326ch4bdh part 1 v1.4

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GT 326 Ch. 4: Time Value of Money (bdh) Part 1

1

Time Value of Money (TVM)

Learning Objectives (Ch 4 Parts 1 !)"

!"lain the TVM #on#e"tCom"ute the $V% PV% &'& and of a in*le Ca+h $lo, ituationCom"ute the $V% PV% &'&% PMT and of an -nnuityCom"ute the PV of a erie+ of ne/en Ca+h $lo,+Perform -ll of the -bo/e 0ith 'therthanannual Payment+Com"oundin*Perform -ll of the -bo/e ,ith $ra#tional (noninte*er) Time Period+Perform -ll of the -bo/e in Ca+e+ 0here Com"oundin* Period+ Per ear

-rent 5ual To Payment+ Per ear-""ly TVM Com"utation+ To Common u+ine++ and Per+onal $inan#e

7e#i+ion+ u#h a+ orro,in* Money% Plannin* for &etirement% and 8n/e+tin*!"lain and +e the $undamental Valuation Con#e"t 9 Pro#e++!"lain ffe#ti/e -nnual &ate+e ffe#ti/e -nnual &ate To Mae a orro,in* or 8n/e+tin* 7e#i+ion;earn

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Time Value of Money0hen money i+ +ome ho, in/e+ted (and not >u+t "la#ed under a mattre++ or

in a +afe)% the amount of money *ro,+-lthou*h money lo+e+ /alue o/er time due to inflation% the amount of mone

in an a##ount that earn+ a "o+iti/e &'& ,ill be *reater in the future than ,hat

it i+ todayThu+ the money in the a##ount ha+ different /alue+ at different "oint+ in timThi+ i+ ,hat the term ?Time Value of Money@ refer+ toThe &'& +hould #om"en+ate for o""ortunity #o+t% inflation and ri+

the in#rea+in* amount of money o/er time shouldmore than mae u"

for the /alue lo+t due to inflation and o""ortunity #o+t+

Time Lines # Cash $lo% &iagrams$or the re+t of thi+ #our+e% ,e ,ill deal ,ith #a+h flo,+ that o##ur o/er +ome

"eriod of time8t i+ e/er +o hel"ful to be able to de"i#t the+e #a+h flo,+ *ra"hi#ally0e ,ill u+e Time ;ine+ (al+o #alled Ca+h $lo, 7ia*ram+) to do thi+ be#au+e

they areA.a mean+ to /i+ually de"i#t #a+h flo,+% both "o+iti/e and ne*ati/e

(in#omin* and out*oin*) +o ,e *et a #learer idea of ,hatB+ ha""enin*a mean+ to in/entory ,hat ,e no, and ,hat ,e donBt no, about a

"roblema tool to hel" u+ de#ide on ,hat ,e need to find 9 do in order to +ol/e

the "roblem

our ba+i# Time ;ine (,ithout #a+h flo,+) loo+ lie thi+:

' 1 !

V 1.2 une =1D

Today The $uture

ote"the time unit+ #an be ,hat e/er they need to beE day+% ,ee+%

month+% year+% et#.

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3

$uture Value"

$uture Value ($V) (a noun):The amount to ,hi#h an in/e+tment *ro,+ ,hen it earn+ a

"o+iti/e rate of return.

Com"oundin* (a /erb):The "ro#e++ of *oin* from todays values(?"re+ent /alue+@) to

/alue+ at +omefuturetime (?future /alue+@).-""lyin* the effe#t+ of TVMThe "ro#e++ of determinin* the $uture Value of a #a+h flo, or

+erie+ of #a+h flo,+.Con/ertin* "re+ent"re/iou+"rior /alue+ to future /alue+

The 8ntere+t &ate&ate of &eturn i+ the #on/er+ion fa#tor:

!am"le (im"le Ca+e): ou de"o+it F1DD in a +a/in*+ a##ount that

"ay+ 6 "er year (1 #om"oundin* "eriod "er year). 0hat amount omoney ,ould you ha/e in thi+ a##ount after 1 yearH (0hat i+ the

future /alue of F1DD I 6 after 1 yearH)8n thi+ e!am"le% there i+ only one "eriod (1 year)E therefore n J 18ntere+t that i+ "aidout o/er only one intere+t earnin* "eriod i+

#alled +im"le intere+t

&ra% a cash flo% *iagram (a time line %ith cash flo%s a**e*):

' 1

$V + ,

PV + -1''r + ./

' 1

$V + ,PV + -1''r + ./

or thi+A..

