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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 ,$.4
Cpt *PV ,04#-$-.,$
Page 6Fin (,, Chapter 4 Lecture *otes
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,-.$$
?i%%erenceB
Time $ / !(-4#3-3.$3
Time ( / !4(4#,6$.$$
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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.$
$$$#,$, =
=gr
CFPV
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xamples 'ith Jultiple Annuities
1 'ant to 'ithdra' !4#$$$ 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 $
Page ,0Fin (,, Chapter 4 Lecture *otes
(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#$$$
cpt FV !-"#"9-.63
*o' 1 hae the %ollo'ing timelineB
And the e8uation isB
-"#"9-.63 / 6#$$$+PV1FA*# ,$.45
1 sole the e8uation lie thisB
Cpt * 4
1 ,$.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(.$4
Pmt !,$#$$$
cpt FV !,-0#46(.(,
Page ,6Fin (,, Chapter 4 Lecture *otes
,$
A / 0#$$$
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#$$$
A / )
,$4
r / ,,.-45
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*o' 1 hae the %ollo'ing timelineB
And the e8uation isB
,-0#46(.(, / (3#44(.$4+FV1F4# ,,.-45 @ A+FV1FA4# ,,.-45
1 sole the e8uation lie thisB
* 4
1 ,,.-4
PV =!(3#44(.$4
cpt Pmt =!,$#$$$
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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*o' 1 hae the %ollo'ing timelineB
And the e8uation isB
,-0#46(.(, / (3#44(.$4+FV1F*# ,,.-45 @ ,$#$$$+FV1FA*# ,,.-45
1 sole the e8uation lie thisB
Cpt * 4
1 ,,.-4
PV =!(3#44(.$4
Pmt =!,$#$$$
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!,#$$$ K -,4.4, / !369.9" today. To help Vito on his booeeping# he 'ill re8uire you to mae%our 'eely payments o% !-4$ to repay the loan. 1% you are brae enough to as# 'hat AP: 'illVito say you are paying) ;hat is the A: you are paying) Assume 4- 'ees in a year.
Periodic rateB
* 9
Cpt 1 ,$.9066 / r24- < r / +,$.9066+4- / 499.(65
PV =!369.9"
Pmt !-4$
FV $
*om 499.(65
Cpt %% ,3#0-$.-95
C27 4-
Page --Fin (,, Chapter 4 Lecture *otes
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1n%lation +or ;hy 1n%lation ?oesnt Jatter
Today 1nterest rate One year
!,$$ ,$5 !,,$
&ot dogs !, 95 !,.$97ou can buy ,$$ ,$4.30"-($6
;hat 'as your rate o% return)
The Fisher %%ect
+, @ : / +, @ r+, @ h
$430"-($".$,$9.,
,$.,=
++
Approximate Fisher %%ect
: r @ h
Fin (,, Chapter 4 Lecture *otesPage -(
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uestion
7ou 'ant to buy a motorcycle one year %rom no'# t'o years %rom no'# and three years %rom no'.The motorcycle currently costs !-$#$$$. 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