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File: Appendix C Time Value of Money
True/False
[QUESTION]
1. The value of $1
today is worth more than $1 one year from now.
Answer: True
Learning
Objective: 0C-01
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Time Value
of Money
[QUESTION]
2. The time value
of money is a concept, which means that the value of $1 increases over time.
Answer: False
Feedback: Time
value of money means that interest causes the value of money received today to
be greater than the value of that same amount of money received in the future.
Learning Objective:
0C-01
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Time Value
of Money
[QUESTION]
3. Simple interest
is interest earned on the initial investment only.
Answer: True
Learning
Objective: 0C-01
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Simple
Interest
[QUESTION]
4. If you put $500
into a savings account that pays simple interest of 8% per year and then
withdraw the money two years later, you will earn interest of $80.
Answer: True
Feedback: Simple
interest = ($500 × 8%) + ($500 × 8%) = $80.
Learning
Objective: 0C-01
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Calculation
of Simple Interest
[QUESTION]
5. If you put $600
into a savings account that pays simple interest of 10% per year and then
withdraw the money two years later, you will earn interest of $126.
Answer: False
Feedback: Simple
interest = ($600 × 10%) + ($600 × 10%) = $120.
Learning
Objective: 0C-01
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Calculation
of Simple Interest
[QUESTION]
6. Compound
interest is interest you earn on the initial investment and on previous
interest.
Answer: True
Learning
Objective: 0C-01
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Compound
Interest
[QUESTION]
7. If you put $200
into a savings account that pays annual compound interest of 8% per year and
then withdraw the money two years later, you will earn interest of $32.
Answer: False
Feedback: Compound
interest = ($200 × 8%) + ($216 × 8%) = $33.28.
Learning
Objective: 0C-01
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Calculation
of Compound Interest
[QUESTION]
8. If you put $300
into a savings account that pays annual compound interest of 10% per year and
then withdraw the money two years later, you will earn interest of $63.
Answer: True
Feedback: ($300 × 10%)
+ ($330 × 10%) = $63.
Learning
Objective: 0C-01
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Calculation
of Compound Interest
[QUESTION]
9. Future value is how much an amount
today will grow to be in the future.
Answer: True
Learning
Objective: 0C-02
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Future Value
[QUESTION]
10. The more frequent the rate of
compounding, the more interest that is earned on previous interest, resulting
in a higher future value.
Answer: True
Learning
Objective: 0C-02
Difficulty: Medium
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Understand
Topic: Future
Value
[QUESTION]
11. Present value indicates how much a
present amount of money will grow to in the future.
Answer: False
Feedback: Present
value indicates the value today of receiving some larger amount in the future.
Learning
Objective: 0C-02
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Present
Value
[QUESTION]
12. The discount rate is the rate at
which someone is willing to give up current dollars for future dollars.
Answer: True
Learning
Objective: 0C-02
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Discount Rate
[QUESTION]
13. An annuity is a series of equal cash
payments over equal time intervals.
Answer: True
Learning
Objective: 0C-03
Difficulty: Easy
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Remember
Topic: Annuity
[QUESTION]
14. The future value of $1,000 invested
today for three years that earns 10% compounded annually is greater than the
future value of a $500 annuity with the same interest rate over the same period.
Answer: False
Feedback: The
three-year annuity represents three payments of $500 (= $1,500), so the annuity
is greater.
Learning
Objective: 0C-02
Learning
Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Future Value of a Single Amount
Topic: Future Value of an Annuity
[QUESTION]
15. The present value of $1,000 received
three years from today with a discount rate of 10% is less than the present
value of a $500 annuity with the same discount rate over the same period.
Answer: True
Feedback: The
three-year annuity represents three payments of $500 (= $1,500), so the present
value of the annuity is greater.
Learning
Objective: 0C-02
Learning
Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN
Measurement
Blooms: Analyze
Topic: Present Value of a Single Amount
Topic: Present Value of an Annuity
Multiple Choice
[QUESTION]
16. The concept that interest
causes the value of money received today to be greater than the value of that
same amount of money received in the future is
referred to as the:
a. Monetary unit assumption.
b. Historical cost principle.
c. Time value of money.
d. Matching principle.
