vw10e-03中文-货币的时间价值

Click to edit Master style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,3-,*,Click to edit Master style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,Click to edit Master style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,第三章,货币的时间价值,货币的时间价值,利息率,单利,复利,贷款的分期偿还,今天的,10,000,美元,!,我们知道了,货币的时间价值,!,利息率,对于今天的,10,000,美元和 十年后的,10,000,美元,你将选择哪一个,?,时间允许你现在有机会延迟消费和,获取利息,.,时间的作用,?,在你的决策中,时间为什么是 非常重要的因素,?,利息的 形式,复利,不仅借,(,贷,),的本金需要支付利息,而且前期的 利息在本期也要计息,.,单利,只就借,(,贷,),的原始金额或本金支付,(,收取,),的利息,.,单利计算公式,公式,SI = P,0,(i)(n),SI:,单利利息额,P,0,:,原始金额,(,第零期,),i:,利息率,n:,期数,SI = P,0,(i)(n) = $1,000(.07)(2) =,$140,单利计算举例,假设投资者按,7%,的单利把,1,000,元存入储蓄帐户,保持,2,年不动,在第,2,年年末,利息额的计算如下,:,终值,是现在的一笔钱和一系列支付款项按给定 的利息率计算所得到的在某个未来时间点的价值,.,单利,(,终值,),存款终值,(,FV,),的计算,:,FV,= P,0,+ SI = $1,000 + $140 =,$1,140,单利,(,现值,),如何理解货币现值的概念,(PV) ?,现值,是未来的一笔钱和一系列支付款项按给 定的利息率计算所得到的现在的价值,.,产生复利的原因,终值,若将,1,000,元以,7%,的利率,(,复利,),存入银行,则,2,年后的复利,终值是多少,?,终值：一笔存款,(,图示,),0,1,2,$1,000,FV,2,7%,FV,1,=,P,0,(1+i),1,=,$1,000,(1.07) =,$1,070,复利,你存入银行的,1000,元在第一年取得了,70,元的利息收入,这与单利法下计算的利息收入相同,.,终值：一笔存款,(,公式,),FV,1,=,P,0,(1+i),1,=,$1,000,(1.07) =,$1,070,FV,2,= FV,1,(1+i),1,=,P,0,(1+i)(1+i) =,$1,000,(1.07)(1.07)=,P,0,(1+i),2,=,$1,000,(1.07),2,=,$1,144.90,在第二年,与单利法相比,你多取得了,4.,90,美元的利息收入,.,终值：一笔存款,(,公式,),FV,1,= P,0,(1+i),1,FV,2,= P,0,(1+i),2,一般的终值公式,:,FV,n,= P,0,(1+i),n,或,FV,n,= P,0,(,FVIF,i,n,) - (,见表,1),一般的终值公式,etc.,1,元的复利终值系数，利率I%. 期数 n 即,(,FVIF,i,n,),.,复利终值系数表,期数,6%,7%,8%,1,1.060,1.070,1.080,2,1.124,1.145,1.166,3,1.191,1.225,1.260,4,1.262,1.311,1.360,5,1.338,1.403,1.469,FV,2,= $1,000 (,FVIF,7%,2,)= $1,000 (1.145)=,$1,145,复利终值计算表,期数,6%,7%,8%,1,1.060,1.070,1.080,2,1.124,1.145,1.166,3,1.191,1.225,1.260,4,1.262,1.311,1.360,5,1.338,1.403,1.469,Julie Miller,想知道她的,10,000,美元存款在复利是,10%,的条件下，,5,年之后的价值是多少？,例题,0 1 2 3 4,5,$10,000,FV,5,10%,基于表,1,的计算：,FV,5,= $10,000 (,FVIF,10%, 5,),= $10,000 (1.611)=,$16,110,小数点差异,解答,基于一般复利公式的计算：,FV,n,= P,0,(1+i),n,FV,5,= $10,000 (1+ 0.10),5,=,$16,105.10,我们用“,72,法则,”,让你的钱翻倍,!,让你的,5,000,元翻倍需要多长时间？（复利年利率为,12%,）,所需要的大概时间是,=,72,/ i%,72,/ 12% =,6,年,实际所需时间是,6.12,年,72,法则,让你的,5,000,元翻倍需要多长时间？