MBA Prep Summer Tech

8/6/2019 MBA Prep Summer Tech

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August, 2000 UT Department of Finance

The Time Value of Money

In order to work the problems in this module, the user should have the use of a

business calculator such as the Hewlett Packard 17BII.

The author grants individuals a limited license to use this presentation. It is

the sole property of the author who holds the corresponding copyrights. The

user agrees not to reproduce, duplicate or distribute any copies of thispresentation in any form.

The author would like to thank the Innovative Technology Center at The

University of Tennessee which supported this project with a grant through the

Teaching with Technology Summer Institute. She would also like to

commend the teachers who helped her design the module.

If you have any comments or suggestions on how to improve this presentation,

please e-mail the author at [email protected].

Copyright 2000 Suzan Murphy

In order to work the problems in this module, the user should have the use of a

business calculator such as the Hewlett Packard 17BII.

The author grants individuals a limited license to use this presentation. It is

the sole property of the author who holds the corresponding copyrights. The

user agrees not to reproduce, duplicate or distribute any copies of thispresentation in any form.

The author would like to thank the Innovative Technology Center at The

University of Tennessee which supported this project with a grant through the

Teaching with Technology Summer Institute. She would also like to

commend the teachers who helped her design the module.

If you have any comments or suggestions on how to improve this presentation,

please e-mail the author at smurp

[email protected].

Copyright 2000 Suzan Murphy


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The Time Value of MoneyThe Time Value of Money What is the Time Value of Money?

Compound Interest

Future Value Present Value

Frequency of Compounding

Annuities Multiple Cash Flows

Bond Valuation

What is the Time Value of Money?

Compound Interest

Future Value Present Value


Annuities Multiple Cash Flows

Bond Valuation


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Obviously, $1,000 today$1,000 today.

Money received sooner rather than later allows

one to use the funds for investment or

consumption purposes. This concept is referred

to as the TIME VALUE OF MONEYTIME VALUE OF MONEY!!

The Time Value of MoneyThe Time Value of Money

Which would you rather have -- $1,000 today$1,000 today or

$1,000 in 5 years?$1,000 in 5 years?


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TIMETIME allows one the opportunity to

postpone consumption and earn

INTERESTINTEREST.

NOT having the opportunity to earn

interest on money is called

OPPORTUNITY COST.

Why TIME?Why TIME?


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How can one compare amounts

in different time periods?

How can one compare amounts

in different time periods?

One can adjust values from different time

periods using an interest rate.

Remember, one CANNOT compare

numbers in different time periods withoutfirst adjusting them using an interest rate.


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Compound InterestCompound Interest

When interest is paid on not only the principal amountinvested, but also on any previous interest earned, this iscalled compound interest.

FV = Principal + (Principal x Interest)

= 2000 + (2000 x .06)

= 2000 (1 + i)

= PV (1 + i)

Note: PV refers to Present Value or Principal


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Ifyou invested $2,000 today in an account that$2,000 today in an account thatpays 6pays 6% interest, with interest compounded

annually, how much will be in the account at theend of two years if there are no withdrawals?

Future Value

(Graphic)

Future Value

(Graphic)

0 1 2

$2,000$2,000

FVFV

6%


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FVFV11 = PVPV (1+i)n = $2,000$2,000 (1.06)2

= $2,247.20$2,247.20

Future Value

(F

ormula)

Future Value

(F

ormula)

FV = future value, a value at some future point in time

PV = present value, a value today which is usually designated as time 0

i = rate of interest per compounding period

n = number of compounding periods

Calculator Keystrokes: 1.06 (2nd yx) 2 x 2000 =


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Future Value

(HP 17 B II Calculator)

Future Value


2

6

2000 +/-

N

I%Yr

PV

2,247.20FV

Exit until you get Fin Menu.

2nd, Clear Data.

Choose Fin, then TVM


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John wants to know how large his $5,000$5,000 deposit will

become at an annual compound interest rate of 8% at

the end of5 years5 years.

F

uture Value ExampleF

uture Value Example

0 1 2 3 4 55

$5,000$5,000

FVFV55

8%


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Calculator keystrokes: 1.08 2nd yx x 5000 =

F

uture ValueS

olutionF

uture ValueS

olution Calculation based on general

formula: FVFVnn = PV (1+i)n

FVFV55 = $5,000 (1+ 0.08)5= $7,346.64$7,346.64


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Future Value


Future Value


8

5000 +/-

FV

N

I%Yr

PV

7,346.64


2nd, Clear Data.


5


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Double Your Money!!!Double Your Money!!!

Quick! How long does it take to double $5,000

at a compound rate of 12% per year

(approx.)?

We will use the RuleRule--ofof--7272..


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The R

ule-of-72The R

ule-of-72

Quick! How long does it take to double $5,000

at a compound rate of 12% per year

(approx.)?

