Intermediate Accounting

Seventeenth Edition

Kieso ● Weygandt ● Warfield

Chapter 6

Accounting and the Time Value of

Money

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Learning Objectives

After studying this chapter, you should be able to:

1.

Describe the fundamental concepts related to the time value of money.

2.

Solve future and present value of 1 problems.

3.

Solve future value of ordinary and annuity due problems.

4.

Solve present value of ordinary and annuity due problems.

5.

Solve present value problems related to deferred annuities, bonds, and expected cash flows.

Copyright ©2019 John Wiley & Sons, Inc.

2

Preview of Chapter 6

Accounting and the Time Value of Money

Basic Time Value Concepts

•

Applications

•

The nature of interest

•

Simple interest

•

Compound interest

•

Fundamental variables

Copyright ©2019 John Wiley & Sons, Inc.

3

Preview of Chapter 6

Single-Sum Problems

•

Future value of single sum

•

Present value of single sum

•

Solving for other unknowns

Annuities (Future Value)

•

Future value of ordinary annuity

•

Future value of annuity due

•

Examples of FV of annuity

Copyright ©2019 John Wiley & Sons, Inc.

4

Preview of Chapter 6

Annuities (Present Value)

•

Present value of ordinary annuity

•

Present value of annuity due

•

Examples of PV of annuity

Copyright ©2019 John Wiley & Sons, Inc.

5

Preview of Chapter 6

Other Time Value of Money Issues

•

Deferred annuities

•

Valuation of long-term bonds

•

Effective-interest method of bond discount/premium amortization

•

Present value measurement

Copyright ©2019 John Wiley & Sons, Inc.

6

Learning Objective 1

Describe the Fundamental Concepts Related to the Time Value of

Money

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

7

Basic Time Value Concepts

Time Value of Money

•

A relationship between time and money.

•

A dollar received today is worth more than a dollar promised at some time in the future.

When deciding among investment or borrowing alternatives, it is essential to be able to compare

today’s dollar and tomorrow’s dollar on the same footing—to “compare apples to apples.”

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

8

Applications of Time Value Concepts

Present Value-Based Accounting Measurements

1.

2.

3.

4.

LO 1

5.

Notes

Leases

Benefits

6.

7.

Long-Term Assets

8.

Pensions and Other Postretirement

Copyright ©2019 John Wiley & Sons, Inc.

Shared-Based Compensation

Business Combinations

Disclosures

Environmental Liabilities

9

The Nature of Interest

•

Payment for the use of money

•

Excess cash received or repaid over the amount lent or borrowed (principal)

Variables in Interest Computation

1.

Principal. The amount borrowed or invested.

2.

Interest Rate. A percentage of the outstanding principal.

3.

Time. The number of years or fractional portion of a year that the principal is outstanding.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

10

Simple Interest (1 year)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year.

Compute the total interest to be paid for the 1 year.

Annual Interest

Interest = p x i x n

= $10,000 x .08 x 1

= $800

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

11

Simple Interest (3 year)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year.

Compute the total interest to be paid for the 3 years.

Total

Interest = p x i x n

Interest

= $10,000 x .08 x 3

= $2,400

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

12

Simple Interest (3 months)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 months at a simple interest rate of 8% per

year, the interest is computed as follows.

Partial Year

Interest = p x i x n

Interest

= $10,000 x .08 x 3/12

= $200

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

13

Compound Interest

•

•

LO 1

Computes interest on

principal and

interest earned that has not been paid or withdrawn

Typical interest computation applied in business situations

Copyright ©2019 John Wiley & Sons, Inc.

14

Compound Interest

Simple vs. Compound Interest

Illustration: Tomalczyk Company deposits $10,000 in the Last National Bank, where it will earn simple interest of 9% per year. It

deposits another $10,000 in the First State Bank, where it will earn compound interest of 9% per year compounded annually. In both

cases, Tomalczyk will not withdraw any interest until 3 years from the date of deposit.

LO 1

Year 1 $10,000.00 x 9%

$ 900.00

$ 10,900.00

Year 2 $10,900.00 x 9%

$ 981.00

$ 11,881.00

Year 3 $11,881.00 x 9%

$1,069.29

$ 12,950.29

Copyright ©2019 John Wiley & Sons, Inc.

15

Compound Interest Tables

Table 6.1 - Future Value of 1

Table 6.2 - Present Value of 1

Table 6.3 - Future Value of an Ordinary Annuity of 1

Table 6.4 - Present Value of an Ordinary Annuity of 1

Table 6.5 - Present Value of an Annuity Due of 1

Number of Periods = number of years × the number of compounding periods per year.

Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

16

Compound Interest Tables

(Excerpt from Table 6.1)

Future Value of 1 at Compound Interest

Period

4%

5%

6%

1

1.04000

1.05000

1.06000

2

1.08160

1.10250

1.12360

3

1.12486

1.15763

1.19102

4

1.16986

1.21551

1.26248

5

1.21665

1.27628

1.33823

How much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of

compound interest.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

17

Compound Interest Tables

Formula for future value factor (FVF) for 1

FVFn ,i = ( 1 + i )

n

Where:

FVFn,i = future value factor for n periods at i interest

n = number of periods

i = rate of interest for a single period

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

18

Compound Interest Tables

Frequency of Compounding

Determine number of periods by multiplying number of years involved by number of compounding periods

per year.

12% Annual Interest Rate over 5 Years

Interest Rate per Compounding Period

Number of Compounding Periods

Compounded

Annually (1)

.12 ÷ 1 = .12

Semiannually (2)

.12 ÷ 2 = .06

Quarterly (4)

.12 ÷ 4 = .03

Monthly (12)

.12 ÷ 12 = .01

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

5 years × 1 compounding per year = 5 periods

5 years × 2 compoundings per year = 10 periods

5 years × 4 compoundings per year = 20 periods

5 years × 12 compoundings per year = 60 periods

19

Compound Interest Tables

Comparison of Different Compounding Periods

A 9% annual interest compounded daily provides a 9.42% yield.

Effective Yield for a $10,000 investment.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

20

Fundamental Variables

LO 1

•

Rate of Interest

•

Number of Time Periods

•

Future Value

•

Present Value

Copyright ©2019 John Wiley & Sons, Inc.

21

Learning Objective 2

Solve Future and Present Value of 1 Problems

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

22

Single-Sum Problems

Two Categories

Unknown Present Value

LO 2

Unknown Future Value

Copyright ©2019 John Wiley & Sons, Inc.

23

Future Value of a Single Sum

Value at a future date of a given amount invested, assuming compound interest.

(

FV = PV FVFn ,i

)

Where:

FV = future value

PV = present value (principal or single sum)

FVFn, i = future value factor for n periods at i interest

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

24

Future Value of a Single Sum

Illustration

Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at

an interest rate of 6%.

Future value = PV( FVFn,i )

= $50, 000(FVF5,6% )

= $50, 000(1+ .06)5

= $50, 000(1.33823)

= $66, 912

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

25

Seventeenth Edition

Kieso ● Weygandt ● Warfield

Chapter 6

Accounting and the Time Value of

Money

This slide deck contains animations. Please disable animations if they cause issues with your device.

Learning Objectives

After studying this chapter, you should be able to:

1.

Describe the fundamental concepts related to the time value of money.

2.

Solve future and present value of 1 problems.

3.

Solve future value of ordinary and annuity due problems.

4.

Solve present value of ordinary and annuity due problems.

5.

Solve present value problems related to deferred annuities, bonds, and expected cash flows.

Copyright ©2019 John Wiley & Sons, Inc.

2

Preview of Chapter 6

Accounting and the Time Value of Money

Basic Time Value Concepts

•

Applications

•

The nature of interest

•

Simple interest

•

Compound interest

•

Fundamental variables

Copyright ©2019 John Wiley & Sons, Inc.

3

Preview of Chapter 6

Single-Sum Problems

•

Future value of single sum

•

Present value of single sum

•

Solving for other unknowns

Annuities (Future Value)

•

Future value of ordinary annuity

•

Future value of annuity due

•

Examples of FV of annuity

Copyright ©2019 John Wiley & Sons, Inc.

4

Preview of Chapter 6

Annuities (Present Value)

•

Present value of ordinary annuity

•

Present value of annuity due

•

Examples of PV of annuity

Copyright ©2019 John Wiley & Sons, Inc.

5

Preview of Chapter 6

Other Time Value of Money Issues

•

Deferred annuities

•

Valuation of long-term bonds

•

Effective-interest method of bond discount/premium amortization

•

Present value measurement

Copyright ©2019 John Wiley & Sons, Inc.

6

Learning Objective 1

Describe the Fundamental Concepts Related to the Time Value of

Money

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

7

Basic Time Value Concepts

Time Value of Money

•

A relationship between time and money.

•

A dollar received today is worth more than a dollar promised at some time in the future.

When deciding among investment or borrowing alternatives, it is essential to be able to compare

today’s dollar and tomorrow’s dollar on the same footing—to “compare apples to apples.”

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

8

Applications of Time Value Concepts

Present Value-Based Accounting Measurements

1.

2.

3.

4.

LO 1

5.

Notes

Leases

Benefits

6.

7.

Long-Term Assets

8.

Pensions and Other Postretirement

Copyright ©2019 John Wiley & Sons, Inc.

Shared-Based Compensation

Business Combinations

Disclosures

Environmental Liabilities

9

The Nature of Interest

•

Payment for the use of money

•

Excess cash received or repaid over the amount lent or borrowed (principal)

Variables in Interest Computation

1.

Principal. The amount borrowed or invested.

2.

Interest Rate. A percentage of the outstanding principal.

