Chapter 4
Valuation: The One‐Period Case (one year from now)
future value FV = PV *(1+R)
Present Value PV = FV /(1+R)
Net Present Value NPV = −Cost + PV
The Multiperiod Case (two years from now and more)
Future Value FV = PV × (1 + r)t
Present Value PV = FV/(1 + r)t
Net Present Value NPV = −Co +( C1/ 1 + r) +( C2/( 1 + r)^2)
Find the variables
r = (FV/PV)1/t – 1
t = ln(FV/PV)/ln(1 + r)
Compounding Periods occur more frequently than once a year (semiannually,
quarterly, monthly, daily)
future value (annual percentage rate ) Co*(1+R/m)^m
Effective Annual Rate EAR = [1 + (APR/m)]m – 1
APR = m[(1 + EAR)1/m – 1]
EAR with continuous compounding EAR = er – 1
COMPOUNDING OVER MANY YEARS
future value FV = PV(1+r/m)^mt
CONTINUOUS COMPOUNDING FV = PVert
