fin222 autumn2015 lectures lecture 3
TRANSCRIPT
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FIN922 CorporateFinance
Dr. Kashif SaleemE-mail: [email protected]
Oce: Room 105 1s! "oor
Consultation Hours for Autumn 2015Su#da$ 1%:00-1&:00 '(hrs)
*uesda$ 1%:+0 , 15:+0 '1hr) 1:+0-
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Discounted CashFlow Valuation
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Lecture Outline
Multiple Cash Flos! Futurean" #resent $alues
Multiple %&ual Cash Flos!Annuities an" #erpetuities
Comparin' (ates! the %)ect
of Compoun"in' Loan *+pes Loan Amorti,ation
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-in'le Cash Flos
Today 1 2 3 4 5
FVPV
Today 1 2 3 4 5
FVPVCompounding
Discounting
In the pre.ious lecture/ e use"sin'le cash os an" mo.e" themforar" an" acar" in time3
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Multiple Cash Flos
4hat if e ha.e morethan onecash o
*he concept 6an"formula7 are
i"entical if esimpl+ loo at theprolem as a series
of si#le 2a$me#!s3
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Multiple Cash FlosFuture $alue 1
-uppose +ou ha.e 81/000 no in asa.in's account that is earnin' :3;ou ant to a"" 8500 one +ear fromno an" 8
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Multiple Cash FlosFuture $alue 1
-impl+ loo at each pa+mentseparatel+ an" compute the F$ of eachas e "i" in the earlier chapter3
Today 1 Year 2 Years
$1,000 $ 500 $ 00
$1,124
$ 530No =ust a"" them upecause the+ are all
a"=uste" to e in >+ear ?@$2,354
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Multiple Cash FlosFuture $alue 1
Today 1 Year 2 Years
$1,000 $ 500 $ 00
$1,0!0$1,!54
$2,354
$1,5!0
Coul" e "o this prolem another a+
rin' each of the cash os forar"
one +ear at a time an" a"" them upeach +ear3
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Multiple Cash FlosFuture $alue 1C
LetBs a"" one more tist to theprolem!4hat oul" e the .alue at +ear 5
if e ma"e no further "eposits intoour sa.in's accountToday 1 2 3 4 5
$1,000
500 00
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Multiple Cash FlosFuture $alue 1C
4e coul" "o this to "i)erenta+s!13 rin' the >+ear to@ 'ure e
pre.iousl+ pro"uce" to +ear.eToday 1 2 3 4 5
$2,#03$1,000
500 00$2,354
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Multiple Cash FlosFuture $alue 1C
4e coul" "o this to "i)erenta+s!23rin' each of the three ori'inal
"ollars to +ear 5 an" a"" them allup3Today 1 2 3 4 5
$2,#03
$1,000
500 00 $1,33#$ !31$ #33
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Multiple Cash Flos#resent $alue
*o compute the present.alue of multiple cashos/ e a'ain =ustrin' the pa+ments into
the present .alue one+ear at a time3
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Multiple Cash Flos#resent $alue D 1
Consi"er recei.in' thefolloin' cash os!
;ear 1 CF E 8200;ear 2 CF E 800;ear ? CF E 800
;ear CF E 8G00If the "iscount rate is 12:/hat oul" this cash o e
orth to"a+
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Multiple Cash Flos#resent $alue D 1
Visually, the time linewould look like this:
Today 1 2 3 4
200
400 !00 #00
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Multiple Cash Flos#resent $alue D 1
*o compute the present .alue ofthis future stream of cash/ e =usttae each +ear to the present/ one
at a time!Today 1 2 3 4
200
400 !00 #001#5
31###420
50#41
1,432%3
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Multiple Cash Flos#resent $alue D1
sin' a calculator/ n" the #$ ofeach cash o an" =ust a"" themup
#$1 E 1
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Multiple Cash Flos#resent $alue D 2
;ou are consi"erin' an in.estment thatill pa+ +ou 81/000 in one +ear/ 82/000 into +ears an" 8?/000 in three +ears3 If
+ou ant to earn 10: on +our mone+/ homuch oul" +ou e illin' to pa+
#$ 6CF17 E 909309
#$ 6CF27 E 1/523G9#$ 6CF?7 E 2/25?39
#$ E 909309 J 1/523G9 J 2/25?39 E
/G1539?
