Accounting tools for business decision making 7 kieo app g

Accounting: Tools for Business Decision Making

Seventh Edition

Kimmel; Weygandt; Kieso

Appendix G

Time Value of Money
Prepared by
COBY HARMON
University of California, Santa Barbara
Westmont College

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Chapter Outline:
Learning Objectives
LO 1 Compute interest and future values.
LO 2 Compute present values.
LO 3 Compute the present value in capital budgeting situations.
LO 4 Use a financial calculator to solve time value of money problems.

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2


Learning Objective 1
Compute Interest and Future Values

LO 1

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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

LO 1

•

Principal (p): Amount borrowed or invested

•

Interest Rate (i): An annual percentage

•

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

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4


Simple Interest
•

Interest computed on principal only

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

Interest =

LO 1

Principal

=

p
$5,000

=

$1, 200

ì
ì

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Rate
i
0.12

×
×

Time
n
2

5


Compound Interest (1 of 3)
•

•

LO 1

Computes interest on

•

principal

•

interest earned that has not been paid or withdrawn

Most business situations use compound interest

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6


Compound Interest (2 of 3)
Illustration: Assume 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 cash until three years from the date of deposit.
Compute the interest to be received and the accumulated year-end balances for Citizens Bank.

LO 1

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7


Compound Interest (3 of 3)

LO 1

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8


Future Value of a Single Amount (1 of 5)
Value at a future date of a given amount invested, assuming compound interest.

FV = p × ( 1 + i )

n

FV = future value of a single amount
P = principal (or present value; the value today)
i = interest rate for one period
n = number of periods

LO 1

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9


Future Value of a Single Amount (2 of 5)
Illustration: The future value of a $1,000 investment earning 9% for three years is $1,295.03.

FV =

p × (1+ i)

n

= $1,000 × ( 1 + .09 )

3

= $1,000 × 1.29503
= $1, 295.03
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Second level
Third level
Fourth level
Fifth level

LO 1

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10


Future Value of a Single Amount (3 of 5)
Another method to compute the future value of a single amount involves a compound interest table.

Table 1 Future Value of 1

(n) Periods

5%

6%

7%

8%

9%

10%

1

1.05000

1.06000

1.07000

1.08000

1.09000

1.10000

2

1.10250

1.12360

1.14490

1.16640

1.18810

1.21000

3

1.15763

1.19102

1.22504

1.25971

1.29503

1.33100

4

1.21551

1.26248

1.31080

1.36049

1.41158

1.46410

5

1.27628

1.33823

1.40255

1.46933

1.53862

1.61051

$1,000
Present Value

LO 1

ì

1.29503

Factor

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=

$1,295.03
Future Value

11


Future Value of a Single Amount (4 of 5)
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?

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Second level
Third level
Fourth level
Fifth level

LO 1

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12


Future Value of a Single Amount (5 of 5)
Table 1 Future Value of 1
(n) Periods

5%

6%

7%

8%

9%

10%

1

1.05000

1.06000

1.07000

1.08000

1.09000

1.10000

2

1.10250

1.12360

1.14490

1.16640

1.18810

1.21000







16

2.18287

2.54035

2.95216

3.42594

3.97031

4.59497

17

2.29202

2.69277

3.15882

3.70002

4.32763

5.05447

18

2.40662

2.85434

3.37993

3.99602

4.71712

5.55992

19

2.52695

3.02560

3.61653

4.31570

5.14166

6.11591

20

2.65330

3.20714

3.86968

4.66096

5.60441

6.72750

$20,000

2.85434

=

ì
Present Value
LO 1

Factor
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$57,086.80
Future Value
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Future Value of an Annuity (1 of 5)
Illustration: Assume you invest $2,000 at the end of each year for three years at 5% interest compounded annually.

LO 1

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Future Value of an Annuity (2 of 5)
Table 1 Future Value of 1

LO 1

(n) Periods

4%

5%

6%

7%

8%

9%

0

1.00000

1.00000

1.00000

1.00000

1.00000

1.00000

1

1.04000

1.05000

1.06000

1.07000

1.08000

1.09000

2

1.08160

1.10250

1.12360

1.14490

1.16640

1.18810

3

1.12486

1.15763

1.19102

1.22504

1.25971

1.29503

Invested

Number of

Future

at End

Compounding

Amount

of Year

Periods

Invested

1

2

$2,000

1.10250

$2,205

2

1

$2,000

1.05000

2,100

3

0

$2,000

1.00000

2,000

3.15250

$6,305

Value of 1
×

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Factor at 5%

Future
=

Value

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Future Value of an Annuity (3 of 5)
When 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.

