FIN222 Autumn2015 Lectures Lecture 3

7/25/2019 FIN222 Autumn2015 Lectures Lecture 3

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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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6-5

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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-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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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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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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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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6-13

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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Visually, the time linewould look like this:

Today 1 2 3 4

200

400 !00 #00


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6-15


*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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;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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6-20

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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6-22

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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6-30

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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6-31

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

FIN222 Autumn2015 Lectures Lecture 3

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