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					                     Stock Valuation


                     Professor Dr. Rainer Stachuletz
                           Corporate Finance

                      Berlin School of Economics


Berlin, 04.01.2006                Fußzeile             1
Debt vs. Equity: Debt



                      Debt securities represent a legally enforceable
                                           claim.


                     Debt securities offer fixed or floating cash flows.


                Bondholders don’t have any control over how the
                               company is run.


Berlin, 04.01.2006                         Fußzeile                        2
Debt vs. Equity: Equity


                     Common stockholders are residual claimants.


        • No claim to earnings or assets until all senior claims are
          paid in full
        • High risk, but historically also high return

                     Stockholders have voting rights on important
                                 company decisions.

         Debt and equity have substantially different marginal benefits
                             and marginal costs.
Berlin, 04.01.2006                     Fußzeile                           3
Preferred Stock

            Preferred stock is a hybrid having some features
          similar to debt and other features similar to equity.

        - Claim on assets and cash flow senior to common stock
        - As equity security, dividend payments are not tax
          deductible for the corporation.
        - For tax reasons, straight preferred stock held mostly by
          corporations.
          Promises a fixed annual dividend payment, but not
         legally enforceable. Firms cannot pay common stock
               dividends if preferred stock is in arrears.
             Preferred stockholders usually do not have voting
                                  rights.
Berlin, 04.01.2006                 Fußzeile                          4
Rights of Common Stockholders


                       Common stockholders’ voting rights can be
                           exercised in person or by proxy.

                     Most US corporations have majority voting, with
                       one vote attached to each common share.

                  Cumulative voting gives minority shareholders
                 greater chance of electing one or more directors.

                     Shareholders have no legal rights to receive
                                     dividends.
Berlin, 04.01.2006                       Fußzeile                      5
Common Stock


              Par value   Little economic relevance today

                          Shares authorized by stockholders to be
              Shares
                           sold by the board of directors without
            authorized         further stockholders approval

             Shares
                               Number of shares owned by
          issued and                 stockholders
         outstanding

             Additional
                          Amount received in excess of par value
              paid-in
                           when corporation initially sold stock
              capital
Berlin, 04.01.2006              Fußzeile                            6
Common Stock


           Market               Market price per share x number of
        capitalization                 shares outstanding



                 Treasury     Stock repurchased by corporation;
                  stock       Usually purchased for stock options



                             Two-for-one split issues one new share
              Stock split   for each already held; reduces per share
                                             price.


Berlin, 04.01.2006               Fußzeile                            7
Investment Banks’ Role in Equity
Offerings

                                                   Trading

             Investment banking               Asset management
               lines of business
                                              Corporate finance



         Investment banks provide advice with structuring
                seasoned and unseasoned issues.

         Seasoned           • Equity issues by firms that already
          offering            have common stock outstanding.

     Unseasoned             • Initial public offering (IPO): issue of
      offering                securities that are not traded yet.
Berlin, 04.01.2006                 Fußzeile                             8
Investment Banks’ Role in Equity
Offerings
                 Firms can choose an investment bank through


          Direct negotiated offer                       Competitive bidding

                               Public security issues can be


                      Best              •   The bank promises its best efforts to sell
                                            the firm’s securities. No guarantees
                     efforts                though about the success of the offering.
                                        • Underwritten offerings, bank
                      Firm                guarantees certain proceeds.
              commitment                • Vast majority of US security offerings
                                          are underwritten.
Berlin, 04.01.2006                           Fußzeile                              9
Investment Bank Services and Costs

                     Services provided by investment banks prior to
                                    security offering

                     –   Primary pre-issue role: provide advice and help plan offer
                     –   Firm seeking capital selects lead underwriter(s).
                     –   Top firm is the lead manager, others are co-managers.
                     –   Offering syndicate organized early in process

                Prior to offering, lead investment bank negotiates
                              underwriting agreement

                     – Sets offer price and spread; details lock-up agreement
                     – Bulge bracket underwriter’s spread usually 7.0% for IPOs
                     – Initial offer price set as range; final price set day before
                       offer
Berlin, 04.01.2006                               Fußzeile                         10
   Services Provided during and
   after a Security Offering

               Lead underwriter sets each syndicate member’s
                               participation.

                     How many shares each member must sell and
                            compensation for each sale

        Almost all IPOs and SEOs have a green shoe option:
          over-allotment option to cover excess demand.

         Lead underwriter responsible for price stabilization
                           after offering.

          After offering, lead underwriter serves as principal
                             market maker.
Berlin, 04.01.2006                      Fußzeile                 11
    Secondary Market
               On the secondary market, investors deal among
                                themselves.

                                   Securities exchanges

             – Centralized locations in which listed securities are bought
               and sold
             – NYSE: the largest exchange in the world, with almost 360
               billion shares listed. Other exchanges: AMEX, regional
               exchanges

                           The Over-the-counter market (OTC)

                     – OTC has no central, physical location; linked by a mass
                       telecommunication network.
                     – A part of the OTC market is made up of stocks traded on
Berlin, 04.01.2006
                       NASDAQ.               Fußzeile                          12
Valuation Fundamentals:
Preferred Stock
        Preferred stock is an equity security that is expected to pay a fixed annual
                                   dividend indefinitely.


