time value of money.ppt
TRANSCRIPT
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Sanjay Dhamija/ FM-I/2015/ TVM
Time Value of Money
Suggested Readings!ha"te# 2$ I M %andey!ha"te# &$ Van 'o#ne / Dhamija
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(hat is Time Value of Money)
Relationshi" *et+een Re,1 today andRe,1 in the futu#e,
T+o methods fo# aounting fo# time.alue of money !om"ounding
Finding the futu#e .alue of a "#esent sum ofmoney
Disounting Finding the "#esent .alue of a futu#e sum of
money
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(hat is Time Value of Money)
Futu#e Value FV Value of a sum afte#
in.esting o.e# one o#
mo#e "e#iods, %#esent Value %V
Value of a sum today+hih is #eei.ed afte#
one yea# o# mo#e"e#iods,
nrCFV )1( +=
nr
CPV
)1( +=
! Sum in.ested today
# Inte#est #ate
! Sum #eei.ed n yea# hene# Inte#est #ate
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Futu#e Value and !om"ounding
The gene#al fo#mula fo# the futu#e .alue of an in.estmento.e# many "e#iods an *e +#itten as
FV C01 3 #n
+he#e C0is ash flo+ at date 0$
r is the a""#o"#iate inte#est #ate$ and
n is the num*e# of "e#iods o.e# +hih the ash is
in.ested, 1 3 #n = Future Value Interest Factor
(FVIFr,n)
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Futu#e Value and !om"ounding
FVIF Ta*le
Interest rate
Period 6% 7% 8%
1 1.0600 1.0700 1.0800
2 1.1236 1.1449 1.1664
3 1.1910 1.2250 1.2597
4 1.2625 1.3108 1.3605
FV of Re,1 afte# th#ee yea#s at the inte#est #ate of 4,6lso te#med as FVIF4$&
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%#esent .alue of a futu#e sum an *e +#itten as
+he#e$ %V %#esent .alue of the futu#e sum !n
n num*e# of yea#s until the "ayment +ill*e #eei.ed
# annual disount o# inte#est #ate
1/13#n is te#med as Present Value Interest
Factor (PVIFr,n)
%#esent Value and Disounting
+=
nn
rCPV
)1(
1
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%#esent Value and Disounting
%VIF Ta*le
Interest rate
Period 7% 8% 9%
1 0.9346 0.9259 0.9174
2 0.8734 0.8573 0.8417
3 0.8163 0.7938 0.7722
4 0.7629 0.7350 0.7084
%V of Re,1 #eei.ed afte# th#ee yea#s at the inte#est #ate of 7,6lso te#med as %VIF7$&
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6nnuities 6 8e.el St#eam
6n annuity is defined as a le.el st#eam of#egula# "ayments that lasts fo# a fi9ednum*e# of "e#iods, Regula# 6nnuity : ash flo+ at the end of
eah "e#iod
6nnuity Due : ash flo+ at the *eginning of
eah "e#iod
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Futu#e Value of an 6nnuity
Futu#e .alue of an annuity an *e +#itten as
+he#e
FVn Futu#e .alue of the annuity at the end of the "e#iod
# The annual #ate of inte#est
n num*e# of yea#s fo# +hih annuity lasts
;13#n-1
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Futu#e Value of an 6nnuity
Interest rate
Period 5% 6% 7%
1 1.000 1.000 1.000
2 2.050 2.060 2.070
3 3.152 3.184 3.215
4 4.310 4.375 4.440
Futu#e .alue of Re,1 #eei.ed "aid "e#iodially fo# = yea#s$ +ith theInte#est #ate *eing at >, 6lso te#med as FVIF6>$=
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%#esent Value of an 6nnuity
The formula for the present value of an annuity is
+he#e
%V %#esent .alue of a #egula# annuity! 6nnual !ont#i*ution at the end of eah "e#iod# The annual #ate of disountn num*e# of yea#s fo# +hih annuity lasts
( )
+
+
= rr
rCPV
n
n
n )1(
11
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%#esent Value of an 6nnuity
Interest rate
Period 7% 8% 9%
19 10.336 9.604 8.950
20 10.594 9.818 9.129
25 11.654 10.675 9.823
