solution manual for investment science by david luenberger

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1、Chapter2TheBasicTheoryofInterest1.(Aniceinheritance)Usethe"72rule".Years=1994-1776=218years.(a)i=3.3%.Yearsrequiredforinheritancetodouble=Zf=8:'=!21.8.Timesdoubled=Hi=10times.$1investedin1776isworth210:'=!$1,000today.(b)i=6.6%.Yearsrequiredtodouble=~:'=!10.9.Timesdoubled=~=20times.$1invested

2、in1776isworth220:'=!$1,000,000today.2.(The72rule)Using(1+r)n=2givesnIn(1+r)=In2.UsingIn(1+r):'=!randIn2=0.69.Wehavenr:'=!0.69andthusn:'=!~:'=!PI.UsinginsteadIn(1+r):'=!r-!r2=r(1-!r)wehavenIn(1+r)=In2orequivalentlynr:'=!~.Forr:'=!0.08,wehave(1-r/2)-1:'=!1.042.Therefore,n:'=!!(0.069)(1.042)=~=

3、~rrt3.(Effectiverates)(a)3.04%(b)19.56%(c)19.25%.4.(Newton'smethod)WehaveI(")=-1+"+"2,I,(,,)=1+2","k+1="k-f'I("k)i"kI("k)I'("k)"k+101132/312/31/97/313/21213/210.002272.238100.61803330.618033-2.2x10-62.236070.61803440.61803402.236080.6180345.(Aprize)PV=$4,682,460.12CHAPTER2.mEBASICmEORYOF

4、INTEREST6.(Sunkcost)ThepaymentstreamforapartmentAis1,000,1,000,1,000,1,0001,000,1,000whileforBitis1,900,900,900,900,900,900.AtanyinterestratePVA

5、endontheinterestrate.At1%permonth,thevaluesarePVA=$11,367.62andPVB=$11,230.87,sotheyshouldswitch.7.(Shortcut)Thecashflowwithwaitingis(-l,O,O,x).WeknowthatPV=-1+x/1.13<-1+3/1.12.Hencex/1.1<3whichmeansx<3.3.8.(Copymachines)Assumethatthemaintenancepaymentsoccuratthebeginningofeachyear.InClement

6、alIRRfromAtoB:(Cashflowsin$1000)f(c)=0=-24+6c+6C2+6c3+6c4+10cs,where1c---.l+rUsingNewton'smethod,wegetc=0.894112,r=0.118Thus,IRRA-B=11.8%>10%.IncrementalIRRfromBtoC:(Cashflowsin$1000)f(c)=0=-5+0.4c+0.4c2+0.4c3+0.4c4+2cs,c=~l+rUsingNewton'smethod(co=1.1),wegetc=1.0862106,r=-0.079Thus,IRRB-c=-

7、7.9%AmovefromAtoBisjustifiedonthebasisofIRR.9.(Anappraisal)ConsiderthePVofthetwofollowingpaymentstreams:(a)Changeroofnow,thenevery20years:001PVl=$20,000xi~(1.05)20i=$32,097(b)Changeroofin5yearsandthenevery20years:PVlPV2="i"i:"OST'=$25,149CHAPTER2.m