                                 Dp
        PS0 =                                            • PS0 = Preferred stock’s market
                                                           price
                                   rp                    •        Dp = next period’s dividend
                                                                  payment
                                                         • rp = discount rate



             An example: Investors require an 11% return on a preferred stock that pays a $2.30 annual
                                           dividend. What is the price?

                                             Dp       $2.3
                                    PS0 =         =        = $20.90 / share
                                             rp       0.11
Berlin, 04.01.2006                                     Fußzeile                                          13
Valuation Fundamentals:
Common Stock


            Value
             of a                                  D1  P
            Share                             P0          1
              of
         Common Stock                              (1  r )1



         • P0 = Present value of the expected stock price at the end of
           period #1
         •       D1 = Dividends received
         • r = discount rate

Berlin, 04.01.2006                         Fußzeile                       14
    Valuation Fundamentals:
    Common Stock

            How is P1 determined?
             - PV of expected stock price P2, plus
               dividends
             - P2 is the PV of P3 plus dividends, etc...
            Repeating this logic over and over, you find that
             today’s price equals PV of the entire dividend
             stream the stock will pay in the future:

                      D1       D2       D3       D4       D5
              P0                                              ....
                   (1  r ) (1  r ) (1  r ) (1  r ) (1  r )
                           1        2        3        4         5



Berlin, 04.01.2006                     Fußzeile                      15
Zero Growth Valuation Model

       To value common stock, you must make
        assumptions about future dividend growth.

                     Zero growth model assumes a constant,
                          non-growing dividend stream.

                                  D1 = D2 = ... = D
      • Plugging constant value D into the common stock
        valuation formula reduces to simple equation for
        a perpetuity:
                                         D1
                                    P0 
                                         r
Berlin, 04.01.2006                     Fußzeile              16
Constant Growth Valuation Model

       Assumes dividends will grow at a constant rate
        (g) that is less than the required return (r)
       If dividends grow at a constant rate forever, you
        can value stock as a growing perpetuity,
        denoting next year’s dividend as D1:

                           D1
                     P0                       Eq.4.6
                          rg
          Commonly called the Gordon growth model
Berlin, 04.01.2006            Fußzeile                      17
Example

  Dynasty Corp. will pay a $3 dividend in one year. If investors expect that
   dividend to remain constant forever, and they require a 10% return on
                  Dynasty stock, what is the stock worth?




                              D1 $3
                          P0       $30
                              r 0.1
        What is the stock worth if investors expect Dynasty’s dividends
                           to grow at 3% per year?

                             D1      $3
                      P0                    $42 ,86
                           r  g 0.10  0.03
Berlin, 04.01.2006                   Fußzeile                                  18
Variable Growth Model Example

                    Estimate the current value of Morris Industries'
                     common stock, P0

              Assume:
              - The most recent annual dividend payment of
                 Morris Industries was $4 per share.
              -        Investors expect that these dividends will
                       increase at an 8% annual rate over the next 3
                       years.
              -        After three years, dividend growth will level
                       out at 5%.
              -        The firm's required return, r , is 12%.

Berlin, 04.01.2006                        Fußzeile                      19
Variable Growth Model
Valuation Steps 1 and 2

 Compute the value of dividends in year 1, 2, and 3 as
  (1+g1)=1.08 times the previous year’s dividend
        Div1= Div0 x (1+g1) = $4 x 1.08 = $4.32
        Div2= Div1 x (1+g1) = $4.32 x 1.08 = $4.67
        Div3= Div2 x (1+g1) = $4.67 x 1.08 = $5.04


 Find the PV of these three dividend payments:
        PV of Div1= Div1  (1+r)1 = $ 4.32  (1.12) = $3.86
        PV of Div2= Div2  (1+r)2 = $ 4.67  (1.12)2 = $3.72
        PV of Div3= Div3  (1+r)3 = $ 5.04  (1.12)3 = $3.59
        Sum of discounted dividends = $3.86 + $3.72 + $3.59 = $11.17


Berlin, 04.01.2006                      Fußzeile                       20
    Variable Growth Model
    Valuation Step 3

          Find the value of the stock at the end of the initial
           growth period using the constant growth model.