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4

0am2le (continue*):

The future /alue in#lude+ the "rin#i"le and the intere+t

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olution Method 2: +e your T8 - 88 Plu+ finan#ial #al#ulator1) Clear your #al#ulator: 2nd% N8TO2) Clear the TVM memorie+: 2nd% C;& TVMO3) et "ayment+ "er year to 1: 2nd% P% 1% T&% CCO4) nter "arameter+:

nter number of "eriod+ 1% O

nter intere+t rate 6% 8O (the #al#ulator a++ume+ youmean it a+ 6)

nter PV 1DD% PVO $ind $V CPT% $VO and /oila $V J () -1'.5'' 6hy i

$V negative,

7m2ortant TVM Conce2t"F1DD today i+ e8uivalentto F1D6 one year from no, if the #urrent

in/e+tment o""ortunity i+ 6and

F1D6 one year from no, (I 6 &'&) i+ e8uivalentto F1DD today

Com2oun* 7nterest

0hat ha""en+ ,hen money i+ left in a ban a##ount for morethan one intere+t "ayin* time "eriod (for more than 1#om"oundin* "eriod)H

!am"le: ou de"o+it F1DD in a +a/in*+ a##ount that "ay+ 6 "eryear. 0hat amount of money ,ould you ha/e in thi+ a##ountafter 2 year+H (0hat i+ the future /alue of F1DD I 6 after 2

year+H) (-bbre/iation notation: $V1DD%6%2yr)7ra, a #a+h flo, dia*ram:

' 1 !

$V + ,

PV + -1''r + ./

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Com2oun* 7nterest (continue*)

!am"le (#ontinued)The a##ount #olle#t+ intere+t after one year (F6 a+ "er "re/iou+e!am"le) ,hi#h re+ult+ in a balan#e of F1D6 ($V1J F1D6)

7urin* the +e#ond year% intere+t i+ "aid on the one year balan#e(i.e. the F1D6 earn+ 6 intere+t)$V2J F1DD(1 K D.D6)(1 K D.D6)

$V1$V2J F1DD(1 K D.D6)

2J -11!5.

0hen an in/e+tment i+ held for more than one intere+t "ayin* "eriod%the intere+t i+ ?#om"ounded@ (intere+t i+ "aid on "re/iou+ly earnedintere+t a+ ,ell a+ on the "rin#i"le)a#h intere+t "ayin* "eriod i+ #alled a ?#om"oundin* "eriod@8n thi+ #onte!t% ?r@ i+ referred to a+ the ?#om"ound rate@

olution Method 2: +e the finan#ial fun#tion+ on your #al#ulator1) Clear TVM Memory: 2nd% C;-& TVMO2) eten+ure "ayment+ "er year J 1: 2nd% P% 1% T&% CC3) nter "arameter+:

nter number of "eriod+ 2% Onter intere+t rate 6% 8O (#al#ulator inter"ret+ it a+ 6)nter PV (1DD) 1DD% PVO$ind $V CPT% $VO and /oila $V J () -11!5.

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!am"le (#ontinued)

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!am"le: 0hat i+ the $V of FLDDD I 6 after L year+H ($ind

$VLDDD%6%L)

PV + :;'''

r + ./

$V + ,

' 1 ! 4 :

$ormula olution:

Cal#ulator $inan#ial $un#tion olution:

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S

-:

-4

-

-!

