of which is to prevent short selling in a declining market
    (since continuous short selling will exacerbate the fall of a falling stock).
   Equity loans can occur for reasons other than short selling. For instance in cases
    where A borrows from B but then doesn’t short to C, A is treated as the legal
    owner of the shares and is therefore entitled to the dividends distributed during
    the course of the loan (which, as previously mentioned, are required to be
    reimbursed by A to B). This might happen in cases where A values the
    distribution received more than the reimbursements given (for taxation reasons,
    for example)
   In lending, B forfeits voting rights to A (to C in the case of the short sale).


                                                                                         9
                       Types of Orders

   Market Orders
    » Buy or sell at the current market price
   Limit Order
    » Buy or sell at a specified price
    » Limit by time period
   Stop Orders
    » Stop-loss: Sell if price falls below certain level
    » Stop-buy: Buy if price rises above certain level
       – Used in conjunction with short selling




                                                           10
                          Valuation
               The Role of Financial Markets

         Primary Market                      Secondary Market

   New securities and investment      Provide price information
    opportunities.                     Transform (short term) savings
                                        into (long term) investments
                                       Liquidity

   Companies need to acquire          Investors need to buy and sell at
    funds at a “correct” price          “correct” prices


                   What is a correct price?
               Do markets generate correct prices?

                                                                            11
                   Stock Market Indices
   Return to holding a security:                           Pricenew  Priceold  Cash
                                                 Return 
                                                                     Priceold
   Stock market indices: average return
     » of stocks in particular market (NYSE Composite, NASDAQ)
     » market segments (e. g., small companies (Russell 2000), value stocks,
       technology stocks)
   General expression: RIndex  iN1 wi Ri

     » Equally weighted wi = 1/N (Value Line Index)
         – Equal to portfolio strategy placing equal dollar amount in each stock
     » Value weighted wi = proportion of market capitalization
       (S&P500,NASDAQ)
         – Return on portfolio where investment is proportional to market
           capitalization.
     » Price weighted (DJIA)
         – Equal to portfolio strategy holding an equal number of shares of each
           stock
                                                                                         12
                                      U. S. Stock Markets

   Major U. S. Stock Exchanges
      New York Stock Exchange (NYSE)
      American Stock Exchange (AMEX)
      Over-The-Counter (OTC)
        » National Association of Securities Dealers (NASDAQ)
   U. S. Stock Market:

                                          Value                    Value          Value           Value
                   Stock Index          10/12/06                  7/01/05        6/30/04         7/04/03
                   Dow Jones Industrial 11,851.33                10,303.44      10,424.19        9,070.21
                   NASDAQ                2,309.40                 2,057.37       2,041.25        1,663.46
                   S&P500                1,350.21                 1,194.44       1,138.58          985.7
                   NYSE Composite*       8,540.86                 7,245.59       6,592.68         558.46
                   AMEX Composite        1,862.42                 1,554.74       1,247.45         976.16
                   Russell 2000           742.48                   643.04         590.03          546.35
*The NYSE Composite index was recalculated to reflect a base value of 5,000 as of Dec/31, 2002
                                                                                                            13
Number of Listed Companies on Nasdaq,
Yearly Comparison with NYSE and AMEX




                                        14
Market Capitalization of Domestically Listed
Companies - NYSE and NASDAQ, 1985 – 2003

($ billions)

      12,000

      10,000

       8,000

       6,000

       4,000

       2,000

               0
                   1985   1987   1989   1991      1993   1995   1997   1999   2001   2003

                                               NYSE   NASDAQ




                                                                                            15
16
    Why “short-termists” are “long-termists”

Shareholders require a rate of return re for buying a share. They buy for
P0 and sell after one year for P1 and receive dividends D1:
                    D P
               P0  1 1
                     1  re

The next buyer also sells after one year:
                     D2  P2         D    D  P2
              P              P0  1  2
                      1  re       1  re 1  re 2
               1


The same holds for P2. Continuing gives:

                      D1      D2         D3
             P0                                ...
                    1  re 1  r e  1  re 
                                     2         3




                             Share price = PV of dividends
                                                                            17
                      Stock Valuation

   Stock Price = PV of future dividends
    » The price an investor is willing to pay for a share of stock depends
      upon:
       – Magnitude and timing of expected future dividends.
       – Risk of the stock.

