CHAPTER 6
Accounting and the Time Value of Money
LEARNING OBJECTIVES
1. Identify accounting topics where the time value of money is relevant.
2. Distinguish between simple and compound interest.
3. Use appropriate compound interest tables.
CHAPTER REVIEW
Basic Time Value Concepts
1. (L.O. 1) Chapter 6 discusses the essentials of compound interest, annuities and present
value. These techniques are being used in many areas of financial reporting where the
2. Compound interest, annuity, and present value techniques can be applied to many of
the items found in financial statements. In accounting, these techniques can be used to
3. (L.O. 2) Interest is the payment for the use of money. It is normally stated as a per–
centage of the amount borrowed (principal), calculated on a yearly basis. For example, an
4. (L.O. 3) Compound interest is the process of computing interest on the principal plus
any interest previously earned. Referring to the example in (3) above, if the loan was for
5. In discussing compound interest, the term period is used in place of years because
interest may be compounded daily, weekly, monthly, and so on. Thus, to convert the
6. Compound interest tables have been developed to aid in the computation of present
7. The following is a summary of the contents of the five types of compound interest tables:
“Future value of 1” table. Contains the amounts to which 1 will accumulate if deposited
now at a specified rate and left for a specified number of periods. (Table 1)
“Present value of 1” table. Contains the amounts that must be deposited now at a specified
8. (L.O. 4) Certain concepts are fundamental to all compound interest problems. These
concepts are:
a. Rate of Interest. The annual rate that must be adjusted to reflect the length of the
compounding period if less than a year.
Single-Sum Problems
9. (L.O. 5) The remaining review paragraphs pertain to present values and future values.
The text material covers the following six major time value of money concepts:
a. Future value of a single sum.
10. Single-sum problems generally fall into one of two categories. The first category consists
of problems that require the computation of the unknown future value of a known single
11. The concept of present value is described as the amount that must be invested now to
produce a known future value. This is the opposite of the compound interest discussion in
Annuities
12. (L.O. 6) An annuity is a series of equal periodic payments or receipts called rents. An
annuity requires that the rents be paid or received at equal time intervals, and that
13. (L.O. 7) The present value of an annuity is the single sum that, if invested at compound
interest now, would provide for a series of equal withdrawals for a certain number of future
periods. If the annuity is an ordinary annuity, the initial sum of money is invested at
More Complex Situations
14. (L.O. 8) A deferred annuity is an annuity in which two or more periods have expired before
the rents will begin. For example, an ordinary annuity of 10 annual rents deferred five
years means that no rents will occur during the first five years, and that the first of the
15. A long-term bond produces two cash flows: (1) periodic interest payments during the life
of the bond, and (2) the principal (face value) paid at maturity. At the date of issue, bond
Present Value Measurement
16. (L.O. 9) International Accounting Standard No. 13 introduces an expected cash flow
approach that uses a range of cash flows and incorporates the probabilities of those cash
LECTURE OUTLINE
This chapter can be covered in two to three class sessions. Most students have had previous
exposure to single sum problems and ordinary annuities, but annuities due and deferred
annuities will be new material for most students. The first class session can be used for
discussing Illustration 6-5.
Some students with a background in math or finance courses may prefer to use exponential
formulas rather than interest tables to find interest factors. Other students with sophisticated
calculators may prefer to “let the calculator do the work.” Remind students that whether they
Some of the journal entries for the accounting applications can be discussed briefly.
The following lecture outline is appropriate for this chapter.
A. (L.O. 1) Introduction: Basic Time Value Concepts.
1. Discuss the importance of the time value of money.
B. Nature of Interest.
1. Interest is payment for the use of money. It is the excess cash received or repaid over
C. (L.O. 2) Simple Interest.
D. (L.O. 3) Compound Interest.
2. Discuss the power of time and compounding. (e.g., “What do the numbers mean?”
3. The term period should be used instead of years.
a. Interest may be compounded more than once a year:
If interest is Number of compounding
compounded periods per year
Annually 1
b. Adjustment when interest is compounded more than once a year.
E. Use of Compound Interest Tables.
1. The tables contain interest factors that simplify the computation of compound interest.
Example: If R$1,000 is deposited today at 9% compound interest, the balance in 3
years can be determined:
a. By repetitive calculation—
2. Describe the five interest tables provided in the text:
a. Table 6-1: Future Value of 1.
F. (L.O. 4) Terminology Used in Compound Interest Problems.
1. Describe the four fundamental variables in compound interest problems:
a. Rate of interest.
2. Describe the difference between single sum and annuity problems.
b. Annuity problems involve a series of equal periodic payments or receipts called
rents.
G. Steps in Solving Compound Interest Problems.
Emphasize the importance of performing Steps 1 and 2 correctly. Whether students
H. (L.O. 5) Specific Problems—Single Sum Problems.
1. Formula for future value:
3. Point out that the present value is always a smaller quantity than the future value.
4. The process of finding the future value is called accumulation compounding. The
process of finding the present value is called discounting.
5. The factors in Table 6-2 are the reciprocal of corresponding factors in Table 6-1.
I. (L.O. 6 and 7) Specific Problems—Ordinary Annuities.
1. Formula for future value of an ordinary annuity:
2. Formula for present value of an ordinary annuity:
4. The factors in Tables 6-3 and 6-4 are not reciprocals of each other.
5. In annuity problems, the rents, interest payments, and number of periods must all be
6. Some confusion may arise in annuity problems because of two different meanings of
the word “period.”
a. For the purpose of looking up interest factors, n equals the number of “periods”
and is always equal to the number of rents.
b. In the phrase “when computing the future value of an ordinary annuity the number
J. (L.O. 6 and 7) Specific Problems—Annuities Due.
1. Formula for future value of annuity due:
2. Formula for present value of annuity due:
3. Point out that:
a. The present value of an annuity due is always smaller than the future value of
K. (L.O. 8) Specific Problems—Deferred Annuities.
1. A deferred annuity does not begin to produce rents until two or more periods have
expired.
b. The differences between the two situations are as follows:
Ordinary Annuity Annuity Due of
of n Rents Deferred n Rents Deferred
for y Periods for y Periods
First rent occurs (y + 1) periods y periods from
c. If a deferred annuity involves solving for a present value, the distinction between
an ordinary annuity and an annuity due has no practical significance. This can be
used, but the same answer will be obtained.)
d. However, if a deferred annuity involves solving for a future value, the distinction
between an ordinary annuity and an annuity due is important. The following
formula is required:
The time diagram for this revised problem is:
1,000
1,000 1,000
The problem involves solving for the future value of an annuity due of
3 rents deferred for 3 periods. The solution is
(1) If the future value is to be determined immediately after the last rent, the
problem may be thought of as an ordinary annuity. The computation described
L. Specific Problems—Bond Valuation Problems.
1. Discuss the distinction between the stated rate of interest and the market or effective
yield rate of interest:
a. The stated interest rate is used to determine the periodic amount of cash interest
M. (L.O. 9) Expected cash flow approach.
1. Explained by IFRS 13.
3. Choosing an appropriate interest rate:
a. rate is not always obvious.