Part Three

							  Part Three


Valuation
       Outline of Valuation

   Discounted Cash Flow Analysis

   Valuation Model

   Risk and Return
          Type of Cash Flow
   A lump sum

        $0      $0         $100     $0

   An annuity of $100:
           $0       $100    $100    $100
                       
   An uneven cash flow stream
         ($50)      $100      $75        $50

           Future Value
   Find the FV of $100 left for 3 years in an
    account paying 10 percent annual
    interest:

 FV = PV(1 + k)" = PV(FVIFk n)
 = $100(1.10)3
 = $100(1.3310) = $133.10.
          Present Value
 Find   the PV of $100 to be received in 3
    years if the appropriate interest rate is
    10 percent:
                     n
 PV = FVn/(1 + k)
 = $100(1/1.10)3 =$100(0.7513) =
  $75.13.
              Annuities
 Ordinary   Annuity:

   PV   $100     $100   $100 FV

 Annuity   Due

 $100   $100     $100    FV
 PV
    Future Value of an Annuity
          (Time Line Approach)

   0   $100      $100           $100
                                $110
                  
                          10%
                  
                                    $121

                                      $331
  Future Value of an Annuity
         (Formula Approach)
 FVAn   = PMT(FVIFA)
 = $100(3.3100) = $331.
 If the annuity is an annuity due,
  then :
 FVAn(Annuity due) = FVAn(1 + k)
 =$331(1.10)= $364.10
 Present Value of an Annuity
            (Time Line Approach)
       0    $100    $100      $100
                    
 10%
                    
  $ 90.91
 82.64 ——————
 75.13—————————
 $248.68
 Present Value of an Annuity
         (Formula Approach)
 PVA= PMT(PVIFA k,n) = $100(2.4869)
 = $248.69.

 The present value of an annuity due is
  PVA(Annuity due) = PVA(1 + k)
 = $248.69(1.10) = $273.56.
    Uneven Cash Flow Stream
   0    $100   $300   $300   $(50)
    10%

 90.91
 247.93
 225.39
 (34.15)
 $530.08
    Finding the Interest Rate
                    $100(1 + x)3 = $125.97
                $100(FVIF k,3) = $125.97
                        FVIF k,3 = 1.2597
 Look at Table of Future Value for K. The
  1.2597 is at Row 3 in the 8% column.
  Therefore,
                  k = 8%.
      General Valuation Model
   The value of any asset can be found as
    the present value of its expected future
    cash flows, CFi, discounted at the rate k:


   V=    CF 1     +     CF2     +     CF3

        (1 +k)1       (1 +k)2       (1 +k)n•
     Bond Valuation
V=l(PVIFA     + M(PVIF k,n)
             k,n)

=$100(PVIFA 10%,10) +
 $1,000(PVIF 10%,10)
=$614.46 + $385.54
=$1,000.
      Yield to Maturity of Bond
   Par value = $1,000
   Current price = $887
   Annual coupon = $100
   Term to maturity = 10 years
     0       1      2 ……… 9         10
      -$887 $100      $100 $100 $100 $1,000
   $887 = $1oo(PVIFA ytm,10) + $1,ooo(PVIFytm, 10)
   YTM = 12%.
      Current Yield of Bond



                     Annual coupon payment
    Current yield =
                        Current price
General Stock Valuation Model
              D1
 P0   =
          ks – g

     D0(1+g)
 =
     kg - g
         Value of Perpetuity

           PMT
V   =
             k
                 $2
    =                 =   $12.50.
             0.16
           Supernormal Growth


   $2.000 $2.600   $3.380   $4.394   $4.658


   g = 30% g = 30% g = 30% g = 6% g = 6%
 PV of Supernormal Dividends
                  PV D1 = $2.600/(1.16)1 = $2.241
                  PV Ds2= $3.380/(1.16)2 = $2.512
                  PV D3 = $4.394/(1.16)3 = $2.815
                                          $7.568
 Stock Price at t = 3

p =    D4        =    $4.658     =   $4.658 = $46.58
      ks -   g       0.16-0.06       0.10
 PV of P3
 $46.58 / (1.16) = $29.84
 Value of Stock
 Po = $7.57 + $29.84 = $37.41.
         Concept of Risk

 Risk
     refers to the possibility that
 some unfavorable event will occur

 Investment risk is associated with
 the probability of low or negative
 returns on an investment.
    Probability Distribution
             (payoff Matrix)


                         Rate of Return
 Demand
                      Comapany Company
  for the Probability
                         A        B
 products
Strong          0.3        100       20
Normal          0.4         15       15
Weak            0.3        -70       10
      Probability of Distribution
                                              Probability of
      Probability of
                                                  Co.B
          Co.A




-70                    100   Rate of Return        10 15 20
             15
Probability   Density
     Expected Rate of Return
Expected rate   of return
                    n
         ˆ
         k       i 1
                          pi ki

= .3(100%)+.4(15%)+.3(-70)
= 15%

                      ˆ
     Deviation  kj  k
Variance and Standard Deviation
                           n
   Variance       2
                          ( Ki  K ) Pi
                                                2

                          i 1

                                  n
    Std   Deviation            (K
                                 i 1
                                        i    K ) Pi
                                                 2




  The smaller the standard deviation, the
  lower the risk associated with the event.
    Coefficient of Variation
 The coefficient of variation shows the
 risk per unit of return and a better
 measure for evaluation risk in situation
 where investments have substantially
 different expected returns.
                                   
 Coefficien of Deviation  CV 
           t
                                   ˆ
                                   K
         Portfolio Return
                    ˆp
Portfolio Re turn  K
           ˆ              ˆ
     ˆ  W K  ....... W K
 W1 K1   2 2            n n
   n
 Wi K i
      ˆ
  i 1
            Portfolio Risk

 The   risk of a portfolio depends not
 only on the standard deviation of
 the individual stocks, but also on
 the correlation between the stocks.
   Portfolio Risk
        m     n
     W W 
        j 1 k 1
                    j   k   jk




  j , k  rj , kjk
           When R = -1
  Year    stock A % Stock B % Portfolio AB %
  1992        40       -10           15
  1993       -10        40           15
  1994        35        -5           15
  1995        -5        35           15
  1996        15        15           15
Average
              15        15           15
 return
standard
            22.6       22.6           0
deviation
           When r = +1
  Year    stock A % Stock B % Portfolio AB %
  1992       -10       -10          -10
  1993        40        40           40
  1994        -5        -5           -5
  1995        35        35           35
  1996        15        15           15
Average
              15        15           15
 return
standard
            22.6       22.6        22.6
deviation
        When +1 > r > -1
  Year    stock A % Stock B % Portfolio AB %
  1992        40        28           34
  1993       -10        20            5
  1994        35        41           38
  1995        -5       -17          -11
  1996        15        3             9
Average
              15        15           15
 return
standard
            22.6       22.6        20.6
deviation
      Classification of Risk
 Total   risk can be separated into two
 parts:


     Market risk

     Company-specific risk
Effects of Portfolio Size on Risk