Slide accounting principles 12e app g

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Appendix G

Time Value of Money

Learning Objectives

G-2

1

Compute interest and future values.

2

Compute present values.

3

Compute the present value in capital budgeting situations.

4

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


LEARNING
OBJECTIVE

1

Compute interest and future values.

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 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:

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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.

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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

Interest = p x i x n

2 FULL YEARS
= $5,000 x .12 x 2

= $1,200

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LO 1


Nature of 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any interest earned that has not been paid or withdrawn.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

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

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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


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 =

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future value of a single amount

p

=

principal (or present value; the value today)

i

=

interest rate for one period

n

=

number of periods
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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

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LO 1


Alternate Method

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

What table do we use?

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LO 1


Future Value of a Single Amount

What factor do we use?

$1,000
Present Value

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x

1.29503

=
Factor

$1,295.03
Future Value

LO 1

Future Value of a Single Amount
Illustration G-5
Demonstration problem—

Illustration:

Using Table 1 for FV of 1

What table do we use?

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LO 1


Future Value of a Single Amount

$20,000
Present Value
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x

2.85434

=
Factor

$57,086.80

Future Value
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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

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Future Value of an Annuity

Illustration:

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

Illustration G-7
Future value of periodic payment computation

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LO 1

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
Demonstration problem—

Illustration:

Using Table 2 for FV of an
annuity of 1

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LO 1


Future Value of an Annuity

What factor do we use?

$2,500
Payment

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x

4.37462

=
Factor

$10,936.55
Future Value

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LEARNING
OBJECTIVE

2

Compute present values.

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:

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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).

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Present Value of a Single Amount

Illustration G-9
Formula for present value

Present Value (PV) = Future Value ÷ (1 + i )
p

n

= principal (or present value)

i = interest rate for one period
n

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= number of periods

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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

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LO 2


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

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 2

Present Value of a Single Amount

What factor do we use?

$1,000
Future Value

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x

.90909

=
Factor

$909.09
Present Value

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Present Value of a Single Amount
Illustration G-11
Finding present value if
discounted for two period

Illustration: If the single amount of $1,000 is to be received in two years and discounted at 10% [PV = $1,000
2

÷ (1 + .10 ], its present value is $826.45 [($1,000 ÷ 1.21).

What table do we use?
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LO 2


Present Value of a Single Amount

What factor do we use?

$1,000
Future Value

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x

.82645

=
Factor

$826.45
Present Value

LO 2

Present Value of a Single Amount

Illustration: Suppose you have a winning lottery ticket and the state gives you the option of taking $10,000 three years from
now or taking the present value of $10,000 now. The state uses an 8% rate in discounting. How much will you receive if you
accept your winnings now?

$10,000
Future Value
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x

.79383

=
Factor

$7,938.30
Present Value
LO 2