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[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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