978-1259722660 Chapter 6 Lecture Note

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CHAPTER 6

TIME VALUE OF MONEY CONCEPTS

Overview

Time value of money concepts, specifically future value and present value, are essential in a

variety of accounting situations. These concepts and the related computational procedures are the

subjects of this chapter. Present values and future values of single amounts and present values and

future values of annuities (series of equal periodic payments) are described separately but shown to

be interrelated.

Learning Objectives

LO6–1 Explain the difference between simple and compound interest.

LO6–2 Compute the future value of a single amount.

LO6–3 Compute the present value of a single amount.

LO6–4 Solve for either the interest rate or the number of compounding periods when present value

and future value of a single amount are known.

LO6–5 Explain the difference between an ordinary annuity and an annuity due situation.

LO6–6 Compute the future value of both an ordinary annuity and an annuity due.

LO6–7 Compute the present value of an ordinary annuity, an annuity due, and a deferred annuity.

LO6–8 Solve for unknown values in annuity situations involving present value.

LO6–9 Briefly describe how the concept of the time value of money is incorporated into the

valuation of bonds, long-term leases, and pension obligations.

Lecture Outline

Part A: Basic Concepts

I. Time Value of Money

A. The time value of money means that money can be invested today to earn interest and

grow to a larger dollar amount in the future.

II. Simple versus Compound Interest

A. Interest is the amount of money paid or received in excess of the amount borrowed or

lent.

1. Simple interest is computed by multiplying an initial investment times both the

applicable interest rate and the period of time for which the money is used.

2. Compound interest includes interest not only on the initial investment but also on the

accumulated interest in previous periods.

III. Valuing a Single Cash Flow Amount

A. The future value (FV) of a single amount is the amount of money that a dollar will grow to

at some point in the future.

1. The future value of a single amount can be calculated by multiplying the initial

investment (I) times (1 + i)

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where: i= interest rate

n= number of compounding periods

2. The future value also can be determined by using Table 1, Future Value of $1.

B. The present value (PV) of a single amount is today’s equivalent of a particular amount in

the future.

1. The present value of a single amount can be calculated by dividing the future value by

(1 + i).

2. As with future value, we can use a table, Table 2, Present Value of $1, to determine

present value.

C. Solving for other values when PV and FV are known

1. There are four variables in the process of adjusting single cash flow amounts for the

time value of money: the present value (PV), the future value (FV), the number of

compounding periods (n), and the interest rate (i).

2. If you know any three of these, the fourth can be determined.

IV. Preview of Accounting Applications of Present Value Techniques—Single Cash Amount

A. Most receivables and payables are valued at the present value of future cash flows,

reflecting an appropriate time value of money.

B. While most notes, loans, and mortgages explicitly state an interest rate that will properly

reflect the time value of money, there can be exceptions.

V. Expected Cash Flow Approach

A. SFAC No. 7 provides a framework for using future cash flows as the basis for accounting

measurement and asserts that the objective in valuing an asset or liability using present

value is to approximate the fair value of that asset or liability.

B. Traditionally, the way uncertainty has been considered in present value calculations has

been by discounting the best estimate of future cash flows applying a discount rate that has

been adjusted to reflect the uncertainty or risk of those cash flows. SFAC No. 7

offers an alternative method called the expected cash flow approach. This approach adjusts

for uncertainty or risk of cash flows by incorporating specific probabilities of cash flows

into the analysis.

Part B: Basic Annuities

I. Ordinary Annuity and Annuity Due

A. An annuity is a series of equal-sized cash flows occurring over equal intervals of time.

B. In an ordinary annuity, cash flows occur at the end of each period.

C. In an annuity due, cash flows occur at the beginning of each period.

II. Future Value of an Annuity

A. The future value of an annuity can be determined by summing the future value of each of

the individual cash payments or by using the appropriate annuity table, Table 3, Future

Value of an Ordinary Annuity of $1, or Table 5, Future Value of an Annuity Due of $1.

B. In the future value of an ordinary annuity (FVA), the last cash payment will not earn any

interest.

C. In the future value of an annuity due (FVAD), the last cash payment will earn interest.

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III. Present Value of an Annuity

A. The present value of an annuity can be determined by summing the present value of each

of the individual cash payments or by using the appropriate annuity table, Table 4, Present

Value of an Ordinary Annuity of $1, or Table 6, Present Value of an Annuity Due.

B. In the present value of an ordinary annuity (PVA), the first cash flow takes place at the end

of the first compounding period.

C. In the present value of an annuity due (PVAD), the first cash flow takes place at the

beginning of the first compounding period.

D. In the present value of a deferred annuity, the first cash flow occurs more than one period

after the date the agreement begins.

