ppt time value of money (ii)

8/8/2019 Ppt Time Value of Money (II)

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Obvio usly, Rs.10 ,000 tod ayRs.10 ,000 tod ay.

You alrea dy re cogniz e that there is TIME TIME VALUE TO MONEY VALUE TO MONEY !!

Wh ich wo uld you pre f er Rs.10 ,000Rs.10 ,000tod ay tod ay or Rs.10 ,000 in 5 year sRs.10 ,000 in 5 year s?

The Interest Rate


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TIMETIMEallows you the opportunity to

pos tpon e cons ump t ion and ear nINTERESTINTEREST.

Why is TIMETIMEsuch an impo rta n t ele me n t

in your de cision ?

W hy Time?


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Types of InterestTypes of Interest

yy Compo und In tere stCompo und In tere st

Intere st pa id (ear ne d) on any pre vious intere st ear ne d , as well as on the princip al bo rrow e d(lent ).

S imple InterestS imple Interest

Interest paid (earned) on only t h e originalamount, or principal borrowed (lent).

Types of Interests


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Assume that you de posi t Rs.1 ,000Rs.1 ,000 at a compo und in tere st rate of 7% for 2 year s2 year s.

0 1 22

Rs. 1 ,000Rs. 1 ,000FVFV22

7%

F uture Value Single Deposite


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FVFV11 = PP00 (1+i)1 = Rs.1 ,000Rs.1 ,000 (1.07 )= Rs.1 ,070Rs.1 ,070

Compo und In tere st You ear ne d Rs.70 in tere st on your Rs.1 ,000

de posi t over the first year .

Th is is the same amo unt of in tere st you wo uldear n und er simp le intere st .

S ingle Value Deposite Formula


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FVFV11 = PP00 (1+i)1 = Rs.1 ,000Rs.1 ,000 (1.07 )= Rs.1 ,070Rs.1 ,070

FVFV22 = FV1 (1+i)1

= PP00 (1+i)(1+i) = Rs1 ,000s1 ,000 (1.07 )(1.07 ) =PP00 (1+i)2 = Rs.1 ,000Rs.1 ,000 (1.07 )2

= Rs.1 ,144.90Rs.1 ,144.90You ear ne d an EXTRA Rs.4.90Rs.4.90 in Year 2 wi th

compo und ov er simp le intere st .

Fu tu re Val u e Single Deposite


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FVIFFVIF i,n is found at t h e end of t h ebook.

Valuation Using Table IValuation Using Table I

Period 6% 7% 8%1 1. 6 1. 7 1. 82 1.124 1.145 1.166

3 1.191 1.225 1.26

4 1.262 1.311 1.365 1.338 1.4 3 1.469


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FVFV11 = P0(1i)1

FVFV22 = P0(1+i)2

Ge neral Future Value Future Value Formula:FVFVnn = P0 (1+i)n

or FVFVnn = P0 (FVIFFVIFi,n) -- See Tabl e ISee Tabl e I

etc.

General Future Value Formula


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See ma wants to know how lar ge her de posi t of Rs.10 ,000Rs.10 ,000tod ay will be com e at a compo und ann ual intere st rate of

10% for 5 year s5 year s.

0 1 2 3 4 55

Rs. 10,000Rs. 10,000

FVFV 55

10%

Ex amples


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y Calculat ion b ase d on Tab le I:FVFV55 = Rs.10 ,000 (FVIFFVIF10% , 5)

= Rs.10 ,000 (1.611)= Rs.16 ,110Rs.16 ,110 [D ue to Rounding ]

C alculation based on general formula:FVFVnn = 0 (1+ i)n

FVFV55 = Rs. 10,000 (1+ 0.10)5

= Rs. 16 ,105 .10Rs. 16 ,105 .10

roblem S olution


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Assume that you nee d Rs.1 ,000Rs.1 ,000 in 2 year s.2 year s. Let sexa min e the proce ss to d eter min e how m uch you nee d to d e posi t tod ay at a disco un t rate of 7%compo und e d ann ually .

0 1 22

Rs. 1 ,000Rs. 1 ,000

7%

P V1P VP V00

P resent Value S ingle Deposite


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PVPV00 = FVFV22 / (1+ i)2 = Rs.1 ,000Rs.1 ,000 / (1 .07 )2 = FVFV22/ (1+ i)2 = Rs.873.44Rs.873.44

0 1 22

Rs. 1 ,000Rs. 1 ,000

7%

P VP V00

P resent Value S ingle Deposite(Formula)


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PVPV00 = FVFV11 / (1+ i)1

PVPV00 = FVFV22 / (1+ i)2

Ge neral Pre se n t Value Pre se n t Value Formula:PVPV00 = FVFVnn / (1+ i)n

or PVPV00 = FVFVnn (PVIFPVIFi,n) -- See Tabl e IISee Tabl e II

etc.