Answer: c
Learning Objective: 0C-01
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Time Value of Money
[QUESTION]
17. The value today of receiving
an amount in the future is referred to as the:
a. Future value of a single amount.
b. Present value of a single amount.
c. Future value of an annuity.
d. Present value of an annuity.
Answer: b
Learning Objective: 0C-02
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Present Value of a
Single Amount
[QUESTION]
18. The value that an amount
today will grow to in the future is referred to as the:
a. Future value of a single amount.
b. Present value of a single amount.
c. Future value of an annuity.
d. Present value of an annuity.
Answer: a
Learning Objective: 0C-02
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Future Value of a
Single Amount
[QUESTION]
19. Reba wishes to know how
much would be in her savings account in five years if she deposits a given sum
in an account that earns 6% interest. She should use a table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: a
Learning Objective: 0C-02
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
20. LeAnn wishes to know how much she should set aside now at 7%
interest in order to accumulate a sum of $5,000 in four years. She should use a
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: b
Learning Objective: 0C-02
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
21. Samuel is trying to determine what it’s worth today to receive
$10,000 in four years at a 7% interest rate. He should use a table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: b
Learning Objective: 0C-02
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
22. Below are excerpts from
interest tables for 8% interest.
|
|
1
|
2
|
3
|
4
|
|
1
|
1.0000
|
0.92593
|
1.08000
|
0.92593
|
|
2
|
2.0800
|
0.85734
|
1.16640
|
1.78326
|
|
3
|
3.2464
|
0.793833
|
1.25971
|
2.57710
|
|
4
|
4.5061
|
0.73503
|
1.36049
|
3.31213
|
Column 2 is an interest
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: b
Learning Objective: 0C-02
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future Value Tables
[QUESTION]
23. Below are excerpts from
interest tables for 8% interest.
|
|
1
|
2
|
3
|
4
|
|
1
|
1.0000
|
0.92593
|
1.08000
|
0.92593
|
|
2
|
2.0800
|
0.85734
|
1.16640
|
1.78326
|
|
3
|
3.2464
|
0.793833
|
1.25971
|
2.57710
|
|
4
|
4.5061
|
0.73503
|
1.36049
|
3.31213
|
Column 3 is an interest
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: a
Learning Objective: 0C-02
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
24. How much will $25,000 grow to in seven years, assuming an
interest rate of 12% compounded annually?
a. $55,267.
b. $46,000.
c. $61,899.
d. $52,344.
Answer: a
Feedback: FV = $25,000 × 2.21068
(Table 1; n = 7; i = 12%) = $55,267.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
[QUESTION]
25. How much will $8,000 grow to in five years, assuming an
interest rate of 8% compounded quarterly?
a. $10,989.
b. $11,755.
c. $11,888.
d. $12,013.
Answer: c
Feedback: FV = $8,000 × 1.48595
(Table 1; n = 20; i = 2%) = $11,888.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
26. What is the value today
of receiving $2,500 at the end of three years, assuming an interest rate of 9%
compounded annually?
a. $1,984.
b. $1,930.
c. $2,104.
d. $3,238.
Answer: b
Feedback: PV = $2,500 × 0.77218
(Table 2; n = 3; i = 9%) = $1,930.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
[QUESTION]
27. What is the value today
of receiving $5,000 at the end of six years, assuming an interest rate of 8%
compounded semiannually?
a. $3,151.
b. $3,203.
c. $3,428.
d. $3,123.
Answer: d
Feedback: PV = $5,000 × 0.62460
(Table 2; n = 12; i = 4%) = $3,123.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
28. Davenport Inc. offers a
new employee a lump-sum signing bonus at the date of employment. Alternatively, the employee can take $30,000
at the date of employment and another $50,000 two years later. Assuming the employee's time value of money
is 8% annually, what lump-sum at employment date would make her indifferent
between the two options?
a. $60,000.
b. $62,867.
c. $72,867.
d. $80,000.
Answer: c
Feedback: The lump-sum
equivalent would be $30,000 + the present value of $50,000 where n=2 and i=8%.
That is, $30,000 + ($50,000 × 0.85734 from Table 2) = $72,867.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Present Value
Alternatives
[QUESTION]
29. Today, Thomas deposited
$100,000 in a three-year, 12% CD that compounds quarterly. What is the maturity
value of the CD?
a. $109,270.
b. $119,410.
c. $142,576.
d. $309,090.
