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Chapter # 02

Time Value of Money

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Reasons behind change of Value

Investment Opportunity

Uncertainty

Inflation

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Time Value of Money

Single Payment

nnuity

Mi!e" Stream

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Future Value (problem# P5-6

s part of your financial planning you $ish topurchase a ne$ car e!actly % years from to"ay&The car you $ish to purchase costs

T'&()00000 to"ay an" your research in"icatesthat its price $ill increase *y +, per year overne!t % years&

a- .stimate the price of the car at the en" of % years&

a- .stimate the price of the car if the rate of inflation is ),

for the first 2 years an" +, for the ne!t / years&

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ou can ma'e a "eposit of T'&(00000 into an account paying 1,

annual interest to"ay& o$ much $illyou get at the en" of )0 years3

Future Value

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Present Value (problem# P5-!"

Mr& 4ahman nee"s T'& (000000 for his"aughter5s marriage purpose after + years

from no$& 6hat single investment heshoul" ma'e to"ay earning (2, annualinterest rate to get the re7uire" amountafter + years3

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Problem o$ P5-!%

8im 9ance has *een offere" an investmentthat $ill pay him :%00 three years from

no$& If his opportunity cost is ;,compoun"e" annually $hat value shoul"he place on this opportunity to"ay3

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umber of year (problem# P5-5

Manuel 4ios has recently opene" a fi!e""eposit $here he has "eposite" T'&

(00000 $ith an annual (0, interest rate&9o$ he $ants to 'no$ ho$ long he shoul"'eep the money $ith this account so thathis "eposit amount "ou*les&

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)emi-annual* +uarterly or Monthly

,ompounding &nterest rate ou have purchase" a % years *on" $ith

(0, annual interest rate $ith a price of T'&20000& The issuing company of the *on"has "eci"e" to provi"e interest 7uarterlyan" ma'e the total payment of interest an"principal at the en" of the maturity&

o$ much $ill you get in total from thisinvestment at the en" of the maturity3

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Future Value of nnuity (problem# P5-""

al Thomas a 2%?year college gra"uate $hishes to retire at age+%& To supplement other sources of retirement income he can"eposit T'& 2000 each year into a ta! "eferre" in"ivi"ual retirementarrangement @I4-& The I4 $ill earn a (0, return over the ne!t )0years&

a& If al ma'es en"?of?year T'& 2000 "eposits into the I4 ho$ much$ill he have accumulate" *y the en" of his si!ty?fifth year3

*& If al "eci"es to $ait until age /% to *egin ma'ing annual en"?of?year T'& 2000 "eposits into the I4 ho$ much $ill he haveaccumulate" *y the en" o" his si!ty?fifth year3

c& Using your fin"ings in parts a an" * "iscuss the impact of "elayingma'ing "eposits into the I4 for (0 years @age 2% to age /%- on theamount accumulate" *y the en" of al5s si!ty?fifth year&

"& 4e$or' part a assuming that the "eposit $ill *e ma"e at the*eginning of each year&

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Present Value of nnuity (problem#P5-".

Mr& Tom plans to retire in e!actly 20 years& is goal isto create a fun" that $ill allo$ him to receive T'&20000 at the en" of each year for the ne!t (0 yearsto meet up his son5s e"ucational e!penses& Mr& Tom'no$s that he $ill *e a*le to earn ((, per year"uring the (0 year perio"&

a& o$ large a fun" $ill he nee" $hen he retires in 20 years toprovi"e the (0?year T'& 20000 retirement annuity3

a& o$ much $ill he nee" to"ay as a single amount to provi"e thefun" calculate" in part a if he earns only 1, per year "uringthe 20 years prece"ing retirement3

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c& 9o$ assume that Mr& Tom $ill earn (0,from no$ through the en" of your

retirement& e $ants to ma'e 20 en"Aof?year "eposits into his retirement accountthat $ill fun" the (0?year stream of T'&20000 annual annuity payments& o$

large "o your annual "eposits have to *e3

Present Value of nnuity

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Time in nnuity ((problem# P5-6!

