5 Time value of money Compinding future value FVDiscounting present value PVInterest rate exchange rate between earlier and later money 哕簽粪飪棂嬰驿。FV = PV(1 + r)t PV = FV / (1 + r)tr = period interest rate, expressed as a decimalt = number of periodsFuture value interest factor = (1 + r)t 复利终值系数1/(1+r) t present value factor 现值系数For a given interest rate – the longer the time period, the lower the present value閘鈐巔挤轡衮麩。For a given time period – the higher the interest rate, the smaller the present value懑滸织擋暈贸戗。r = (FV / PV)1/t – 1t = ln(FV / PV) / ln(1 + r)6 Discounted Cash Flow ValuationFuture and Present Values of Multiple Cash FlowsYou think you will be able to deposit $4,000 at the end of each of the next three years in a bank account paying 8 percent interest、 You currently have $7,000 in the account、 How much will you have in three years? In four years?蓮賀辏兑顛辐渎。Today (year 0 CF): 3 N; 8 I/Y; -7,000 PV; CPT FV = 8,817、98 FV = 7000(1、08)3 = 8,817、98 勻贈憚痈鸥鲍厨。Year 1 CF: 2 N; 8 I/Y; -4000 PV; CPT FV = 4,665、60 FV = 4,000(1、08)2 = 4,665、60 渎购賡騁鮫铱绢。Year 2 CF: 1 N; 8 I/Y; -4000 PV; CPT FV = 4,320 FV = 4,000(1、08) = 4,320 鍵紱纖扪氲锰蓠。Year 3 CF: value = 4,000Total value in 3 years = 8817、98 + 4665、60 + 4320 + 4000 = 21,803、58 妆藍鸪恆鱘娱軋。Value at year 4: 1 N; 8 I/Y; -21803、58 PV; CPT FV = 23,547、87 气霽装彥覷认頗。You are offered an investment that will pay you $200 in one year, $400 the next year, $600 the next year and $800 at the end of the next year 、 You can earn 12 percent on very similar investments、 What is the most you should pay for this one?绀幀厩楊癘颼崢。Point out ...