IV. Financial Calculators and Excel

Financial calculators can be used to solve future and present value problems. Also, many

professionals choose to use spreadsheet software, such as Excel, to solve time value of money

problems. These spreadsheets can be used in a variety of ways. A template can be created using

the formulas or you can use the software’s built-in financial functions.

V. Solving for Unknown Values in Present Value Situations

A. In present value problems involving annuities, there are four variables: present value of an

annuity (PVA or PVAD), the amount of each annuity payment, the number of periods (n),

and the interest rate (i).

B. If you know any three of these, the fourth can be determined.

VI. Preview of Accounting Applications of Present Value Techniques—Annuities

A. Because financial instruments typically specify equal periodic payments, accounting

applications incorporating the time value of money concept quite often involve annuity

situations.

B. Three examples are:

1. The valuation of long-term bonds.

2. The valuation of long-term leases.

3. The valuation of pension obligations.

VII.Summary of Time Value of Money Concepts

A. Illustration 6-22 summarizes the time value of money concepts discussed in this chapter.

PowerPoint Slides

Three PowerPoint presentations of the chapter are available in the Connect Library:

1. With “Concept Checks” useful for classroom presentation, permitting the

instructor to intersperse in the presentation short exercises students can be asked

to solve individually or in small groups before the solution is “revealed” by the

instructor. {These are available only within Instructor Resources.}

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2. Without the “Concept Checks” so students don’t have the solutions before being

asked to solve individually or in small groups.

3. Accessible PowerPoint Presentations. Accessibility is becoming even more

important in the education marketplace. Students and instructors with

disabilities use many different assistive technologies, and McGraw-Hill

Education is working to increase compatibility and access that will not only

help those with disabilities achieve better learning outcomes, but also serve the

institutions that are teaching these students. Accessible PowerPoint allows slide

content to be read by a screen reader and provides alternative text descriptions

for any image files used that enrich the learning experience. Accessible

PowerPoint is also designed with high-contrast color palettes and uses texture

when possible, instead of color to denote different aspects of the imagery used

within the slide.

Note: The slides are intended to provide comprehensive coverage of the chapter, but

they can be easily edited to allow instructors to change numbers and content in

illustrations or to delete slides pertaining to topics they choose to omit or

deemphasize. (Using your students’ names for company names in the Concept

Checks or Illustrations can be fun.)

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Suggestions for Class Activities

1. Real World Scenario

An important accounting application of present value techniques illustrated in this chapter is the

valuation of bonds. Occasionally, corporations issue zero-coupon bonds or notes. These instruments

pay no stated interest over their life. For example, in 1997, Costco Wholesale Corporation issued

20-year, zero-coupon bonds with a maturity value of $900 million. The company received $450

million upon issuance of these bonds.

Suggestions:

Have the class consider the Costco zero-coupon bonds. What is the approximate interest rate

implicit in these bonds when they were issued in 1997?

Points to Note:

Students must solve for the unknown interest rate when PV and FV are known. In millions:

$450 = $900 × ?

present future

value value

$450 ÷ $900 = .50

Present value of $1: n = 20, i = ?

When you consult the present value table, Table 2, you search row 20 (n = 20) for this value. The

rate is approximately 3.5%. The company’s debt disclosure note reports that these notes were sold to

yield 3.5%.

In 1997, corporate AAA bond yields averaged in excess of 7%. You might ask the class to locate

the bonds in Costco’s 10-K to see if there are any clues as to why the company was able to issue

these bonds at approximately half of the going rate for corporate bonds. The answer is that these

bonds are convertible into common stock. In fact, at the end of Costco’s 2011 fiscal year, the book

value of these bonds was only $31 million, indicating that the majority of the issue had either been

converted to common stock or repurchased by Costco.

2. Professional Skills Development Activities

The following are suggested assignments from the end-of-chapter material that will help your

students develop their communication, research, analysis, and judgment skills.

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Communication Skills. In addition to Communication Case 6–3, Judgment Case 6–5 can be

adapted to ask students to choose one of the two alternatives and write a memo supporting their

position. Judgment Case 6–5 and Real World Case 6–6 do well as group assignments. Problem

6–5 and Ethics Case 6–1 create good class discussions. Problems 6–9 and 6–13, and Analysis

Case 6–4 are suitable for student presentation(s).

Research Skills. In their careers, our graduates will be required to locate and extract relevant

information from available resource material to determine the correct accounting practice,

perhaps identifying the appropriate authoritative literature to support a decision. Real World

Cases 6–6 and 6–7 can be adapted to require students to research the authoritative literature on

incorporating the time value of money in valuation.

