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1. 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.
4. Identify variables fundamental to solving interest problems.
5. Solve future and present value of 1 problems.
6. Solve future value of ordinary and annuity due problems.
7. Solve present value of ordinary and annuity due problems.
8. Solve present value problems related to deferred annuities and bonds.
9. Apply expected cash flows to present value measurement.
CHAPTER REVIEW
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 relative
values of cash inflows and outflows are measured and analyzed. The material presented
in Chapter 6 will provide a sufficient background for application of these techniques to
topics presented in subsequent chapters.
2. (L.O. 1) 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 measure the relative values of cash inflows and outflows, evaluate alternative
investment opportunities, and determine periodic payments necessary to meet future
obligations. It is frequently used when market-based fair value information is not readily
available. Some of the accounting items to which these techniques may be applied are:
(a) notes receivable and payable, (b) leases, (c) pensions and other post-retirement
benefits, (d) long-term assets, (e) stock-based compensation, (f) business
combinations, (g) disclosures, and (h) environmental liabilities.
Nature of Interest
3. Interest is the payment for the use of money. It is normally stated as a percentage of the
amount borrowed (principal), calculated on a yearly basis.
Simple Interest
4. (L.O. 2) Simple interest is computed on the amount of the principal only. The formula for
simple interest can be expressed as p × i × n where p is the principal, i is the rate of
interest for one period, and n is the number of periods.
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2. Compound Interest
5. (L.O. 3) Compound interest is the process of computing interest on the principal plus
any interest previously earned. Compound interest is common in business situations
where capital is financed over long periods of time. Simple interest is applied to short-
term investments and debts due in one year or less. How often interest is compounded
can make a substantial difference in the level of return achieved, or the cost of borrowing.
6. In discussing compound interest, the term period is used in place of years because
interest may be compounded daily, weekly, monthly, and so on. To convert the annual
interest rate to the compounding period interest rate, divide the annual interest rate
by the number of compounding periods in a year. The number of periods over which
interest will be compounded is calculated by multiplying the number of years involved by
the number of compounding periods in a year.
Compound Interest Tables
7. (L.O. 3) Compound interest tables have been developed to aid in the computation of
present values and annuities. Careful analysis of the problem as to which compound
interest tables will be applied is necessary to determine the appropriate procedures to
follow. The contents of the five types of compound interest tables follow:
Future value of 1. Contains the amounts to which 1 will accumulate if deposited now
at a specified rate and left for a specified number of periods. (Table 6-1)
Present value of 1. Contains the amount that must be deposited now at a specified rate
of interest to equal 1 at the end of a specified number of periods. (Table 6-2)
Future value of an ordinary annuity of 1. Contains the amount to which periodic
rents of 1 will accumulate if the rents are invested at the end of each period at a
specified rate of interest for a specified number of periods. (This table may also be
used as a basis for converting to the amount of an annuity due of 1.) (Table 6-3)
Present value of an ordinary annuity of 1. Contains the amounts that must be
deposited now at a specified rate of interest to permit withdrawals of 1 at the end of
regular periodic intervals for the specified number of periods. (Table 6-4)
Present value of an annuity due of 1. Contains the amounts that must be deposited
now at a specified rate of interest to permit withdrawals of 1 at the beginning of regular
periodic intervals for the specified number of periods. (Table 6-5)
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.
b. Number of Time Periods. The number of compounding periods (a period may be
equal to or less than a year).
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3. c. Future Amount. The value at a future date of a given sum or sums invested
assuming compound interest.
d. Present Value. The value now (present time) of a future sum or sums discounted
assuming compound interest.
9. (L.O. 5) The remaining concepts in this chapter cover the following six major time value of
money concepts:
a. Future value of a single sum.
b. Present value of a single sum.
c. Future value of an ordinary annuity.
d. Future value of an annuity due.
e. Present value of an ordinary annuity.
f. Present value of an annuity due.
