Sir Nabeel Tmv4

8/8/2019 Sir Nabeel Tmv4

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PROFESSIONAL ONESPROFESSIONAL ONES


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TheTime ValueTheTime Valueof Mon

eyof Mon

ey

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ASSIGNED TOASSIGNED TO

M.NazimM.Nazim Saleem #905115Saleem #905115 InamUllahInamUllah #905110#905110

ShumailaShumaila IllyasIllyas #905160#905160

SamreenSamreen NazNaz #905161#905161 ErumErum Tariq #905144Tariq #905144

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ASSIGNED BY:ASSIGNED BY:

SirSir NabeelNabeel

(Course Co(Course Co--ordinatorordinator))

Financial ManagementFinancial Management

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The Time Value of MoneyThe Time Value of MoneyWould you prefer toWould you prefer to

have Rs1 million nowhave Rs1 million now

ororRs1 million 10 yearsRs1 million 10 years

from now?from now?Of course, we would allOf course, we would all

prefer the money now!prefer the money now!

This illustrates that thereThis illustrates that thereis an inherent monetaryis an inherent monetary

value attached to time.value attached to time.


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What is The Time Value ofWhat is The Time Value of

Money?Money?A Rupees received today is worth moreA Rupees received today is worth more

than a Rupees received tomorrowthan a Rupees received tomorrow This is because a Rupees received todayThis is because a Rupees received today

can be invested to earn interestcan be invested to earn interest

The amount of interest earned depends onThe amount of interest earned depends onthe rate of return that can be earned onthe rate of return that can be earned on

the investmentthe investment Time value of money quantifies theTime value of money quantifies the

value of a Rupees through timevalue of a Rupees through time


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Uses of Time Value of MoneyUses of Time Value of Money Time Value of Money, or TVM, is a conceptTime Value of Money, or TVM, is a concept

that is used in all aspects of financethat is used in all aspects of finance

including:including: Bond valuationBond valuation

Stock valuationStock valuation

Accept/reject decisions for project managementAccept/reject decisions for project management

Financial analysis of firmsFinancial analysis of firms

And many others!And many others!


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FormulasFormulas Common formulas that are used in TVM calculations:Common formulas that are used in TVM calculations:**

Present value of a lump sum:Present value of a lump sum:

PV = CFPV = CFtt/ (1+r)/ (1+r)tt

OROR PV = FVPV = FVtt/ (1+r)/ (1+r)tt

Future value of a lump sum:Future value of a lump sum:

FVFVtt= CF= CF00 * (1+r)* (1+r)ttOROR FVFVtt= PV * (1+r)= PV * (1+r)

tt

Present value of a cash flow stream:Present value of a cash flow stream:

nn

PV =PV = 77[CF[CFtt/ (1+r)/ (1+r)tt]]

t=0t=0


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Formulas (continued)Formulas (continued) Future value of a cash flow stream:Future value of a cash flow stream:

nn

FV =FV = 77[CF[CFtt* (1+r)* (1+r)nn--tt

]]t=0t=0

Present value of an annuity:Present value of an annuity:

PVA = PMT * {[1PVA = PMT * {[1--(1+r)(1+r)--tt]/r}]/r}

Future value of an annuity:Future value of an annuity:

FVAFVAtt= PMT * {[(1+r)= PMT * {[(1+r)tt1]/r}1]/r}

* List adapted from the Prentice Hall Website


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VariablesVariables wherewhere

r = rate of returnr = rate of return

t = time periodt = time period n = number of time periodsn = number of time periods

PMT = paymentPMT = payment

CF = Cash flow (the subscripts t and 0 mean atCF = Cash flow (the subscripts t and 0 mean attime t and at time zero, respectively)time t and at time zero, respectively)

PV = present value (PVA = present value of anPV = present value (PVA = present value of anannuity)annuity)

FV = future value (FVA = future value of anFV = future value (FVA = future value of anannuity)annuity)


