Chapter 5
Time Value of
Money
3-1
After studying Chapter 5
you should be able to:
1.
2.
3.
4.
3-2
Understand what is meant by "the time value of money."
Understand the relationship between present and future value.
Describe how the interest rate can be used to adjust the value of
cash flows – both forward and backward – to a single point in
time.
Calculate both the future and present value of: (a) an amount
invested today; (b) a stream of equal cash flows (an annuity);
and (c) a stream of mixed cash flow.
The Time Value of Money

The Interest Rate

Simple Interest

Compound Interest

3-3
Compounding More Than
Once per Year
The Interest Rate
Which would you prefer -- $10,000
today or $10,000 in 5 years?
Obviously, $10,000 today.
You already recognize that there is
TIME VALUE TO MONEY!!
3-4
Why TIME?
Why is TIME such an important
element in your decision?
TIME allows you the opportunity to
postpone consumption and earn
INTEREST.
3-5
Types of Interest
 Simple
Interest
Interest paid (earned) on only the original
amount, or principal, borrowed (lent).
 Compound
Interest
Interest paid (earned) on any previous
interest earned, as well as on the
principal borrowed (lent).
3-6
Simple Interest Formula
Formula
3-7
SI = P0(i)(n)
SI:
Simple Interest
P0:
Deposit today (t=0)
i:
Interest Rate per Period
n:
Number of Time Periods
Simple Interest Example
 Assume
that you deposit $1,000 in an
account earning 7% simple interest for
2 years. What is the accumulated
interest at the end of the 2nd year?
SI
3-8
= P0(i)(n)
= $1,000(.07)(2)
= $140
Simple Interest (FV)
 What
is the Future Value (FV) of the
deposit?
FV
 Future
= P0 + SI
= $1,000 + $140
= $1,140
Value is the value at some future
time of a present amount of money, or a
series of payments, evaluated at a given
interest rate.
3-9
Simple Interest (PV)
 What
is the Present Value (PV) of the
previous problem?
The Present Value is simply the
$1,000 you originally deposited.
That is the value today!
 Present
3-10
Value is the current value of a
future amount of money, or a series of
payments, evaluated at a given interest
rate.
examples
If
u know that pv=1000
Interest
Future
How
rate = 6%
value = 1180
u can caculate number of
years for this investment?
3-11
examples
If
u know that during 3 years
Ur
future value is 1180
Interest
Can
rate is 6%
u compute ur initial value for
this investment
3-12
examples
If
u invest 1000 dollars by 6%
simply interest rate during:
26
9
weeks
months
240
days
How
3-13
u can calculate ur future
value
Why Compound Interest?
Future Value (U.S. Dollars)
Future Value of a Single $1,000 Deposit
3-14
20000
10% Simple
Interest
7% Compound
Interest
10% Compound
Interest
15000
10000
5000
0
1st Year 10th
Year
20th
Year
30th
Year
Distinguish invest 1000
dollars by 6% simply or
compounded rate for 3
years

3-15
then mention which is bettre for
investor ?
Future Value
Single Deposit (Graphic)
Assume that you deposit $1,000 at
a compound interest rate of 7% for
2 years.
0
7%
1
2
$1,000
FV2
3-16
Future Value
Single Deposit (Formula)
FV1 = P0 (1+i)1
= $1,000 (1.07)
= $1,070
Compound Interest
You earned $70 interest on your $1,000
deposit over the first year.
This is the same amount of interest you
would earn under simple interest.
3-17
Future Value
Single Deposit (Formula)
FV1
= P0 (1+i)1
FV2
= FV1 (1+i)1
= P0 (1+i)(1+i) = $1,000(1.07)(1.07)
= P0 (1+i)2
= $1,000(1.07)2
= $1,144.90
= $1,000 (1.07)
= $1,070
You earned an EXTRA $4.90 in Year 2 with
compound over simple interest.
3-18
General Future
Value Formula
FV1 = P0(1+i)1
FV2 = P0(1+i)2
etc.
General Future Value Formula:
FVn = P0 (1+i)n
or
3-19
FVn = P0 (FVIFi,n) -- See Table I
Valuation Using Table I
FVIFi,n is found on Table I
at the end of the book.
3-20
Period
1
2
3
4
5
6%
1.060
1.124
1.191
1.262
1.338
7%
1.070
1.145
1.225
1.311
1.403
8%
1.080
1.166
1.260
1.360
1.469
Using Future Value Tables
FV2
= $1,000 (FVIF7%,2)
= $1,000 (1.145)
= $1,145 [Due to Rounding]
Period
6%
7%
8%
1
1.060
1.070
1.080
2
1.124
1.166
1.145
3
1.191
1.225
1.260
4
1.262
1.311
1.360
5
1.338
1.403
1.469
3-21
Story Problem Example
Julie Miller wants to know how large her deposit
of $10,000 today will become at a compound
annual interest rate of 10% for 5 years.
0
1
2
3
4
5
10%
$10,000
FV5
3-22
Story Problem Solution