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
sum of money that is invested now for a certain number of periods at a certain interest
rate. The second category consists of problems that require the computation of the
unknown present value of a known single sum of money in the future that is discounted
for a certain number of periods at a certain interest rate.
Present Value
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
which the present value was known and the future value was determined. An example of
the type of question addressed by the present value method is: What amount must be
invested today at 6% interest compounded annually to accumulate $5,000 at the end of
10 years? In this question the present value method is used to determine the initial dollar
amount to be invested. The present value method can also be used to determine the
number of years or the interest rate when the other facts are known.
Future Value of an Annuity
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
compound interest be applied. The future value of an annuity is the sum (future value)
of all the rents (payments or receipts) plus the accumulated compound interest on them.
If the rents occur at the end of each time period, the annuity is known as an ordinary
annuity. If rents occur at the beginning of each time period, it is an annuity due. Thus, in
determining the amount of an annuity for a given set of facts, there will be one less
interest period for an ordinary annuity than for an annuity due.
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4. Present Value of an Annuity
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
the beginning of the first period and withdrawals are made at the end of each subsequent
period. If the annuity is an annuity due, the initial sum of money is invested at the
beginning of the first period and withdrawals are made at the beginning of each period.
Thus, the first rent withdrawn in an annuity due occurs on the day after the initial sum of
money is invested. When computing the present value of an annuity, for a given set of
facts, there will be one less discount period for an annuity due than for an ordinary
annuity.
Deferred Annuities
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
10 rents will occur at the end of the sixth year. An annuity due of 10 annual rents deferred
five years means that no rents will occur during the first five years, and that the first of the
10 rents will occur at the beginning of the sixth year. The fact that an annuity is a deferred
annuity affects the computation of the present value. However, the future value of a
deferred annuity is the same as the future value of an annuity not deferred because
there is no accumulation or investment on which interest may accrue.
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
buyers determine the present value of these two cash flows using the market rate of
interest.
16. (L.O. 9) Concepts Statement No. 7 introduces an expected cash flow approach that uses
a range of cash flows and incorporates the probabilities of those cash flows to provide
a more relevant measurement of present value. The FASB takes the position that after
computing the expected cash flows, a company should discount those cash flows by the
risk-free rate of return, which is defined as the pure rate of return plus the expected
inflation rate.
Financial Calculators
*17. Business professionals, after mastering the above concepts, will often use a financial
(business) calculator to solve time value of money problems. When using financial
calculators, the five most common keys used to solve time value of money problems are:
where:
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N
N I I PV
PV PMT
PMT FV
FV

5. N = number of periods.
I = interest rate per period (some calculators use I/YR or i).
PV = present value (occurs at the beginning of the first period).
PMT = payment (all payments are equal in amount, and the time between each payment
is the same).
FV = future value (occurs at the end of the last period).
ILLUSTRATION 6-1SIMPLE INTEREST VS. COMPOUND INTEREST
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6. ILLUSTRATION 6-2
FUNDAMENTAL VARIABLES IN COMPOUND
INTEREST PROBLEMS
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7. ILLUSTRATION 6-3
SINGLE SUM TIME DIAGRAMS
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8. ILLUSTRATION 6-3 (continued)
ANNUITY TIME DIAGRAMS
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9. ILLUSTRATION 6-4
STEPS IN SOLVING COMPOUND INTEREST PROBLEMS
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10. ILLUSTRATION 6-5
EXAMPLES OF COMPOUND INTEREST PROBLEMS
P
R
O
B
L
E
M
S
S
O
L
U
T
I
O
N
S
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11. ILLUSTRATION 6-5 (continued)
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12. ILLUSTRATION 6-5 (continued)
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13. ILLUSTRATION 6-5 (continued)
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14. ILLUSTRATION 6-5 (continued)
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15. ILLUSTRATION 6-5 (continued)
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16. ILLUSTRATION 6-6
BOND VALUATION
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17. ILLUSTRATION 6-7
EXPECTED CASH FLOWS AND PRESENT VALUE
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