Fin 311 Chapter 05

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Chapter 5 Discounted Cash Flow Valuation

Compounding Periods Other Than Annual

Lets examine monthly compounding problems.

Future Value

Suppose you inest !"#$$$ today and get an interest rate o% " percent compounded monthly. &o'much 'ill you hae in ( years)

FV = $9,000(FVIF9%/!,("#(!##

* (+,- / (0

1 "2,- / $.345

PV !"#$$$Pmt $

Cpt FV !,,#333.6,

7ou can see 1 hae introduced another ariable. This ariable# m# is the number o% compoundingperiods per year. 1% it is monthly compounding# them m is e8ual to ,-. 1% it is 8uarterlycompounding# them m is e8ual to 9. The number o% years is multiplied by m and the annualpercentage rate +AP: is diided by m.

Present Value

Assume you need !4$$#$$$ in ($ years and can earn an interest rate o% 0 percent compoundedmonthly. &o' much 'ill you hae to inest today)

V = $500,000(VIF%/!,("0#(!##

* ($+,- / (0$

1 02,- / $.45

Cpt PV !6(#$-$."0

Pmt $

FV !4$$#$$$

1nterest :ate

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7ou hae !,$#$$$ and need !,-#4$$ in -.4 years. ;hat interest rate must you earn to accomplishyour goal) Assume monthly compounding.

$0,000 = $!,500(VIFr/!,(!&5#(!##

* -.4+,- / ($Cpt 1 $.39005 / r2,- < r / +$.3900+,- / 6."4"5

PV =!,$#$$$

Pmt $

FV !,-#4$$

*umber o% Periods

7ou hae !,$$#$$$ and need !,-4#$$$. 7our inestment 'ill earn a rate o% ,4.34 5 compoundedmonthly. &o' many years be%ore you accomplish your goal)

$00,000 = $!5,000(VIF5&'5/!,(t#(!##

Cpt * ,3.,, / t+,- < t/,3.,,2,- / ,.9( years

1 ,4.342,- / ,.(,-45

PV =!,$$#$$$

Pmt $

FV !,-4#$$$

This method %or calculating the di%%erent ariables in the lump sum e8uations can be applied touneen# perpetuity# and annuity cash %lo's.

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>neen Cash Flo's

Suppose you are going to receie !,$#$$$ in one year# !,4#$$$ in t'o years and three years# and!-$#$$$ in %ie years. 1% the appropriate interest rate is ,$ percent# 'hat is the alue o% the cash%lo's today) ?ra' the time line.

PV / ,$#$$$+PV1F ,#,$5 @ ,4#$$$+PV1F -#,$5 @ ,4#$$$+PV1F (#,$5 @ -$#$$$+PV1F 4#,$5

* / , * / - * / ( * / 4

1 / ,$5 1 / ,$5 1 / ,$5 1 / ,$5

Cpt PV !"#$"$.", CptPV

!,-#("0.0" CptPV

!,,#-0".3- CptPV

!,-#9,6.9(

Pmt / $ Pmt / $ Pmt / $ Pmt / $

FV / ,$#$$$ FV / ,4#$$$ FV / ,4#$$$ FV / -$#$$$

PV$/ !"#$"$.", @ !,-#("0.0" @ !,,#-0".3- @ !,-#9,6.9( / !94#,34.34

;hat i% 1 'ant to no' the alue at year 4)

FV4/ ,$#$$$+FV1F 9#,$5 @ ,4#$$$+FV1F (#,$5 @ ,4#$$$+FV1F -#,$5 @ -$#$$$

* / 9 * / ( * / - * / $

1 / ,$5 1 / ,$5 1 / ,$5 1 / ,$5

PV / ,$#$$$ PV / ,4#$$$ PV / ,4#$$$ PV / -$#$$$

Pmt / $ Pmt / $ Pmt / $ Pmt / $

Cpt FV / ,9#09,.$$ Cpt FV/

,"#"04.$$ Cpt FV/

,6#,4$.$$ Cpt FV/

-$#$$$

V4/ !,9#09,.$$ @ !,"#"04.$$ @ !,6#,4$.$$ @ !-$#$$$.$$ / !3-#340.$$

Fin (,, Chapter 4 Lecture *otesPage (

$ , - 9( 4

,$#$$$ ,4#$$$ ,4#$$$ -$#$$$

r / ,$5

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Another approach isB

FV / PV+FV1Fr#t < FV / !94#,34.34+FV1F,$5#4

* / 4

1 / ,$5

PV / 94#,34.34

Pmt / $

Cpt FV / 3-#340.$$

Cash Flo' ;orsheet

The cash %lo' 'orsheet is another alternatie to soling this problem. The cash %lo' 'orsheetis initiated 'ith the CF ey. Push this ey and you see CF$.

