Time value of money -Theory.docx

SM Nahidul Islam Dept. of Finance & Banking (2nd batch)

1. Define Define Time Time value of money money & State State the role / importa importance nce / significa significance nce of time value value of  money Answer:  ime !alue of mone" is the p#emise that an in!esto# p#efe#s to #ecei!e a pa"ment of a fi$ed amount of mone" toda"% #athe# than an eual amount in the futu#e% all else being eual. he significance of the concept of time !alue of mone" could be stated as belo' a. Inve Invest stme ment nt Dec Decis isio ion: n: In!estment In!estment decision decision is conce#ned conce#ned 'ith the allocation allocation of capital capital into long te#m in!estment p#o*ects. he cash flo' f#om longte#m in!estment occu#s at diffe#ent point in time in the futu#e. he" a#e not compa#able to each othe# and against the cost of the p#o*ect spent at  p#esent. o o make them compa#able% the futu#e cash flo's a#e discounted back to p#esent !alue. he concept of time !alue of mone" is useful to secu#ities in!esto#s. he" use !aluation models 'hile making in!estment in secu#ities such as stock and bonds. hese secu#it" !aluation models conside# time !alue of cash flo's f#om secu#ities. b. Fina Financ ncin ing g Deci Decisi sion on:: Financing decision is conce#ned 'ith designing optimum capital st#uctu#e and #aising funds f#om least cost sou#ces. he concept of time !alue of mone" is euall" useful in financi financing ng decisio decision% n% especi especiall all" " 'hen 'hen 'e deal deal 'ith 'ith compa# compa#ing ing the cost cost of diffe# diffe#ent ent sou#ce sou#cess of  financing. he effecti!e #ate of inte#est of each sou#ce of financing is calculated based on time !alue of mone" concept. Simila#l"% in leasing !e#sus bu"ing decision% 'e calculate the p#esent !alue of  cost of leasing and cost of bu"ing. he p#esent !alue of costs of t'o alte#nati!es is compa#ed against each othe# to decide on app#op#iate sou#ce of financing.

Beside Besides% s% the concept concept of time time !alue !alue of mone" mone" is also also used used in e!aluat e!aluating ing p#opos p#oposed ed c#edit c#edit polici policies es and the fi#m+s efficienc" in managing cash collection unde# cu##ent assets manage ment.

2. h hyy money money has has time time valu value! e!

Answer: he time !alue of mone" is the !alue of mone" figu#ing in a gi!en amount of

inte#est ea#ned inte#est  ea#ned o!e# a

gi!en amount of time. Mone" has time !alue fo# the follo'ing #easons

1. Present Present consump consumption tion pre prefer ferenc ence: e:  people  people p#efe#  p#efe# p#esent consumption to futu#e consumption. he" can be induced to dela" consumption but onl" b" b " offe#ing them mo#e in the futu#e. 2. Uncertai tainty nty  ,nce#taint" is the state of mind of an indi!idual 'ho is unable to make an" estimate of futu#e e!ents. Does not gi!e an" odds and all outcomes% e$pected o# not% a#e possible. 3. Inte Intere rest st rate rate::  he e$istence of inte#est #ate s in the econom" p#o!ides mone" 'ith its time !alue uite apa#t f#om the attitudes of an" one pe#son o# the in!estment oppo#tunities a!ailable to a  pa#ticula# fi#m. 4. Inflation Inflation occu#s 'hen gene#al p#ice le!el goes up% the suppl" of mone" goes up and demand fo# mone" goes do'n. 5. Defation: Defation occurs when general price level goes down, the supply o 

money goes down and the Supply o Goods goes up.

". De Descr scrib ibee Ti Time li line ne

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SM Nahidul Islam Dept. of Finance & Banking (2nd batch)

Answer: Time line is a horizontal line on which time zero appears at the letmost end and uture periods are mared rom let to right! can "e used to depict investment cash fow. To illustrate how to construct a timeline, assume that a riend owes you money. #e has agreed to repay the loan "y maing two payments o $1%,%%% at the end o each o the ne&t two years. 'e represent this inormation on a timeline as ollows:

 

Date

)ash fow

%

 6ear 1

1

 6ear (

T*. %

1%,%%%

(

1%,%%%

+n a word, Time line is a graphical representation used to show the timing o cash fows. #. hat is the $ifference bet%een future value an$ present value! hich approach is generally  preferre$ by financial managers! hy!

Answer: The dierences "etween -resent value and uture value are given "elow:

Present value

Future value Futu#e !alue is the !alue of a p#esent amount at a futu#e date% is calculated b" appl"ing compound inte#est o!e# a specific time pe#iod.

