Vb - Florida International University by QEg9iD

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									                                       FORMULA SHEET #2
The Expected Value, or Mean () of a Probability Distribution:

                   =  (V x P)

 where:  = the expected value, or mean
        V = the possible value for some variable
        P = the probability of the value V occurring
         = the sum of (summation sign)

The Standard Deviation of a Probability Distribution:

                   = [  P(V - )2 ] (.5)

 where:     =    standard deviation
        V    =     the value the variable can take
        P    =    the probability of the value V occurring
            =    the expected value, or mean

The Coefficient of Variation of a Probability Distribution:

                              Standard Deviation               
                  CV     =    --------------------------   =   ----
                                      Mean                      

The Expected Rate of Return of a Portfolio, E(Rp), Comprised of Two Assets, a and b:

                  E(Rp) = [ wa x E(Ra) ] + [ wb x E(Rb) ]

 where:     wa    =   the weight, or percentage of the portfolio invested in Asset a
          E(Ra)   =   the expected return of Asset a
            wb    =   the weight, or percentage of the portfolio invested in Asset b
          E(Rb)   =   the expected return of Asset b

The Standard Deviation of a Two-Asset Portfolio:

                  p = [ wa2a2 + wb2b2 + 2 wawbra,bab ] (.5)

 where:     p = the standard deviation of the two-asset portfolio comprised of assets a and b
            wa = the weight, or percentage of the portfolio invested in Asset a
            a = the standard deviation of the returns of Asset a
           ra,b = the correlation coefficient of the cash flows of Asset a and Asset b
            wb = the weight, or percentage of the portfolio invested in Asset b
            b = the standard deviation of the returns of Asset b
The Capital Asset Pricing Model (CAPM):

                 kp = kRF + [ ( kM - kRF ) x ]

 where:     kp   =   the required rate of return appropriate for the investment
           kRF   =   the risk-free rate of return
            kM   =   the expected (required) rate of return on the overall market
                =   the beta of the asset


Present Value of a Perpetuity:

                              PMT
                 PVP     =    -------
                                k

 where: PVP = Present value of a perpetuity
        PMT = Amount of each of the perpetual annuity payments
          k = Discount rate


The Bond Valuation Formula (Algebraic Version):

                Present Value               Present Value of 
   Bond Value =  of Interest 
                                         + the Return of the
                                                               
                 Payments                      Principal     

                              1 – (1 + kd)-n                M
          Vb         = INT x ------------------- +     -------------
                                   kd                   (1 + kd)n

 where:     Vb = Current market value of the bond
          INT = Dollar amount of each periodic interest payment
            n = Number of periods to maturity (also number of interest payments remaining)
           M = Principal payment received at maturity (par value of the bond)
           kd = Required rate of return (per period) on the bond


The Bond Valuation Formula (Table Version):

                 Vb = INT x (PVIFAk,n) + M x (PVIFk,n)

 where: PVIFAk,n = Present Value Interest Factor for an Annuity
         PVIFk,n = Present Value Interest Factor for a Lump Sum
The Current Yield on a Bond:

                             INT
               CY      =    ---------
                              Vb


The Estimated Yield to Maturity on a Bond:

                                INT + [(M – Vb)/n]
               Estimated YTM = --------------------------
                                    (M + 2Vb)/3

 where: INT    =    Dollar amount of yearly interest payment
         Vb    =    Current market value of the bond
           n   =    Number of years to maturity
          M    =    Principal payment received at maturity (par value of the bond)


The Present Value of a Preferred Stock:

                             Dp
               Vp      =   --------
                             kp

 where: Vp = Current market value of the preferred stock
        Dp = Amount of the preferred stock dividend
        kp = Required rate of return on this issue of preferred stock


Formula for the Yield on Preferred Stock:

                             Dp
               kp     =    -------
                             Pp

 where:   kp = Yield on investment that an investor can expect if the shares are purchased at
               the current market price Pp and the preferred dividend Dp is paid forever
          Dp = Amount of the preferred stock dividend
          Pp = Current market price of the preferred stock
The Constant Growth Version of the Dividend Valuation Model (Gordon Model):

                             D0(1 + g)                     D1
               P0       =    ------------    or   P0   = ----------       (Note: ks must be  g)
                               ks – g                     ks – g

 where:   P0   =   Current price of the common stock (intrinsic or theoretical value)
          D0   =   The dollar amount of the last actual dividend on the stock
          D1   =   The dollar amount of the dividend on the stock expected one period from now
          ks   =   Required rate of return on the stock
           g   =   Expected constant growth rate of the dividends on the stock



The Yield, or Total Return, on Common Stock:

                                         dividend  growth
               Expected rate of return =  yield  +  rate 

                                                   D1
                                        ks    =    ----       +       g
                                                   P0

 where:     P0     =   Current price of the common stock (intrinsic or theoretical value)
            D1     =   The dollar amount of the dividend on the stock expected one period from now
            ks     =   Required (expected) rate of return on the stock
             g     =   Expected constant growth rate of the dividends on the stock



Common Stock Valuation under Supernormal Growth (two-stage growth):

           D0(1 + gs)                                   D0(1 + gs)Ns x (1 + gn)
P0   =                                             Ns
          --------------- x { 1 - (1 + gs / 1 + ks) } + -------------------------------- x (1 + ks)-Ns
             ks – gs                                            ks – gn

 where:     P0     =   Current price of the common stock (intrinsic or theoretical value)
            D0     =   The dollar amount of the last actual dividend on the stock
            ks     =   Required rate of return on the stock
            gn     =   Expected constant growth rate of the dividends on the stock
            gs     =   Expected supernormal growth rate of the dividends on the stock
            Ns     =   Number of years of initial (supernormal) growth
Formula for the Conversion Value of a Convertible Bond:

               Conversion Value = Conversion Ratio x Stock Price


Approximate Value of a Right, Stock Trading Rights-On:

                    M0 - S
               R = -------------
                     N + 1

 where:    R   =   Approximate market value of a right
          M0   =   Market price of the common stock, selling rights-on
           S   =   Subscription price
           N   =   Number of rights needed to purchase one of the new shares of common stock


Approximate Value of a Right, Stock Trading Ex-Rights:

                    Mx - S
               R = -------------
                        N

 where:    R   =   Approximate market value of a right
          Mx   =   Market price of the common stock, selling ex-rights
           S   =   Subscription price
           N   =   Number of rights needed to purchase one of the new shares of common stock


The Exercise Value of a Warrant:

               XV = (M – XP) x #

 where:   XV = Exercise value of a warrant
           M = Market price of the stock
          XP = Exercise price of a warrant
           # = Number of shares that may be purchased if the warrant is exercised

								
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