VIEWS: 2 PAGES: 5 POSTED ON: 9/22/2012
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 = [ wa2a2 + wb2b2 + 2 wawbra,bab ] (.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