6-1
CHAPTER 6
Accounting and the Time Value of Money
ASSIGNMENT CLASSIFICATION TABLE (BY TOPIC)
Topics
Questions
Brief
Exercises
Exercises
Problems
1.
Present value concepts.
1, 2, 3, 4,
5, 9, 17
15, 17
c. Unknown number of
periods.
4, 9
10, 15
2
d. Unknown interest rate.
15, 18
3, 11, 16
9, 10, 11, 14
2, 7
e. Unknown present value.
8, 19
2, 7, 8,
10, 14
3, 4, 5, 6,
8, 12, 17,
18, 19
1, 4, 7, 9,
13, 14
Value of a series of irregular
deposits; changing interest
rates.
3, 5, 8
Valuation of leases,
pensions, bonds; choice
between projects.
6
7, 12, 13,
14, 15
3, 5, 6, 8, 9,
10, 11, 12,
13, 14, 15
Deferred annuity.
Expected Cash Flows.
20, 21, 22
13, 14, 15
Use of tables.
13, 14
8
1
3.
Present and future value
problems:
a. Unknown future amount.
7, 19
1, 5, 13
2, 3, 4, 7
b. Unknown payments.
10, 11, 12
6, 12,
8, 16, 17
2, 6
6-2
ASSIGNMENT CLASSIFICATION TABLE (BY LEARNING OBJECTIVE)
Learning Objectives
Brief
Exercises
Problems
1. Identify accounting topics where the time
value of money is relevant.
5. Solve future and present value of 1 problems.
1, 2, 3,
4, 7, 8
1, 2, 3, 5,
7, 9, 10
6. Solve future value of ordinary and annuity
due problems.
5, 6, 9, 13
2, 7
14, 16, 17
7, 8, 9, 10,
13, 14
8. Solve present value problems related
to deferred annuities and bonds.
6, 11, 12, 15
value measurement.
13, 14, 15
2. Distinguish between simple and compound
interest.
2
1
4. Identify variables fundamental to solving
interest problems.
6-3
ASSIGNMENT CHARACTERISTICS TABLE
Item
Description
Level of
Difficulty
Time
(minutes)
E6-1
Using interest tables.
Simple
5–10
E6-2
Simple and compound interest computations.
Simple
5–10
E6-9
Unknown rate.
Moderate
5–10
E6–10
Unknown periods and unknown interest rate.
Simple
10–15
E6–11
Evaluation of purchase options.
Moderate
10–15
E6–12
Analysis of alternatives.
Simple
10–15
E6–13
Computation of bond liability.
Moderate
15–20
E6–14
Computation of pension liability.
Moderate
15–20
E6–15
Investment decision.
Moderate
15–20
E6–16
Retirement of debt.
Simple
10–15
E6–17
Computation of amount of rentals.
Simple
10–15
E6–18
Least costly payoff.
Simple
10–15
E6–19
Least costly payoff.
Simple
10–15
E6–20
Expected cash flows.
Simple
5–10
E6–21
Expected cash flows and present value.
Moderate
15–20
P6-1
Various time value situations.
Moderate
15–20
P6-2
Various time value situations.
Moderate
15–20
P6-3
Analysis of alternatives.
Moderate
20–30
P6-4
Evaluating payment alternatives.
Moderate
20–30
P6-5
Analysis of alternatives.
Moderate
20–25
P6-6
Purchase price of a business.
Moderate
25–30
P6-7
Time value concepts applied to solve business problems.
30–35
P6-8
Analysis of alternatives.
Moderate
20–30
P6-9
Analysis of business problems.
30–35
P6–10
Analysis of lease vs. purchase.
30–35
P6–11
Pension funding.
25–30
P6–12
Pension funding.
Moderate
20–25
P6–13
Expected cash flows and present value.
Moderate
20–25
P6–14
Expected cash flows and present value.
Moderate
20–25
P6–15
Fair value estimate.
20–25
E6-3
Computation of future values and present values.
Simple
10–15
E6-4
Computation of future values and present values.
Moderate
15–20
E6-5
Computation of present value.
Simple
10–15
E6-6
Future value and present value problems.
Moderate
15–20
E6-7
Computation of bond prices.
Moderate
12–17
E6-8
Computations for a retirement fund.