Table 2 Future Value of an Annuity of 1

LO 1

(n) Periods

5%

6%

7%

8%

9%

10%

1

1.00000

1.00000

1.00000

1.00000

1.00000

1.00000

2

2.05000

2.06000

2.07000

2.08000

2.09000

2.10000

3

3.15250

3.18360

3.21490

3.24640

3.27810

3.31000

4

4.31013

4.37462

4.43994

4.50611

4.57313

4.64100

5

5.52563

5.63709

5.75074

5.86660

5.98471

6.10510

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16

Future Value of an Annuity (4 of 5)
Illustration: John and Char Lewis’s daughter, Debra, has just started high school. They decide to start a
college fund for her and will invest $2,500 in a savings account at the end of each year she is in high school (4
payments total). The account will earn 6% interest compounded annually. How much will be in the college
fund at the time Debra graduates from high school?

LO 1

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Future Value of an Annuity (5 of 5)
Table 2 Future Value of an Annuity of 1

(n) Periods

5%

6%

7%

8%

9%

10%

1

1.00000

1.00000

1.00000

1.00000

1.00000

1.00000

2

2.05000

2.06000

2.07000

2.08000

2.09000

2.10000

3

3.15250

3.18360

3.21490

3.24640

3.27810

3.31000

4

4.31013

4.37462

4.43994

4.50611

4.57313

4.64100

5

5.52563

5.63709

5.75074

5.86660

5.98471

6.10510

What factor do we use?
$2,500
Payment

LO 1

ì

4.37462
Factor
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=

$10,936.55
Future Value
18


Learning Objective 2

Compute Present Values

LO 2

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19


Present Value
•.

Present value is the value now of a given amount to be paid or received in the future, assuming compound interest

•.

Present value variables

L O2

•

Dollar amount to be received (future amount)

•

Length of time until amount is received (number of periods)

•

Interest rate (the discount rate)

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20


Present Value of a Single Amount (1 of 9)

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

n

p = principal (or present value)
i = interest rate for one period
n = number of periods

LO 2

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21


Present Value of a Single Amount (2 of 9)
Illustration: The computation of $1,000 discounted at 10% for one year is as follows.

PV

=

FV ÷ ( 1 + i )

n

= $1,000 ÷ ( 1 + .10 )
= $1,000 ÷ 1.10
= $909.09

1

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Second level
Third level
Fourth level
Fifth level

LO 2

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22


Present Value of a Single Amount (3 of 9)
Alternate
Calculation

Table 3 Present Value of 1

(n) Periods

6%

7%

8%

9%

10%

11%

1

.94340

.93458

.92593

.91743

.90909

.90090

2

.89000

.87344

.85734

.84168

.82645

.81162

3

.83962

.81630

.79383

.77218

.75132

.73119

4

.79209

.76290

.73503

.70843

.68301

.65873

5

.74726

.71299

.68058

.64993

.62092

.59345

What factor do we use?

$1,000
Future Value
LO 2

ì

.90909
Factor

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=

$909.09
Present Value
23


Present Value of a Single Amount (4 of 9)
Illustration: If the single amount of $1,000 is to be received in two years and discounted at 10%

its present value is $826.45 [($1,000 ữ 1.21).

What table do we use?

LO 2

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24


Present Value of a Single Amount (5 of 9)
Alternate

Calculation

Table 3 Present Value of 1
(n) Periods

6%

7%

8%

9%

10%

11%

1

.94340

.93458

.92593

.91743

.90909

.90090

2

.89000

.87344

.85734

.84168

.82645

.81162

3

.83962

.81630

.79383

.77218

.75132

.73119

4

.79209

.76290

.73503

.70843

.68301

.65873

5

.74726

.71299

.68058

.64993

.62092

.59345

What factor do we use?

$1,000

Future Value
LO 2

ì

.82645
Factor

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=

$826.45
Present Value
25