-resent value is the value today o a stream o payments to "e received in the uture at a given cost o capital. +t represents the original investment that +t represents what that investment will we have in hand today grow to when interest is earned on a seuential renewal o investment. -resent value techniues measure cash 3uture value techniues measure cash fow at the start o a pro/ect0s lie zero fow at the end o a pro/ect0s lie time2. -resent value o an annuity helps to 3uture value o an annuity helps to calculate how much money needs to "e calculate how much money needs to paid. "e invested today, in order to receive a certain payment in the uture. Formula: Formula:  FV 

-45

n

(1 +i)

'here, 34 is uture

value, -4 is present value, i is annual interest rate, n is num"er o years.

34 5 -4

(1 + i )n 'here, 34 is uture

value, -4 is present value, i is annual interest rate, n is num"er o years.

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SM Nahidul Islam Dept. of Finance & Banking (2nd batch) Financial manage#s p#efe# p#esent !alue to futu#e !alue because the" t"picall" make decisions at time -e#o% befo#e the sta#t of a p#o*ect.

. 'o% are present value an$ future value calculations relate$! Answer: #esent !alue calculations a#e the e$act in!e#se of compound inte#est calculations. ,sing compound inte#est% one attempts to find the futu#e !alue of a p#esent amount/ using p#esent !alue% one attempts to find the p#esent !alue of an amount to be #ecei!ed in the futu#e.

(. Define an$ $ifferentiate among the three basic patterns of cash flo%: )1* a single amount+ )2* an annuity+ an$ )"* a mi,e$ stream. Answer: 0 single amount cash flo' #efe#s to an indi!idual% stand alone% !alue occu##ing at one point in time. 0n annuit" consists of an unb#oken se#ies of cash flo's of eual dolla# amount occu##ing o!e# mo#e than one pe#iod.

0 mi$ed st#eam is a patte#n of cash flo's o!e# mo#e than one time pe#iod and the amount of cash associated 'ith each pe#iod 'ill !a#".

-. hat is the $ifference bet%een an or$inary annuity an$ an annuity $ue! hich is more valuable! hy!  ns%er: 0n o#dina#" annuit" is an annuit" 'hose pa"ments a#e made at the end of each pe#iod (e.g. a month% a "ea#). 1n the othe# hand% an annuit" due is an annuit" 'hose pa"ments a#e made at the beginning of each pe#iod (e.g. a month% a "ea#).

he o#dina#" annuit" is the mo#e common. Fo# othe#'ise identical annuities and inte#est #ates% the annuit" due #esults in a highe# futu#e !alue because cash flo's occu# ea#lie# and ha!e mo#e time to compound.

8. Why is interest charged? Answer: There are several reasons or interest to "e /usti7a"ly charged that are given "elow: 1. Risk o deault: +t is possi"le that the "orrower may not repay the money. The ris o deault is dierent or each "orrower! more credit8worthy "orrowers have a lower ris o deault. 9evertheless, there is always a ris and the lender ought to "e compensated or this ris. 2. Opportunity cost: The lender could gainully employ the capital elsewhere instead o lending to the "orrower. This is called opportunity cost. y lending the money to a speci7c "orrower, the lender closes all other avenues to use it or gain.

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SM Nahidul Islam Dept. of Finance & Banking (2nd batch)

3. Infation: The value o money decreases with time "ecause o infation. + $1%% is lent today and will "e repaid ; years rom now, the same $1%% will "e worth euivalent to only $%%% dollars is deposited into a "an account and the annual interest rate is =?. #ow much is the interest ater > years@

Ase the ollowing simple interest ormula: + 5 pB r B n 'here - 5 the principal or money deposited i 5 the rate o interest n 5 num"er o years

 

'e get: + 5 pB r B t + 5 >%%%B =? B > + 5 >%%%B %.%= B > + 5 1(=% dollars. !ompound interest: compound interest is the interest earned not only on the original principal, "ut also on all interests earned previously. + we use compound interest or the situation a"ove, the interest will "e computed as ollow:

+nterest at the end o the 7rst year: + 5 >%%%B %.%= B 1 + 5 ;(% dollars 9ew principal is now >%%% C ;(% 5 >;(% +nterest at the end o the second year: + 5 >;(%B %.%= B 1 + 5 ;>.E dollars 9ew principal is now >;(% C ;>.E 5 >EE.E +nterest at the end o the third year: + 5 >EE.EB %.%= B 1 + 5 ;F;.(>= dollars 9ew principal is now >EE.E C ;F;.(>= 5 %;=.=>= +nterest at the end o the ourth year: + 5 %;=.=>= B %.%= B 1 + 5 >%;.1%F=> dollar 9ew principal is now %;=.=>= C >%;.1%F=> 5 >>1.  Total interest earned 5 >>1.  >%%% 5 1>>1..  The dierence in money "etween compound interest and simple interest is

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SM Nahidul Islam Dept. of Finance & Banking (2nd batch)

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