（复利年利率为,12%,）,假定你在,2,年后需要,1,000,美元，那么在贴现率是,7%,的条件下,你现在需要向银行存入多少钱,?,0,1,2,$1,000,7%,PV,1,PV,0,现值：一笔存款（图示）,PV,0,=,FV,2,/ (1+i),2,=,$1,000,/ (1.07),2,=,FV,2,/ (1+i),2,=,$873.44,现值：一笔存款（公式）,0,1,2,$1,000,7%,PV,0,PV,0,=,FV,1,/ (1+i),1,PV,0,=,FV,2,/ (1+i),2,一般现值计算公式：,PV,0,=,FV,n,/ (1+i),n,或,PV,0,=,FV,n,(,PVIF,i,n,) -,见表,2,一般的现值公式,etc.,期数为,n,的复利现值系数（,PVIF,i,n,）,复利现值系数表,期数,6%,7%,8%,1,.943,.935,.926,2,.890,.873,.857,3,.840,.816,.794,4,.792,.763,.735,5,.747,.713,.681,PV,2,=,$1,000,(PVIF,7%,2,)=,$1,000,(.873)=,$873,Due to Rounding,复利现值计算表,期数,6%,7%,8%,1,.943,.935,.926,2,.890,.873,.857,3,.840,.816,.794,4,.792,.763,.735,5,.747,.713,.681,例题,Julie Miller,想知道为了在5年后取得10,000,美元，在贴现率是,10%,的条件下，现在应当向银行存入多少钱？,0 1 2 3 4,5,$10,000,PV,0,10%,基于一般公式的计算：,PV,0,=,FV,n,/ (1+i),n,PV,0,=,$10,000,/ (1+ 0.10),5,=,$6,209.21,基于表,1,的计算：,PV,0,=,$10,000,(,PVIF,10%, 5,),=,$10,000,(.621)=,$6,210.00,Due to Rounding,解答,年金的种类,普通年金,:,收付款项发生在每个期末。,先付年金,:,收付款项发生在每个期初。,年金是一定期限内一系列相等金额的收付款项,年金举例,学生贷款支付年金,汽车贷款支付年金,保险预付年金,抵押支付年金,退休收入年金,年金分析,0 1 2 3,$100 $100 $100,(,普通年金,),第一年年末,(,先付年金,),第一年年初,今日,每年相同的现金流,(,先付年金,),第一年年末,FVA,n,= R(1+i),n-1,+ R(1+i),n-2,+ . + R(1+i),1,+ R(1+i),0,普通年金终值,- FVA,R R R,0 1 2,n,n+1,FVA,n,R,:,年金金额,年末,i%,. . .,FVA,3,= $1,000(1.07),2,+ $1,000(1.07),1,+ $1,000(1.07),0,= $1,145 + $1,070 + $1,000 =,$3,215,$1,000 $1,000 $1,000,0 1 2,3,4,$3,215 = FVA,3,年末,7%,$1,070,$1,145,普通年金终值举例,FVA,n,= R (FVIFA,i%,n,),FVA,3,= $1,000 (FVIFA,7%,3,)= $1,000 (3.215) =,$3,215,年金终值系数表,期数,6%,7%,8%,1,1.000,1.000,1.000,2,2.060,2.070,2.080,3,3.184,3.215,3.246,4,4.375,4.440,4.506,5,5.637,5.751,5.867,FVAD,n,= R(1+i),n,+ R(1+i),n-1,+ . + R(1+i),2,+ R(1+i),1,=,FVA,n,(1+i),先付年金终值,- FVAD,R R R,0 1 2,n,n+1,FVAD,n,R,:,年金金额,年初,i%,. . .,FVAD,3,= $1,000(1.07),3,+ $1,000(1.07),2,+ $1,000(1.07),1,= $1,225 + $1,145 + $1,070 =,$3,440,先付年金终值举例,$1,000 $1,000 $1,000 $1,070,0 1 2,3,4,FVAD,3,= $3,440,年初,7%,$1,225,$1,145,FVAD,n,= R (FVIFA,i%,n,)(1+i),FVAD,3,= $1,000 (FVIFA,7%,3,)(1.07)= $1,000 (3.215)(1.07) =,$3,440,年金终值系数表,期数,6%,7%,8%,1,1.000,1.000,1.000,2,2.060,2.070,2.080,3,3.184,3.215,3.246,4,4.375,4.440,4.506,5,5.637,5.751,5.867,PVA,n,= R/(1+i),1,+ R/(1+i),2,+ . + R/(1+i),n,普通年金现值,- PVA,R R R,0 1 2,n,n+1,PVA,n,R,:,年金金额,年末,i%,. . .,PVA,3,= $1,000/(1.07),1,+ $1,000/(1.07),2,+ $1,000/(1.07),3,= $934.58 + $873.44 + $816.30 =,$2,624.32,普通年金现值举例,$1,000 $1,000 $1,000,0 1 2,3,4,$2,624.32 = PVA,3,年末,7%,$934.58,$873.44,$816.30,PVA,n,= R (PVIFA,i%,n,),PVA,3,= $1,000 (PVIFA,7%,3,)= $1,000 (2.624) =,$2,624,年金现值系数表,期数,6%,7%,8%,1,0.943,0.935,0.926,2,1.833,1.808,1.783,3,2.673,2.624,2.577,4,3.465,3.387,3.312,5,4.212,4.100,3.993,PVAD,n,= R/(1+i),0,+ R/(1+i),1,+ . + R/(1+i),n-1,=,PVA,n,(1+i),先付年金现值,- PVAD,R R R,0 1 2,n,n+1,PVAD,n,R,:,年金金额,年初,i%,. . .,PVAD,n,= $1,000/(1.07),2,+ $1,000/(1.07),1,+ $1,000/(1.07),0,=,$2,808.02,先付年金现值举例,$1,000.00 $1,000 $1,000,0 1 2,3,4,PVAD,n,=,$2,808.02,年初,7%,$ 934.58,$ 873.44,PVAD,n,= R (PVIFA,i%,n,)(1+i),PVAD,3,= $1,000 (PVIFA,7%,3,)(1.07) = $1,000 (2.624)(1.07) =,$2,808,年金现值系数表,期数,6%,7%,8%,1,0.943,0.935,0.926,2,1.833,1.808,1.783,3,2.673,2.624,2.577,4,3.465,3.387,3.312,5,4.212,4.100,3.993,1.,完全地了解问题,2.,判断这是一个现值问题还是一个终值问题,3.,画一条时间轴,4.,标示出代表时间的箭头，并标出现金流,5.,决定问题的类型：单利、复利终值、,年金问题、混合现金流,6.,解决问题,解决货币时间价值问题所要 遵循的步骤,Julie Miller,想收到以下现金，若按,10%,贴现，则现值是多少？,混合现金流举例,0 1 2 3 4,5,$600 $600 $400 $400 $100,PV,0,10%,1.,分割成不同的时间，分别计算单个 现金流量的现值；,2.,解决混合现金流，将问题分成 年金问题、组合问题、单利问题；,3.,把每组问题归结为现值。,如何解答,?,每年一次计息期条件下,0 1 2 3 4,5,$600 $600 $400 $400 $100,10%,$545.45,$495.87,$300.53,$273.21,$ 62.09,$1677.15 =,混合现金流的现值,不同计息期条件下,(#1),0 1 2 3 4,5,$600 $600 $400 $400 $100,10%,$1,041.60,$ 573.57,$ 62.10,$1,677.27 =,混合现金流的现值,按表计算,$600(PVIFA,10%,2,) = $600(1.736) = $1,041.60,$400(PVIFA,10%,2,)(PVIF,10%,2,) = $400(1.736)(0.826) = $573.57,$100 (PVIF,10%,5,) = $100 (0.621) = $62.10,不同计息期条件下,(#2),0 1 2 3 4,$400 $400 $400 $400,PV,0,等于,$1677.30.,0 1 2,$200 $200,0 1 2 3 4 5,$100,$1,268.00,$347.20,$62.10,加,加,一般公式,: FV,n,=,PV,0,(1 + i/m),mn,n:,期数,m:,一年中计息的次数,i:,年利率,FV,n,m,: n,年后的终值,PV,0,:,现金流的现值,复利的计息频率,Julie Miller,有,1,000,元想进行为期,2,年的投资，年利率为,12%.,每年一次计息,FV,2,=,1,000,(1+ .12/1),(1)(2),=,1,254.40,半年一次计息,FV,2,=,1,000,(1+ .12/2),(2)(2),=,1,262.48,频率对现金流的影响,按季度计息,FV,2,=,1,000,(1+ .12/4),(4)(2),=,1,266.77,按月计息,FV,2,=,1,000,(1+ .12/12),(12)(2),=,1,269.73,按日计息,FV,2,=,1,000,(1+,.12/365,),(365)(2),=,1,271.20,频率对现金流的影响,实际年利率,在对名义利率按每年计息期长短等因素 进行调整后的利率。,(1 + i / m ),m,- 1,实际年利率,Basket Wonders (BW),在银行有,1,000,美元的信用贷款，每季度按,6%,的利息率支付利息，则,BW,的实际年利率 是多少（,EAR,）,?,EAR,= ( 1 + 6% / 4 ),4,- 1 = 1.0614 - 1 = .0614,或,6.14%!,BW,公司的实际年利率,1.,计算每期偿付金额,.,2.,确定,t,时期内的利率,.,(Loan Balance at t-1) x (i% / m),3.,计算本金偿付额。,(Payment - Interest from Step 2),4.,计算年末偿还金额。,(Balance -,principal payment,from Step 3),5.,重复第,2,步骤。,贷款分期偿付的步骤,Julie Miller,从银行取得了,10,000,美元的贷款，年利率为,12%,，分,5,年偿还。,第一步,:,计算每期偿付金额,PV,0,= R (PVIFA,i%,n,),$10,000,= R (PVIFA,12%,5,),$10,000,= R (3.605),R,=,$10,000,/ 3.605 =,$2,774,偿还贷款举例,年末,偿还金额,利息,本金,贷款余额,0,-,-,-,$10,000,1,$2,774,$1,200,$1,574,8,426,2,2,774,1,011,1,763,6,663,3,2,774,800,1,974,4,689,4,2,774,563,2,211,2,478,5,2,775,297,2,478,0,$13,871,$3,871,$10,000,由于小数计算差异，最后一次偿付稍高于前期偿付。,偿还贷款举例,分期偿还贷款的作用,2.,外部债务,-,外部债务可以用于 一个企业的日常经营活动。,1.,利息费用,-,利息费用可以减少 公司的应税所得。,