    » The stock’s discount rate, re, is the rate of return investors can
      expect to earn on securities with similar risk.

    » Where are capital gains?



                                                                             18
                      Another Application:
                     Estimating the required return on equity



   Holders of stock receive returns in two forms:
    » Dividend payouts
    » Capital gains (stock price appreciation P1-P0)

                   D1 P  P0
            re        1
                   P0     P0

       – typically larger fraction of returns
    » Capital gain reflects growth in future dividend payments
   Note:
    » The expected rate of return is not equal to the dividend yield
    » The expression is in terms of the prospective yield, not the historic yield

                                                                                    19
             The “Constant Growth” Formula

Assumption: Dividends grow at a constant rate g forever:

        D2  D1 (1  g ), Dt  Dt 1 (1  g ) ...  D1 (1  g ) t 1  D0 (1  g ) t

Then:
                                                   D 1  g 
                                                             t 1
                           D    D (1  g )                                      D1
                     P0  1  1              ...  1                ... 
                         1  re (1  re ) 2         1  re t                re  g


                                     Prospective Dividend per Share
                     Share Price 
                                      Expected return - growth rate

   Issues:
     » constant growth



                                                                                        20
Simplifying the Dividend Discount Model

   Constant Dividends
    g  0  D1  D2 ...  D

    Then the pricing relation simplifies to:

                           D         D
     P0  P  Pt  ... 
           1                   re 
                           re        P0

     » Stock similar to perpetual bond
   If dividends are constant, then we have that:

                          Capital gains are zero
                Expected return on equity = Dividend yield
                                                             21
                   Constant Dividends
                          Two Examples

   Example 1: RJR Nabisco has preferred stock outstanding with a fixed
    dividend per share of $2.50. Similar securities command a return of
    9.6%. What is the per share price of the stock?



   Example 2: Consider a company that pays every period a dividend of:
     » $3 per share in bad years (Probability = 50%)
     » $15 per share in good years (Probability = 50%)
    If the required rate of return is 18%, what is the share price?




                                                                          22
     Valuation with Growing Dividends
                   An Example: Valuation of XYZ


Consider data for XYZ:
   » Number of shares: 856,695
   » Market capitalization       $46.31m
   » Historic dividend           $1.60 per share
   » Forecasted Dividend:        $1.75 per share
        – What valuation do you obtain for XYZ, depending on g and r?




                                                                        23
                          Valuation of XYZ

   Alternative valuations:
                                            Growth Rate (g)
            Return (re)    3%       4%         5%           6%       7%
               7%         $37.48   $49.97     $74.96     $149.92     N/A
               8%         $29.98   $37.48     $49.97     $74.96    $149.92
               9%         $24.99   $29.98     $37.48     $49.97    $74.96
              10%         $21.42   $24.99     $29.98     $37.48    $49.97
              11%         $18.74   $21.42     $24.99     $29.98    $37.48
              12%         $16.66   $18.74     $21.42     $24.99    $29.98

Example:
   856,695*$1.75=$1.499m

                   Dforecast   $1.499m
    MCAPXYZ                             $37.48m
                rXYZ  g XYZ 0.09  0.05

                                                                             24
                     Valuing a Business
                            A Hybrid Approach



    Sometimes equity analysts have knowledge about the
     immediate, but not the distant future
      » Dividend forecasts for immediate future (2-5 years)
      » Assume constant growth for distant future (>5 years)
      » How do you change the model?
    Dividends




                                                     Time
                                                               25
    Modifying the Constant Growth Model

   The formula for a T-year horizon can be written as:
                 t T      Dt                PT
     P0  t 1                      
                        1  re t 1  re T
    Apply the constant growth model to get the price in period T:
          1  g DT      DT 1
    PT               
            re  g       re  g

    Then the current value of the share is:
                   Dt                    1         DT 1
P0  t 1
         t T
                               
                1  re   t
                                   1  re T     re  g




                                                                    26
                     Valuing a Business

   Consider a company with cash flows from operations of $1
    million for the most recent year.
    »   The company’s cash flows are expected to grow at a rate of 10% for
        the next 5 years and at a constant rate of 5% thereafter.
    »   To generate this increase in cash flows, the company is required to
        reinvest 50% of its cash flows for the first 5 years and 25% of its
        cash flows thereafter.
    »   Given the risk of the business, the required rate of return is 15%.


