公司理財計算題匯總

第第頁公司理財計算題匯總

公司理財計算題匯總

金融工程三班奚紅勝

第四章：凈現(xiàn)值：P73

Sincethisbondhasnointerimcouponpayments,itspresentvalueissimplythe

presentvalueofthe$1,000thatwillbereceivedin25years.Note:Aswillbediscussedinthenextchapter,thepresentvalueofthepaymentsassociatedwithabondisthepriceofthatbond.

PV=$1,000/1.125=$92.30PV=$1,500,000/1.0827=$187,780.23

a.Atadiscountrateofzero,thefuturevalueandpresentvaluearealwaysthesame.

Remember,FV=PV(1+r)t.Ifr=0,thentheformulareducestoFV=PV.Therefore,thevaluesoftheoptionsare$10,000and$20,000,respectively.Youshouldchoosethesecondoption.b.Optionone:$10,000/1.1=$9,090.91Optiontwo:$20,000/1.15=$12,418.43Choosethesecondoption.c.Optionone:$10,000/1.2=$8,333.33Optiontwo:$20,000/1.25=$8,037.55Choosethefirstoption.

d.YouareindifferentattheratethatequatesthePVsofthetwoalternatives.

Youknowthatratemustfallbetween10%and20%becausetheoptionyouwouldchoosediffersattheserates.Letrbethediscountratethatmakesyouindifferentbetweentheoptions.

$10,000/(1+r)=$20,000/(1+r)5(1+r)4=$20,000/$10,000=2

1+r=1.18921r=0.18921=18.921%

PV=$5,000,000/1.1210=$1,609,866.18a.$1,000/0.1=$10,000

b.$500/0.1=$5,000isthevalueoneyearfromnowoftheperpetualstream.

Thus,thevalueoftheperpetuityis$5,000/1.1=$4,545.45.

$2,420/0.1=$24,200isthevaluetwoyearsfromnowof

theperpetualstream.Thus,thevalueoftheperpetuityis$24,200/1.12=$20,000.

Theeasiestwaytodothisproblemistousetheannuityfactor.Theannuityfactor

mustbeequalto$12,800/$2,000=6.4;rememberPV=CATr.Theannuityfactorsareintheappendixtothetext.Tousethefactortabletosolvethisproblem,scanacrosstherowlabeled10yearsuntilyoufind6.4.Itisclosetothefactorfor9%,6.4177.Thus,therateyouwillreceiveonthisnoteisslightlymorethan9%.Youcanfindamorepreciseanswerbyinterpolatingbetweennineandtenpercent.