-1

'

FutureValueof$1

! 4 . < 1'

Number of Periods

r = 15%

r= 10%

r = 5%

r = 0%

Future Value as a Function of

Time and Rate of Return

=ey Points"The greater the interest rate#rate of return; the bigger the

future valueThe longer the investment is hel*; the bigger the future value

6hich factor (r or time) has the greatest influence on $V,

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1D

Present Value"

Money that i+ e!"e#ted to be re#ei/ed or "aid in the future doe+ no

ha/e the +ame /alue a+ todayB+ money be#au+e of TVM

8n order to determined ,hat future money i+ ,orth in term+ oftodayB+ dollar+% ,e ha/e to re/er+e the effe#t+ of TVME thi+ i+ referred

to a+ discounting

Pre+ent Value (PV) (a noun): the /alue today (the /alue in today+dollar+) of a future #a+h flo, or +erie+ of #a+h flo,+.7i+#ountin* (a /erb):

The "ro#e++ of *oin* fromfuture valuestopresent values.(The ?re/er+e@ of #om"oundin*.)&e/er+in* the effe#t of TVMThe "ro#e++ of findin* the Pre+ent Value of a future #a+h flo, o+erie+ of #a+h flo,+.Con/ertin* future dollar+ into ?todayB+@ dollar+

3asic formula for fin*ing Present Value: PV J $V (1 K r)n

The 1(1 K r)n"ortion of the formula i+ #alled the ?Pre+ent Value8ntere+t $a#tor@ (PV8$r%n) and #an be found on a PV8$ table

1(1 K r)ni+ al+o #alled the ?di+#ountin*@ fa#tor0hen ?r@ i+ u+ed to di+#ount% it i+ referred to a+ the ?di+#ount rate@

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Present Value"!am"le (im"le Ca+e): 0hat i+ the Pre+ent Value of F2DD di+#ounted for 1year I 4 "er yearH (-bbre/iation notation: PV2DD%4%1) 8n other ,ord+% ho,

mu#h ,ould ,e ha/e to de"o+it today into an a##ount that "ay+ 4 "er year inorder to ha/e F2DD one year from no,H

7ra, a #a+h flo, dia*ram:

' 1

$V + -!''

PV + ,

r + 4/

olution Method 1: +e the $ormulaPV J $V (1 K r)n

J F2DD (1 K D.D4)1

J F2DD (1.D4)1

J F2DD 1.D4 J -1>!5'

olution Method 2: +e your finan#ial #al#ulator

1) Clear TVM Memory: 2nd% C;-& TVMO

2) eten+ure "ayment+ "er year J 1: 2nd% P% 1% T&% CCO

3) nter "arameter+:nter number of "eriod+ 1% Onter intere+t rate 4% 8Onter $V 2DD% $VO$ind PV CPT% PVO and /oila PV J(?) -1>!5'

6hy *i* %e use 4/ to *iscount the future cash flo%,

@ns%er"8t i+ the +"e#ified #om"ound rate8t i+ the rate at ,hi#h ,e e!"e#t our in/e+tment to *ro, to a#hie/e

a future /aluein#e di+#ountin* i+ the o""o+ite of #om"oundin*% ,e mu+t

di+#ount at that e!a#t +ame rate in order to find the "re+ent /alue

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!am"le: 0hatB+ the PV of FLDDD di+#ounted for 3 year+ I12H

($ind PVLDDD%12%3)

A -4;4.45!> -:;'''5''

$V

+ -;::' (1 9 '51!) + -;>A (1 9 '51!) + -4;4.45!> (1 9 '51!)

' 1 !

$V + -:'''

r + 1!/

PV + ,

$ormula olution:


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Very 7m2ortant $inancial Conce2ts"

Be?%or* the eam2le from 25 1!" ou are #on+iderin* "ur#ha+in* +e#urity that "romi+e+ to "ay FL%DDD three year+ from no,. 0hat i+thi+ +e#urity theoreti#ally ,orth today (orA.. ,hat i+ it+ fair maret/alueH) if your be+t in/e+tment o""ortunity yield+ 12H

@ns%er" -;::'

$inancial Valaution Princi2le" The 2resent value of any financialasset *e2en*s on usable; after?ta cash flo% it is e2ecte* to2ro*uce in the future

ut% due to the Time Value of Money% ,e ha/e to di+#ount tho+ee!"e#ted future #a+h flo,+ in order to #on/ert them into todayB+dollar+.