30 12.409 11.258 10.274
%#esent .alue of Re,1 #eei.ed "aid "e#iodially fo# &0 yea#s$ +ith theInte#est #ate *eing at 4 ",a,, 6lso te#med as %VIF64$&0
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%e#"etuity
6 onstant st#eam of ash flo+s that lasts fo#e.e#,
The formula for the present value of a perpetuity is
r
CPV=
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Im"lied Rate of Retu#n
To find the #ate of inte#est +he#einflo+ and outflo+s a#e gi.en
6n in.estment of Rs,1$000 *eomesRs,2$000 in ? yea#s 1000 9 FVIF#$ ? 2000
FVIF #$? 2000/ 1000 2
8oo@ fo# the fato# 2 in FVIF ta*le inthe #o+ fo# ? yea#s
# 7 a""#o9imately
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Sin@ing Fund Fato#To om"ute the amount that has to *e
in.ested at the end of e.e#y yea# fo# a"e#iod of AnB yea#s at @ #ate of inte#est$
in o#de# to aumulate a gi.en amount atthe end of the "e#iod,
It is the in.e#se of the FVIF6,
SFF 1/ FVIF6 #$n
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!a"ital Reo.e#y Fato#!a"ital Reo.e#y Fato# hel"s in om"uting
8oan installment to liCuidate a loan
6mount that an *e +ithd#a+n "e#iodially +hen
a "a#tiula# amount is in.ested no+,The !a"ital Reo.e#y Fato# is the in.e#se of
%VIF6!RF 1/ %VIF6
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Installment St#utu#e
!ost of Cui"ment Rs,50 la@hs
ReCui#ed #ate of #etu#n 1>
8ease %e#iod 5 yea#s
Residual Value Eil
Cuated
8R 9 %VIF61>$5 Rs,50 la@hs
8R Rs,50 la@hs/%VIF61>$5 Rs,50 la@hs/&,24= Rs,15,242 8
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Installment St#utu#e
Ste""ed - 10 in#ease e.e#y yea#ea# 8R %VIF1>$y 8R 9 %VIF 1>$y1 8 ,7>2 ,7>2 8
2 89 1,1 ,4=& ,714& 8& 8 9 1,1G2 ,>=1 ,445> 8= 8 9 1,1G& ,552 ,4&=485 8 9 1,1G= ,=4> ,>?>? 8
&,77>5 8&,77>5 8 Rs,50 la@hs8 Rs,12,7>5$12,7>5$ 1=,152$ 15,5>4$ 14,12&$ 17,7&>
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Installment St#utu#e
Hallooned - 5 la@hs fo# fi#st fou# yea#s
5 9 %VIF61>$= 3 8 9 %VIF 1>$5 Rs,50 la@hs
5 9 2,4?7 3 8 9 ,=4> Rs 50 la@hs
11,1?2 3 ,=4> 8 Rs, 50 la@hs
8 50-11,1?2/,=4> Rs,71,5& 8a@hs
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Installment St#utu#e
Defe##ed fo# 2 yea#s8 9 %VIF 1>$& 3 8 9 %VIF 1>$= 3 8 9 %VIF
1>$5 Rs,50 8a@hs
8 9 0,>=1 3 8 ,552 3 8 ,=4> Rs,50 la@hs
8 1,>>? Rs,50 la@hs
8 50/1,>>? Rs,2?,?57
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Installment St#utu#e
6d.ane Installments : Cuated Rental+ith one ad.ane installment
8R 3 8R 9 %VIF61>$= Rs,50 la@hs8R38R 9 2,4?7 Rs,50 8a@hs
&,4?7 8R Rs,50 8a@hs
8R Rs,50 la@hs/&,4?7 Rs,50 la@hs/&,4?7 Rs,1&,1>5 8
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Rental St#utu#e-!om"a#ison
!ear "#uate$ %teppe$ &alloone$ 'eferre$ $vane
0 13.165
1 15.272 12.865 5.00 *il 13.165
2 15.272 14.152 5.00 *il 13.165
3 15.272 15.567 5.00 29.958 13.165
4 15.272 17.123 5.00 29.958 13.165
5 15.272 18.836 81.53 29.958 *il
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TVM Fo#mulas
Futu#e Value %#esent Value
nrAFV )1( +=
nr
APV
)1( +=
( )
+=
r
rAFV
n
RA
11+ ( )
+
+=
rr
rxAPV
n
n
RA
)1(
11
r)(1++=
RAAD FVFV r)(1+ +=
RAAD
PVPV
n)(r,-/-
1=SFF
n)(r,/-
1=CRF
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8ea#ning
Time Value of Money Disounting !om"ounding
6nnuity Regula# 6nnuity Due
Im"lied Rate of Retu#n 6""liations of Time Value of Money
Sin@ing Fund !a"ital Reo.e#y
Jse of Finanial Ta*les and 9el funtions
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9"lo#eK,,
D!F a""#oahes to .aluation
Hills Disounting
Rental Disounting / 8ease RentalDisounting
Ma#@ to Ma#@et 8ossK,