6-1

PREVIEW OF CHAPTER 6

6-2

Intermediate Accounting

16th Edition

Kieso ● Weygandt ● Warfield

6

Accounting and the Time

Value of Money

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.

4 Solve present value of ordinary

and annuity due problems.

5 Solve present value problems

related to deferred annuities,

bonds, and expected cash flows.

3 Solve future value of ordinary

and annuity due problems.

6-3

LO 1

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

When deciding

deciding among

among investment

investment or

or

borrowing

borrowing alternatives,

alternatives, itit is

is essential

essential to

to be

be

able

able to

to compare

compare today’s

today’s dollar

dollar and

and

tomorrow’s

tomorrow’s dollar

dollar on

on the

the same

same footing—to

footing—to

“compare

“compare apples

apples to

to apples.”

apples.”

6-4

LO 1

Applications of Time Value Concepts

Present Value-Based Accounting

Measurements

1. Notes

2. Leases

3. Pensions and Other

Postretirement

Benefits

5. Shared-Based

Compensation

6. Business Combinations

7. Disclosures

8. Environmental Liabilities

4. Long-Term Assets

6-5

LO 1

BASIC TIME VALUE CONCEPTS

The Nature of Interest

6-6

Payment for the use of money.

Excess cash received or repaid over the amount lent

or borrowed (principal).

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

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.

Interest = p x i x n

Annual

Interest

= $10,000 x .08 x 1

= $800

Federal law requires the disclosure of interest rates on an annual basis.

6-7

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

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.

Interest = p x i x n

Total

Interest

= $10,000 x .08 x 3

= $2,400

6-8

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

Interest computed on the principal only.

Illustration: If Barstow borrows $10,000 for 3 months at a 8%

per year, the interest is computed as follows.

Partial

Year

Interest = p x i x n

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

= $200

6-9

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest

6-10

Computes interest on

►

principal and

►

interest earned that has not been paid or withdrawn.

Typical interest computation applied in business

situations.

LO 1

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.

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%

ILLUSTRATION 6-1

Simple vs. Compound Interest

6-11

$1,069.29 $ 12,950.29

LO 1

WHAT DO THE NUMBERS MEAN?

A PRETTY

GOOD START

WHAT’S

YOUR PRINCIPLE

The continuing debate on Social Security reform provides a great context to

illustrate the power of compounding. One proposed idea is for the government

to give $1,000 to every citizen at birth. This gift would be deposited in an

account that would earn interest tax-free until the citizen retires. Assuming the

account earns a modest 5% annual return until retirement at age 65, the

$1,000 would grow to $23,839. With monthly compounding, the $1,000

deposited at birth would grow to $25,617.

Why start so early? If the government waited until age 18 to deposit the money,

it would grow to only $9,906 with annual compounding. That is, reducing the

time invested by a third results in more than a 50% reduction in retirement

money. This example illustrates the importance of starting early when the

power of compounding is involved.

6-12

LO 1

BASIC TIME VALUE CONCEPTS

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 x the number of compounding

periods per year.

Compounding Period Interest Rate = annual rate divided by the

number of compounding periods per year.

6-13

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

ILLUSTRATION 6-2

Excerpt from Table 6-1

FUTURE VALUE OF 1 AT COMPOUND INTEREST

(Excerpt From Table 6-1, Page 1

How much principal plus interest a dollar accumulates to at the end of

each of five periods, at three different rates of compound interest.

6-14

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

Formula to determine the future value factor (FVF) for 1:

Where:

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

n

i

6-15

= number of periods

= rate of interest for a single period

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

Determine the number of periods by multiplying the number

of years involved by the number of compounding periods

per year.

ILLUSTRATION 6-4

Frequency of Compounding

6-16

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

A 9% annual interest compounded daily provides a 9.42%

yield.

Effective Yield for a $10,000 investment.

6-17

ILLUSTRATION 6-5

Comparison of Different

Compounding Periods

LO 1

BASIC TIME VALUE CONCEPTS

Fundamental Variables

Rate of Interest

Future Value

Number of Time Periods

Present Value

ILLUSTRATION 6-6

Basic Time Diagram

6-18

LO 1

6

Accounting and the Time

Value of Money

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.

