Time Value of Money.ppt

7/24/2019 Time Value of Money.ppt

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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


2/25

(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


3/25

(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


4/25

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)


5/25

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$&


6/25

%#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


7/25

%#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$&


8/25

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


9/25

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


10/25

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>$=


11/25

%#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


12/25

%#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=


14/25

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


16/25

!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


17/25

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


18/25


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&>


19/25


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


20/25


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


21/25


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


22/25

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


23/25

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


24/25

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,

Time Value of Money.ppt

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