# chuong gioi thieu Time Value of Money Ke toan quan tri

Appendix
A- 1

Time Value of Money

Managerial Accounting
Fifth Edition
Weygandt Kimmel Kieso
Appendix
A- 2

study objectives
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 values in capital budgeting
situations.

8.
Appendix
A- 3

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

Basic
Basic Time
Time Value
Value Concepts
Concepts
Time Value of Money
In accounting (and finance), the term indicates
that a dollar received today is worth more than
a dollar promised at some time in the future.

Appendix
A- 4

Nature
Nature of
of Interest
Interest
Payment for the use of money.
Excess cash received or repaid over the
amount invested or borrowed (principal).
Variables involved in financing transaction:
1. Principal (p) - Amount borrowed or invested.
2. Interest Rate
3. Time

(i) – An annual percentage.

(n) - The number of years or portion of

a year that the principal is borrowed or
invested.
Appendix
A- 5

SO 1 Distinguish between simple and compound interest.

Nature
Nature of
of Interest
Interest
Simple Interest
Interest computed on the principal only.
Illustration:
On January 2, 2010, assume you borrow \$5,000 for 2
years at a simple interest of 12% annually. Calculate
the annual interest cost.
Illustration A-1

Interest = p x i x n

FULL YEAR

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

Appendix
A- 6

SO 1 Distinguish between simple and compound

Nature
Nature of
of Interest
Interest
Compound Interest
Computes interest on
 the principal and
 any interest earned that has not been

paid or withdrawn.
interest.

Appendix
A- 7

SO 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 BankOne,
where it will earn simple interest of 9% per year, and you
deposit another \$1,000 in CityCorp, where it will earn
compound interest of 9% per year compounded annually. Also
assume that in both cases you will not withdraw any cash
until three years from the date of deposit.
Illustration A-2

Appendix
A- 8

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

SO 1 Distinguish between simple and compound interest.

Future
Future Value
Value of
of aa Single
Single Amount
Amount
The future value is the value at a future date of
a given amount invested assuming compound
Illustration A-3
interest.
Future value computation

Appendix
A- 9

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Single
Single Amount
Amount
Illustration: If you earn a 9% rate of return,
compute the future value of \$1,000 at the end of
three years:

Illustration A-4

Appendix
A- 10

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Single
Single Amount
Amount
Illustration: If you earn a 9% rate of return,
compute the future value of \$1,000 at the end of
three years:

Illustration A-4

What table do we use?
Appendix
A- 11

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Single
Single Amount
Amount

What factor do we use?
\$1,000
Appendix
A- 12

Present
Value

x

1.29503
Factor

=

\$1,295.03
Future
Value

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Single
Single Amount
Amount
Illustration: John and Mary Rich invested \$20,000 in a
savings account paying 6% interest at the time their son,
Mike, was born. The money is to be used by Mike for his
college education. On his 18th birthday, Mike withdraws
the money from his savings account. How much did Mike
withdraw from his account?
Illustration A-5

Appendix
A- 13

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Single
Single Amount
Amount

\$20,000
Appendix
A- 14

Present
Value

x

2.85434
Factor

=

\$57,086.80
Future
Value

SO 2 Solve for future value of a single

Future
Future Value
Value of
of aa Annuity
Annuity
The Future Value of an Annuity is the sum of
all the payments (receipts) plus the
accumulated compound interest on them. In
computing the future value of an annuity, it is
necessary to know
1. the interest rate,
2. the number of compounding periods, and
3. the amount of the periodic payments or
receipts.
Appendix
A- 15

SO 3 Solve for future value of an

Future
Future Value
Value of
of aa Annuity
Annuity
Illustration: Assume that you invest \$2,000 at the end
of each year for three years at 5% interest compounded
annually. Compute the future value.
Illustration A-6

Appendix
A- 16

SO 3 Solve for future value of an

Future
Future Value
Value of
of aa Annuity
Annuity

Illustration A-7

Appendix
A- 17

Solution on
notes page

SO 3 Solve for future value of an

Future
Future Value
Value of
of aa Annuity
Annuity

What factor do we use?
\$2,000
Annual
Investment
Appendix
A- 18

x

3.15250
Factor

=

\$6,305
Future
Value

SO 3 Solve for future value of an

Present
Present Value
Value Variables
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 paid or received in the
future,
2. Length of time until amount is paid or
3. Interest rate (the discount rate).
Appendix
A- 19

SO 4 Identify the variables fundamental to solving present value

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

Present Value = Future Value / (1 +
i )n
i = interest rate for one period
n = number of periods

Appendix
A- 20

SO 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 A-10

Appendix
A- 21

SO 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
can also compute the present value of \$1,000 for
one year by using a present value table.
Illustration A-10

What table do we use?
Appendix
A- 22

SO 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
Appendix
A- 23

x

.90909
Factor

=

\$909.09
Present
Value

SO 5 Solve for present value of a single amount.

Present
Present Value
Value of
of aa Single
Single Amount
Amount
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.
Illustration A-11

What table do we use?
Appendix
A- 24

SO 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
Appendix
A- 25

x

.82645
Factor

=

\$826.45
Present
Value

SO 5 Solve for present value of a single amount.

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