Approx.Yearsto Double = 7272 / i%

7272 / 12% = 6 Years6 Years[Actual Time is 6.12 Years]


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Present ValuePresent Value

Since FV = PV(1 + i)n.

PVPV = FVFV / (1+i)n.

Discounting is the process of translating a

future value or a set of future cash flows

into a present value.


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Assume that you need to have exactly $4,000$4,000 saved10 years from now.years from now. How much must you deposittoday in an account that pays 6% interest,

compounded annually, so that you reach your goal of$4,000?

0 55 10

$4,000$4,000

6%

PVPV00

Present Value

(Graphic)

Present Value

(Graphic)


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PVPV00 = FVFV / (1+i)2 = $4,000$4,000 / (1.06)10

= $2,233.58$2,233.58

Present Value

(F

ormula)

Present Value

(F

ormula)

0 55 10

$4,000$4,000

6%

PVPV00


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Present Value


Present Value


10

6

4000

PV

N

I%Yr

FV

-2,233.57


2nd, Clear Data.



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Joann needs to know how large of a deposit to

make today so that the money will grow to $2,500$2,500

in 5 years. Assume todays deposit will grow at a5 years. Assume todays deposit will grow at a

compound rate ofcompound rate of 4% annually.

Present Value ExamplePresent Value Example

0 1 2 3 4 55

$2,500$2,500

PVPV00

4%


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Calculation based on general

formula: PVPV00 = FVFVnn / (1+i)n

PVPV00 = $2,500/(1.04)$2,500/(1.04)55

= $2,054.81

Calculator keystrokes: 1.04 2nd yx 5 =2nd 1/x X 2500 =

Present Value SolutionPresent Value Solution


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Present Value


Present Value


5

4

2,500 +/-

N

I%Yr

FV

2,054.81PV


2nd, Clear Data.



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Finding n oriwhen one

knows PV and FV

Finding n oriwhen one

knows PV and FV

If one invests $2,000 today and hasIf one invests $2,000 today and has

accumulated $2,676.45 after exactly fiveaccumulated $2,676.45 after exactly fiveyears, what rate of annual compoundyears, what rate of annual compound

interest was earned?interest was earned?


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(HP

17 BII

Calculator)(HP

17 BII

Calculator)

5

2000 +/-

2,676.45

I%Yr

N

PV

FV

6.00


2nd, Clear Data.



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General Formula:

FVn = PVPV00(1 + [i/m])mn

n: Number of Years

m: Compounding Periods per Year

i: Annual Interest Rate

FVn,m: FV at the end of Year n

PVPV00: PV of the Cash Flow today

Frequency of

Compounding

Frequency of

Compounding


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Example Suppose you deposit $1,000 in an account that

pays 12% interest, compounded quarterly. How

much will be in the account after eight years ifthere are no withdrawals?

PV = $1,000

i = 12%/4 = 3% per quarter

n = 8 x 4 = 32 quarters


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Solution based on formula:

FV= PV (1 + i)n

= 1,000(1.03)32

= 2,575.10

Calculator Keystrokes:

1.03 2nd yx 32 X 1000 =


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Future Value, Frequency of

Compounding (HP 17 B II Calculator)

Future Value, Frequency of

Compounding (HP 17 B II Calculator)

32

3

1000 +/-

N

I%Yr

PV

2,575.10FV


2nd, Clear Data.



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AnnuitiesAnnuities

Examples of Annuities Include:Student Loan Payments

Car Loan PaymentsInsurance Premiums

Mortgage Payments

Retirement Savings

An AnnuityAn Annuityrepresents a series of

equal payments (or receipts) occurring

over a specified number of equidistantperiods.


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FVAFVA33 = $1,000(1.07)2 + $1,000(1.07)1 +

$1,000(1.07)0 = $3,215$3,215

If one saves $1,000 a year at the end of every year for threeIf one saves $1,000 a year at the end of every year for three

years in an account earning 7% interest, compoundedyears in an account earning 7% interest, compounded

annually, how much will one have at the end of theannually, how much will one have at the end of the

third year?third year?

Example of an Ordinary

Annuity --

FVA

Example of an Ordinary

Annuity --

FVA

$1,000 $1,000 $1,000

0 1 2 33 4

$3,215

= FVA$3,215

= FVA33

End of Year

7%

$1,070

$1,145


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Future Value


Future Value


1,000 +/-

3

7

FV

PMT

N

I%Yr

3,214.90


2nd, Clear Data.



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PVAPVA33 = $1,000/(1.07)1 + $1,000/(1.07)2 +

$1,000/(1.07)3 = $2,624.32$2,624.32

If one agrees to repay a loan by paying $1,000 a year atIf one agrees to repay a loan by paying $1,000 a year at

the end of every year for three years and the discountthe end of every year for three years and the discount

rate is 7%, how much could one borrow today?rate is 7%, how much could one borrow today?