4 Solve present value of ordinary

and annuity due problems.

5 Solve present value problems

related to deferred annuities,

bonds, and expected cash flows.

3 Solve future value of ordinary

and annuity due problems.

6-19

LO 2

SINGLE-SUM PROBLEMS

Two Categories

Unknown Present Value

Unknown Future Value

ILLUSTRATION 6-6

Basic Time Diagram

6-20

LO 2

SINGLE-SUM PROBLEMS

Future Value of a Single Sum

Value at a future date of a given amount invested, assuming

compound interest.

Where:

FV = future value

PV = present value (principal or single sum)

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

6-21

LO 2

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%.

= $66,912

ILLUSTRATION 6-7

Future Value Time Diagram (n = 5, i = 6%)

6-22

LO 2

Future Value of a Single Sum

Alternate

Calculation

Illustration: Bruegger Co. wants to determine the future value

of $50,000 invested for 5 years compounded annually at an

interest rate of 6%.

What table

do we use?

ILLUSTRATION 6-7

Future Value Time Diagram (n = 5, i = 6%)

6-23

LO 2

Future Value of a Single Sum

Alternate

Calculation

i=6%

n=5

What factor do we use?

$50,000

Present Value

6-24

x

1.33823

Factor

=

$66,912

Future Value

LO 2

Future Value of a Single Sum

Illustration: Assume that Commonwealth Edison Company

deposited $250 million in an escrow account with Northern

Trust Company at the beginning of 2017 as a commitment

toward a power plant to be completed December 31, 2020. How

much will the company have on deposit at the end of 4 years if

interest is 10%, compounded semiannually?

Present Value

$250,000,000

0

1

Future Value?

2

3

4

5

6

What table do we use?

6-25

LO 2

PREVIEW OF CHAPTER 6

6-2

Intermediate Accounting

16th Edition

Kieso ● Weygandt ● Warfield

6

Accounting and the Time

Value of Money

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.

4 Solve present value of ordinary

and annuity due problems.

5 Solve present value problems

related to deferred annuities,

bonds, and expected cash flows.

3 Solve future value of ordinary

and annuity due problems.

6-3

LO 1

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

When deciding

deciding among

among investment

investment or

or

borrowing

borrowing alternatives,

alternatives, itit is

is essential

essential to

to be

be

able

able to

to compare

compare today’s

today’s dollar

dollar and

and

tomorrow’s

tomorrow’s dollar

dollar on

on the

the same

same footing—to

footing—to

“compare

“compare apples

apples to

to apples.”

apples.”

6-4

LO 1

Applications of Time Value Concepts

Present Value-Based Accounting

Measurements

1. Notes

2. Leases

3. Pensions and Other

Postretirement

Benefits

5. Shared-Based

Compensation

6. Business Combinations

7. Disclosures

8. Environmental Liabilities

4. Long-Term Assets

6-5

LO 1

BASIC TIME VALUE CONCEPTS

The Nature of Interest

6-6

Payment for the use of money.

Excess cash received or repaid over the amount lent

or borrowed (principal).

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

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.

Interest = p x i x n

Annual

Interest

= $10,000 x .08 x 1

= $800

Federal law requires the disclosure of interest rates on an annual basis.

6-7

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

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.

Interest = p x i x n

Total

Interest

= $10,000 x .08 x 3

= $2,400

6-8

LO 1

BASIC TIME VALUE CONCEPTS

Simple Interest

Interest computed on the principal only.

Illustration: If Barstow borrows $10,000 for 3 months at a 8%

per year, the interest is computed as follows.

Partial

Year

Interest = p x i x n

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

= $200

6-9

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest

6-10

Computes interest on

►

principal and

►

interest earned that has not been paid or withdrawn.

Typical interest computation applied in business

situations.

LO 1

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.

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%

ILLUSTRATION 6-1

Simple vs. Compound Interest

6-11

$1,069.29 $ 12,950.29

LO 1

WHAT DO THE NUMBERS MEAN?