1n this example# the cash %lo's areB

CF$ $

CF, ,$#$$$ F, ,

CF- ,4#$$$ F- -

CF( $ F( ,

CF9 -$#$$$ F9 ,

1 ,$

Cpt *PV 94#,34.34

Perpetuities

A perpetuity is an een cash %lo' that occurs at een time interals %oreer.

7ou 'ill receie !34#$$$ per year %oreer 'ith the %irst payment occurring one year %rom today. 1%the interest rate is 0 percent# 'hat is the alue o% the perpetuity today) ?ra' the time line.

rate

PerpetuityPVPerpetuity=

$$$#-4$#,$0.$

$$$#34==PerpetuityPV

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Suppose the perpetuity payments in the preious problem start " years %rom today. ;hat is thealue o% the cash %lo's no') ?ra' the time line.

* / 6

1 / 05

Cpt PV / 369#-04.90

Pmt / $

Cpt FV / ,#-4$#$$$

Annuities

An ordinary annuity is constant cash %lo' that occurs at constant and een time interals %or a%inite time. The cash %lo's are at the end o% the time period.

PV o% an Annuity

Suppose you are o%%ered !,$#$$$ per year %or three years. 1% the interest rate is ,$ percent# 'hat isthe alue o% the cash %lo's today)

;e no' seeral 'ays o% calculating the present alue. &ere is oneB

Lets loo at Table A( in the ,$ percent column and the ( period ro'. 7ou %ind -.9606. 7ou cansee that another 'ay to calculate the PV o% an annuity is to multiply the %actor %rom Table A( bythe annuity.

Fin (,, Chapter 4 Lecture *otesPage 4

-,

$."$",

$.6-09

$.34,(

$ (

,$#$$$ ,$#$$$ ,$#$$$

"#$",

3#4,(

6#-09

!-9#606 -.9606

r / ,$5

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The 8uation Approach

The e8uation %or the PV o% an annuity isB

( ) ( )4-.606#-9!,$.$

,$.,

,,

$$$#,$,

,,

(

=

=

+

= rr

APV

t

A

The Table Approach

PVA/ A+PV1FAr#t

PVA/ ,$#$$$+PV1FA,$5#(

PVA/ ,$#$$$+-.9606

PVA/ -9#606

The Calculator Approach

* / (

1 / ,$5

Cpt PV / !-9#606.4-

Pmt / ,$#$$$

FV / $

PV i% the interest rate is ,-5 / !-9#$,6.(,

PV at 65 / !-4#33$."3

;e can use the cash %lo' 'orsheet

CF$ $

CF, ,$#$$$ F, (

1 ,$

Cpt *PV -9#606.4-


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Future Value o% Annuities

7ou are planning to sae !4#$$$ per year %or the next ($ years to'ard retirement 'ith the %irstpayment occurring one year %rom today. 1% you can earn an ,, percent interest rate# 'hat 'ill thealue o% your retirement port%olio be)

The 8uation Approach

( ) ( ) (".,$9#""4,,.$

,,,.,$$$#4,,

($

==+=rrAFV

t

A

The Table Approach

FVA/ A+FV1FAr#t

FVA/ 4#$$$+FV1FA,,5#($

FVA/ 4#$$$+,"".$-

FVA/ ""4#,$$

The Calculator Approach

* / ($

1 / ,,5

PV / $

Pmt / 4#$$$

Cpt FV / !""4#,$9.("

;e cannot directly use the cash %lo' 'orsheet. This calculator does not hae a D*FVE %unction.

