PowerPoint file Business Valuation by mikeholy

VIEWS: 27 PAGES: 37

									Business Valuation

      PREPARED BY
   KELDON BAUER, PHD
       FOR FIL 240
                              Introduction

 The valuation of all financial securities is based on
 the expected PV of future cash flows.



                    E CF 1  E CF 2       E CF n 
    P0  E CF0                       
                    1  k  1  k 2
                                             1  k n
            n
                  E CF t 
           1  k 
           t 0
                         t
                    Introduction

                       n
                             E CFt 
               P0     1  k 
                      t 0
                                   t

 E[CFt] = Expected cash flow at time t.
 k = The required return (based on economic conditions
  & riskiness).
 Value increases as cash flow increases or k decreases.
                   Bond Valuation


 Two major components
   Interest payments (an annuity).

   Principal (future lump-sum).




                  n

                 1  k   1  k 
                        Interest      Par
     ValueB                     t          n
                 t 1
                             B          B

             = PV of Annuity + PV of Par Value
       Bond Valuation - Example 1


 The value of a 15 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 10%.

        VB  PV of Annuity + PV of Par Value
                          1    
                   1-
                  1+ 0.05 30 
           = 500 
                               10,000 1 
                                                     30 
                       0.05              1  0.05 
                                                        
                               
                               
            7,686.23  2,313.77  10,000
       Bond Valuation - Example 2


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 10%.

       VB  PV of Annuity + PV of Par Value
                        1   
                 1-
                1+ 0.05 14 
         = 500 
                             10,000 1 
                                                  14 
                     0.05             1  0.05 
                                                     
                            
                            
          4,949.32  5,050.68  10,000 - Same as before!
       Bond Valuation - Example 3


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 8%.

     VB  PV of Annuity + PV of Par Value
                      1   
               1-
              1+ 0.04 14 
       = 500 
                           10,000 1 
                                                14 
                   0.04             1  0.04 
                                                   
                          
                          
        5,28156  5,774.75  11,056.31 - More than before!
               .
       Bond Valuation - Example 4


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 12%.

     VB  PV of Annuity + PV of Par Value
                       1   
                1-
               1+ 0.06 14 
        = 500 
                            10,000 1 
                                                 14 
                    0.06             1  0.06 
                                                    
                           
                           
         9,070.50  4,647.49  9,070.50 - Less than before!
                     Some Conclusions

 Return or loss on bonds comes from two
 components.
 Interest Payment (Current Yield) = (Interest Payment)/VB
 Change in Face Value (Capital Gain) = (VEnding - VBeginning)/VBeginning
           Current Yield - Example


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 8%.

                                            Interest Payment 
                                          
    Current Yield = # of Payments per year                   
                                              Value of Bond t 
                                           
                        500
                  2            9.04%
                     11,056.31
       Capital Gains Yield - Example


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 8%.
                                                    Value t+1  Value t 
  Capital Gains Yield =  # of Payments per year                       
                                                        Value t         
                           10,948.56  11,056.31
                      2                          104%
                                                      .
                                11,056.31
           Total Yield - Example


 The value of a 7 year $10,000 bond, paying
 semi-annual payments of $500, when market
 rate is 8%.

   Total Yield = Current Yield + Capital Gains Yield
                9.04%  104%  8.00%  market rate
                          .
                    Some Conclusions

 When market rate = kB the bond sells at par or face
  value.
 When market rate < kB the bond sells at a premium.
    When interest rates go down, bond prices go up.
 When market rate > kB the bond sells at a discount.
                    Some Conclusions

 As time to maturity approaches zero, market value
 approaches face value.
    If a 15 year, 10% coupon bond at 5% 10% and 15% market rates
     were sold on the market, the values of the bond would be as
     shown in the following graph.
                       Value of a 10% Coupon Bond
               1,600
                            Market Rate =5%
               1,400
               1,200
Market Value




                            Market Rate =10%
               1,000
                800
                            Market Rate =15%
                600
                400
                200
                   0
                -1      1        3       5      7     9   11   13   15
                                               Time
                Some Conclusions

 As time to maturity approaches zero, market value
 approaches the face value of the bond.
               Yield to Maturity (YTM)

 Yield to Maturity (YTM): The effective interest rate
  earned on the bond.
 Your calculator can calculate it directly.
    Input the n, PV (Market Value), PMT (semi-annual payments),
     FV (Par Value), and have it compute i (then adjust).
               YTM - Example


 What is the yield-to-maturity of a bond with
 current market value of $950.51, a par value of
 $1,000 (which is returned in seven years),
 making a coupon payment of $45 every six
 months?



                Answer: 10.00%
                    Bond Values

 If one knows the market interest rate, the maturity,
 the coupon payments, and the par value, one can
 calculate the bond’s value by using one’s calculator!
          Bond Values - Example


 What is the market value of a bond with current
 market rate of 10%, a par value of $1,000
 (which is returned in seven years), making a
 coupon payment of $54 every six months?




