8/6/2019 MBA Prep Summer Tech
1/51
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
Copyright 2000 Suzan Murphy
8/6/2019 MBA Prep Summer Tech
2/51
August, 2000 UT Department of Finance
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
Frequency of Compounding
Annuities Multiple Cash Flows
Bond Valuation
8/6/2019 MBA Prep Summer Tech
3/51
August, 2000 UT Department of Finance
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?
8/6/2019 MBA Prep Summer Tech
4/51
August, 2000 UT Department of Finance
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?
8/6/2019 MBA Prep Summer Tech
5/51
August, 2000 UT Department of Finance
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.
8/6/2019 MBA Prep Summer Tech
6/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
7/51
August, 2000 UT Department of Finance
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%
8/6/2019 MBA Prep Summer Tech
8/51
August, 2000 UT Department of Finance
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 =
8/6/2019 MBA Prep Summer Tech
9/51
August, 2000 UT Department of Finance
Future Value
(HP 17 B II Calculator)
Future Value
(HP 17 B II Calculator)
2
6
2000 +/-
N
I%Yr
PV
2,247.20FV
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
10/51
August, 2000 UT Department of Finance
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%
8/6/2019 MBA Prep Summer Tech
11/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
12/51
August, 2000 UT Department of Finance
Future Value
(HP 17 B II Calculator)
Future Value
(HP 17 B II Calculator)
8
5000 +/-
FV
N
I%Yr
PV
7,346.64
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
5
8/6/2019 MBA Prep Summer Tech
13/51
August, 2000 UT Department of Finance
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..
8/6/2019 MBA Prep Summer Tech
14/51
August, 2000 UT Department of Finance
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]
8/6/2019 MBA Prep Summer Tech
15/51
August, 2000 UT Department of Finance
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.
8/6/2019 MBA Prep Summer Tech
16/51
August, 2000 UT Department of Finance
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)
8/6/2019 MBA Prep Summer Tech
17/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
18/51
August, 2000 UT Department of Finance
Present Value
(HP 17 B II Calculator)
Present Value
(HP 17 B II Calculator)
10
6
4000
PV
N
I%Yr
FV
-2,233.57
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
19/51
August, 2000 UT Department of Finance
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%
8/6/2019 MBA Prep Summer Tech
20/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
21/51
August, 2000 UT Department of Finance
Present Value
(HP 17 B II Calculator)
Present Value
(HP 17 B II Calculator)
5
4
2,500 +/-
N
I%Yr
FV
2,054.81PV
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
22/51
August, 2000 UT Department of Finance
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?
8/6/2019 MBA Prep Summer Tech
23/51
August, 2000 UT Department of Finance
(HP
17 BII
Calculator)(HP
17 BII
Calculator)
5
2000 +/-
2,676.45
I%Yr
N
PV
FV
6.00
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
24/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
25/51
August, 2000 UT Department of Finance
Frequency of Compounding
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
8/6/2019 MBA Prep Summer Tech
26/51
August, 2000 UT Department of Finance
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 =
8/6/2019 MBA Prep Summer Tech
27/51
August, 2000 UT Department of Finance
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
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
28/51
August, 2000 UT Department of Finance
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.
8/6/2019 MBA Prep Summer Tech
29/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
30/51
August, 2000 UT Department of Finance
Future Value
(HP 17 B II Calculator)
Future Value
(HP 17 B II Calculator)
1,000 +/-
3
7
FV
PMT
N
I%Yr
3,214.90
Exit until you get Fin Menu.
2nd, Clear Data.
Choose Fin, then TVM
8/6/2019 MBA Prep Summer Tech
31/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
32/51
8/6/2019 MBA Prep Summer Tech
33/51
August, 2000 UT Department of Finance
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%
8/6/2019 MBA Prep Summer Tech
34/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
35/51
August, 2000 UT Department of Finance
Multiple Cash Flow Solution
(HP 17 B II Calculator)
Multiple Cash Flow Solution
(HP 17 B II Calculator)
FIN
Flow(0)=?
Flow(1)=?
Flow(2)=?
CFLO
0
500
600
Exit until you get Fin Menu.
2nd, Clear Data.
Flow(3)=? 10,700
NVP
I%5
Calc
Exit
# Times (2) = 1
Input# Times (1) = 1
Input
Input
Input
Input
Input
8/6/2019 MBA Prep Summer Tech
36/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
37/51
August, 2000 UT Department of Finance
Bond Valuation Solution
(HP 17 B II Calculator)
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
8/6/2019 MBA Prep Summer Tech
38/51
August, 2000 UT Department of Finance
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
8/6/2019 MBA Prep Summer Tech
39/51
8/6/2019 MBA Prep Summer Tech
40/51
August, 2000 UT Department of Finance
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?
8/6/2019 MBA Prep Summer Tech
41/51
August, 2000 UT Department of Finance
Solution (HP 17 B II Calculator)
Problem #1
Solution (HP 17 B II Calculator)
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.
8/6/2019 MBA Prep Summer Tech
42/51
August, 2000 UT Department of Finance
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.
8/6/2019 MBA Prep Summer Tech
43/51
August, 2000 UT Department of Finance
Possible Answers - Problem 2
$400
$431.01
$452.56
Need a
Hint?
Need a
Hint?
8/6/2019 MBA Prep Summer Tech
44/51
August, 2000 UT Department of Finance
Solution (HP 17 B II Calculator)
Problem #2
Solution (HP 17 B II Calculator)
Problem #2Exit until you get Fin Menu.
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
8/6/2019 MBA Prep Summer Tech
45/51
August, 2000 UT Department of Finance
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%.
8/6/2019 MBA Prep Summer Tech
46/51
August, 2000 UT Department of Finance
Possible Solutions - Problem 3
$1,000
$921.37
$1021.37
Need a
Hint?
Need a
Hint?
8/6/2019 MBA Prep Summer Tech
47/51
August, 2000 UT Department of Finance
Solution (HP 17 B II Calculator)
Problem #3
Solution (HP 17 B II Calculator)
Problem #3Exit until you get Fin Menu.
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
8/6/2019 MBA Prep Summer Tech
48/51
August, 2000 UT Department of Finance
Congratulations!
You obviously understand this material.
Now try the next problem.
The Interactive Exercises are found on slide
#37.
8/6/2019 MBA Prep Summer Tech
49/51
August, 2000 UT Department of Finance
Comparing PV to FV
Remember, both quantities must be present
value amounts or both quantities must be
future value amounts in order to becompared.
8/6/2019 MBA Prep Summer Tech
50/51
August, 2000 UT Department of Finance
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.
8/6/2019 MBA Prep Summer Tech
51/51
August, 2000 UT Department of Finance
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).
Top Related