Simple
10–15
6-4
SOLUTIONS TO CODIFICATION EXERCISES
CE6-1
(a) According to the Master Glossary, present value is a tool used to link uncertain future amounts
(cash flows or values) to a present amount using a discount rate (an application of the income
approach) that is consistent with value maximizing behavior and capital market equilibrium.
1. 820 Fair Value Measurements and Disclosures > 10 Overall > 35 Subsequent Measurement
35–33 Those valuation techniques include the following:
a. Present value techniques
2. 820 Fair Value Measurements and Disclosures > 10 Overall > 55 Implementation General,
paragraph 55-4 >>> Present Value Techniques
55-4 FASB Concepts Statement No. 7, Using Cash Flow Information and Present Value in
Accounting Measurements, provides guidance for using present value techniques to
measure fair value. That guidance focuses on a traditional or discount rate adjustment
CE6-2
Answers will vary. By entering the phrase “present value” in the search window, a list of references to
the term is provided. The site allows you to narrow the search to assets, liabilities, revenues, and
expenses.
6-5
CE6-2 (Continued)
50-1 The changes in the carrying amount of goodwill during the period shall be disclosed, including
the following (see Example 3 [paragraph 350-20–55-24]):
a. The aggregate amount of goodwill acquired.
> Goodwill Impairment Loss
50-2 For each goodwill impairment loss recognized, all of the following information shall be dis-
closed in the notes to the financial statements that include the period in which the impair-
ment loss is recognized:
a. A description of the facts and circumstances leading to the impairment.
(b) Liability reference: 410 Asset Retirement and Environmental Obligations > 20 Asset Retirement
Obligations > 30 Initial Measurement
Determination of a Reasonable Estimate of Fair Value
30-1 An expected present value technique will usually be the only appropriate technique with which
to estimate the fair value of a liability for an asset retirement obligation. An entity, when
using that technique, shall discount the expected cash flows using a credit-adjusted risk-free
rate. Thus, the effect of an entity’s credit standing is reflected in the discount rate rather
6-6
CE6-2 (Continued)
(c) Revenue or Expense reference: 720 Other Expenses> 25 Contributions Made> 30 Initial Measurement
CE6-3
Interest cost includes interest recognized on obligations having explicit interest rates, interest imputed
According to the discussion at: 835 Interest> 30 Imputation of Interest
05-1 This Subtopic addresses the imputation of interest.
05-2 Business transactions often involve the exchange of cash or property, goods, or services for a
note or similar instrument. When a note is exchanged for property, goods, or services in a
bargained transaction entered into at arm’s length, there should be a general presumption that
05-3 This Subtopic provides guidance for the appropriate accounting when the face amount of a note
does not reasonably represent the present value of the consideration given or received in the
6-7
ANSWERS TO QUESTIONS
1. Money has value because with it one can acquire assets and services and discharge obligations.
The holding, borrowing or lending of money can result in costs or earnings. And the longer the
time period involved, the greater the costs or the earnings. The cost or earning of money as a
2. Some situations in which present value measures are used in accounting include:
(a) Notes receivable and payable—these involve single sums (the face amounts) and may
involve annuities, if there are periodic interest payments.
(b) Leases—involve measurement of assets and obligations, which are based on the present value
3. Interest is the payment for the use of money. It may represent a cost or earnings depending upon
whether the money is being borrowed or loaned. The earning or incurring of interest is a function
4. The interest rate generally has three components:
(a) Pure rate of interest—This would be the amount a lender would charge if there were no
possibilities of default and no expectation of inflation.
(b) Expected inflation rate of interest—Lenders recognize that in an inflationary economy, they
5. (a) Present value of an ordinary annuity at 8% for 10 periods (Table 6-4).
(b) Future value of 1 at 8% for 10 periods (Table 6-1).
(c) Present value of 1 at 8% for 10 periods (Table 6-2).
(d) Future value of an ordinary annuity at 8% for 10 periods (Table 6-3).
6-8
Questions Chapter 6 (Continued)
6. He should choose quarterly compounding, because the balance in the account on which interest
will be earned will be increased more frequently, thereby resulting in more interest earned on the
investment. This is shown in the following calculation:
7. $26,897.80 = $20,000 X 1.34489 (future value of 1 at 21/2 for 12 periods).
8. $44,671.20 = $80,000 X .55839 (present value of 1 at 6% for 10 periods).
10.
Amount paid each year =
$40,000
(present value of an ordinary annuity at 12% for 4 years).
3.03735
Amount paid each year = $13,169.37.
11.