Calculation based on general formula:
FVn = P0 (1+i)n
FV5 = $10,000 (1+ 0.10)5
= $16,105.10
 Calculation
based on Table I:
FV5 = $10,000 (FVIF10%, 5)
= $10,000 (1.611)
= $16,110 [Due to Rounding]
3-23
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 “Rule-of-72”.
3-24
The “Rule-of-72”
Quick! How long does it take to
double $5,000 at a compound rate
of 12% per year (approx.)?
Approx. Years to Double = 72 / i%
72 / 12% = 6 Years
[Actual Time is 6.12 Years]
3-25
Example
3-26
you know that price of BMW always 20000
dollars. U like to buy one-currently u have only
7752 dollars-how many years will it take for your
initial investment of 7752 dollars to grow 20000- if
it is invested at 9% compounded annually
using table of ( FVIF)

If

ALSO IF u have currently 11167 dollars invested
for 10 years- what is interest rate u need to get
price of BMW –using same table
Present Value
Single Deposit (Graphic)
Assume that you need $1,000 in 2 years.
Let’s examine the process to determine
how much you need to deposit today at a
discount rate of 7% compounded annually.
0
7%
1
2
$1,000
PV0
3-27
PV1
Present Value
Single Deposit (Formula)
PV0 = FV2 / (1+i)2
= FV2 / (1+i)2
0
7%
= $1,000 / (1.07)2
= $873.44
1
2
$1,000
PV0
3-28
General Present
Value Formula
PV0 = FV1 / (1+i)1
PV0 = FV2 / (1+i)2
etc.
General Present Value Formula:
PV0 = FVn / (1+i)n
or
3-29
PV0 = FVn (PVIFi,n) -- See Table II
Valuation Using Table II
PVIFi,n is found on Table II
at the end of the book.
Period
1
2
3
4
5
3-30
6%
.943
.890
.840
.792
.747
7%
.935
.873
.816
.763
.713
8%
.926
.857
.794
.735
.681
Using Present Value Tables
PV2
3-31
= $1,000 (PVIF7%,2)
= $1,000 (.873)
= $873 [Due to Rounding]
Period
6%
7%
8%
1
.943
.935
.926
2
.890
.873
.857
3
.840
.816
.794
4
.792
.763
.735
5
.747
.713
.681
Story Problem Example
Julie Miller wants to know how large of a
deposit to make so that the money will
grow to $10,000 in 5 years at a discount
rate of 10%.
0
1
2
3
4
5
10%
$10,000
PV0
3-32
Story Problem Solution

Calculation based on general formula:
PV0 = FVn / (1+i)n
PV0 = $10,000 / (1+ 0.10)5
= $6,209.21

Calculation based on Table I:
PV0 = $10,000 (PVIF10%, 5)
= $10,000 (.621)
= $6,210.00 [Due to Rounding]
3-33
example
What
is present value of an
investment yields 500 dollars to
be received in 5 years and 1000
dollars to be received in 10 years
if u know that discount rate is 4%
for both
3-34
example
If
present value=676 and future
value= 1000 dollars and discount
rate was =4% so number of years
was 8 years using PVIF table
Mention:
3-35
true or falce and why.
Types of Annuities
 An
Annuity represents a series of equal
payments (or receipts) occurring over a
specified number of equidistant periods.
 Ordinary
Annuity: Payments or receipts
occur at the end of each period.
 Annuity
Due: Payments or receipts
occur at the beginning of each period.
3-36
Examples of Annuities
3-37

Student Loan Payments

Car Loan Payments

Insurance Premiums

Mortgage Payments

Retirement Savings