Answer: c
Feedback: FV = $100,000 × 1.42576
(Table 1; n = 12; i = 3%) = $142,576.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
30. Carol wants to invest
money in a 6% CD that compounds semiannually. Carol would like the account to
have a balance of $50,000 five years from now. How much must Carol deposit to
accomplish her goal?
a. $35,069.
b. $43,131.
c. $37,205.
d. $35,000.
Answer: c
Feedback: PV = $50,000 × 0.74409 (Table 2; n = 10; i = 3%) =
$37,205.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
31. Shane wants to invest
money in a 6% CD that compounds semiannually. Shane would like the account to
have a balance of $100,000 four years from now. How much must Shane deposit to
accomplish his goal?
a. $88,848.
b. $78,941.
c. $25,336.
d. $22,510.
Answer: b
Feedback: PV = $100,000 ×0.78941 (Table 2; n = 8; i = 3%) = $78,941.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
32. Bill wants to give Maria
a $500,000 gift in seven years. If money is worth 6% compounded semiannually,
what is Maria's gift worth today?
a. $66,110.
b. $81,310.
c. $406,550.
d. $330,560.
Answer: d
Feedback: PV = $500,000 ×0.66112 (Table 2; n = 14; i = 3%) =
$330,560.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
33. At the end of the next
four years, a new machine is expected to generate net cash flows of $8,000,
$12,000, $10,000, and $15,000, respectively. What are the cash flows worth
today if a 3% interest rate properly reflects the time value of money in this
situation?
a. $41,557.
b. $47,700.
c. $32,403.
d. $38,108.
Answer: a
Feedback: PV = ($8,000 × 0.97087)
+ ($12,000 × 0.94260) + ($10,000 × 0.91514) + ($15,000 × 0.88849) = $41,557.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of Uneven Cash Flows
[QUESTION]
34. Monica wants to sell her
share of an investment to Barney for $50,000 in three years. If money is worth
6% compounded semiannually, what would Monica accept today?
a. $8,375.
b. $41,874.
c. $11,941.
d. $41,000.
Answer: b
Feedback: PV = $50,000 ×0.83748 (Table 2; n = 6; i = 3%) = $41,874.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
35. How much must be invested now at 9% interest to accumulate to
$10,000 in five years?
a. $9,176.
b. $6,499.
c. $5,500.
d. $5,960.
Answer: b
Feedback: PV = $10,000 ×0.64993 (Table 2; n = 5, i = 9%) = $6,499.
Learning Objective: 0C-02
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
[QUESTION]
36. The value today of
receiving a series of equal payments in the future is referred to as the:
a. Future value of a single amount.
b. Present value of a single amount.
c. Future value of an annuity.
d. Present value of an annuity.
Answer: d
Learning Objective: 0C-03
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Present Value of an
Annuity
[QUESTION]
37. The value that a series
of equal payments will grow to in the future is referred to as the:
a. Future value of a single amount.
b. Present value of a single amount.
c. Future value of an annuity.
d. Present value of an annuity.
Answer: c
Learning Objective: 0C-03
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Future Value of an
Annuity
[QUESTION]
38. A series of equal
periodic payments is referred to as:
a. The time value of money.
b. An annuity.
c. The future value.
d. Interest.
Answer: b
Learning Objective: 0C-03
Difficulty: Easy
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Remember
Topic: Annuity
[QUESTION]
39. How much will $5,000 invested at the end of each year grow to
in six years, assuming an interest rate of 7% compounded annually?
a. $35,766.
b. $26,813.
c. $23,833.
d. $7,504.
Answer: a
Feedback: FVA = $5,000 × 7.1533
(Table 3; n = 6; i = 7%) = $35,766.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of an Annuity
[QUESTION]
40. How much will $1,000 invested at the end of each year grow to
in 20 years, assuming an interest rate of 10% compounded annually?
a. $6,728.
b. $8,514.
c. $83,159.
d. $57,275.
Answer: d
Feedback: FVA = $1,000 × 57.2750
(Table 3; n = 20; i = 10%) = $57,275.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of an Annuity
[QUESTION]
41. What is the value today
of receiving $5,000 at the end of each year for the next 10 years, assuming an
interest rate of 12% compounded annually?
a. $87,744.
b. $28,251.
c. $50,000.
d. $15,529.