              Answer: $1,039.59
                     Interest Rate Risk

 Two types of interest rate risk associated with bond
 value.
    Price Risk
    Reinvestment Risk
 Price Risk: The risk of change in price give change in
 interest.
    As interest increases, value decreases.
             Price Risk - Effect of Maturity
                       Value of 10% Coupon Bond

             1,600
             1,400
             1,200
Bond Value




             1,000                               1-Year Bond
               800
               600
               400                               14-Year Bond
               200
                 0
                  0%   5%   10%      15%        20%       25%   30%
                                  Market Rate
                    Interest Rate Risk

 Reinvestment Risk: The risk of worse reinvestment
 opportunities when repaid.
    When interest rates increase reinvestment opportunities
     improve.
 Note: Price and Reinvestment Risks go in opposite
 directions.
             Price Risk - Effect of Payment
                     14 Year Debt Instrument - 10% Contract Rate

             2,500
             2,000
Bond Value




             1,500                                           Coupon Bond
                                                             Zero Coupon
             1,000                                           Monthly Loan
              500
                0
                 0%      5%    10%   15%   20%   25%   30%
                                 Market Rate
 Equity Valuation - Dividend Based Models

 The first economic based valuation models assessed
  the present value of expected dividends.
 Myron Gordon applied the previous equation to
  expected dividends, assuming a constant growth
  rate.
    Since stocks never mature, n must be allowed to approach
     infinity.
             Dividend Based Models

 The Gordon Constant Growth Model:


             D0 1  g  D0 1  g      D0 1  g 
                                    2                 
  [1]   P0                         
              1  k s  1  k s 2
                                          1  k s 

         multiplyin g both sides by
                                       1  g 
                                      1  k s 
  [2]     1  g  P  D0 1  g 2  D0 1  g 3   D0 1  g 
         1  k s  0
                        1  k s 2     1  k s 3     1  k s 
        Gordon Constant Growth Model

 Subtracting [2] from [1]:


             P0 
                    1  g  P  D0 1  g 
                   1  k s  0 1  k s 
               1  k s 1  g  D0 1  g 
               1  k  1  k   1  k 
           P0                   
                     s        s            s

                   k s  g  D0 1  g 
                   1  k   1  k 
               P0          
                         s         s
        Gordon Constant Growth Model

 Solving for PV:


         k s  g  1  k s  D0 1  g   1  k s 
     P0                               
         1  k  k  g  1  k   k  g         
               s  s               s     s       

                   D0 1  g    ˆ
                                 D1
              P0              
                   ks  g  ks  g 
             Free Cash Flow Models

 Many stocks do not offer a dividend.
 If the same assumptions are made, except that free
 cash flow, not dividends are being valued, the same
 process can be used to derive another valuation
 model:



                        FCF0 1  g 
                   P0 
                         k s  g 
           What Affects Stock Prices?

                         FCF0 1  g 
                    P0 
                          k s  g 
 Stock prices should therefore depend on:
  Expected cash flow.
  Growth rate.

  The company’s required return.
               What Affects Stock Prices?

 Required return is a function of the Capital Asset
 Pricing Model (CAPM):

                   k s  RF  km  RF  s
    Therefore ks depends on:
      Interest rates.
      Systematic risk of the firm.
      Market risk aversion.
        Non-Constant Growth Valuation

 Since constant growth is unlikely, we will now
  consider how to value stock under non-constant
  growth.
 First, project dividends (or free cash flows) as far as
  practical.
 From there estimate a constant growth rate.
 Then take the PV as we discussed in an earlier
  chapter.
       Non-Constant Growth - Example


 If Buford’s Bulldozer is expected to pay the
 following dividends, and then grow indefinitely
 at 4.5% (assuming a discount rate of 14.50%),
 what would its stock value be?
                    T im e Div idends
                       1      1 .25
                       2      2.7 5
                       3      1 .50
                       4      2.80
                       5      3.20
        Non-Constant Growth - Example

 First we consider the price of the stock at time five.




                      3.20(1  0.045) 3.344
                D5 1  g
         P5                                  $33.44
                k  g 0145  0.045 010
                  s
                           .               .
       Non-Constant Growth - Example

 Next we sum all period cash flows.


    T im e Div idends Stock Value      T otal
       1      1 .25                     1 .25
       2      2.7 5                     2.7 5
       3      1 .50                     1 .50
       4      2.80                      2.80
       5      3.20       33.44         36.64
Non-Constant Growth - Example


    0           1     2       3       4       5
        14.5%



           $1.25    $2.75   $1.50   $2.80   $36.64


  $ 1.09
 $ 2.10
 $ 1.00
 $ 1.63
 $18.62
 $24.44 = Present Value
           Other Valuation Methods

 Book Value Method.
 Liquidation Value Method.
 Price/Earnings (P/E) Multiples.

								
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