Fin (,, Chapter 4 Lecture *otesPage 3

A / 4#$$$

($$

r / ,,5

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7ou 'ill receie !4$#$$$ per year %or ,$ years 'ith the %irst payment occurring 3 years %romtoday. 1% the appropriate interest rate is ,$.4 percent# 'hat is the alue o% the cash %lo's today)

The 8uation

V$/ 4$#$$$+PV1FA,$.45#,$ +PV1F,$.45#0

* / ,$ * / 01 / ,$.45 1 / ,$.45

Cpt PV !($$#3(6.09 CptPV

!,04#-$-.,$

Pmt / 4$#$$$ Pmt / $

FV / $ FV / !($$#3(6.09

;e can use the cash %lo' 'orsheet

CF$ $

CF, $ F, 0

CF- 4$#$$$ F- ,$

1 ,$.4

Cpt *PV ,04#-$-.,$


r / ,$.45

,03

A / 4$#$$$

$

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Annuity Payments

7ou 'ant to retire in 9$ years 'ith !,.4 million. 7ou plan to sae an e8ual amount each year and%eel you can earn an interest rate o% ,, percent. &o' much do you hae to sae each year)

The 8uation

,#4$$#$$$ / A+FV1FA9$# ,,5

* 9$

1 ,,.$$

PV $

Cpt Pmt !-#436.$"

FV ,#4$$#$$$

7ou 'ant to buy a car that costs !-"#$$$. 7ou plan to put !-#$$$ do'n and %inance the remainder%or 4 years. The dealer o%%ers you a loan 'ith a 9.4 percent annual interest rate 'ith monthlycompounding. &o' much are your payments)

The 8uation

-3#$$$ / A+PV1FA+4+,-# 9.452,-

* +4+,- / 0$

1 9.42,- / $.(34PV -3#$$$

Cpt Pmt !4$(.(0

FV $

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Annuity 1nterest :ates

7ou 'ant to hae !- million 'hen you retire in (4 years. 7ou plan to inest !0#$$$ each year to%und your retirement. ;hat interest rate do you hae to earn)

The 8uation

-#$$$#$$$ / A+FV1FA(4# r

* (4

Cpt 1 ,$.6"

PV $

Pmt =!0#$$$

FV -#$$$#$$$

7ou plan to put !-$#$$$ do'n on your ne' house. The house sells %or !-$$#$$$ and you 'ant toget a ($ year %ixed rate mortgage. 1% the highest payment you can a%%ord is !,#,-4 per month# 'hatis the highest interest rate you could a%%ord)

The 8uation

,6$#$$$ / A+PV1FA($+,-# r2,-

* ($+,- / (0$

Cpt 1 $.4(-35 / r2,- < r / +$.4(-3+,- / 0.("5

PV =,6$#$$$

Pmt ,#,-4

FV $

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Comparing Cash Flo's

Suppose a 8uarterbac and 'ide receier hae both signed ne' contracts. The 8uarterbacscontract calls %or an immediate signing bonus o% !0 million and an annual salary o% !9 million %orthree years. The 'ide receiers contract calls %or a signing bonus o% !(.4 million and an annual

salary o% !4 million %or three years. Assuming all salary payments are at the end o% the year andthe interest rate is ,6 percent# 'hich contract is 'orth more)

The 8uation

GB

PV / 0#$$$#$$$ @ 9#$$$#$$$+PV1FA(# ,65

* (

1 ,65

Cpt PV 6#0"3#$",.3-

Pmt 9#$$$#$$$

FV $

PV / !6#0"3#$",.3- @ 0#$$$#$$$ / !,9#0"3#$",.3-

FV / !-9#,93#3"-.$$

;ide receierB

PV / (#4$$#$$$ @ 4#$$$#$$$+PV1FA(# ,65

* (

1 ,65

Cpt PV !,$#63,#(09.04

Pmt 4#$$$#$$$

FV $

PV / !,$#63,#(09.04 @ (#4$$#$$$ / !,9#(3,#(09.04

FV / !-(#0,-#0,-.$$

?i%%erenceB

Time $ / !(-4#3-3.$3

Time ( / !4(4#,6$.$$

Fin (,, Chapter 4 Lecture *otesPage ,,

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7ou are trying to plan %or retirement on ,$ years. 7ou currently hae !-$$#$$$ in a bond accountand !9$$#$$$ in a stoc account. 7ou plan to add !,$#$$$ per year at the end o% each o% the next,$ years to your bond account. The stoc account earns ,-.45 and the bond account earns 6.45.;hen you retire# you plan to 'ithdra' an e8ual amount %or the next -$ years +at the end o% eachyear and hae nothing le%t. Additionally# 'hen you retire you 'ill trans%er your money to an

account that earns 3.-45. &o' much can you 'ithdra' each year)