Example of anOrdinary

Annuity --

PVA

Example of anOrdinary

Annuity --

PVA

$1,000 $1,000 $1,000

0 1 2 33 4

$2,624.32 = PVA$2,624.32 = PVA33

End of Year

7%

$934.58$873.44$816.30


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Suppose an investment promises a cash flow of $500 in one

year, $600 at the end of two years and $10,700 at the end of

the third year. If the discount rate is 5%, what is the value of

this investment today?

Multiple Cash Flows ExampleMultiple Cash Flows Example

0 1 2 3

$500 $600 $10,700$500 $600 $10,700

PVPV00

5%5%


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Multiple Cash Flow SolutionMultiple Cash Flow Solution

0 1 2 3

$500 $600 $10,700$500 $600 $10,700

5%

$476.19$476.19$544.22$544.22$9,243.06$9,243.06

$10,263.47$10,263.47== PVPV00 of the Multipleof the MultipleCash FlowsCash Flows


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Multiple Cash Flow Solution


Multiple Cash Flow Solution


FIN

Flow(0)=?

Flow(1)=?

Flow(2)=?

CFLO

0

500

600


2nd, Clear Data.

Flow(3)=? 10,700

NVP

I%5

Calc

Exit

# Times (2) = 1

Input# Times (1) = 1

Input

Input

Input

Input

Input


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Bond Valuation ProblemBond Valuation Problem

Find todays value of a coupon bond with a

maturity value of $1,000 and a coupon rate of

6%. The bond will mature exactly ten years from

today, and interest is paid semi-annually. Assumethe discount rate used to value the bond is 8.00%

because that is your required rate of return on an

investment such as this.

Interest = $30 every six months for 20 periods

Interest rate = 8%/2 = 4% every six months


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Bond Valuation Solution


Bond Valuation Solution

(HP 17 B II Calculator)Exit until you get Fin Menu.

2nd, Clear Data

FIN TVM

1000

30

4

20

PV

PMT

FV

I%YR

N

-864.09

0 1 2 . 20

30 30 30

1000


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Welcome to the Interactive

Exercises Choose a problem; select a solution

To return to this page (slide 37), use Power Points

Navigation Menu

Choose Go and By Title

1122

33


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Possible Answers - Problem 1

$25,000 in cash today

$30,000 in cash to be received two years

from now Either option O.K.

Need a Hint?Need a Hint?Need a Hint?Need a Hint?


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Solution (HP 17 B II Calculator)

Problem #1


Problem #1Exit until you get Fin Menu.

2nd, Clear Data

Choose FIN, then TVM

I%YR

N

FV

-25,720.16PV

30,000

8

2

Compare PV of $30,000, which is $25,720.16

to PV of $25,000. $30,000 to be received 2

years from now is better.


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Problem #2

What is the value of $100 per year for four

years, with the first cash flow one year from

today, if one is earning 5% interest,compounded annually? Find the value of

these cash flows four years from today.


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Possible Answers - Problem 2

$400

$431.01

$452.56

Need a

Hint?

Need a

Hint?


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Problem #2



2nd, Clear Data

Choose FIN, then TVM

PMT

FVA

=100(1.05)3

+ 100(1.05)2

+ 100(1.05)1

+ 100(1.05)0

100

I%YR

N

431.01

4

5

FV

0 1 2 3 4

100 100 100 100


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Problem #3

What is todays value of a $1,000 face value

bond with a 5% coupon rate (interest is paid

semi-annually) which has three yearsremaining to maturity. The bond is priced

to yield 8%.


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Possible Solutions - Problem 3

$1,000

$921.37

$1021.37

Need a

Hint?

Need a

Hint?


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Problem #3



2nd, Clear Data

FIN TVM

1000

25

4

6

PV

PMT

FV

I%YR

N

921.37

0 1 2 . 12

25 25 25

1000


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Congratulations!

You obviously understand this material.

Now try the next problem.

The Interactive Exercises are found on slide

#37.


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Comparing PV to FV

Remember, both quantities must be present

value amounts or both quantities must be

future value amounts in order to becompared.


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How to solve a time value of

money problem. The value four years from today is a

future value amount.

The expected cash flows of $100 per yearfor four years refers to an annuity of $100.

Since it is a future value problem and there

is an annuity, you need to solve for aFUTURE VALUE OF AN ANNUITY.


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Valuing a Bond

The interest payments represent an annuity and

you must find the present value of the annuity.

The maturity value represents a future valueamount and you must find the present value of this

single amount.

Since the interest is paid semi-annually, discount

at HALF the required rate of return (4%) andTWICE the number of years to maturity (6

periods).

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