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Types of TVM CalculationsTypes of TVM Calculations There are many types of TVM calculationsThere are many types of TVM calculations

The basic types will be covered in this reviewThe basic types will be covered in this review

module and include:module and include: Present value of a lump sumPresent value of a lump sum

Future value of a lump sumFuture value of a lump sum

Present and future value of cash flow streamsPresent and future value of cash flow streams

Present and future value of annuitiesPresent and future value of annuities Keep in mind that these forms can, should,Keep in mind that these forms can, should,

and will be used in combination to solve moreand will be used in combination to solve morecomplex TVM problemscomplex TVM problems


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Basic RulesBasic Rules The following are simple rules that you should always use noThe following are simple rules that you should always use no

matter what type of TVM problem you are trying to solve:matter what type of TVM problem you are trying to solve:

1.1. Stop and think: Make sure you understand what theStop and think: Make sure you understand what theproblem is asking. You will get the wrong answer if youproblem is asking. You will get the wrong answer if youare answering the wrong question.are answering the wrong question.

2.2. Draw a representative timeline and label the cash flowsDraw a representative timeline and label the cash flowsand time periods appropriately.and time periods appropriately.

3.3. Write out the complete formula using symbols first andWrite out the complete formula using symbols first andthen substitute the actual numbers to solve.then substitute the actual numbers to solve.

While these may seem like trivial and time consuming tasks,While these may seem like trivial and time consuming tasks,they will significantly increase your understanding of thethey will significantly increase your understanding of thematerial and your accuracy rate.material and your accuracy rate.


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Present Value of a Lump SumPresent Value of a Lump Sum Present value calculations determinePresent value calculations determine

what the value of a cash flow received inwhat the value of a cash flow received in

the future would be worth today (time 0)the future would be worth today (time 0)

The process of finding a present value isThe process of finding a present value iscalled discounting (called discounting (hint: it gets smallerhint: it gets smaller))

The interest rate used to discount cashThe interest rate used to discount cashflows is generally called the discount rateflows is generally called the discount rate


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Example of PV of a Lump SumExample of PV of a Lump Sum How much would Rs100 received five years from nowHow much would Rs100 received five years from now

be worth today if the current interest rate is 10%?be worth today if the current interest rate is 10%?

1.1. Draw a timelineDraw a timeline

The arrow represents the flow of money and theThe arrow represents the flow of money and the

numbers under the timeline represent the time period.numbers under the timeline represent the time period.

Note that time period zero is today.Note that time period zero is today.

0 1 2 3 4 5

Rs10

0

?i = 10%


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2.2. Write out the formula using symbols:Write out the formula using symbols:

PV =PV = CFCFtt/ (1+r)/ (1+r)tt

3.3. Insert the appropriate numbers:Insert the appropriate numbers:

PV = 100 / (1 + .1)PV = 100 / (1 + .1)55

4.4. Solve the formula:Solve the formula:

PV = Rs62.09PV = Rs62.09

Example of PV of a Lump SumExample of PV of a Lump Sum


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Future Value of a Lump SumFuture Value of a Lump SumYou can think of future value as theYou can think of future value as the

opposite of present valueopposite of present value

Future value determines the amountFuture value determines the amountthat a sum of money invested today willthat a sum of money invested today willgrow to in a given period of timegrow to in a given period of time

The process of finding a future value isThe process of finding a future value iscalled compounding (called compounding (hint: it getshint: it getslargerlarger))


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Example of FV of a Lump SumExample of FV of a Lump Sum How much money will you have in 5 years if you investHow much money will you have in 5 years if you invest

Rs100 today at a 10% rate of return?Rs100 today at a 10% rate of return?