Analysis Skills. The “Broaden Your Perspective” section includes Analysis Cases that direct

students to gather, assemble, organize, process, or interpret data to provide options for making

business and investment decisions. In addition to Analysis Case 6–2, Problems 6–1, 6–3, 6–5,

6–9, and 6–13; Communication Case 6–3; and Judgment Case 6–5 also provide opportunities

to develop and sharpen analytical skills.

Judgment Skills. The “Broaden Your Perspective” section includes Judgment Cases that require

students to critically analyze issues to apply concepts learned to business situations in order to

evaluate options for decision making and provide an appropriate conclusion. In addition to

Judgment Case 6–5, Analysis Case 6–2 also requires students to exercise judgment.

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Assignment Chart

Learning Est. time

Questions Objective(s) Topic (min.)

6–1 1 Interest 5

6–2 1 Compound interest 5

6–3 1 Effective rate or yield 5

6–4 2 Future value 5

6–5 3 Present value 5

6–6 3 Monetary versus nonmonetary assets and

liabilities

6–7 5 Annuity 5

6–8 5 Ordinary annuity versus an annuity due 5

6–9 3,5 Present value table relationships 5

6–10 5 Time diagram-ordinary annuity 5

6–11 5 Time diagram-annuity due 5

6–12 7 Deferred annuity 5

6–13 8 Explain how to compute unknown annuity

payment

6–14 8 Compute unknown annuity payment 5

6–15 9 Long-term leases 5

Brief Learning Est. time

Exercises Objective(s) Topic (min.)

6–1 1 Simple versus compound interest 5

6–2 2 Future value; single amount 5

6–3 4 Future value; solving for unknown; single amount 5

6–4 3 Present value; single amount 5

6–5 4 Present value; solving for unknown; single

amount

6–6 6 Future value; ordinary annuity 5

6–7 6 Future value; annuity due 5

6–8 7 Present value; ordinary annuity 5

6–9 7 Present value; annuity due 5

6–10 7 Deferred annuity 10

6–11 8 Solve for unknown; annuity 5

6–12 9 Price of a bond 10

6–13 9 Lease payment 10

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Learning Est. time

Exercises Objective(s) Topic (min.)

6–1 2 Future value; single amount 10

6–2 2 Future value; single amounts 10

6–3 3 Present value; single amounts 10

6–4 3 Present value; multiple, unequal amounts 10

6–5 3 Noninterest-bearing note; single payment 10

6–6 4 Solving for unknowns; single amounts 20

6–7 6 Future value; annuities 20

6–8 7 Present value; annuities 10

6–9 8 Solving for unknowns; annuities 20

6–10 4,8 Future value; solving for annuities and single

amount

6–11 3,6,7 Future and present value 20

6–12 7 Deferred annuities 15

6–13 8 Solving for unknown annuity payment 10

6–14 8 Solving for unknown interest rate 10

6–15 8 Solving for unknown annuity amount 10

6–16 7,8 Deferred annuities; solving for annuity amount 15

6–17 9 Price of a bond 10

6–18 9 Price of a bond; interest expense 15

6–19 9 Lease payments 10

6–20 8,9 Lease payments; solve for unknown interest rate 15

6–21 1,2,3,5 Concepts; terminology 15

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Learning Est. time

Problems Objective(s) Topic (min.)

6–1 3,7 Analysis of alternatives 20

6–2 6,7,9 Present and future value 25

6–3 3,7 Analysis of alternatives 15

6–4 3,7 Investment analysis 20

6–5 3,7 Investment decision; varying rates 25

6–6 3,8 Solving for unknowns 20

6–7 8 Solving for unknown 20

6–8 7 Deferred annuities 15

6–9 7 Deferred annuities 15

6–10 3,7 Noninterest-bearing note; annuity and lump-sum

payment

6–11 8,9 Solving for unknown lease payment 20

6–12 8,9 Solving for unknown lease payment;

compounding periods of varying length

6–13 3,7,9 Lease vs. buy alternatives 15

6–14 7,9 Deferred annuities; pension obligation 25

6–15 3,7,9 Bonds and leases; deferred annuities 30

 Star Problems

Learning Est. time

Cases Objective(s) Topic (min.)

Ethics Case 6–1 1 Rate of return 20

Analysis Case 6–2 3,7 Bonus alternatives; present value analysis 15

Communication Case 6–3 7 Present value of annuities 60

Analysis Case 6–4 7 Present value of an annuity 15

Judgment Case 6–5 3,7 Replacement decision 15

Real World Case 6–6 3,9 Zero-coupon bonds; Johnson & Johnson 20

Real World Case 6–7 3,9 Leases; Southwest Airlines 20

Target Case 3,7,9 Accounting for leases; Target 20

Air France—KLM Case 9IFRS; accounting for pensions; Air France 30

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