Answer: b
Feedback: PVA = $5,000 × 5.65022
(Table 4; n = 10; i = 12%) = $28,251.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
42. What is the value today
of receiving $3,000 at the end of each year for the next three years, assuming
an interest rate of 3% compounded annually?
a. $8,486.
b. $8,251.
c. $9,000.
d. $9,273.
Answer: a
Feedback: PVA = $3,000 × 2.82861
(Table 4; n = 3; i = 3%) = $8,486.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
43. Tammy wants to buy a car
that costs $10,000 and wishes to know the amount of the monthly payments, which
will be made at the end of the month, with interest of 12% on the unpaid
balance. She should use a table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: d
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
44. George Jones is planning on a cruise for his 70th birthday
party. He wants to know how much he should set aside at the end of each month
at 6% interest to accumulate the sum of $4,800 in five years. He should use a
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: c
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
45. Zulu Corporation hires a
new chief executive officer and promises to pay her a signing bonus of $2
million per year for 10 years, starting at the end of the first year. The value
of this signing bonus is:
a. The present value of the annuity.
b. The future value of the annuity.
c. $20 million.
d. $0 because no cash is owed immediately.
Answer: a
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present Value of an
Annuity
[QUESTION]
46. Sandra won $5,000,000 in the state lottery, which she has
elected to receive at the end of each month over the next thirty years. She will receive 7% interest on unpaid
amounts. To determine the amount of her monthly check, she should use a table
for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: d
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
47. Below are excerpts from
interest tables for 8% interest.
|
|
1
|
2
|
3
|
4
|
|
1
|
1.0000
|
0.92593
|
1.08000
|
0.92593
|
|
2
|
2.0800
|
0.85734
|
1.16640
|
1.78326
|
|
3
|
3.2464
|
0.793833
|
1.25971
|
2.57710
|
|
4
|
4.5061
|
0.73503
|
1.36049
|
3.31213
|
Column 4 is an interest
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: d
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future
Value Tables
[QUESTION]
48. Below are excerpts from
interest tables for 8% interest.
|
|
1
|
2
|
3
|
4
|
|
1
|
1.0000
|
0.92593
|
1.08000
|
0.92593
|
|
2
|
2.0800
|
0.85734
|
1.16640
|
1.78326
|
|
3
|
3.2464
|
0.793833
|
1.25971
|
2.57710
|
|
4
|
4.5061
|
0.73503
|
1.36049
|
3.31213
|
Column 1 is an interest
table for the:
a. Future value of $1.
b. Present value of $1.
c. Future value of an annuity of $1.
d. Present value of an annuity of $1.
Answer: c
Learning Objective: 0C-03
Difficulty: Medium
AICPA: Reflective Thinking
AACSB: BB Critical Thinking
Blooms: Understand
Topic: Present and Future Value Tables
[QUESTION]
49. Quaker State Inc. offers
a new employee a lump-sum signing bonus at the date of employment. Alternatively, the employee can take $8,000
at the date of employment plus $20,000 at the end of each of his first three
years of service. Assuming the
employee's time value of money is 10% annually, what lump-sum at employment
date would make him indifferent between the two options?
a. $23,026.
b. $57,737.
c. $62,711.
d. None of the above is correct.
Answer: b
Feedback: The lump-sum equivalent would be $8,000 + the present
value of a $20,000 annuity where n=3, and i=10%. That is, $8,000 + ($20,000 × 2.48685 from
Table 4) = $57,737.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Present Value Alternatives
[QUESTION]
50. At the end of each
quarter, Patti deposits $500 into an account that pays 12% interest compounded
quarterly. How much will Patti have in the account in three years?
a. $7,096.
b. $7,013.
c. $7,129.
d. $8,880.
Answer: a
Feedback: FVA = $500 × 14.1920 (Table 3; n = 12; i = 3%) = $7,096.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of an Annuity
Topic: Interest Compounding
More Than Annually
[QUESTION]
51. Miller borrows $300,000
to be paid off in three years. The loan payments are semiannual with the first
payment due in six months, and interest is at 6%. What is the amount of each
payment?
a. $55,379.
b. $106,059.
c. $30,138.
d. $60,276.