General P resent Value Formula


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P VIFP VIFi,n is found at t h e end of t h ebook.

Valuation Using Table IIValuation Using Table II

P eriod 6% 7% 8%1 .943 .935 .9262 .89 .873 .8573 .84 .816 .794

4 .792 .763 .7355 .747 .713 .681


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P VP V22 = Rs. 1 ,000Rs. 1 ,000 (P VIF7% ,2)= Rs. 1 ,000Rs. 1 ,000 (. 73 )= Rs. 73Rs. 73 [Due to Rounding]

Using Present Value TablesUsing Present Value Tables

P eriod % 7% 8%1 .943 .935 .9262 .890 . .8573 .840 .816 .794

4 .792 .763 .7355 .747 .713 .681


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Mo ha n w an ts to know how lar ge of a de posi t tomake so that the mon ey will grow to Rs.10 ,000Rs.10 ,000 in5 year s5 year s at a disco un t rate of 10%.

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Rs. 10,000Rs. 10,000P VP V00

10%

Ex ample


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y Calculat ion b ase d on g e neral formula:PVPV00 = FVFVnn / (1+ i)n

PVPV00 = Rs.10 ,000Rs.10 ,000 / (1+ 0.10 )5= Rs.6 ,209.21Rs.6 ,209.21

y Calculat ion b ase d on Tab le I:

PVPV00 = Rs.10 ,000Rs.10 ,000 (PVIFPVIF10% , 5)= Rs.10 ,000Rs.10 ,000 (.621)= Rs.6 ,210.00Rs.6 ,210.00 [D ue to Rounding ]

S olution


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yy Ordin ary Annu ityOrdin ary Annu ity : Payme nts o r re ce ipts occ ur at the e nd of ea ch per iod.

yy Annu ity DueAnnu ity Due : Pay me nts o r re ce ipts occ ur at the be ginning of ea ch per iod.

An Annuity An Annuity represents a series of equalpayments (or receipts) occurring over aspecified number of equidistant periods.

Types of Annuities


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Ex amples of Annuities

Stu de n t Loan Payme n ts

Car Loan Payme n tsInsura nce Pre miumsMo rt gage Payme n ts

Ret ire me n t Savings


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Parts of an AnnuityParts of an Annuity

0 1 2 3

Rs. 100 s. 100 Rs. 100

(Ordinary Annuity)EndEnd of

P eriod 1EndEnd of

P eriod 2

Today EqualEqual C as h Flows

Each

1 P eriod Apart

EndEnd of P eriod 3


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Parts of an AnnuityParts of an Annuity

0 1 2 3

Rs. 100 Rs. 100 Rs. 100

(Annuity Due)BeginningBeginning of

P eriod 1BeginningBeginning of

P eriod 2

Today EqualEqual C as h FlowsEac h 1 P eriod Apart

BeginningBeginning of P eriod 3


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FVAFVAnn = R (FVAIF i% ,n)FVAFVA 33 = Rs. 1 ,000 (FVAIF 7% ,3)

= Rs. 1 ,000 (3 .21 5 ) = Rs. 3 ,21 5Rs. 3 ,21 5

Valuation Using Annuity TableValuation Using Annuity Table

Pe ri % 7% %1 1.000 1.000 1.0002 2.060 2.070 2.0803 3.184 3 .215 3.246

4 4.375 4.440 4.5065 5.637 5.751 5.867


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1. Rea d p rob lem th oroughly2. Deter min e if it is a PV or FV prob lem

3. Deter min e if so lut ion invo lve s a sing le CF, ann u ity strea m(s) , or mixed f low4. So lve the prob lem5. Che ck wi th financial calculat or (op t ion al)

S teps to solve T imeValue of Money P roblems


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Mo ha n wi ll re ce ive the set of cash f lowsbelow. What is the Pre se n t Value Pre se n t Value at a

disco un t rate of 10%10%?

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Rs. 600 Rs. 600 Rs.400Rs. 600 Rs. 600 Rs.400Rs.400 Rs. 100Rs.400 Rs. 100P VP V00

10%10%

M ix ed Flows Ex ample


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1. So lve a pi ece pi ece- - a t a t -- aa -- tim etim e by

disco un t ing ea ch pi ece

pi ece

back to t=0.2. So lve a groupgroup -- a t a t -- aa -- tim etim e by first

brea king p rob lem in to g roups of ann u itystrea ms and any sing le cash f low g roup.The n disco un t ea ch groupgroup back to t=0.

H ow to S olve?

ppt time value of money (ii)

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