Thus" The o/erridin*% all im"ortant% ne/ertobefor*otten $inanciaValuation Process is" The theoretical value (fair maret value orno?arbitrageD 2rice) of any financial asset is *etermine* by*iscounting all future e2ecte* cash flo%s to the 2resent (i5e5 fin*the PV E t + ' of all cash flo%s) an* a**ing them u2

Thi+ i+ the "re+ent /alue of the a++et.

Thi+ i+ ,hat the a++et i+ theoreti#ally ,orth today% ,ithout "rofit+%fee+ or other tran+a#tion #o+t+Thi+ i+ the fair maret /aluenoarbitra*e "ri#e of the a++et today%,ithout "rofit+% fee+ or other tran+a#tion #o+t+

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Fse the $inancial Valuation Process to Mae a &ecision

!am"le: Con+ider t,o different in/e+tment o"tion+:'"tion -: $or an initial #o+t of FS%DDD you re#ei/e F12%6DD at the enof four year+.'"tion : $or an initial in/e+tment of F2D%DDD you re#ei/e F26%DDDat the end of four year+our be+t in/e+tment o""ortunity yield+ 6 ".a. ( "er annum).0hi#h i+ the be+t in/e+tment o"tionH

te" 1: $ind the "re+ent /alue of the future #a+h flo,+ of both o"tion+'"tion -: J4% 8J6% $VJ126DD% CPT PV: PV J ->;>

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Other =ey Points"Com"oundin* mean+ ,ere main* number+ bi**erE ,ere *ro,in*itE ,ere *oin* to the ri*ht on the timeline$V+ are bi**er number+ than PV+E #he# your an+,er7i+#ountin* mean+ ,ere main* the number+ +mallerE ,ere

+hrinin* itE ,ere *oin* to the left on the time linePV+ are +maller number+ than $V+E #he# your an+,er

' 17i+#ountin*

Com"oundin*

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Holving for 7nterest Bate (or 7BB)

!am"le: our broer "ro"o+e+ an in/e+tment +#heme that ,ill "ay

you F1DDD one year from no, for an initial #o+t of FSDD today. 0ha

i+ the annual return on thi+ in/e+tmentH

7ra, a #a+h flo, dia*ram

'

$V + -1'''

r + ,/

PV + ->''

ol/e for r u+in* the PV (or $V) formula: $VnJ PV(1 K r)

n

F1DDD J FSDD(1 K r)1

F1DDDFSDD J (1 K r)1

(1.1111)1J 1 K r

r J 1.1111 1

r J D.1111 J 1151111/"er year


1) Clear your #al#ulator: 2nd% C;-& TVMO


3) nter "arameter+:nter number of "eriod+ 1% Onter PV SDD% K#?% PVOnter $V 1DDD% $VO$ind 8 CPT% 8O and /oila 8 J 1151111/"er year

olution Method 3:

(e, 'ld) 'ld J (1DDD SDD) SDD ! 1DD J 1151111/

1

ote" One of the t%o cash in2uts

must be negative

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1Q


you F1DDD t,o year+ from no, for an initial #o+t of FSDD today.

0hat i+ the annual return on thi+ in/e+tmentH

'

$V + -1'''

r + ,/

PV + ->''

ol/e for r u+in* the PV or $V formula:

$VnJ PV(1 K r)n

F1DDD J FSDD(1 K r)2

F1DDDFSDD J (1 K r)2

(1.1111)12J 1 K r

r J 1.DL4DS3 1

r J D.DL4S3 J :54'>/"er year

Holving for 7nterest Bate (or 7BB)


This is the return over ! years; not an annual rate

7m2ortant Point" &ate+ of &eturn are al,ay+ e!"re++ed on an annua

ba+i+. 6hy,

6hy canIt you use (e%?Ol*) # Ol*,

!1


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1R


0hy donBt you >u+t multi"ly the annual rate of return (L.4DS3) by

2 (to "rodu#e 1D.R1R6) H


you F1DDD t,o year+ from no, for an initial #o+t of FSDD today. 0ha

i+ the totalreturn on thi+ in/e+tmentH

!am"le: ' years

Cal#ulator $inan#ial $un#tion olution:1) Clear your #al#ulator: 2nd% C;-& TVMO


3) nter "arameter+:nter 8 6% 8Onter PV 1DDD% K% PVO

nter $V 2DDD% $VO$ind % CPT% O and /oila J 115>'

' n + ,

$V + -!'''