Answer: a
Feedback: $300,000/5.41719 (Table 4; n = 6; i = 3%) = $55,379.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating Loan
Payment Amount
Topic: Interest Compounding
More Than Annually
[QUESTION]
52. Claudine Corporation
will deposit $5,000 into a money market account at the end of each year for the
next five years. How much will accumulate by the end of the fifth and final
payment if the account earns 9% interest?
a. $32,617.
b. $29,924.
c. $27,250.
d. $26,800.
Answer: b
Feedback: FVA = $5,000 × 5.9847 (Table 3; n = 5; i = 9%) = $29,924.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of an Annuity
[QUESTION]
53. What is the value today
of receiving five annual payments of $500,000, beginning one year from now,
assuming an 11% discount rate?
a. $2,500,000.
b. $2,225,000.
c. $1,847,950.
d. $2,115,270.
Answer: c
Feedback: PVA = $500,000 × 3.69590 (Table 4; n = 5; i = 11%) =
$1,847,950.
Learning Objective: 0C-03
Difficulty: Hard
AICPA: Analytic
AACSB: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of an Annuity
Problems
[QUESTION]
54. Compute the future value
of the following invested amounts at the specified periods and interest rates.
|
|
Invested
|
Interest
|
Number of
|
|
Item
|
Amount
|
Rate
|
Periods
|
|
a.
|
$20,000
|
8%
|
10
|
|
b.
|
$30,000
|
4%
|
8
|
|
c.
|
$10,000
|
12%
|
15
|
Answer: a. $43,178; b.
$41,057; c. $54,736.
Feedback:
a. FV = $20,000 × 2.15892
(Table 1; n = 10; i = 8%) = $43,178.
b. FV = $30,000 × 1.36857
(Table 1; n = 8; i = 4%) = $41,057.
c. FV = $10,000 × 5.47357
(Table 1; n = 15; i = 12%) = $54,736.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
[QUESTION]
55. Anthony would like to have $18,000
to buy a new car in three years. Currently, he has saved $15,000. If he puts $15,000
in an account that earns 6% interest, compounded annually, will he be able to buy
the car in three years?
Answer: No.
Feedback: FV = $15,000 × 1.19102
(Table 1; n = 3; i = 6%) = $17,865, which is less than the $18,000 desired amount.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
[QUESTION]
56. Michaela would like to have $10,000
for a European vacation in four years. Currently, she has saved $8,000. If she puts
$8,000 in an account that earns 6% interest, compounded annually, will she be
able to take the vacation in four years?
Answer: Yes.
Feedback: FV = $8,000 × 1.26248
(Table 1; n = 4; i = 6%) = $10,100, which is more than the $10,000 desired amount.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Future Value of a Single Amount
[QUESTION]
57. Compute the present
value of the following single amounts to be received at the end of the
specified period at the given interest rate.
|
|
Invested
|
Interest
|
Number of
|
|
Item
|
Amount
|
Rate
|
Periods
|
|
a.
|
$40,000
|
7%
|
20
|
|
b.
|
$20,000
|
6%
|
25
|
|
c.
|
$50,000
|
11%
|
10
|
Answer: a. $10,337; b.
$4,660; c. $17,609.
Feedback:
a. PV = $40,000 × 0.25842
(Table 2; n = 20; i = 7%) = $10,337.
b. PV = $20,000 × 0.23300
(Table 2; n = 25; i = 6%) = $4,660.
c. PV = $50,000 × 0.35218
(Table 2; n = 10; i = 11%) = $17,609.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
[QUESTION]
58. Compute the present
value of the following single amounts to be received at the end of the
specified period at the given interest rate.
|
|
Invested
|
Interest
|
Number of
|
|
Item
|
Amount
|
Rate
|
Periods
|
|
a.
|
$1,500
|
10%
|
1
|
|
b.
|
$1,500
|
10%
|
2
|
|
c.
|
$1,500
|
10%
|
3
|
|
d.
|
$1,500
|
10%
|
4
|
Answer: a. $1,364; b.