2.2. Write out the formula using symbols:Write out the formula using symbols:

FVFVtt= CF= CF00 * (1+r)* (1+r)tt

00 11 22 33

Rs100Rs100 ??i = 10%i = 10%

44 55


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Example of FV of a Lump SumExample of FV of a Lump Sum3.3. Substitute the numbers into the formula:Substitute the numbers into the formula:

FV = Rs100 * (1+.1)FV = Rs100 * (1+.1)55

4.4. Solve for the future value:Solve for the future value:FV = Rs161.05FV = Rs161.05


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Some Things to NoteSome Things to Note In both of the examples, note that if you were toIn both of the examples, note that if you were to

perform the opposite operation on the answers (i.e.,perform the opposite operation on the answers (i.e.,find the future value of Rs62.09 or the present valuefind the future value of Rs62.09 or the present value

of Rs161.05) you will end up with your originalof Rs161.05) you will end up with your originalinvestment of Rs100.investment of Rs100. This illustrates how present value and future valueThis illustrates how present value and future value

concepts are intertwined. In fact, they are the sameconcepts are intertwined. In fact, they are the sameequation . . .equation . . . Take PV =Take PV = FVFVtt/ (1+r)/ (1+r)

ttand solve forand solve for FVFVtt. You will get. You will get FVFVtt==PV * (1+r)PV * (1+r)tt..


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AnnuitiesAnnuitiesAn annuity is a cash flow stream in which theAn annuity is a cash flow stream in which the

cash flows are all equal and occur at regularcash flows are all equal and occur at regular

intervals.intervals. Note that annuities can be a fixed amount, anNote that annuities can be a fixed amount, an

amount that grows at a constant rate overamount that grows at a constant rate overtime, or an amount that grows at varioustime, or an amount that grows at various

rates of growth over time. We will focus onrates of growth over time. We will focus onfixed amounts.fixed amounts.


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Example of PV of an AnnuityExample of PV of an Annuity Assume that Ahmed owns an investment that willAssume that Ahmed owns an investment that will

pay her Rs100 each year for 20 years. The currentpay her Rs100 each year for 20 years. The currentinterest rate is 15%. What is the PV of thisinterest rate is 15%. What is the PV of thisannuity?annuity?


00 11 22 33 .. 1919 2020

Rs100Rs100Rs100Rs100Rs100Rs100Rs100Rs100 Rs100Rs100

??

i = 15%i = 15%


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Example of PV of an AnnuityExample of PV of an Annuity2.2. Write out the formula using symbols:Write out the formula using symbols:

PVA = PMT * {[1PVA = PMT * {[1--(1+r)(1+r)--tt]/r}]/r}

3.3. Substitute appropriate numbers:Substitute appropriate numbers:

PVA = Rs100 * {[1PVA = Rs100 * {[1--(1+.15)(1+.15)--2020]/.15}]/.15}

4.4. Solve for the PVSolve for the PV

PVA = Rs100 * 6.2593PVA = Rs100 * 6.2593

PVA = Rs625.93PVA = Rs625.93


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Example of FV of an AnnuityExample of FV of an Annuity Assume that Ahmed owns an investment that willAssume that Ahmed owns an investment that will

pay her Rs100 each year for 20 years. The currentpay her Rs100 each year for 20 years. The currentinterest rate is 15%. What is the FV of thisinterest rate is 15%. What is the FV of thisannuity?annuity?


00 11 22 33 .. 1919 2020

Rs100Rs100Rs100Rs100Rs100Rs100Rs100Rs100 Rs100Rs100

i = 15%i = 15%

??


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Example of FV of an AnnuityExample of FV of an Annuity2.2. Write out the formula using symbols:Write out the formula using symbols:

FVAFVAtt= PMT * {[(1+r)= PMT * {[(1+r)tt1]/r}1]/r}

3.3. Substitute the appropriate numbers:Substitute the appropriate numbers:

FVAFVA2020 = Rs100 * {[(1+.15)= Rs100 * {[(1+.15)20201]/.151]/.15

4.4. Solve for the FV:Solve for the FV:FVAFVA2020 = Rs100 * 102.4436= Rs100 * 102.4436

FVAFVA2020 = Rs10,244.36= Rs10,244.36

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