The Gond Account 8uation

VG,$/ !-$$#$$$+FV1F,$# 6.45 @ ,$#$$$+FV1FA,$# 6.45

* ,$ * ,$

1 6.45 1 6.45

PV !-$$#$$$ PV

Pmt Pmt !,$#$$$

Cpt FV 94-#,"0.0" @ Cpt FV ,96#(4$."" / 0$$#493.06

Or

* ,$

1 6.45

PV !-$$#$$$

Pmt !,$#$$$

Cpt FV 0$$#493.06

The Stoc Account 8uation

VS,$/ !9$$#$$$+FV1F,$# ,-.45

* ,$

1 ,-.45

PV !9$$#$$$

Pmt $

Cpt FV ,#-"6#"-6.9,

7ou 'ill hae !0$$#493.06 @ ,#-"6#"-6.9, / !,#6""#930.$"

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The :etirement 8uation

!,#6""#930.$" / A+PV1FA-$# 3.-45

* -$

1 3.-45

PV !,#6""#930.$"

Cpt Pmt !,6-#3"4.36

FV $

7ou are planning to sae %or the college education o% your children. They are t'o years apartH one'ill begin college in ,4 years and the other 'ill begin college in ,3 years. Assume both 'ill be onthe %our year plan. 7ou estimate each childs education 'ill cost !-(#$$$ per year# payable at thebeginning o% each school year. The annual interest rate is 0.4 percent. &o' much must you deposit

each year in an account to %und your childrens education) 7ou 'ill mae your last deposit 'henyour oldest child enters college.

CF$ -(#$$$

CF, -(#$$$ F, ,

CF- 90#$$$ F- -

CF( -(#$$$ F( -

1 0.4

Cpt *PV !,43#6"".(-

* ,4

1 0.45

PV $

Cpt Pmt !0#4-".46

FV !,43#6"".(-

Iro'ing Perpetuities

7ou 'ill receie perpetuity 'ith a payment o% !,$#$$$ next year. The payment 'ill gro' by -.4percent per year %oreer. 1% the appropriate interest rate is 6 percent# 'hat is the alue o% the cash%lo's today)

,6.,6,#,6,!$-4.$$6.$

$$$#,$, =

=gr

CFPV

Fin (,, Chapter 4 Lecture *otesPage ,(

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xamples 'ith Jultiple Annuities

1 'ant to 'ithdra' !4#$$$ a year %or the next %ie years and !6#$$$ a year %or the %ollo'ing %ieyears. 1 can earn ,$.4 percent. &o' much do 1 hae to inest today) 1 am asing %or the presentalue o% these t'o annuities. There are seeral 'ays to calculate this alue. First# 1 dra' the time

line.

The next step is to 'rite an e8uation %or the present alueB

V$/ 4#$$$+PV1FA4# ,$.45 @ 6#$$$+PV1FA4# ,$.45+PV1F4# ,$.45

* 4 * 4 * 4

1 ,$.4 1 ,$.4 1 ,$.4

Pmt !4#$$$ Pmt !6#$$$ FV !-"#"9-.63

cpt PV !,6#3,9.-" cpt PV !-"#"9-.63 cpt PV !,6#,34.(-

V$/ ,6#3,9.-" @ ,6#,34.(-

/ !(0#66".0,

Page ,9Fin (,, Chapter 4 Lecture *otes

A / 4#$$$

A / 6#$$$

,$4$

r / ,$.45

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&ere is another 'ay

* 4

1 ,$.4

cpt PV !-"#"9-.63

Pmt !6#$$$

*o' my time line loos lie thisB

This is the e8uationBV$/ 4#$$$+PV1FA4# ,$.45 @ -"#"9-.63+PV1F4# ,$.45

* 4

1 ,$.4

cpt PV !(0#66".0,

Pmt !4#$$$

FV !-"#"9-.63

The cash %lo' 'orsheet is the last 'ay 1 'ill sho' you.