Amount deposited each year =
12.
Amount deposited each year =
$200,000
[future value of an annuity due at 10% for 4 years
(4.64100 X 1.10)].
5.10510
Amount deposited each year = $39,176.51.
13. The process for computing the future value of an annuity due using the future value of an ordinary
14. The basis for converting the present value of an ordinary annuity table to the present value of an
annuity due table involves multiplying the present value of an ordinary annuity factor by one plus
the interest rate.
6-9
Questions Chapter 6 (Continued)
15. Present value = present value of an ordinary annuity of $25,000 for 20 periods at? percent.
16. 4.96764 Present value of ordinary annuity at 12% for eight periods.
2.40183 Present value of ordinary annuity at 12% for three periods.
2.56581 Present value of ordinary annuity at 12% for eight periods, deferred three periods.
The present value of the five rents is computed as follows:
2.56581 X $20,000 = $51,316.20.
18. $27,600 = PV of an ordinary annuity of $6,900 for five periods at? percent.
$27,600
= PV of an ordinary annuity for five periods at? percent.
$6,900
SOLUTIONS TO BRIEF EXERCISES
BRIEF EXERCISE 6-1
8% annual interest
8% annual interest, compounded semiannually
i = 4%
PV = $15,000 FV = ?
6-11
BRIEF EXERCISE 6-2
12% annual interest
12% annual interest, compounded quarterly
i = 3%
PV = ? FV = $25,000
BRIEF EXERCISE 6-3
i = ?
PV = $30,000 FV = $150,000
2
20 21
PV = FV (PVF21, i)
$30,000 = $150,000 (PVF21, i)
FVF21, i = 5.0000
PVF21, i = .20000
i = 8%
i = 8%
BRIEF EXERCISE 6-4
i = 5%
PV = $10,000 FV = $17,100
0
?
n = ?
PV = FV (PVFn, 5%)
$17,100 = $10,000 (FVFn, 5%)
n = 11 years
n = 11 years
6-13
BRIEF EXERCISE 6-5
First payment today (Annuity Due)
i = 12%
R = FV – AD =
$8,000 $8,000 $8,000 $8,000 $8,000 ?
0
1
2
18
19 20
n = 20
First payment at year-end (Ordinary Annuity)
i = 12%
FV – OA =
?
$8,000 $8,000 $8,000 $8,000 $8,000
1
2
18
19 20
6-14
BRIEF EXERCISE 6-6
i = 11%
FV – OA =
R = ? ? ? ? $250,000
0
1
2
8
9 10
n = 10
BRIEF EXERCISE 6-7
12% annual interest
i = 12%
PV = ? FV = $300,000
0
1
2
3
4 5
n = 5
BRIEF EXERCISE 6-8
With quarterly compounding, there will be 20 quarterly compounding periods,
at 1/4 the interest rate:
BRIEF EXERCISE 6-9
i = 10%
FV – OA =
R = $100,000
$16,380 $16,380 $16,380
0
1
2
n
n = ?
6-16
BRIEF EXERCISE 6-10
First withdrawal at year-end
i = 8%
PV – OA = R =
? $30,000 $30,000 $30,000 $30,000 $30,000
0
1
2
8
9 10
First withdrawal immediately
i = 8%
PV – AD =
?
R =
$30,000 $30,000 $30,000 $30,000 $30,000
0
2
8
9 10
6-17
BRIEF EXERCISE 6-11
i = ?
PV = R =
$793.15 $75 $75 $75 $75 $75
0
1
2
10
11 12
n = 12
BRIEF EXERCISE 6-12
i = 8%
PV =
$300,000 R = ? ? ? ? ?
0
18
19 20
BRIEF EXERCISE 6-13
i = 12%
R =
12/31/11
12/31/12
12/31/17
BRIEF EXERCISE 6-14
i = 8%
PV – OA = R =
? $25,000 $25,000 $25,000 $25,000
0
1
2
3
4
5
6
6-19
BRIEF EXERCISE 6-15
i = 8%
PV = ?
PV – OA = R = $2,000,000
? $140,000 $140,000 $140,000 $140,000 $140,000
BRIEF EXERCISE 6-16
PV – OA = $20,000
$4,727.53 $4,727.53 $4,727.53 $4,727.53
0
1
2
5 6
0
1
2
8
9 10
BRIEF EXERCISE 6-17
PV – AD = $20,000
$? $? $? $?
0
1
2
5 6