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Annuities an" #erpetuitiesKenitions
Annuit+ nite series of e&ual
pa+ments that occur at re'ularinter.also If the rst pa+ment occurs at the en" of the
perio"/ it is calle" an or"inar+ annuit+
o If the rst pa+ment occurs at the e'innin'of the perio"/ it is calle" an annuit+ "ue
Most prolems are or"inar+ annuities
#erpetuit+ innite series of
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#erpetuities asicFormulas
Perpetuity: PV = C / r
Annuity:
[ ]
[ ] [ ])1FVIFrC1)r1(
rC
r
1)r1(CFV
)PVIF1rC
)r1(
11
rC
r
)r1(
11
CPV
tt
t
t
=+=
+=
=
+=
+
=
A it S i f
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Annuity: Saving for aCar
After carefull+ 'oin' o.er +ouru"'et/ +ou ha.e "etermine"+ou can a)or" to pa+ 8?2 permonth toar"s a ne sports car3
;ou call up +our local an an"n" out that the 'oin' rate is
1: per month for G months3Ho much can +ou orro
A it - i f
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Annuit+! -a.in' for aCar
;ou orro mone+ *OKA;so +ou nee" to compute thepresent .alue3
Formula!
54.999,2301.
)01.1(11
63248
=
=PV
[ ])PVIF1rC
)r1(
11rC
r
)r1(
11
CPVt
t
=
+=
+
=
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House
;ou are rea"+ to u+ a house/ an" +ou ha.e820/000 for a "on pa+ment an" closin'costs3 Closin' costs are estimate" to e :of the loan .alue3 ;ou ha.e an annualsalar+ of 8?/000/ an" the an is illin' to
allo +our monthl+ mort'a'e pa+ment toe e&ual to 2G: of +our monthl+ income3
*he interest rate on the loan is : per +earith monthl+ compoun"in' 635: per month7
for a ?0D+ear e" rate loan313 Ho much mone+ ill the an loan +ou
23 Ho much can +ou o)er for the house
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Annuit+! u+in' aHouse D Continue"
an loanMonthl+ income E ?/000 12 E ?/000Maimum pa+ment E 32G6?/0007 E G0
?012 E ?0 Nr E 035C E G0 month#$ E 810/105
*otal #riceClosin' costs E 30610/1057 E 5/0Kon pa+ment E 20/000 5/0 E 1/?9*otal #rice E 10/105 J 1/?9 E 815/501
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Fin"in' the #a+ment
-uppose +ou ant to orro 820/000 fora ne car3 ;ou can orro at G: per+ear/ compoun"e" monthl+
6G12 E 3
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Annuities
-uppose +ou e'in sa.in' for +ourretirement + "epositin' 82/000 per +earin an I(A3 If the interest rate is
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Annuit+ Kue
;ou are sa.in' for a ne house an" +ounee" 20: "on to 'et a loan3 ;ou put810/000 per +ear in an account pa+in'G:3 *he rst pa+ment is ma"e to"a+3
Ho much ill +ou ha.e at the en" of ?+ears
6+ou mae a total of three 810/000
pa+ments7F$ E 8?5/01312
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#erpetuit+ %ample
-uppose the Fellini Compan+ants to sell preferre" stoc at8100 per share3 A similar issue of
preferre" stoc alrea"+outstan"in' has a price of 80per share an" o)ers a "i.i"en" of
81 e.er+ &uarter3
4hat "i.i"en" ill Fellini ha.e too)er if the preferre" stoc is
oin to sell
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#erpetuit+
#erpetuit+ formula! #$ EC r
Current re&uire" return!0 E 1 r
r E 3025 or 235: per &uarter
Ki.i"en" for ne preferre"!100 E C 3025
C E 2350 per &uarter
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*erms an" Formulas
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Qroin' Annuit+
A 'roin' stream of cashos ith a e"maturit+
t
t
r
gC
r
gC
r
CPV
)1(
)1(
)1(
)1(
)1(
1
2 ++++
+++
+=
++
=
t
r
g
gr
CPV)1()1(1
ro n' nnu +!
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ro n' nnu +!%ample
A "ene"Denet retirement plano)ers to pa+ 820/000 per +ear for 0+ears an" increase the annual pa+ment+ threeDpercent each +ear3
4hat is the present .alue atretirement if the "iscount rate is 10percent
57.121,265$10.1
03.1
103.10.
000,20$ 40
=
=PV
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Qroin' #erpetuit+
A 'roin' stream of cashos that lasts fore.er
++++
+++
+=
3
2
2 )1(
)1(
)1(
)1(
)1( r
gC
r
gC
r
CPV
grCPV
=
Qro in' #erpet it
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Qroin' #erpetuit+%ample
*he epecte" "i.i"en" net +ear is813?0/ an" "i.i"en"s are epecte"to 'ro at 5: fore.er3
If the "iscount rate is 10:/ hat isthe .alue of this promise""i.i"en" stream
00.26$05.10.