$1,240; c. $1,127; d. $1,025.
a. PV = $1,500 × 0.90909 (Table 2; n = 1; i = 10%) = $1,364.
b. PV = $1,500 × 0.82645 (Table 2; n = 2; i = 10%) = $1,240.
c. PV = $1,500 × 0.75131 (Table 2; n = 3; i = 10%) = $1,127.
d. PV = $1,500 × 0.68301 (Table 2; n = 4; i = 10%) = $1,025.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
[QUESTION]
59. If you had an investment opportunity
that promises to pay you $20,000 in three years and you could earn a 10% annual
return investing your money elsewhere, what is the most you should be willing
to invest today in this opportunity?
Answer: $15,026.
Feedback: PV = $20,000 × 0.75131
(Table 2; n = 3; i = 10%) = $15,026.
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
[QUESTION]
60. Touche Manufacturing is
considering a rearrangement of its manufacturing operations. A consultant
estimates that the rearrangement should result in after-tax cash savings of
$6,000 the first year, $10,000 for the next two years, and $12,000 for the next
two years. Assuming a 12% discount rate, calculate the total present value of
the cash flows.
Answer: $34,882.
Feedback
|
Year
|
Cash Flow
|
PV
|
Present Value
|
|
|
1
|
$ 6,000
|
0.89286 (Table 2; n = 1; i = 12%)
|
$ 5,357
|
|
|
2
|
10,000
|
0.79719 (Table 2; n = 2; i = 12%)
|
7,972
|
|
|
3
|
10,000
|
0.71178 (Table 2; n = 3; i = 12%)
|
7,118
|
|
|
4
|
12,000
|
0.63552 (Table 2; n = 4; i = 12%)
|
7,626
|
|
|
5
|
12,000
|
0.56743 (Table 2; n = 5; i = 12%)
|
6,809
|
|
|
|
|
Total PV of Cash
Savings
|
$34,882
|
|
|
|
|
|
|
|
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of Uneven Cash Flows
[QUESTION]
61. Price Mart is
considering outsourcing its billing operations. A consultant estimates that
outsourcing should result in after-tax cash savings of $9,000 the first year,
$15,000 for the next two years, and $18,000 for the next two years. Assuming a
12% discount rate, calculate the total present value of the cash flows.
Answer: $52,324.
Feedback:
Year
|
Cash Flow
|
PV
|
Present Value |
|
|
1
|
$ 9,000
|
0.89286 (Table 2; n = 1; i = 12%)
|
$ 8,036
|
|
|
2
|
15,000
|
0.79719 (Table 2; n = 2; i = 12%)
|
11,958
|
|
|
3
|
15,000
|
0.71178 (Table 2; n = 3; i = 12%)
|
10,677
|
|
|
4
|
18,000
|
0.63552 (Table 2; n = 4; i = 12%)
|
11,439
|
|
|
5
|
18,000
|
0.56743 (Table 2; n = 5; i = 12%)
|
10,214
|
|
|
|
|
Total PV of Cash
Savings
|
$52,324
|
|
Learning Objective: 0C-02
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of Uneven Cash Flows
[QUESTION]
62. Hillsdale is considering
two options for comparable computer software. Option A will cost $25,000 plus
annual license renewals of $1,000 for three years, which includes technical
support. Option B will cost $20,000 with technical support being an add-on
charge. The estimated cost of technical support is $4,000 the first year,
$3,000 the second year, and $2,000 the third year. Assume the software is
purchased and paid for at the beginning of year one, but that technical support
is paid for at the end of each year. The discount rate is 8%. Ignore income
taxes. Determine which option should be chosen based on present value
considerations.
Answer: Option A should be
chosen because it has the lower cost based on present value considerations.
Feedback:
|
Option A.
|
|
|
|
|
Year
|
Cash Flow
|
PV
|
Present Value
|
|
0
|
$25,000
|
1.00000
|
$25,000
|
|
1
|
1,000
|
0.92593 (Table 2; n = 1; i = 8%)
|
926
|
|
2
|
1,000
|
0.85734 (Table 2; n = 2; i = 8%)
|
857
|
|
3
|
1,000
|
0.79383 (Table 2; n = 3; i = 8%)
|
794
|
|
|
|
|
$27,577
|
|
|
|
|
|
|
Option B.
|
|
|
|
|
Year
|
Cash Flow
|
PV
|
Present Value
|
|
0
|
$20,000
|
1.00000
|
$20,000
|
|
1
|
4,000
|
0.92593 (Table 2; n = 1; i = 8%)
|
3,704
|
|
2
|
3,000
|
0.85734 (Table 2; n = 2; i = 8%)
|
2,572
|
|
3
|
2,000
|
0.79383 (Table 2; n = 3; i = 8%)
|
1,588
|
|
|
|
|
$27,864
|
Learning Objective: 0C-02
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Decision Making
Blooms: Analyze
Topic: Determining Present
Value Alternatives
[QUESTION]
63. Incognito Company is
contemplating the purchase of a machine that provides it with net after-tax
cash savings of $80,000 per year for 5 years. Assuming an 8% discount rate,
calculate the present value of the cash savings.