PV + -1'''

r+ ./

ote" One of the t%o cash in2uts

must be negative

olving for the number of 2erio*s (n)

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1S

@nnuities

7efinition: a +erie+ of e5ual "ayment+ made at fi!ed inter/al+ for a

+"e#ified number of "eriod+

!am"le+"

ote" The "ayment+ o##ur at the end of ea#h "eriod. The+e are e!am"le+ of

an -nnuity in -rrear+% al+o #alled and 'rdinary -nnuity

' 1 !

Pmt Pmt Pmt

Trust $un*

0n*o%ment (PV)

' 1 !

Pmt Pmt Pmt0n*o%ment (PV)

Pmt Pmt Pmt

Princi2le (PV)

Loan

' 1 !

Pmt Pmt PmtPrinci2le (PV)

' 1 !

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2D

!am"le ($uture Value): 8f you de"o+ited F3DD a year (at the end ofthe year) into a +a/in*+ a##ount that "ay+ L -P&% ,hat ,ould thea##ount balan#e be after 3 year+H (-bbre/iation notation: $V-F3DD%L%3)

' 1 !

'' '' ''

r+ :/

$V + ,

$ormula olution:Pro#e++: Com"ound all of the #a+h flo,+ to t J 3 and add them u"$V J C$

1

(1 K r)2K C$2

(1 K r)1K C$3

J 3DD(1 K D.DL)2K 3DD(1 K D.DL)1K 3DD J 3DD(1.DL)2K 3DD(1.DL)1K 3DD

J 3DD(1.1D2L) K 3DD(1.DL) K 3DDJ 33D.QLDD K 31L.DDDD K 3DD

J ->4:5A:

6e can fin* the PV an* $V of annuitiesThereB+ an added "arameter% the ?"ayment@ (PMT):

annuitie+ in/ol/e "eriodi# "ayment+ in addition to im"lied#om"ound intere+t "ayment+The+e additional "ayment+ o##ur throu*hout the life of the

annuity at +"e#ified "eriod+all of the+e additional "ayment+ are the +ame

C$1(1 9 r)!

C$!(1 9 r)1

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!am"le: (#ontinued) ): 8f you de"o+ited F3DD a year (at the end ofthe year) into a +a/in*+ a##ount that "ay+ L -P&% ,hat ,ould thea##ount balan#e be after 3 year+H (-bbre/iation notation: $V-F3DD%L%3

ote"there are L "arameter+ but you only #are about 4 of them (1 ofthem i+ irrele/ant)E +o if you no, 3% you #an find the 4 th

6hich 2arameter is irrelevant in this eam2le,

Cal#ulator $inan#ial $un#tion olution:1) Clear your #al#ulator: 2nd% C;-& TVMO2) eten+ure "ayment+ "er year J 13) nter "arameter+:

nter 3% Onter 8& L% 8Onter Pmt 3DD% PMTO

$ind $V CPT% $VO and /oila $V J() ->4:5A:

' 1 !

'' '' ''

r+ :/

$V + ,

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!am"le ($uture Value): 8f you de"o+ited FLDD a year (at the end ofthe year) into a +a/in*+ a##ount that "ay+ S -P&% ,hat ,ould thea##ount balan#e be after 2 year+H (-bbre/iation notation: $V-FLDD%S%2)

' 1 !

:'' :''

$V + ,

$ormula olution:


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3LD Time Value of Money Part 1

24

&etirement !am"le ($uture Value): 8f you de"o+ited F6DDD a year(at the end of the year) into a +a/in*+ a##ount that "ay+ S ".a.%

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2L

!am"le (Present Value): ou re#ently ,on a #ourt +ettlement that"romi+e+ to "ay FL%DDD a year (at the end of the year) for 3 year+.0hat i+ the e5ui/alent "re+ent /alue of thi+ a,ardH our o""ortunit#o+t of #a"ital i+ L.DDDD "er year. (-bbre/iation notation:(PV-FLDDD%L%3) -++ume that the number of "ayment+ "er year and the

number of #om"oundin* "eriod+ "er year are the +ame.