30.1$ =
=PV
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6%A(7
*his is the actual rate pai" 6orrecei.e"7 after accountin' forcompoun"in' that occurs "urin' the
+ear
If +ou ant to compare to alternati.ein.estments ith "i)erent
compoun"in' perio"s/ +ou nee" tocompute the %A( an" use that forcomparison3
Annual #ercenta'e (ate
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Annual #ercenta'e (ate6A#(7
*his is the annual ratethat is &uote" + la onall loans3
+ "enition! A#( Eperio" rate times thenumer of perio"s per+ear
Annual #ercenta'e (ate
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Annual #ercenta'e (ate6A#(7
Conse&uentl+/ to 'et the perio" rate erearran'e the A#( e&uation!
#erio" rate E A#( numer
of perio"s per +ear
;ou shoul" N%$%("i.i"e the e"ective rate+ the numer of perio"s per +ear it ill
NO*'i.e +ou the perio" rate
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Computin' A#(s
13 4hat is the A#( if the monthl+ rateis 35:
356127 E :
23 4hat is the A#( if the semiannualrate is 35:
35627 E 1:?3 4hat is the monthl+ rate if the A#(
is 12: ith monthl+ compoun"in'
12 12 E 1:
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*hin's to (ememer
;ou AL4A;- nee" tomae sure that thei#!eres! ra!e an" the !ime
2eriod ma!ch3
If +ou are looin' at
annual perio"s/ +ounee" an annual rate3
If +ou are looin' at
monthl+ perio"s/ +ou
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*hin's to (ememer
If +ou ha.e an A#(ase" on monthl+
compoun"in'/ +ou ha.eto use monthl+ perio"sfor lump sums/ or
a"=ust the interest rateappropriatel+ if +ouha.e pa+ments other
than monthl+
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%A( D Formula
(ememer that the
A#(is the &uote" rate/ an"
>m@ is the numer of
compoun"in' perio"s per +ear
1m
APR1EAR
m
+=
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%'a#$le
-uppose +ou can earn 1: per month on81 in.este" to"a+3
4hat is the A#(
16127 E 12:
Ho much are +ou e)ecti.el+ earnin'
F$ E 161301712E 1312G
(ate E 61312G 17 1
E 312G E 123G:
Computin' %A(s
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Computin' %A(s%ample 6continue"7
-uppose +ou put it in anotheraccount an" earn ?: per &uarter3
4hat is the A#(?67 E 12:
Ho much are +ou e)ecti.el+
earnin'F$ E 16130?7 E 131255
(ate E 6131255 17 1
E 31255 E 12355:
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/II
;ou are looin' at to sa.in's accounts3 Onepa+s 5325:/ ith "ail+ compoun"in'3 *heother pa+s 53?: ith semiannual
compoun"in'34hich account shoul" +ou use
First account!%A( E 61 J 30525?57?5 1 E 53?9:
-econ" account!%A( E 61 J 305?272 1 E 53?
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%A(s
If +ou ha.e an e)ecti.e rate/ hocan +ou compute the A#((earran'e the %A( e&uation an"+ou 'et!
( )1%A&)(1#AP& #1
+=
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A#( D %ample
-uppose +ou ant to earn an e)ecti.erate of 12: an" +ou are looin' at anaccount that compoun"s on a monthl+
asis3 4hat A#( must the+ pa+
[ ]
11.39%or
8655152113.1)12.1(12 12/1 =+=APR
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Compoun"in'
-ometimes in.estments or loans are'ure" ase" on continuous compoun"in'
%A( E e& 1F$ E #$3 ert
#$ E F$3 eDrt*he e is a special function on the calculatornormall+
"enote" + e
%ample! 4hat is the e)ecti.e annual rate of
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*+pes of Loans
#ure Kiscount Loan
InterestDonl+ Loan
Amorti,e" ith Fie"
#rincipal pa+ment Amorti,e" ith Fie"#a+ment
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#ure Kiscount Loans
*reasur+ ills are ecellent eamples ofpure "iscount loans3 *he principalamount is repai" at some future "ate/
ithout an+ perio"ic interest pa+ments3
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#ure Kiscount Loans
If a *Dill promises to repa+ 810/000in 12 months an" the maretinterest rate is < percent/ ho
much ill the ill sell for in themaret
#$ E 89/?53
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%ample
Consi"er a 5D+ear/ interestDonl+ loan
ith a
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Fie" #rincipal#a+ment D %ample
suppose a usiness taes outa 85/000/ .eD+ear loan at 9percent3 *he loan a'reementcalls for the orroer to pa+the interest on the loanalance each +ear an" to
re"uce the loan alance each+ear + 81/0003 ecause theloan amount "eclines +
81/000 each +ear/ it is full+
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Formulas
#erpetuit+! #$ EC r
Annuit+!
+=
+
=
r
rCFV
r
rCPV
t
t
1)1(
)1(
11
F l
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Formulas6continue"7
+
+
=t
r
g
gr
CPV
)1(
)1(1
gr
CPV
=
F l
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Formulas6continue"7
1m
APR1EAR
m
+=
+= 1-EAR)(1mAPRm
1