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Formulas - Formulas Future value and present value n FV =...

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Formulas: Future value and present value: FV = PV ° (1 + i ) n ; PV = FV (1 + i ) n Non-annual compounding and e/ective annual interest rate: FV = PV ° ° 1 + i m ± m ° n ; Eff:Int:Rate = ° 1 + i m ± m ± 1 Present value and future value of an (ordinary) annuity: PV = PMT ° ( 1 ± 1 (1+ i ) n i ) ; FV = PMT ° ² (1 + i ) n ± 1 i ³ PV (or FV) of Annuity Due: (1 + i ) ° PV ( or FV ) of ordinary annuity : Present value of a perpetuity and a growing perpetuity: PV = PMT i ; PV = PMT i ± g Price of an n -period zero-coupon bond ( FV : face value; y : yield to maturity): P 0 = FV (1 + y ) n Price of an n -period coupon bond ( PMT : coupon; FV : face value; y : yield to maturity): P 0 = n X t =1 PMT (1 + y ) t ! + FV (1 + y ) n Market value of a stock ( ^ D t : expected amount of dividend at t ; r is the stock°s required rate of return): P 0 = 1 X t =1 ^ D t (1 + r ) t : Gordon°s constant dividend growth model: P 0 = ^ D 1 r ± g : Expected return on a portfolio, ° R p : ° R p = n X i =1 w i ° ° r i ; n X i =1 w i = 1 : CAPM formula (Security Market Line formula) ° R i = R f + ° i ´ ° R m ± R f µ ; ° i = Cov ~ R i ; ~ R m · V ar ~ R m · = ± i
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