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paid or withdrawn.

Most business situations use compound

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

received, and

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.

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.

Most business situations use compound

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

received, and

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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