FV - Future Value 

PV - Present Value

R - Compouand annual return

n - Investment horizon

EAR - Effective Annual Rate

Pn - Price at the end of n

Pn-1 - Price at the end of n-1

Simple Valuation

FV = PV * (1+R)^n

PV = FV/ (1+R)^n

R = (FV/PV)^(1/n) - 1

n = ln(FV/PV)/ln(1+R)

If n is infinite

If n is infinite and Growing FV

Compounding

Compounding occurs m times per year  --> FV = PV(1+R/m)^(n*m)

Conitnuos Compounding - m is infinite --> FV = PV*e^(R*n), e = 2.71828

Effective Annual Rate (EAR)

Compounding occurs m times per year  --> PV(1+R/m)^(n*m) = PV(1+ EAR)^n  --> EAR = (1+R/m)^(m) - 1

Conitnuos Compounding - m is infinitve --> PV*e^(R*n)= PV(1+ EAR)^n --> EAR = e^(R)- 1

Net return over n period --> Rn = (Pn - Pn-1)/Pn-1

Gross return over n period --> 1 + Rn = (Pn)/Pn-1

Multiple period returns

Net Return, Rn(2) = (Pn - Pn-2)/Pn-2 = (Pn/Pn-2) - 1

Relationship to 1 period returns

Net Return, Rn(2) = (Pn/Pn-2) - 1 = (Pn/Pn-1) * (Pn-1/Pn-2) - 1 = (1+Rn) * (1+Rn-1) - 1

Gross Return,1+Rn(2) = (1+Rn) * (1+Rn-1)

!!! 2 period gross return = the product of 2 1-period gross returns

Net Return, Rn(k) = (Pn / Pn-k) - 1

Gross Return,1+Rn(k)  = (1+Rn) * (1+Rn-1) * (1+Rn-2) ....... * (1+Rn-k+1)

Portfolio Return Calculations

SA = % of Stock B, RA = return of Stock A

SB = % of Stock B, RB = return of Stock B

SA + SB = 100%

Rp = SA*RA + SB * RB

Dn = dividend received

Net Return, R = (Pn + Dn - Pn-1)/ Pn-1

Gross Return, 1 + R =  (Pn + Dn)/ Pn-1

Ifn = Inflation over period n

Deflated price by using Inflation, Pr = P/Ifn

Return with Infaltion, Ri = (Pr - Prn-1) / Prn-1

                                            = ( (P/Ifn) - (Pn-1/Ifn-1))/ (Pn-1/Ifn-1)