' 1 !

:''' :''' :'''

r + :/

PV + ,

$ormula olution:

Pro#e++: 7i+#ount all of the #a+h flo,+ ba# to t J D and add them u

PV J C$1(1 K r)1K C$2(1 K r)

2K C$3(1 K r)3

J LDDD(1 K D.DL)1K LDDD(1 K D.DL)2K LDDD(1 K D.DL)3

J LDDD(1.DL)1K LDDD(1.DL)2K LDDD(1.DL)3J LDDD1.DL K LDDD1.1D2L K LDDD1.1LQ6

J 4%Q61.SD4R K 4%L3L.14Q4 K 4%31S.2R13

J -1;.1.5!4

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@nnuities (continue*)




3) nter "arameter+:nter 3% Onter 8 L% 8Onter PMT LDDD% PMTO$ind PVCPT% PVO and /oila PV J () -1;.1.5!4

6hy *i* %e use :/ to *iscount the future cash flo%s,

@ns%er" 7t is the O22ortunity Cost of Ca2ital

Thi+ i+ the rate ,e e!"e#t our in/e+t to *ro, (#om"ound)The o""o+ite of #om"oundin* i+ di+#ountin*0e mu+t u+e the +ame rate for the di+#ount rate to find PV

7m2ortant @ssum2tion" The number of "ayment+ "er year

#orre+"ond+ to the number of #om"oundin* "eriod+ "er year. nle++

other,i+e +"e#ified% thi+ i+ u+ually the #a+e. ;ater ,e ,ill di+#u++

,hat to do ,hen thi+ i+ not the #a+e.

@nother 7m2ortant @ssum2tion" Payment+ are rein/e+ted at thedi+#ount rate. nle++ other,i+e +"e#ified% thi+ i+ u+ually the #a+e.

;ater ,e ,ill di+#u++ ,hat to do ,hen thi+ i+ not the #a+e.

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-nnuity 7ue

The "re/iou+ e!am"le+ ,ere ?ordinary@ annuitie+ or ?annuity in

arrear+@E all "ayment+ o##urred at the end of the "eriod (?deferred

"ayment+@)-n annuity in ,hi#h "ayment+ o##ur at the be*innin* of a "eriod i+

#all an ?annuity due@ 0am2les,

!am"le: our #om"any i+ #on+iderin* lea+in* a ,arehou+e for 3year+ I F3%DDD "er year% "aid at the be*innin* of ea#h year. 0hat i

the PV of the lea+e if the a""ro"riate o""ortunity #o+t i+ 6H

7ra, a #a+h flo, dia*ram

' 1 !

''' ''''''

i + ./

PV + ,

$ormula olution:

Pro#e++: 7i+#ount all of the #a+h flo,+ ba# to t J D and add them u"

PV J C$1K C$2(1 K r)1K C$3(1 K r)

2

J 3DDD K 3DDD(1 K D.D6)1K 3DDD(1 K D.D6)2

J 3DDD K 3DDD(1.D6)1K 3DDD(1.D6)2

J 3DDD K 3DDD1.D6 K 3DDD1.1236

J 3DDD K 2%R3D.1RRQ K 2%66S.SRS3

J -

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2R


-nnuity 7ue (#ontinued)

!am"le (#ontinued)



2) eten+ure "ayment+ "er year J 1:

3) et "ayment timin* to beginningof year: 2nd% G% 2nd% T%

CCO (ote: ?G@ shoul*a""ear in your #al#ulator di+"lay)

4) nter "arameter+:nter 3% Onter 8 6% 8Onter Pmt 3DDD% PMTO$ind PV CPT% PVO and /oila PV J -

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2S

$ormula olution:

Pro#e++: Com"ound all of the #a+h flo,+ to t J 3 and add them u"

$V J C$1(1 K r)3K C$2(1 K r)