A PRETTY

GOOD START

WHAT’S

YOUR PRINCIPLE

The continuing debate on Social Security reform provides a great context to

illustrate the power of compounding. One proposed idea is for the government

to give $1,000 to every citizen at birth. This gift would be deposited in an

account that would earn interest tax-free until the citizen retires. Assuming the

account earns a modest 5% annual return until retirement at age 65, the

$1,000 would grow to $23,839. With monthly compounding, the $1,000

deposited at birth would grow to $25,617.

Why start so early? If the government waited until age 18 to deposit the money,

it would grow to only $9,906 with annual compounding. That is, reducing the

time invested by a third results in more than a 50% reduction in retirement

money. This example illustrates the importance of starting early when the

power of compounding is involved.

6-12

LO 1

BASIC TIME VALUE CONCEPTS

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 x the number of compounding

periods per year.

Compounding Period Interest Rate = annual rate divided by the

number of compounding periods per year.

6-13

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

ILLUSTRATION 6-2

Excerpt from Table 6-1

FUTURE VALUE OF 1 AT COMPOUND INTEREST

(Excerpt From Table 6-1, Page 1

How much principal plus interest a dollar accumulates to at the end of

each of five periods, at three different rates of compound interest.

6-14

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

Formula to determine the future value factor (FVF) for 1:

Where:

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

n

i

6-15

= number of periods

= rate of interest for a single period

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

Determine the number of periods by multiplying the number

of years involved by the number of compounding periods

per year.

ILLUSTRATION 6-4

Frequency of Compounding

6-16

LO 1

BASIC TIME VALUE CONCEPTS

Compound Interest Tables

A 9% annual interest compounded daily provides a 9.42%

yield.

Effective Yield for a $10,000 investment.

6-17

ILLUSTRATION 6-5

Comparison of Different

Compounding Periods

LO 1

BASIC TIME VALUE CONCEPTS

Fundamental Variables

Rate of Interest

Future Value

Number of Time Periods

Present Value

ILLUSTRATION 6-6

Basic Time Diagram

6-18

LO 1

6

Accounting and the Time

Value of Money

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.

4 Solve present value of ordinary

and annuity due problems.

5 Solve present value problems

related to deferred annuities,

bonds, and expected cash flows.

3 Solve future value of ordinary

and annuity due problems.

6-19

LO 2

SINGLE-SUM PROBLEMS

Two Categories

Unknown Present Value

Unknown Future Value

ILLUSTRATION 6-6

Basic Time Diagram

6-20

LO 2

SINGLE-SUM PROBLEMS

Future Value of a Single Sum

Value at a future date of a given amount invested, assuming

compound interest.

Where:

FV = future value

PV = present value (principal or single sum)

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

6-21

LO 2

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%.

= $66,912

ILLUSTRATION 6-7

Future Value Time Diagram (n = 5, i = 6%)

6-22

LO 2

Future Value of a Single Sum

Alternate

Calculation

Illustration: Bruegger Co. wants to determine the future value

of $50,000 invested for 5 years compounded annually at an

interest rate of 6%.

What table

do we use?

ILLUSTRATION 6-7

Future Value Time Diagram (n = 5, i = 6%)

6-23

LO 2

Future Value of a Single Sum

Alternate

Calculation

i=6%

n=5

What factor do we use?

$50,000

Present Value

6-24

x

1.33823

Factor

=

$66,912

Future Value

LO 2

Future Value of a Single Sum

Illustration: Assume that Commonwealth Edison Company

deposited $250 million in an escrow account with Northern

Trust Company at the beginning of 2017 as a commitment

toward a power plant to be completed December 31, 2020. How

much will the company have on deposit at the end of 4 years if

interest is 10%, compounded semiannually?

Present Value

$250,000,000

0

1

Future Value?

2

3

4

5

6

What table do we use?

6-25

LO 2

## Test bank with answers intermediate accounting 12e by kieso chapter 01

## Test bank with answers intermediate accounting 12e by kieso chapter 02

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