Week 3 T - yes PDF

Preview

Summary

yes...

Description

FIN222Week3_TCH4:P3,7,8,10,14CH5:P2,12,23(8Questions) CHAPTER4TIMEVALUEOFMONEY:VALUINGCASHFLOWSTREAMS 3  

Youplantodeposit$500inabankaccountnowand$300attheendofoneyear. Iftheaccountearns3%interestperyear,whatwillthebalancebeintheaccountright afteryoumaketheseconddeposit?



 

0   500

 

1  

  300

 FV1=500(1.03)+300=$815

7  

Youwanttoendowascholarshipthatwillpay$10000peryearforever,startingone yearfromnow. Iftheschool’sendowmentdiscountrateis7%,whatamountmustyoudonatetoendow thescholarship? 0 1 2 …                  10,000 10,000 …



      PV=10,000/0.07=$142,857.14         

1

8.HowwouldyouranswertoProblem7changeifyouendowitnow,butitmakesthefirst awardtoastudent10yearsfromtoday? Thisisadeferredperpetuity.

 

0  

1  

 



 

0

910 …           

11…    

0

10,000..

…

10,000

Step1:Thevalueinyear9(=PV9)is10,000/0.07=$142,857.14.  142, 857.14  $77, 704.82 . Step2:Thevaluetoday(=PV0)is 1.079 

Becauseyourendowmentwillhave10yearstoearninterestbeforemakingitsfirstpayment,you canendowthescholarshipformuchless.



Thevalueofyourendowmentmustreach$142,857.14theyearbeforeitstarts(innineyears).



Ifyoudonate$77,704.82today,itwillgrowat7%interestfornineyears,justreaching$142,857.14, oneyearbeforethefirstpayment.

 10.Whatisthepresentvalueof$1000paidattheendofeachofthenext100yearsiftheinterest rateis7%peryear?  

0   

1 2 3                1000 1000 1000 

PV 

PV 

C r

  

  



  

100   1000

1   1  (1  r )n    

1000  1   14, 269.25  1   0.07  1.07100 

    Page2of8

14.  

Youfigurethatthetotalcostofuniversitywillbe$100000peryear18yearsfromtoday. Ifyourdiscountrateis8%compoundedannually,whatisthepresentvaluetodayofthree yearsofuniversitycostsstarting18yearsfromtoday? Thisisadeferredannuity. 0

1

17

18

19

20

0

0

100,000

100,000

100,000

Step1:Thevalueoftheannuityinyear17(=PV17), PV 

C r

 1  100, 000  1  1  (1  r ) n   0 .08 1  (1 .08 )3   $257,709 .70    

Step2:Togetitsvaluetoday(=PV0),weneedtodiscountthatlump sumamountbacktothepresent: 257,709.70

1.08 

17

 $69,650.93

CHAPTER5:INTERESTRATES 2.    

YouareconsideringtwowaysoffinancinganEasterholiday. Youcouldputitonyourcreditcard,at15%APR,compoundedmonthly,orborrowthe moneyfromyourparents,whowantan8%interestpaymenteverysixmonths. Whichisthelowerrate?

EAR  󰇛1  

CreditCard EAR  󰇛1 



  󰇜  1 

0.15  󰇜  1  0.1608  16.08% 12

Parents EAR  󰇛1  0.08󰇜  1  0.1664  16.64%

 Youshoulduseyourcreditcardbecausetheeffectiveannualrate(EAR)islower.   Page3of8

12.   

 Youhavejusttakenouta$20000carloanwitha6%APR,compoundedmonthly. PV=20,000,r=0.06/12=0.005 Theloanisforfiveyears.n=5*12=60 Whenyoumakeyourfirstpaymentinonemonth,howmuchofthepaymentwillgo towardtheprincipaloftheloanandhowmuchwillgotowardinterest?

C=?(Let’ssolveforit!)

PV  20,000 

C 

C r

 1  1    (1  r )n   

1 C   1  60  0.005  1.005 

20,000  0.005 1   1  1.00560   

  $386.66



The interestinthe firstmonth willbe the $20,000borrowed multipliedby0.5% permonth: (20000)(0.005)=$100.



So,ofyourfirstpaymentof$386.66,$100willgotowardinterestand$286.66willgotoward principal.