2K C$3 (1 K r)1

J 3DDD(1 K D.D6)3K 3DDD(1 K D.D6)2K 3DDD(1 K D.D6)1

J 3DDD(1.D6)3K 3DDD(1.D6)2K 3DDD(1.D6)1

J 3DDD(1.1S1D) K 3DDD(1.1236) K 3DDD(1.D6)

J 3LQ3.DDDD K 3%3QD.RDDD K 3%1RD.DDD J -1';1!5

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3D


$in*ing the Payment of an @nnuity (Or*inary or &ue)

!am"le: ou "lan to +tart a +a/in*+ fund to "ay for your #hildB+

#olle*e edu#ation. ou e+timate that you ,ill need F1LD% 1L year+

from no,. our finan#ial ad/i+orbroer +ay+ he #an earn your money

Q.L. ou "lan to mae an annual #ontribution to thi+ fund at the end

of ea#h year.

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31


$in*ing the 7nterest Bate of an @nnuity (Or*inary or &ue)

umeri#al olution+e+ the e5uation+ ,e already #o/ered&e5uire+ trial 9 error% iterati/e +olution te#hni5ue+ouBre on your o,n

+in* our Cal#ulator:

!am"le: ou are #on+iderin* either buyin* a #om"uter or lea+in* one

I FQ2L "er year ("aid at the be*innin* of the year) for 3 year+. The

#urrent /alue of the #om"uter i+ F2%DDD. ou donBt ha/e that mu#h

#a+h but you #an *et a loan for R. 0hi#h ,ould #o+t le++% buyin* or

ea+in*H -++ume the #om"uter i+ ,orth FD at the end of 3 year+ (D

+al/a*e /alue). (

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32


$in*ing the 7nterest Bate of an @nnuity (Or*inary or &ue)

!am"le (#ontinued)

Cal#ulator $inan#ial $un#tion olution:1) Clear your #al#ulator: 2nd% C;-& TVMO2) eten+ure "ayment+ "er year J 13) et "ayment timin* to be*innin* of year (?G@ shoul*a""ear ithe di+"lay)3) nter "arameter+:

nter 3% Onter PV 2DDD% K% PVOnter PMT Q2L% PMTO$ind 8 CPT% 8O and /oila 8 J >5'!'./

@ns%er"in#e you #an borro, money I R% "ur#ha+in* the#om"uter i+ the better o"tion

!am"le: (#ontinued) 0hat ,ill your "ayment+ be if you borro,money to buy the #om"uterH (ote: loan+ are u+ually ordinaryannuitie+)

'1

! r +

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33

ut the annual 2ayment for borro%ing is greater than that for

asing5 Jo% can borro%ing (in this case) be better than leasing,

es2onse" Convert the lease from an annuity *ue to an or*inary

nnuity an* solve for the annual 2ayment using >5'!'./ @PBhen com2are to the loan 2ayments

al#ulator $inan#ial $un#tion olution:1) Clear your #al#ulator: 2nd% C;-& TVMO2) eten+ure "ayment+ "er year J 1

3) et "ayment timin* to end of year (?G@ shoul* not a""ear inhe di+"lay)3) nter "arameter+:nter 3% Onter PV 2DDD% K% PVOnter 8 R% 8O$ind PMT CPT% PMTO and /oila PMT J -AA.5'A

!am"le: (#ontinued)

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34

!am"le:

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GT 326 Ch L: 8ntere+t &ate+ (bdh) (The Co+t of Money)

The O22ortunity Cost of Ca2ital (from Ch L)

The be+t a/ailable e!"e#ted return offered in the maret on an

in/e+tment of #om"arable ri+ and len*th (term)The return the in/e+tor for*oe+ on an alternati/e in/e+tment of

e5ui/alent ri+ and term ,hen the in/e+tor tae+ on the alternati/e

in/e+tment

Point"one al,ay+ u+e+ hi+her '""ortunity Co+t of Ca"ital a+ the

di+#ount#om"ound rate ,hen +ol/in* TVM "roblem+% if the rate i+

not already *i/en

326ch4bdh part 1 v1.4

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