CF$ $

CF, 4#$$$ F, 4

CF- 6#$$$ F- 4

1 ,$.4

Cpt *PV (0#66".0,

Lets loo at this time line again. 1 could as the %ollo'ing8uestionB

1 'ant to 'ithdra' !4#$$$ a year %or 4 years and hae!-"#"9-.63 le%t in the inestment account. &o' much do 1hae to deposit today i% 1 can earn ,$.4 percent)

1 no' the ans'er is !(0#66".0,

;or this outside o% class.

Fin (,, Chapter 4 Lecture *otesPage ,4

A / 4#$$$

4$

r / ,$.45

-"#"9-.63

$

A / 4#$$$

4

r / ,$.45

-"#"9-.63

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Lets loo at this problem in a di%%erent 'ay. 1 'ill inest !(0#66".0, today in an asset that 'illearn ,$.4 percent. 1 plan to 'ithdra' !4#$$$ a year %or the next %ie years. &o' much can 1'ithdra' each year %or the next 4 years) ;e no' the ans'er is !6#$$$ but ho' 'ould 'ecalculate it) &ere is the time lineB

(0#66".0, / 4#$$$+PV1FA4# ,$.45 @ A+PV1FA4# ,$.45+PV1F4# ,$.45

* 4

1 ,$.4

PV =!(0#66".0,

Pmt !4#$$$

cpt FV !-"#"9-.63

*o' 1 hae the %ollo'ing timelineB

And the e8uation isB

-"#"9-.63 / A+PV1FA4# ,$.45

1 sole the e8uation lie thisB

* 4

1 ,$.4

PV !-"#"9-.63

cpt Pmt !6#$$$FV $


(0#66".0,

$

A / 4#$$$

A / )

,$4r / ,$.45

4

A / )

,$

r / ,$.45

-"#"9-.63

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1 'ill inest !(0#66".0, today in an asset that 'ill earn ,$.4 percent. 1 plan to 'ithdra' !4#$$$ ayear %or the next %ie years and !6#$$$ a year a%ter the %irst %ie year period. &o' many years can1 'ithdra' the !6#$$$) ;e no' the ans'er is 4 years but ho' 'ould 'e calculate it) &ere isthe time lineB

(0#66".0, / 4#$$$+PV1FA4# ,$.45 @ 6#$$$+PV1FA*# ,$.45+PV1F4# ,$.45

* 4

1 ,$.4

PV =(0#66".0,

Pmt !4#$$$

cpt FV !-"#"9-.63



-"#"9-.63 / 6#$$$+PV1FA*# ,$.45


Cpt * 4

1 ,$.4

PV =!-"#"9-.63

Pmt !6#$$$

Fin (,, Chapter 4 Lecture *otesPage ,3

(0#66".0,

$

A / 4#$$$

A / 6#$$$

* / )4

r / ,$.45

-"#"9-.63

4

A / 6#$$$

*

r / ,$.45

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1 'ill inest !0#$$$ a year %or the next %ie years and !,$#$$$ a year %or the %ollo'ing %ie years inan asset that earns ,,.-4 percent. &o' much do 1 hae at the end o% ,$ years) 1 am asing %or the%uture alue o% these t'o annuities. There are seeral 'ays to calculate this alue. First# 1 dra'the time line.

The next step is to 'rite an e8uation %or the %uture alueB

V,$/ 0#$$$+FV1FA4# ,,.-45+FV1F4# ,,.-45@ ,$#$$$+FV1FA4# ,,.-45

* 4 * 4 * 4

1 ,,.-4 1 ,,.-4 1 ,,.-4

Pmt !0#$$$ PV !(3#44(.$4 Pmt !,$#$$$

cpt FV !(3#44(.$4 cpt FV !0(#""9.6" cpt FV !0-#466.9-

V,$/ 0(#""9.6" @ 0-#466.9- / !,-0#46(.(,

&ere is another 'ay

* 4

1 ,,.-4

PV $

Pmt !0#$$$

cpt FV !(3#44(.$4

*o' my time line loos lie thisB

This is the e8uationB

V,$/ (3#44(.$4+FV1F4# ,,.-45 @ ,$#$$$+FV1FA4# ,,.-45* 4

1 ,,.-4

PV !(3#44(.$4

Pmt !,$#$$$

cpt FV !,-0#46(.(,


,$

A / 0#$$$

A / ,$#$$$

4$

r / ,,.-45

4

A / ,$#$$$

,$

r / ,,.-45

(3#44(.$4

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The cash %lo' 'orsheet is the last 'ay 1 'ill sho' you.