   What is the value of the business?



                                                                              27
                Valuing a Business (cont.)

Step 1: Find the present value of the first 5 dividends.
                    Year 1     Year 2    Year 3     Year 4    Year 5
    Operating
    Cash Flows         1.10       1.21      1.33       1.46     1.61
    New Capital
    Investment        -0.55      -0.61     -0.67      -0.73    -0.81
    Net Cash
    Flow (Div)         0.55       0.60      0.66       0.73     0.80
    Present
    Value              0.48       0.45      0.43       0.42     0.40

Present value= CF(1)+...+CF(5)=0.48+0.45+0.43+0.42+0.40=2.18

                                                                       28
               Valuing a Business (Cont.)

   Step 2: Find the present value of the dividends after year 5.
     »   Value of business at the end of the 5th year.




     »   Find present value (as of time 0) of this figure.




   Step 3: Add result from steps 1 and 2 to get the total present value of the
    company


                                                                                  29
                 Expected Returns and the
                 Dividend Growth Model
   Use the growth model formula to solve for the required rate of return:
                                     D
                                re  1  g
                                     P0
   Note that you can synthesize with the previous result,
                                  D PP
                            re  1  1 0
                                  P0     P0
    to show:
                               P1  P0
                          g            P1  1  g P0
                                  P0
Therefore, if dividends grow at a constant rate, then
    » share prices grow at the same rate:
                                            P  1  g P0
                                             1

     » yield stays constant:
                               D1 D2
                                       ...
                               P0   P1
                                                                             30
                             P/E-ratios

   Start with basic pricing formula:
                   D1    dE1                      D1
          P0                        where d        Payout Ratio
                 re  g re  g                    E1
   Algebra yields:
                             P0    d
                                
                             E1 re  g
    » Which assumption does one make when arguing that stocks with a
      low P/E are undervalued?
   Some more algebra gives us:
                                      E1
                             re  d      g
                                      P0
    » Implications for re?
                                                                       31
       Growth Stocks and Value Stocks

   Value of stock depends on two components:
    » Profits generated by assets in place, past capital budgeting
      decisions
    » Profits generated by growth opportunities in the future
   Decompose value of stock:
                        E1   gP  1  d E1
                  P 
                   0          0
                        re         re
                                 gP  1  d E1
                   PVGO          0
                                       re

   P/E Ratio
                      P    1    PVGO
                       0
                             
                      E1   re    E1
                                                                     32
       Historical and Prospective Ratios:
   Expected values have to be estimated
   Use model to forecast future yields or multiples:
                   D1  1  g D0
                   E1  1  g E0
   Historic:
                   P0 d 1  g          D0 re  g
                                ,          
                   E0   re  g           P0   1 g

   Prospective:   P0    d             D1
                            ,             re  g
                   E1 re  g           P0
   Example
    d = 0.5, g = 10%, r = 12%
     » Prospective:           DY=2.0%,            PE=25
     » Historic:              DY=1.81%,           PE=27.5
                                                            33
           Historical Yields and Growth

   You can use the expression for the historic yield to infer the growth
    rate:
           r  D0 P0 Expected return  Yield
        g e          
           1  D0 P0           1  Yield
    Consider the “Alphabet” industry:
                             DEF           ABC          XYZ
       MCAP ($million)      30.92         40.71        46.31
       No. of shares       702,500      1,187,000     856,695
       Share Price         $44.01         $34.30      $54.06
       Dividend p. share    $1.35         $1.43        $1.60
       Dividend Yield       3.07%         4.17%        2.96%
       EPS                  $5.03         $3.72        $6.06
       P/E ratio             8.75          9.22         8.92


                                                                            34
            Growth rates in the Industry
   Infer growth rate in the “Alphabet” industry
    Expected Returns          Implied growth rates
                        DEF           ABC             XYZ
          9%           5.76%         4.64%           5.87%
          10%          6.73%         5.60%           6.84%
          11%          7.70%         6.56%           7.81%
          12%          8.67%         7.52%           8.78%
          13%          9.64%         8.48%           9.75%
          14%          10.61%        9.44%           10.72%
          15%          11.58%       10.40%           11.69%

    Example:

                                0.12  0.0417
      g ABC  Exp. ret .12%                 0.0752  7.52%
                                   1.0417
                                                                 35
Valuing a Company Using P/E-Multiples

   The three steps of using P/E multiples company valuation
    1 Find sample of comparable companies
    2 Compute average of their P/E ratios
    3 Multiply earnings by average P/E from step 2.


