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Chapter 9, Part 2
Time Value of Money
1. Present Value of a Single Amount
2. Present Value of an Annuity
3. Future Value of a Single Amount
4. Future Value of an Annuity
1
Introduction
The value of a dollar today will decrease
over time. Why?
 Two components determine the “time value”
of money:

– interest rate (i) for discounting and
compounding.
– number of periods (n) for discounting and
compounding.

For external financial reporting, we are
concerned primarily with present value
concepts.
 For investment decisions, we are also
concerned with future value concepts.
2
Introduction


Future Value concepts:
– What amount do we need to invest today to
accumulate a specific amount at retirement?
– What yearly amounts do we need to invest
to accumulate a specific future amount in an
education fund?
Present Value concepts:
– What is the value today of a payment
coming some time in the future?
– What is the value today of a series of equal
payments received each year for the next 20
years?
3
Present Value Concepts
To record activities in the general ledger
dealing with future cash flows, we should
calculate the present value of the future
cash flows using present value formulas or
techniques.
 Types of activities that require PV
calculations:

– investment decisions
– long term notes payable and notes receivable
– bonds payable and bond investments
4
Types of Present Value Calculations

PV of a single sum (PV1): discounting a
future value of a single amount that is to be
paid or received in the future.

PV of an annuity (PVA): discounting a set
of payments, equal in amount over equal
periods of time, where the first payment is
made at the end of each period.
5
1.Present Value of a Single Sum (PV1)
All present value calculations presume a discount
rate (i) and a number of periods of discounting (n).
There are 4 different ways you can calculate PV1:
n
1. Formula: PV1 = FV1 [1/(1+i) ]
2. Tables: see page 370, Table 9-2
PV1 Table
PV1 = FV1(
)
i, n
3.Calculator (if you have time value functions).
4.Excel spreadsheet.
(Note: we will use tables in class and on exams.)
6
Illustration 1: Long Term Notes Payable

May be interest bearing or non-interest bearing
(we will look at non-interest bearing).
 May be serial notes (periodic payments) or term
notes (balloon payments). We will look at balloon
payments here (serial payments, or annuities,
later).
 Illustration 1: On January, 2, 2008, Pearson
Company purchases a section of land for its new
plant site. Pearson issues a 5 year non-interest
bearing note, and promises to pay $50,000 at the
end of the 5 year period. What is the cash
equivalent price of the land, if a 6 percent
discount rate is assumed?
7
Illustration1 Solution
See page 370, Table 9-2
PV1 Table
PV1 = FV1(
)
i, n
PV1 Table
PV1 =
(
)
i=6%, n=5
Journal entry Jan. 2, 2008:
8
Illustration1 Solution, continued
Journal entry, December 31, 2008, assuming
Pearson uses the straight-line method to
recognize interest expense (12,650 / 5):
Carrying value on B/S at 12/31/2008?
Carrying value on B/S at 12/31/2012?
9
Illustration 2: Investment
Holliman Company wants to accumulate
$500,000 at the end of 10 years. What amount
must it invest today to achieve that balance,
assuming a 6% interest rate, compounded
annually?
PV1 Table
PV1 =
(
)
=
i=6%, n=10
What if the interest is compounded semiannually?
PV1 Table
PV1 =
(
)
=
10
2. Present Value of an Annuity (PVA)
An annuity is defined as equal payments over equal
periods of time. (Specifically, we are using an
ordinary annuity, which assumes that each payment
occurs at the end of each period.)
PVA calculations presume a discount rate (i), where
(A) = the amount of each annuity, and (n) = the
number of annuities (or rents), which is the same as
the number of periods of discounting. There are 4
different ways you can calculate PVA:
1. Formula: PVA = A [1-(1/(1+i)n)] / i
2. Tables: see page 372, Table 9-4 (We will use this.)
PVA Table
PVA = A(
)
i, n
3.Calculator (if you have time value functions).
4.Excel spreadsheets.
11
Illustration 3: Long Term Notes Payable

Illustration 3: On January, 2, 2008, Pearson
Company purchases a section of land for its new
plant site. Pearson issues a 5 year non-interest
bearing note, and promises to pay $10,000 per
year at the end of each of the next 5 years. What
is the cash equivalent price of the land, if a 6
percent discount rate is assumed?
12
Illustration 3 Solution
See page 372, Table 9-4
PVA Table
PVA =
A(
)
i, n
PVA Table
PVA =
(
)
i=6%, n=5
Journal entry Jan. 2, 2008:
13
Illustration 4: Annuity Income

Illustration 4: On January, 2, 2008, Donna Smith
won the lottery. She was offered an annuity of
$100,000 per year for the next 20 years, or
$1,000,000 today as an alternative settlement.
Which option should Donna choose. Assume that
she can earn an average 4 percent return on her
investments for the next 20 years.
 Solution: calculate the present value of the annuity
at a discount rate of 4%.
14
Illustration 4 Solution
See page 372, Table 9-4
PVA Table
PVA =
A(
)
i, n
PVA Table
PVA =
(
)
i=4%, n=20
Which should she choose?
At approximately what interest (discount) rate
would she choose differently? (Based on
whole percentage rate.)
15
Types of Future Value Calculations

FV of a single sum (FV1): compounding a
future value of a single amount that is to be
accumulated in the future. Example:
– projected future value of a savings bond.

FV of an annuity (FVA): compounding the
future value of a set of payments, equal in
amount over equal periods of time, where
the first payment is made at the end of the
first period. Examples:
– projected balance in a retirement account.
– amount of payments into retirement fund.
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3.Future Value of a Single Sum (FV1)
There are 4 different ways you can calculate the
FV1:
n
1. Formula: FV1 = PV1 [(1+i) ]
2. Tables: see page 369, Table 9-1
FV1 Table
FV1 = PV1(
)
i, n
3.Calculator (if you have time value functions).
4.Excel spreadsheet.
(Note: we will use tables in class and on exams.)
17
Illustration 5: Investment
Holliman Company wants to invest $200,000 cash
it received from the sale of land. What amount
will it accumulate at the end of 10 years,
assuming a 6% interest rate, compounded
annually?
FV1 Table
FV1 =
PV1
(
)
i, n
FV1 Table
FV1 =
(
)
=
i=6%, n=10
18
4.Future Value of an Annuity (FVA)
FVA calculations presume a compound rate (i), where
(A) = the amount of each annuity, and (n) = the
number of annuities (or rents), which is the same as
the number of periods of compounding. There are 4
different ways you can calculate FVA:
1. Formula: FVA = A [(1+i)n - 1] / i
2. Tables: see page 371, Table 9-3 (We will use this.)
FVA Table
FVA = A(
)
i, n
3.Calculator (if you have time value functions).
4.Excel spreadsheets.
19
Illustration 6: Future Value of Investment
Jane Smith wants to invest $10,000 each year for the
next 20 years, for her retirement. What balance will
she have at the end of 20 years, assuming a 6%
interest rate, compounded annually?
FVA Table
FVA =
A
(
)
=
i, n
FVA Table
FVA =
(
) =
i=6%, n=20
20
Illustration 7: Future Value of Investment
James Holliman wants to accumulate $200,000 at the
end of 10 years, for his son’s education fund. What
equal amount must he invest annually to achieve that
balance, assuming a 6% interest rate, compounded
annually?
FVA Table
FVA =
A
(
)
=
i, n
FVA Table
=
(
)
i=6%, n=10
21