Miss& Salto $ishes to "etermine ho$ long it$ill ta'e to repay a loan $ith initial

procee"s of T'& ()000 $here annual en"?of Ayear installment payments of T'& 2)%0are re7uire"& If she can *orro$ at a (2,annual rate of interest ho$ long $ill it ta'e

for her to repay the loan fully3

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&nterest rate for an nnuity nna $as seriously inBure" in an in"ustrial acci"ent& She sue" the

responsi*le parties an" $as a$ar"e" a Bu"gment of T'& 2000000&To"ay she an" her la$yer are atten"ing a meeting $ith the"efen"ants& The "efen"ants have ma"e an initial offer of T'& (%+000per year for 2% years& nna plans to counteroffer at T'& 2%%000 per

year for ne!t 2% years& oth the offer an" the counter offer have apresent value of T' 2000000 the amount of the Bu"gment& othassume payments at the en" of each year&

a& 6hat interest rate assumption have the "efen"ants use" in theiroffer3

*& 6hat interest rate assumption have nna use" in their offer3

c& nna is $illing to settle for an annuity that carries an interest rateassumption of 1,& 6hat annual payment $oul" *e accepta*le toher3

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ou have "eci"e" to purchase a car *yta'ing a *an' loan $ith annual interest rate

of (2, compoun"e" monthly *asis& ou$ill ta'e the loan for D years an" for thatyou are rea"y to ma'e an installmentpayment of T'& (%000 per month& >in" out

ma!imum ho$ much you can prevail as*an' loan right no$3

)emi-annual* +uarterly or Monthly

,ompounding &nterest rate

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In your employer organiEation you contri*ute inyour provi"ent fun" T'& 2%00 every month& TheorganiEation has promise" you to provi"e ((,

annual interest compoun"e" monthly *asis& ou$or'e" for this organiEation for last % years an"no$ have "eci"e" to s$itch to a ne$ companyafter t$o years from no$& o$ much $ill you *ea*le to claim from your current employer un"erprovi"ent fun"3

)emi-annual* +uarterly or Monthly

,ompounding &nterest rate

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Perpetuity of nnuity

On completion of her intro"uctory finance course Marla$as so please" $ith the amount of useful an"interesting 'no$le"ge she gaine" that she convince"her parents $ho $ere $ealthy alumni of the university

she $as atten"ing to create am en"o$ment& Theen"o$ment is to allo$ three nee"y stu"ents to ta'e theintro"uctory finance course each year in perpetuity& Theguarantee" annual cost of tuition an" *oo's for thecourse is :+00 per stu"ent& The en"o$ment $ill *e

create" *y ma'ing a single payment to the university&The university e!pects to earn e!actly +, per year onthese fun"s& o$ large an initial single payment mustMarla5s parents ma'e to the university to fun" theen"o$ment3

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Mi/ed )tream

@a- arte Systems Inc& a ma'er of electronic e7uipment isconsi"ering selling to a $ell?'no$n har"$are chain the rights tomar'et its home security system& The propose" "eal call for thehar"$are chain to pay arte T'& /0000 T'& 2%000 an" T'&

)0000 at the en" of ( 2 an" / year respectively&If arte applies a re7uire" rate of return of (2, to them $hatis the present value of this series of payment3

@*- In the a*ove case say arte $ill receive T'& /0000 an" T'&

2%000 in ( F 2 year respectively an" then from year /?% $illreceive T'& (%000 at the en" of each year& =astly it $ill receiveT'& (0000 at the en" of +th year& 9o$ calculate the presentvalue of the cash flo$ stream&

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0oan morti1ation )chedule

8ohn Messino *orro$e" T'&(%0000 at a(), annual rate of interest to *e repai"

over % years& The loan is amortiEe" intofive e7ual annual en" of year payments&

@a- Calculate the annual en"?of?yearpayment&

@*- Prepare a loan amortiEation sche"ule&

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Than' ou