1
Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved.
Time Value of
Money
Concepts
6
6-2
Time Value of Money
Interest is the
rent paid for the use
of money over time.
That’s right! A dollar
today is more valuable
than a dollar to be
received in one year.
6-3
Learning Objectives
Explain the difference between simple and
compound interest.
2
6-4
Simple Interest
Interest amount = P × i × n
Assume you invest $1,000 at 6% simple interest
for 3 years.
You would earn $180 interest.
($1,000 × .06 × 3 = $180)
(or $60 each year for 3 years)
6-5
Compound Interest
Compound interest includes interest not only on

Assume we will save $1,000 for three years and
earn 6% interest compounded annually.
$1,000.00 × 1.06 = $1,060.00
and
$1,060.00 × 1.06 = $1,123.60
and
$1,123.60 × 1.06 = $1,191.02
4
6-10
Writing in a more efficient way, we can say . . . .
$1,000 × 1.06 × 1.06 × 1.06 = $1,191.02
or
$1,000 × [1.06]
3
= $1,191.02
Future Value of a Single Amount
6-11
$1,000 × [1.06]
3
= $1,191.02
We can generalize this as . . .
FV = PV (1 +
i
)
n
Future
Value
Present
Value
Interest

known future amount.
This is a present value question.
Present value of a single amount is today’s
equivalent to a particular amount in the future.
Present Value of a Single Amount
6
6-16
Remember our equation?
FV = PV (1 + i)
n
We can solve for PV and get . . . .
FV
(1 +
i
)
n
PV =
Present Value of a Single Amount
6-17
Find the
Present Value
of $1 table in
your textbook.
Hey, it looks
familiar!
Present Value of a Single Amount
6-18
Assume you plan to buy a new car in 5
years and you think it will cost $20,000 at
that time.

Number
of Compounding
Periods
There are four variables needed when
determining the time value of money.
If you know any three of these, the fourth
can be determined.
Solving for Other Values
8
6-22
Suppose a friend wants to borrow $1,000 today
and promises to repay you $1,092 two years
from now. What is the annual interest rate you
would be agreeing to?
a. 3.5%
b. 4.0%
c. 4.5%
d. 5.0%
Determining the Unknown Interest Rate
6-23
Suppose a friend wants to borrow $1,000 today
and promises to repay you $1,092 two years
from now. What is the annual interest rate you
would be agreeing to?
a. 3.5%
b. 4.0%
c. 4.5%
d. 5.0%
Determining the Unknown Interest Rate
Present Value of $1 Table

note does, in fact, include interest.
We impute an appropriate interest
rate for a loan of this type to use
as the interest rate.
No Explicit Interest
6-26
Statement of Financial Accounting Concepts No. 7
“Using Cash Flow Information and Present Value in
Accounting Measurements”
The objective of
valuing an asset or
liability using
present value is to
approximate the fair
value of that asset
or liability.
Expected Cash Flow
×
Risk-Free Rate of Interest
Present Value
Expected Cash Flow Approach
6-27
Learning Objectives
Explain the difference between an ordinary
annuity and an annuity due.
10
6-28
An annuity is a series of equal periodic
payments.
Basic Annuities

What will be the fund balance at the end of 10
years?
Future Value of an Ordinary Annuity
Amount of annuity 2,500.00$
Future value of ordinary annuity of $1
(i = 8%, n = 10)
×
14.4866
Future value 36,216.50$
12
6-34
Future Value of an Annuity Due
To find the future
value of an annuity
due, multiply the
amount of a single
payment or receipt
by the future value
of an ordinary
annuity factor.
6-35
Compute the future value of $10,000
invested at the beginning of each of the
next four years with interest at 6%
compounded annually.
Future Value of an Annuity Due
Amount of annuity 10,000$
FV of annuity due of $1
(i=6%, n=4)
×

Annuity Factor Value
PV1 10,000$ 0.90909 9,090.90$
PV2 10,000 0.82645 8,264.50
PV3 10,000 0.75131 7,513.10
PV4 10,000 0.68301 6,830.10
Total 3.16986 31,698.60$
Present Value of an Ordinary Annuity
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6-40
PV of $1 Present
Annuity Factor Value
PV1 10,000$ 0.90909 9,090.90$
PV2 10,000 0.82645 8,264.50
PV3 10,000 0.75131 7,513.10
PV4 10,000 0.68301 6,830.10
Total 3.16986 31,698.60$
Can you find this value in the Present Value of
Ordinary Annuity of $1 table?
Present Value of an Ordinary Annuity
More Efficient Computation
$10,000 × 3.16986 = $31,698.60
6-41
How much must a person 65 years old invest
today at 8% interest compounded annually to
provide for an annuity of $20,000 at the end
of each of the next 15 years?
a. $153,981
b. $171,190
c. $167,324
d. $174,680

is expected to occur more than one
period after the date of the
agreement.
Present Value of a Deferred Annuity
6-45
On January 1, 2006, you are considering an investment
that will pay $12,500 a year for 2 years beginning on
December 31, 2008. If you require a 12% return on
your investments, how much are you willing to pay for
this investment?
1/1/06 12/31/06 12/31/07 12/31/08 12/31/09 12/31/10
Present
Value?
$12,500 $12,500
1 2 3 4
Present Value of a Deferred Annuity
Payment
PV of $1
i = 12%
PV n
1 12,500$ 0.71178 8,897$ 3
2 12,500 0.63552 7,944 4
16,841$
16
6-46
On January 1, 2006, you are considering an investment
that will pay $12,500 a year for 2 years beginning on
December 31, 2008. If you require a 12% return on
your investments, how much are you willing to pay for
this investment?

Future Value
PV of $1
n=2, i = 12%
PV
21,126$ 0.79719 16,841$
6-48
Learning Objectives
Solve for unknown values in annuity situations
involving present value.
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6-49
In present value problems involving annuities,
there are four variables:
Solving for Unknown Values in Present
Value Situations
Present value of an
ordinary annuity or
Present value of an
annuity due
The amount of the
annuity payment
The number of
periods
The interest rate
If you know any three of these, the fourth can be
determined.
6-50
Solving for Unknown Values in Present
Value Situations
Assume that you borrow $700 from a friend and

PV of ordinary annuity of $1
(i=8%, n=4)
÷
3.31213
Annuity am ount 211.34$
18
6-52
Learning Objectives
Briefly describe how the concept of the time
value of money is incorporated into the
valuation of bonds, long-term leases, and
pension obligations.
6-53
Because financial instruments
typically specify equal periodic
payments, these applications quite
often involve annuity situations.
Accounting Applications of Present Value
Techniques—Annuities
Long-term
Bonds
Long-term
Leases
Pension
Obligations
6-54
Valuation of Long-term Bonds
Calculate the Present Value
of the Lump-sum Maturity
Payment (Face Value)

recording of an asset
and corresponding
liability at the present
value of future lease
payments.
6-56
Valuation of Pension Obligations
Some pension plans
create obligations during
employees’ service periods
that must be paid during
their retirement periods.
The amounts contributed
during the employment
period are determined
using present value
computations of the
estimate of the future
amount to be paid during
retirement.
6-57
End of Chapter 6