Typically, early in loans, much of the payment goes toward interest, but as the principal decreases and the payments stay the same, more and more of each payment goes toward principal.

$Opening balance

$C

$Principal

$Interest

$Closingbalance





=C‐Interest

=Openingbalance*0.005

=Openingbalance‐ Principal

20,000

386.66

286.66

100

19713.34

19713.34

386.66

288.09

98.57

19425.25

      Page4of8

23    

 Themortgageonyourhouseisfiveyearsold. Itrequiredmonthlypaymentsof$1402,hadanoriginaltermof30yearsandhadan interestrateof10%(APR). Intheinterveningfiveyears,interestrateshavefallenandsoyouhavedecidedto refinance—thatis,youwillrollovertheoutstandingbalanceintoanewmortgage. Thenewmortgagehasa30‐yearterm,requiresmonthlypayments,andhasaninterestrate of6.625%(APR).

a.

Whatmonthlyrepaymentswillberequiredwiththenewloan?  OLDMORTGAGE C=1402,r=0.1/12=0.008333,n=25yearsleft*12=300

‐5   

0       

…   1402…

   

25years

 



    1402 

TodeterminetheoutstandingbalanceasofTODAY(0),

PV  PV  ‐5  

0          

1402 0.008333

C r

  1 1  (1  r )n    

1   1  1.008333 300   $154, 286.22   

…   1402… 

    

25years  

            Page5of8

  1402 



NEWMORTGAGE C=?,r=0.06625/12=0.005521,n=30yearsleft*12=360,PV=154,286.22  0        154,286.22 C  

PV 

154, 286.22  C 

…   C… 

C r

 30years      C  

 1  1    (1  r )n   

C 0.005521

1   1  1.005521 360    

154,286.22 * 0.005521  $987.91 1   1  1.005521360   

b. Ifyoustillwanttopayoffthemortgage in25 years, what monthlypaymentshouldyou makeafteryourefinance? NEWMORTGAGEwiththenewn C=?,r=0.06625/12=0.005521,PV=154,286.22,n=25yearsleft*12=300  0        154,286.22 

C…



C









PV  154, 286.22 

C 

  

 

C

C r

 25years    

…

1   1   (1  r )n   

C 0.005521

1   1  1.005521300    

154, 286.22 * 0.005521  $1053.83  1    1  1.005521300        Page6of8

c. Supposeyouarewillingtocontinuemakingmonthlypaymentsof$1402.Howlongwillit takeyoutopayoffthemortgageafterrefinancing? NEWMORTGAGEwithC=1402 C=1402,r=0.06625/12=0.005521,PV=154,286.22,n=?

 0  …n=?            154,286.22 1402 1402…     

PV 

C r



 

1   1   (1  r )n   

 1402  1 1    $154, 286.22  0.005521  1.005521n   

Naturallogarithm(Ln(X))isthelogarithmtothebaseeofanumber:Eg.Ln(2)(easily solvablebyacalculator!),Ln(2)=0.69314718...... Naturallogarithmpowerrule:Ln(XY)=Y*Ln(X):Eg.Ln(28)=8*Ln2

Usingtheabovelogpowerrule,pleasesolveforn.

1 0.005521    1  1.005521n   $154, 286.22 * 1402   1  0.607571 1 1.005521n 1 1  0.607571  1.005521n 1 0.392429  1.005521n 1 1.005521n  0.392429 n 1.005521  2.54823  n Ln1.005521  Ln 2.54823 n * Ln1.005521  Ln 2.54823 Ln 2.54823 n  169.8929 Ln1.005521 Itwilltakeyouabout170months. 170months/12=14.1666667years=14years2months Page7of8

d. Supposeyouarewillingtocontinuemakingmonthlypaymentsof$1402,andwanttopay off the mortgage in 25 years. How much additional cash can you borrow today as part of the refinancing?  C=1402,r=0.06625/12=0.005521,n=25yearsleft*12=300,PV=? Theamountofadditionalborrowing=PVcomputed–$154,286.22  0        PV=?

  

25years    

1402…  



1402

 

1402

PV 

…

C r

1   1   (1  r )n   



PV 

1402  1  1     $205,259.23  0.005521  1.005521300 

Henceyoucanborrowanadditional$205,259.23–$154,286.22=$50,973.01

       

Page8of8...