CF$ $ * ,$

CF, 0#$$$ F, 4 1 ,,.-4

CF- ,$#$$$ F- 4

PV 9(#466."9Pmt $

1 ,,.-4 Cpt FV ,-0#46(.(,

Cpt *PV 9(#466."9

Lets loo at this problem in a di%%erent 'ay. 1 'ant !,-0#46(.(, in ,$ years. 1 plan to inest!0#$$$ a year %or the next 4 years in an asset that 'ill earn ,,.-4 percent. &o' much must 1 inesteach year %or the last 4 years in order to meet my goal) ;e no' the ans'er is !,$#$$$ but ho''ould 'e calculate it) &ere is the time lineB

,-0#46(.(, / 0#$$$+FV1FA4# ,,.-45+FV1F4# ,,.-45@ A+FV1FA4# ,,.-45

* 4

1 ,,.-4

PV $

Pmt !0#$$$

cpt FV !(3#44(.$4

Fin (,, Chapter 4 Lecture *otesPage ,"

,-0#46(.(,

$

A / 0#$$$

A / )

,$4

r / ,,.-45

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,-0#46(.(, / (3#44(.$4+FV1F4# ,,.-45 @ A+FV1FA4# ,,.-45


* 4

1 ,,.-4

PV =!(3#44(.$4

cpt Pmt =!,$#$$$

FV ,-0#46(.(,

1 'ant !,-0#46(.(, in ,$ years. 1 plan to inest !0#$$$ a year %or the next 4 years and then!,$#$$$ a year in an asset that 'ill earn ,,.-4 percent. &o' many years must 1 inest the!,$#$$$) ;e no' the ans'er is 4 years but ho' 'ould 'e calculate it) &ere is the time lineB

,-0#46(.(, / 0#$$$+FV1FA4# ,,.-45+FV1F*# ,,.-45@ ,$#$$$+FV1FA*# ,,.-45

* 4

1 ,,.-4

PV $

Pmt !0#$$$

Cpt FV !(3#44(.$4

Page -$Fin (,, Chapter 4 Lecture *otes

4

A / )

,$

r / ,,.-45

(3#44(.$4

,-0#46(.(,

r / ,,.-45

,-0#46(.(,

$

A / 0#$$$

A / ,$#$$$

* / )4

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,-0#46(.(, / (3#44(.$4+FV1F*# ,,.-45 @ ,$#$$$+FV1FA*# ,,.-45


Cpt * 4

1 ,,.-4

PV =!(3#44(.$4

Pmt =!,$#$$$

FV ,-0#46(.(,

Suppose you borro' !-$$$ and you are going to mae annual payments o% !3$$ each year %or (years. ;hat is the annual rate o% this loan)

7ou 'ant to receie !4$$$ per year %or the next 4 years. &o' much 'ould you need to deposittoday i% you can earn " percent)

;hat rate 'ould you need to earn i% you only hae !,4#$$$ to deposit)

Suppose you hae !,4#$$$ to deposit and can earn " percent.

