Financial accounting 9th kieso kimmel appendix g

G-1


Appendix

G

Time Value of Money
Accounting in Action

Learning Objectives
After studying this chapter, you should be able to:
[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] Compute the present values in capital budgeting situations.
[9] Use a financial calculator to solve time value of money problems.
G-2


Basic Time Value Concepts
Time Value of Money
Would you rather receive $1,000 today or in a year
from now?
Today! “Interest Factor”

G-3

Nature of Interest


Payment for the use of money.



Difference between amount borrowed or invested
(principal) and amount repaid or collected.

Elements involved in financing transaction:

G-4

1.

Principal (p): Amount borrowed or invested.

2.

Interest Rate (i): An annual percentage.

3.

Time (n): Number of years or portion of a year that
the principal is borrowed or invested.

LO 1

Nature of Interest
Simple Interest


Interest computed on the principal only.

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

2 FULL
YEARS

G-5

Interest = p x i x n
= $5,000 x .12 x 2
= $1,200
LO 1


Nature of Interest
Compound Interest




G-6

Computes interest on
►

the principal and

►

any interest earned that has not been paid or
withdrawn.

Most business situations use compound interest.

LO 1


Nature of Interest - Compound 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 G-2
Simple versus compound interest

G-7

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


Appendix

G

Time Value of Money
Accounting in Action

Learning Objectives
After studying this chapter, you should be able to:
[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] Compute the present values in capital budgeting situations.
[9] Use a financial calculator to solve time value of money problems.
G-8


Future Value Concepts
Future Value of a Single Amount
Future value of a single amount is the value at a future
date of a given amount invested, assuming compound
interest.
Illustration G-3
Formula for future value

FV = future value of a single amount
p
i
n
G-9

= principal (or present value; the value today)
= interest rate for one period
= number of periods
LO 2

Future Value of a Single 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 G-4
Time diagram

G-10

LO 2


Future Value of a Single 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 G-4
Time diagram

What table do we use?
G-11

LO 2

Future Value of a Single Amount

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

G-12

x

1.29503
Factor

=

$1,295.03
Future Value
LO 2


Future Value of a Single Amount
Illustration G-5
Demonstration problem—
Using Table 1 for FV of 1

Illustration:

What table do we use?
G-13

LO 2


Future Value of a Single Amount

$20,000
Present Value
G-14

x

2.85434
Factor

=

$57,086.80
Future Value
LO 2


Appendix

G

Time Value of Money
Accounting in Action

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

[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] Compute the present values in capital budgeting situations.
[9] Use a financial calculator to solve time value of money problems.
G-15


Future Value Concepts
Future Value of an 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 payments (receipts), and
3. amount of the periodic payments (receipts).

G-16

LO 3


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

Illustration G-6
Time diagram for a three-year annuity

G-17

LO 3


Future Value of an Annuity
Illustration:
Invest = $2,000
i = 5%
n = 3 years

Illustration G-7

G-18

Advance slide in presentation mode to reveal answers.

LO 3


Future Value of an 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 G-8
Illustration:

G-19

Demonstration problem—
Using Table 2 for FV of an
annuity of 1

LO 3


Future Value of an Annuity

What factor do we use?
$2,500
Payment

G-20

x

4.37462
Factor

=

$10,936.55
Future Value
LO 3


Appendix

G

Time Value of Money
Accounting in Action

Learning Objectives
After studying this chapter, you should be able to:
[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] Compute the present values in capital budgeting situations.
[9] Use a financial calculator to solve time value of money problems.
G-21


Present Value Concepts
Present Value Variables
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 (future amount).
2. Length of time until amount is received (number of
periods).
3. Interest rate (the discount rate).

G-22

LO 4


Appendix

G

Time Value of Money
Accounting in Action

Learning Objectives
After studying this chapter, you should be able to:
[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] Compute the present values in capital budgeting situations.
[9] Use a financial calculator to solve time value of money problems.
G-23


Present Value Concepts
Present Value of a Single Amount
Illustration G-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

G-24

LO 5


Present Value of a Single 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 G-10
Finding present value if
discounted for one period

G-25

LO 5