   Example: Value XYZ
    »   Use ABC and DEF as comparables
    »   Average P/E=(8.75+9.22)/2=8.99
    »   Estimated value of XYZ share=8.99*$6.06=$54.45
    »   Market price per share is $54.06 (= 46.31m/856,695)


                                                               36
    Valuation Ratios and Stock Market
                Outlook
    Stock market valuation ratios have been at extreme levels a
     few years ago by historical standards.
    When stock prices are very high relative to indicators of
     fundamental values (such as dividends and earnings), prices
     tend to fall in the future ...
    Consider two measures of fundamental values:
     – (i) dividend-price ratio (D/P ratio), or dividend yield.
     – (ii) price-earnings ratio (P/E ratio).




                                                                   37
    Valuation Ratios and Stock Market
           Outlook (continued)
   The dividend-price ratio is measured as previous year’s
    total dividends divided by current stock price
    »   D/P ratios have normally moved in the range from 3% to 7%
        (with an extreme of much less than 2% a few years ago).
   The price-earnings ratio is measured as current stock price
    divided by previous year’s total earnings
    »   P/E ratios have normally moved in the range 8–20.
    »   Graham and Dodd (1934) said that one should use an average of
        earnings of “no less than five years, preferably seven or ten
        years”.




                                                                        38
                                             P/E ratio 1880-2003


                        50
                        45
                        40
 Price-Earnings Ratio




                        35
                        30
                        25
                        20
                        15
                        10
                         5
                         0

                          80     90     00      10     20     30     40            50     60     70     80     90     00
                        18     18     19      19     19     19     19            19     19     19     19     19     20
                                                                          Year




Source: Robert Shiller




                                                                                                                           39
                                                           Dividend yield
                                     18
                                       81




                                                0%
                                                     2%
                                                          4%
                                                               6%
                                                                    8%
                                                                         10%
                                                                               12%
                                                                                     14%
                                                                                           16%
                                     18 .01
                                       84




     Source: Robert Shiller
                                     18 .04
                                       87
                                          .0
                                      18 7
                                        90
                                     18 .1
                                       94
                                     18 .01
                                       97
                                     19 .04
                                       00
                                          .0
                                      19 7
                                        03
                                     19 .1
                                       07
                                     19 .01
                                       10
                                     19 .04
                                       13
                                          .0
                                      19 7
                                        16
                                     19 .1
                                       20
                                     19 .01
                                       23
                                     19 .04
                                       26
                                          .0
                                      19 7
                                        29
                                     19 .1
                                       33
                                     19 .01
                                       36
                                     19 .04
                                       39
                                          .0
                                      19 7
                                        42
                                     19 .1
                                       46
                              Year   19 .01
                                       49
                                     19 .04
                                       52
                                          .0
                                      19 7
                                        55
                                     19 .1
                                       59
                                     19 .01
                                       62
                                     19 .04
                                       65
                                          .0
                                      19 7
                                        68
                                     19 .1
                                                                                                 D/P ratio 1880-2002




                                       72
                                     19 .01
                                       75
                                     19 .04
                                       78
                                          .0
                                      19 7
                                        81
                                     19 .1
                                       85
                                     19 .01
                                       88
                                     19 .04
                                       91
                                          .0
                                      19 7
                                        94
                                     19 .1
                                       98
                                     20 .01
                                       01
                                          .0
                                            4
40
                                Summary

   Stocks and equity securities can be valued by using present value
    techniques
    » The discounting horizon does not depend on the investment horizon of
      individual investors in the stock market
   Investors are compensated through cash dividends and through
    capital gains
    » Required returns on equity are generally not equal to the dividend yield, but
      to the dividend yield plus the growth rate
   P/E-ratios should be used with caution:
    » Depends on simplifying assumptions



                                                                                      41

				
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