3.

Time. The number of years or fractional portion of a year that the principal is outstanding.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

10

Simple Interest (1 year)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year.

Compute the total interest to be paid for the 1 year.

Annual Interest

Interest = p x i x n

= $10,000 x .08 x 1

= $800

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

11

Simple Interest (3 year)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 years at a simple interest rate of 8% per year.

Compute the total interest to be paid for the 3 years.

Total

Interest = p x i x n

Interest

= $10,000 x .08 x 3

= $2,400

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

12

Simple Interest (3 months)

Interest computed on the principal only.

Illustration: Barstow Electric Inc. borrows $10,000 for 3 months at a simple interest rate of 8% per

year, the interest is computed as follows.

Partial Year

Interest = p x i x n

Interest

= $10,000 x .08 x 3/12

= $200

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

13

Compound Interest

•

•

LO 1

Computes interest on

principal and

interest earned that has not been paid or withdrawn

Typical interest computation applied in business situations

Copyright ©2019 John Wiley & Sons, Inc.

14

Compound Interest

Simple vs. Compound Interest

Illustration: Tomalczyk Company deposits $10,000 in the Last National Bank, where it will earn simple interest of 9% per year. It

deposits another $10,000 in the First State Bank, where it will earn compound interest of 9% per year compounded annually. In both

cases, Tomalczyk will not withdraw any interest until 3 years from the date of deposit.

LO 1

Year 1 $10,000.00 x 9%

$ 900.00

$ 10,900.00

Year 2 $10,900.00 x 9%

$ 981.00

$ 11,881.00

Year 3 $11,881.00 x 9%

$1,069.29

$ 12,950.29

Copyright ©2019 John Wiley & Sons, Inc.

15

Compound Interest Tables

Table 6.1 - Future Value of 1

Table 6.2 - Present Value of 1

Table 6.3 - Future Value of an Ordinary Annuity of 1

Table 6.4 - Present Value of an Ordinary Annuity of 1

Table 6.5 - Present Value of an Annuity Due of 1

Number of Periods = number of years × the number of compounding periods per year.

Compounding Period Interest Rate = annual rate divided by the number of compounding periods per year.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

16

Compound Interest Tables

(Excerpt from Table 6.1)

Future Value of 1 at Compound Interest

Period

4%

5%

6%

1

1.04000

1.05000

1.06000

2

1.08160

1.10250

1.12360

3

1.12486

1.15763

1.19102

4

1.16986

1.21551

1.26248

5

1.21665

1.27628

1.33823

How much principal plus interest a dollar accumulates to at the end of each of five periods, at three different rates of

compound interest.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

17

Compound Interest Tables

Formula for future value factor (FVF) for 1

FVFn ,i = ( 1 + i )

n

Where:

FVFn,i = future value factor for n periods at i interest

n = number of periods

i = rate of interest for a single period

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

18

Compound Interest Tables

Frequency of Compounding

Determine number of periods by multiplying number of years involved by number of compounding periods

per year.

12% Annual Interest Rate over 5 Years

Interest Rate per Compounding Period

Number of Compounding Periods

Compounded

Annually (1)

.12 ÷ 1 = .12

Semiannually (2)

.12 ÷ 2 = .06

Quarterly (4)

.12 ÷ 4 = .03

Monthly (12)

.12 ÷ 12 = .01

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

5 years × 1 compounding per year = 5 periods

5 years × 2 compoundings per year = 10 periods

5 years × 4 compoundings per year = 20 periods

5 years × 12 compoundings per year = 60 periods

19

Compound Interest Tables

Comparison of Different Compounding Periods

A 9% annual interest compounded daily provides a 9.42% yield.

Effective Yield for a $10,000 investment.

LO 1

Copyright ©2019 John Wiley & Sons, Inc.

20

Fundamental Variables

LO 1

•

Rate of Interest

•

Number of Time Periods

•

Future Value

•

Present Value

Copyright ©2019 John Wiley & Sons, Inc.

21

Learning Objective 2

Solve Future and Present Value of 1 Problems

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

22

Single-Sum Problems

Two Categories

Unknown Present Value

LO 2

Unknown Future Value

Copyright ©2019 John Wiley & Sons, Inc.

23

Future Value of a Single Sum

Value at a future date of a given amount invested, assuming compound interest.

(

FV = PV FVFn ,i

)

Where:

FV = future value

PV = present value (principal or single sum)

FVFn, i = future value factor for n periods at i interest

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

24

Future Value of a Single Sum

Illustration

Bruegger Co. wants to determine the future value of $50,000 invested for 5 years compounded annually at

an interest rate of 6%.

Future value = PV( FVFn,i )

= $50, 000(FVF5,6% )

= $50, 000(1+ .06)5

= $50, 000(1.33823)

= $66, 912

LO 2

Copyright ©2019 John Wiley & Sons, Inc.

25

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