Answer: $319,417.
Feedback: PVA = $80,000 × 3.99271
(Table 4; n = 5; i =8%) = $319,417.
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
64. Samson Inc. is
contemplating the purchase of a machine that will provide it with net after-tax
cash savings of $100,000 per year for 8 years. Assuming a 10% discount rate,
calculate the present value of the cash savings.
Answer: $533,493.
Feedback: PVA = $100,000 × 5.33493
(Table 4; n = 8; i = 10%) = $533,493.
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
65. DON Corp. is
contemplating the purchase of a machine that will produce net after-tax cash
savings of $20,000 per year for 5 years. At the end of five years, the machine
can be sold to realize after-tax cash flows of $5,000. Assuming a 12% discount
rate, calculate the total present value of the cash savings.
Answer: $74,933.
Feedback:
|
PVA = $20,000 × 3.60478 (Table 4; n = 5; i = 12%)
|
$72,096
|
|
PV = $5,000 × 0.56743 (Table 2; n = 5; i = 12%)
|
2,837
|
|
PV of Cash Savings
|
$74,933
|
|
|
|
Learning Objective: 0C-02
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Measurement
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
66. Baird Bros. Construction
is considering the purchase of a machine at a cost of $125,000. The machine is
expected to generate cash flows of $20,000 per year for ten years and can be
sold at the end of ten years for $10,000. The discount rate is 10%. Assume the
machine would be paid for on the first day of year one, but that all other cash
flows occur at the end of the year. Ignore income tax considerations. Determine
if Baird should purchase the machine.
Answer: Baird Bros.
Construction should buy the machine.
Feedback:
|
Present value of cash outflows
|
|
$125,000
|
|
Present value of cash inflows:
|
|
|
|
Annual cash flows - $20,000 × 6.14457 (Table 4; n = 10; i = 10%)
|
$122,891
|
|
|
Residual value - $10,000 ×0.38554 (Table 2; n = 10; i = 10%)
|
3,855
|
126,746
|
|
Positive present value of net cash flows
|
|
$ 1,746
|
Learning Objective: 0C-02
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Decision Making
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Calculating the
Present Value of an Annuity
[QUESTION]
67. Dobson Contractors is
considering buying equipment at a cost of $75,000. The equipment is expected to
generate cash flows of $15,000 per year for eight years and can be sold at the
end of eight years for $5,000. The discount rate is 12%. Assume the equipment
would be paid for on the first day of year one, but that all other cash flows
occur at the end of the year. Ignore income tax considerations. Determine if
Dobson should purchase the machine.
Answer: Dobson Construction
should buy the machine.
Feedback:
|
Present value of cash outflows
|
|
$75,000
|
|
Present value of cash inflows:
|
|
|
|
Annual cash flows - $15,000 × 4.96764 (Table 4; n = 8; i = 12%)
|
$74,515
|
|
|
Residual value - $5,000 ×0.40388 (Table 2; n = 8; i = 12%)
|
2,019
|
76,534
|
|
Positive present value of net cash flows
|
|
$ 1,534
|
Learning Objective: 0C-02
Learning Objective: 0C-03
Difficulty: Hard
AACSB: Analytic
AICPA: FN Decision Making
Blooms: Analyze
Topic: Calculating the
Present Value of a Single Amount
Topic: Calculating the
Present Value of an Annuity
Essay
The following
answers point out the key phrases that should appear in students' answers. They are not intended to be examples of
complete student responses. It might be helpful to provide detailed
instructions to students on how brief or in-depth you want their answers to be.
[QUESTION]
68. Briefly explain why the value of $100 received today is
greater than the value of $100 received one year from now.