&o' many years could you receie the !4$$$ payment)

&o' much could you receie each year %or 4 years)

Fin (,, Chapter 4 Lecture *otesPage -,

(3#44(.$4

r / ,,.-45

4

A / ,$#$$$

*

,-0#46(.(,

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%%ectie Annual :ates +A:

A: / ,AP:,

+

m

m

>se the 1nterest :ate Conersion ;orsheet

,-5 monthly compounding / ,-.065

,-5 semiannual compounding / ,-.(05

,-5 daily compounding / ,-.345

A: ersus AP:

Suppose you go Vito# a local loan shar# to in8uire about the interest rate on loans. 7ou are told theinterest 'ill be a 4 percent discount loan. 1% you borro' !,#$$$ %or one month# the net interest 'illo'e 'ill beB !,#$$$+, @ .$49K !,#$$$ / !-,4.4,. Since this is a discount loan# you 'ill receie!,#$$$ K -,4.4, / !369.9" today. To help Vito on his booeeping# he 'ill re8uire you to mae%our 'eely payments o% !-4$ to repay the loan. 1% you are brae enough to as# 'hat AP: 'illVito say you are paying) ;hat is the A: you are paying) Assume 4- 'ees in a year.

Periodic rateB

* 9

Cpt 1 ,$.9066 / r24- < r / +,$.9066+4- / 499.(65

PV =!369.9"

Pmt !-4$

FV $

*om 499.(65

Cpt %% ,3#0-$.-95

C27 4-

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1n%lation +or ;hy 1n%lation ?oesnt Jatter

Today 1nterest rate One year

!,$$ ,$5 !,,$

&ot dogs !, 95 !,.$97ou can buy ,$$ ,$4.30"-($6

;hat 'as your rate o% return)

The Fisher %%ect

+, @ : / +, @ r+, @ h

$430"-($".$,$9.,

,$.,=

++

Approximate Fisher %%ect

: r @ h

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uestion

7ou 'ant to buy a motorcycle one year %rom no'# t'o years %rom no'# and three years %rom no'.The motorcycle currently costs !-$#$$$. 7ou can earn a ,$ percent return# and the price o% themotorcycle 'ill increase at 9 percent per year. &o' much do you hae to deposit today in order to

be able to pay cash %or each motorcycle)

*ominal cash %lo's

CF$ $

CF, -$#6$$ F, ,

CF- -,#0(- F- ,

CF( --#9"3.-6 F( ,

1 ,$5

Cpt *PV !4(#06".(-

:eal cash %lo's

CF$ $ * 9

CF, -$#$$$ F, ( 1 4.30"-($65

o

r

Cpt

PV !4(#06".(-1 4.30"-($65 Pmt !-$#$$$

Cpt *PV !4(#06".(- FV $

Page -9Fin (,, Chapter 4 Lecture *otes

-,$ (

-$#6$$ -,#0(- --#9"3.-6

r / ,$5

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Assume that it is anuary ,# -$$6. 7ou plan to retire in 9$ years on anuary ,# -$96 and 'ant toplan you dream retirement. 7ou hae !4#$$$ saed in an account that 'ill earn an ,, percentreturn compounded monthly. ;hen you retire# you 'ant to be able to 'ithdra' !-$#$$$ per month%or the next -4 years 'ith the %irst 'ithdra'al on anuary ,# -$96. 1n addition# on anuary ,# -$4,#you 'ant to be able to 'ithdra' !,4$#$$$ to trac do'n the original cast members o% DGeerly

&ills "$-,$E and DGu%%y the Vampire SlayerE to get their autographs. 7ou also 'ant to leae!-4$#$$$ to your grandchildren on anuary ,# -$3(. ;hen you retire you 'ill earn an 6 percentreturn compounded monthly. &o' much must you deposit each month into the account earning an,, percent compounded monthly %or the next 9$ years to mae your dream happen assuming the%irst deposit is at the end o% the month and the last deposit is on ?ecember (,# -$93)

You will have:

Enter 480 11%/12 $!000

N I/Y PV PM

T

FV

Solve for $"##!120

You &ee': (A&&uity )ue*

Enter "00 8% / 12 $20!000

N I/Y PV PM

T

FV

Solve for $2!#1!2#0!

4

Enter "+ 8%/12 $10!000

N I/Y PV PM

T

FV

Solve for $118!0881#

Enter "00 8%/12 $20!000

N I/Y PV PM

T

FV

Solve for $"4!0#1"

You are ,hort: $2!#1!2#04 - 118!0881# - "4!0#1" . "##!120 $2!"44!2+2

You mu,t ,ave: (A&&uity )ue*

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Enter 480 11% / 12 $2!"44!2+2

N I/Y PV PM

T

FV

Solve for $228

Fin 311 Chapter 05

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