          Calculate next period dividend by multiplying D3 by
           1+g2, the lower constant growth rate:
                      D4 = D3 x (1+ g2) = $ 5.04 x (1.05) = $5.292
          Then use D4=$5.292, g =0.05, r =0.12 in Gordon
                     model:

                            D 4 = $5.292 = $5.292 = $75 .60
                     P3 =
                          r - g 2 0.12 - 0.05 0.07


Berlin, 04.01.2006                           Fußzeile                21
Variable Growth Model
Valuation Step 3

 Find the present value of this stock price by
  discounting P3 by (1+r)3




           PV0 =    P 3 = $75 .60 = $75 .60 = $53 .81
                 (1  r )3 (1.12 )3 1.405




Berlin, 04.01.2006                 Fußzeile             22
Variable Growth Model
Valuation Step 4

 Add the PV of the initial dividend stream (Step 2) to the PV
  of stock price at the end of the initial growth period (P3):

                     P0 = $11.17 + $53.81 = $64.98



                                                        Current
                                                     (end of year 0)
                                                       stock price

               Remember: Because future growth rates might
               change, the variable growth model allows for a
                    changes in the dividend growth rate.
Berlin, 04.01.2006                        Fußzeile                     23
Valuing the Enterprise: Free Cash
Flow Valuation

        Discount
        Discount estimates of free cash flow that the firm
                   will generate in the future.


             Use weighted average cost of capital (WACC) to
                     discount the free cash flows.

        WACC: after-tax weighted average required return
           on all types of securities that firm issues.
                 We have an estimate of total value of the firm.
                 How can we use this to value the firm’s shares?
Berlin, 04.01.2006                    Fußzeile                     24
Value of firm’s shares


                                VS = VF– VD - VP
                       • VS = value of firm’s common shares
                       • VF = total enterprise value
                       • VD = value of firm’s debt
                       • VP = value of firm’s preferred stock


              An example....
                                                       First quarter of 2001, traded
              Morton Restaurant                           in the $20 - $25 range
              Group (MRG)

             We can use the free cash flow approach to estimate
                          the value of MRG shares.
Berlin, 04.01.2006                          Fußzeile                                   25
   An Example:
   Mortons Restaurant Group

                                  • At end of 2000, MRG’s debt market
                                    value was $66 million.
                                  • No preferred stock
                     MRG          • 4,148,002 shares outstanding
                                  • Free cash flow in 2000 was $4.8
                                    million.
                                  • Revenues and operating profits grew
                                    at 14% between 1998 and 2000.
         Assume that Mortons will experience 14% FCF
       growth from 2000 to 2004 and 7% annual growth
                         thereafter.

                      Mortons’ WACC is approximately 11%.
Berlin, 04.01.2006                     Fußzeile                       26
An Example:
Mortons Restaurant Group
          End of Year   Growth Status   Growth Rate (%)         FCF Calculation



                 2000   Historic             Given              $4,800,000


                 2001   Fast                  14                $4,800,000 x (1.14)1 = $5,472,000


                 2002   Fast                  14                $4,800,000 x (1.14)2 = $6,238,080


                 2003   Fast                  14                $4,800,000 x (1.14)3 = $7,111,411


                 2004   Fast                  14                $4,800,000 x (1.14)4 = $8,107,009


                 2005   Stable                 7                $8,107,009 x (1.07)1 = $8,674,499




               Use variable growth equation to estimate
                       Mortons enterprise value.
Berlin, 04.01.2006                                   Fußzeile                                       27
An Example:
Mortons Restaurant Group

          FCF0 1  g1    FCF0 1  g1        FCF0 1  g1 
                               1                   2                 N
     VF                                  ...                
            (1  r )1
                             (1  r ) 2
                                                  (1  r ) N


           1        FCFN 1 
                 
       (1  r ) N
                     r  g2 

                     $5,472,000 $6,238,080 $7,111,411 $8,107,009
     VF 2001                1
                                        2
                                                   3
                                                              4
                                                                 
                       (1.11)     (1.11)     (1.11)     (1.11)
        1         $8,674,499 
               
        (1.11) 4 0.11  0.07 
                              
      $4,929,730  $5,062,966  $5,199,802  $5,340,338  $142,854,029
      $163,386,865


Berlin, 04.01.2006                      Fußzeile                         28
An Example:
Mortons Restaurant Group
                                VF = 163,386,865
                                VD = $66,000,000
                                VP = $0


                     VS = $163,386,865 - $66,000,000 - $0 =
                                  $97,386,865

               Divide total share value by 4,148,002 shares
                  outstanding to obtain per-share value:

                            $97 ,386 ,865
                     VF                   $23 .40
                             4,148 ,002

Berlin, 04.01.2006                    Fußzeile                29
   Common Stock Valuation
   Other Options

                       • The value shown on the balance
       Book value        sheet of the assets of the firm, net of
                         liabilities shown on the balance sheet


       Liquidation     • Actual net amount per share likely to
                         be realized upon liquidation and
          value          payment of liabilities

                       • Reflects the amount investors will
            P/E          pay for each dollar of earnings per
                         share
           multiples   • P / E multiples differ between and
                         within industries.
                       • Especially helpful for privately-held
                         firms.
Berlin, 04.01.2006           Fußzeile                            30
    Stock Valuation



              Preferred stock has both debt and equity-like features.

              Common stock represents residual claims on firms’
               cash flows

              Investment bankers play an important role in helping
               firms issue new securities

              The same principles apply to valuation of both
               preferred and common stock


Berlin, 04.01.2006                    Fußzeile                        31

				
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