Answer: The $100 received today
can be invested to receive interest. Simple
interest is computed only on the initial investment amount. Compound interest
includes not only interest on the initial investment, but also interest on the
accumulated interest to date.
Learning Objective: 0C-01
Difficulty: Medium
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Understand
Topic Time Value of Money
[QUESTION]
69. Briefly describe the difference between simple interest and
compound interest.
Answer: Simple interest is
computed only on the initial investment amount. Compound interest includes not
only interest on the initial investment, but also interest on the accumulated
interest to date.
Learning Objective: 0C-01
Difficulty: Medium
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Understand
Topic: Simple Interest versus Compound
Interest
[QUESTION]
70. Two banks each have stated CD rates of 12%. Bank A compounds
quarterly and Bank B compounds semiannually. Explain which bank offers the
better CD.
Answer: The yield on a CD
increases with more frequent compounding periods. Therefore, since both CDs
have the same stated rate of 12%, Bank A, that compounds quarterly, offers a
better yield than Bank B with semiannual compounding.
Learning Objective: 0C-01
Difficulty: Hard
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Evaluate
Topic: Compound Interest
[QUESTION]
71. Explain the difference
between present value and future value.
Answer: Present
value tells us the value today of receiving some amount in the future. Future
value is the value that an amount today will grow to in the future. The
difference between the present value and the future value is the time value of
money.
Learning Objective: 0C-02
Difficulty: Medium
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Understand
Topic: Present Value versus
Future Value
[QUESTION]
72. Which three factors are
necessary in calculating the present value of a single amount?
Answer: You need to know (1) the future amount, (2) the
interest rate per period, and (3) the number of periods.
Learning Objective: 0C-02
Difficulty: Easy
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Remember
Topic: Calculating Present Value of a Single Amount
[QUESTION]
73. What is
the relationship between the present value of a single amount and the present
value of an annuity?
Answer: The present value of a single
amount is the value today of receiving that amount in the future; whereas, the
present value of an annuity is the sum of the present values of a series of equal
cash payments.
Learning Objective: 0C-02
Learning Objective: 0C-03
Difficulty: Medium
AACSB: Reflective Thinking
AICPA: BB Critical Thinking
Blooms: Understand
Topic: Present Value of a Single Amount
Topic: Present Value of an Annuity
Matching
[QUESTION]
74. Listed below are ten
terms followed by a list of phrases that describe or characterize five of the
terms. Match each phrase with the best term placing the letter designating the
term in the space provided.
Terms:
a. Annuity
b. Future value of a single amount
c. Discount rate
d. Future value of an annuity
e. Interest
f. Compound interest
g. Present value of a single amount
h. Time value of money
i. Simple interest
j. Present value of an annuity
Phrases:
_____ A dollar now is worth
more than a dollar later.
_____ A series of equal
periodic payments.
_____ Accumulation of a
series of equal payments.
_____ Interest
earned on the initial investment and on previous interest.
_____ Accumulation of an
amount with interest.
Answer: h; a; d; f; b
Learning
Objective: 0C-01
Learning
Objective: 0C-02
Learning
Objective: 0C-03
Difficulty: Medium
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Understand
Topic: Time Value
of Money
Topic: Time Value
of a Single Amount
Topic: Time Value
of an Annuity
[QUESTION]
75. Listed below are ten
terms followed by a list of phrases that describe or characterize five of the
terms. Match each phrase with the best term placing the letter designating the
term in the space provided.
Terms:
a. Annuity
b. Future value of a single amount
c. Discount rate
d. Future value of an annuity
e. Interest
f. Compound interest
g. Present value of a single amount
h. Time value of money
i. Simple interest
j. Present value of an annuity
Phrases:
_____ Amount today equivalent to a specified future amount.
_____ The rate at which future dollars are equal to current dollars.
_____ Interest earned on the initial investment only.
_____ The factor that causes money today to be worth more than the same
amount in the future.
_____ Current worth of a series of equal payments received in the future.
Answer: g; c; i; e; j
Learning
Objective: 0C-01
Learning
Objective: 0C-02
Learning
Objective: 0C-03
Difficulty: Medium
AACSB: Reflective
Thinking
AICPA: BB Critical
Thinking
Blooms: Understand
Topic: Time Value
of Money
Topic: Time Value
of a Single Amount
Topic: Time Value
of an Annuity
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