# 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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