Financial Accounting Tools for Business Decision Making apendix d time value of MOney

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TIME VALUE
OF MONEY

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D

Financial Accounting, Seventh Edition


Learning
Learning Objectives
Objectives
After studying this chapter, you should be able to:

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1.

Distinguish between simple and compound interest.

2.

Solve for future value of a single amount.

3.

Solve for future value of an annuity.

4.

Identify the variables fundamental to solving present value problems.

5.

Solve for present value of a single amount.

6.

Solve for present value of an annuity.

7.

Compute the present value of notes and bonds.

8.

Use a financial calculator to solve time value of money problems.


Basic
Basic Time
Time Value
Value Concepts
Concepts
Time Value of Money
Would you rather receive $1,000 today or in a year
from now?

Today! “Interest Factor”

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Nature
Nature of
of Interest
Interest


Payment for the use of money.



Excess cash received or repaid over the amount
borrowed (principal).

Variables involved in financing transaction:

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1.

Principal (p) - Amount borrowed or invested.

2.

Interest Rate (i) – An annual percentage.

3.

Time (n) - The number of years or portion of a year
that the principal is borrowed or invested.

LO 1 Distinguish between simple and compound interest.


Nature
Nature of
of Interest
Interest
Simple Interest


Interest computed on the principal only.

Illustration:
Assume you borrow $5,000 for 2 years at a simple interest
of 12% annually. Calculate the annual interest cost.
Illustration D-1

Interest = p x i x n

FULL YEAR

= $5,000 x .12 x 2
= $1,200

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LO 1 Distinguish between simple and compound interest.


Nature
Nature of
of Interest
Interest
Compound Interest




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Computes interest on
►

the principal and

►

any interest earned that has not been paid or
withdrawn.

Most business situations use compound interest.

LO 1 Distinguish between simple and compound interest.

Nature
Nature of
of Interest
Interest -- Compound
Compound Interest
Interest
Illustration: Assume that you deposit $1,000 in Bank Two, where it
will earn simple interest of 9% per year, and you deposit another
$1,000 in Citizens Bank, where it will earn compound interest of 9%
per year compounded annually. Also assume that in both cases you
will not withdraw any interest until three years from the date of deposit.
Illustration D-2
Simple versus compound interest

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Year 1 $1,000.00 x 9%

$ 90.00

$ 1,090.00

Year 2 $1,090.00 x 9%

$ 98.10

$ 1,188.10

Year 3 $1,188.10 x 9%

$106.93

$ 1,295.03

LO 1 Distinguish between simple and compound interest.


Future
Future Value
Value of
of aa Single
Single Amount
Amount
Future value of a single amount is the value at a future
date of a given amount invested, assuming compound
interest.

FV = p x (1 + i )n
FV =
p =
i =
n =
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Illustration D-3
Formula for future value

future value of a single amount
principal (or present value; the value today)
interest rate for one period

number of periods
LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of aa Single
Single Amount
Amount
Illustration: If you want a 9% rate of return, you would
compute the future value of a $1,000 investment for three
years as follows:

Illustration D-4

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LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of aa Single
Single Amount
Amount

Alternate
Method

Illustration: If you want a 9% rate of return, you would
compute the future value of a $1,000 investment for three
years as follows:
Illustration D-4

What table do we use?
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LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of aa Single
Single Amount
Amount

What factor do we use?
$1,000
Present Value

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x

1.29503
Factor

=

$1,295.03
Future Value

LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of aa Single
Single Amount
Amount
Illustration:

Illustration D-5

What table do we use?
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LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of aa Single
Single Amount
Amount

$20,000
Present Value
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x

2.85434
Factor

=

$57,086.80
Future Value

LO 2 Solve for a future value of a single amount.


Future
Future Value
Value of
of an
an Annuity
Annuity
Future value of an annuity is the sum of all the payments
(receipts) plus the accumulated compound interest on
them.
Necessary to know the
1. interest rate,
2. number of compounding periods, and

3. amount of the periodic payments or receipts.

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LO 3 Solve for a future value of an annuity.


Future
Future Value
Value of
of an
an Annuity
Annuity
Illustration: Assume that you invest $2,000 at the end of
each year for three years at 5% interest compounded
annually.
Illustration D-6

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LO 3 Solve for a future value of an annuity.


Future
Future Value
Value of
of an
an Annuity
Annuity
Illustration:

Invest = $2,000
i = 5%
n = 3 years

Illustration D-7

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LO 3 Solve for a future value of an annuity.


Future
Future Value
Value of
of an
an Annuity
Annuity
When the periodic payments (receipts) are the same in each
period, the future value can be computed by using a future
value of an annuity of 1 table.
Illustration:

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Illustration D-8

LO 3 Solve for a future value of an annuity.


Future

Future Value
Value of
of an
an Annuity
Annuity

What factor do we use?
$2,500
Payment

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x

4.37462
Factor

=

$10,936.55
Future Value

LO 3 Solve for a future value of an annuity.


Present
Present Value
Value Concepts
Concepts
The present value is the value now of a given amount to

be paid or received in the future, assuming compound
interest.
Present value variables:
1. Dollar amount to be received in the future,
2. Length of time until amount is received, and
3. Interest rate (the discount rate).

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LO 4 Identify the variables fundamental to solving present value problems.


Present
Present Value
Value of
of aa Single
Single Amount
Amount
Illustration D-9
Formula for present value

Present Value = Future Value / (1 + i )n
p = principal (or present value)
i = interest rate for one period
n = number of periods

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LO 5 Solve for present value of a single amount.

Present
Present Value
Value of
of aa Single
Single Amount
Amount
Illustration: If you want a 10% rate of return, you would
compute the present value of $1,000 for one year as
follows:

Illustration D-10

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LO 5 Solve for present value of a single amount.


Present
Present Value
Value of
of aa Single
Single Amount
Amount
Illustration D-10

Illustration: If you want a 10% rate of return, you can also
compute the present value of $1,000 for one year by using
a present value table.

What table do we use?
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LO 5 Solve for present value of a single amount.


Present
Present Value
Value of
of aa Single
Single Amount
Amount

What factor do we use?
$1,000
Future Value
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x

.90909
Factor

=

$909.09
Present Value

LO 5 Solve for present value of a single amount.

Present
Present Value
Value of
of aa Single
Single Amount
Amount
Illustration D-11

Illustration: If you receive the single amount of $1,000 in
two years, discounted at 10% [PV = $1,000 / 1.102], the
present value of your $1,000 is $826.45.

What table do we use?
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LO 5 Solve for present value of a single amount.