Chapter 6 Time Value of Money Concepts
59. 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 five years after she joins the company. The
liability for this bonus when the CEO is hired:
a. Is the present value of a deferred annuity.
b. Is the present value of an annuity due.
c. Is $20 million.
d. Is zero because no cash is owed for five years.
60. Which of the following must be known to compute the interest rate paid from financing an
asset purchase with an annuity?
a. Fair value of the asset purchased, number and dollar amount of the annuity payments.
b. Present value of the annuity, dollar amount and timing of the annuity payments.
c. Fair value of the asset and timing of the annuity payments.
d. Number of annuity payments and future value of the annuity.
61. 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.
Chapter 6 Time Value of Money Concepts
62. 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 these answer choices is correct.
63. Garland Inc. offers a new employee a lump-sum signing bonus at the date of employment,
June 1, 2016. Alternatively, the employee can take $39,000 at the date of employment plus
$10,000 each June 1 for five years, beginning in 2020. Assuming the employee’s time value
of money is 9% annually, what lump sum at employment date would make him indifferent
between the two options?
a. $44,035.
b. $40,855.
c. $69,035.
d. $65,855.
64. On January 1, 2016, Glanville Company sold goods to Otter Corporation. Otter signed an
installment note requiring payment of $15,000 annually for six years. The first payment was
made on January 1, 2016. The prevailing rate of interest for this type of note at date of
issuance was 8%.
Chapter 6 Time Value of Money Concepts
Glanville should record sales revenue in January 2016 of:
a. $90,000.
b. $69,343.
c. $74,891.
d. None of these answer choices is correct.
65. Loan C has the same principal amount, payment amount, and maturity date as Loan D.
However, Loan C is structured as an annuity due, while Loan D is structured as an ordinary
annuity. Loan C’s interest rate is:
a. Higher than Loan D.
b. Less than Loan D.
c. The same as Loan D.
d. Indeterminate compared to Loan D.
66. 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 first of the month, with interest of 12% on the unpaid
balance. She should use a table for the:
a. Present value of 1.
b. Present value of an ordinary annuity of 1.
c. Present value of an annuity due of 1.
d. Future value of an annuity due of 1.
67. George Jones is planning on a cruise for his 70th birthday party. He wants to know how much
Chapter 6 Time Value of Money Concepts
he should set aside at the beginning 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 an ordinary annuity of 1.
b. Future value of an annuity due of 1.
c. Future value of 1.
d. Present value of an annuity due of 1.
68. Sandra won $5,000,000 in the state lottery, which she has elected to receive at the end of each
month over the next 30 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. Present value of an annuity due of 1.
b. Future value of an annuity due of 1.
c. Present value of an ordinary annuity of 1.
d. Future value of an ordinary annuity of 1.
69. First Financial Auto Loan Department wishes to know the payment required at the first of
each month on a $10,500, 48-month, 11% auto loan. To determine this amount, First Financial
would:
a. Multiply $10,500 by the present value of 1.
b. Divide $10,500 by the future value of an ordinary annuity of 1.
c. Divide $10,500 by the present value of an annuity due of 1.
d. Multiply $10,500 by the present value of an ordinary annuity of 1.
Chapter 6 Time Value of Money Concepts
70. Koko Company pays $10 million at the beginning of each year for 10 years to Mocha Inc. for
a building with a fair value of $75 million. What interest rate is Mocha earning on financing
this land sale?
a. Between 13% and 14%.
b. Between 7% and 8%.
c. Between 5.5% and 6%.
d. Cannot be determined from the given information.
71. Kunkle Company wishes to earn 20% annually on its investments. If it makes an investment
that equals or exceeds that rate, it considers it a success. Assume that it invests $2 million and
gets $500,000 in return at the end of each year for X years. What is the minimum value of X
for which it will consider the investment a success? Assume that it can’t invest for fractional
parts of a year.
a. 4 years.
b. 6 years.
c. 7 years.
d. 9 years.
9.
72. Chancellor Ltd. sells an asset with a $1 million fair value to Sophie Inc. Sophie agrees to
make six equal payments, one year apart, commencing on the date of sale. The payments
include principal and 6% annual interest. Compute the annual payments.
a. $166,651.
b. $135,252.
c. $203,351.
d. $191,852.
Chapter 6 Time Value of Money Concepts
73. You borrow $20,000 to buy a boat. The loan is to be paid off in monthly installments over one
year at 18% interest annually. The first payment is due one month from today. What is the
amount of each monthly payment?
a. $1,667.
b. $1,511.
c. $1,834.
d. None of the above.
74. Fenland Co. plans to retire $100 million in bonds in five years, so it wishes to create a fund by
making equal investments at the beginning of each year during that period in an account it
expects to earn 8% annually. What amount does Fenland need to invest each year?
a. $15,783,077.
b. $17,045,650.
c. $23,190,400.
d. Cannot be determined from the given information.
Chapter 6 Time Value of Money Concepts
Matching Pair Questions
75. Listed below are 5 terms followed by a list of phrases that describe or characterize each of the
terms. Match each phrase with the number for the correct term.
TERM
PHRASE
NUMBER
1. Future value
A dollar now is worth more than a dollar later.
___
2. Future value of an
annuity due
A series of equal periodic payments.
___
3. Annuity
Accumulation of a series of equal payments with the last
payment accruing interest.
___
4. Future value of an
ordinary annuity
Accumulation of a series of equal payments with the last
payment accruing no interest.
___
5. Time value of money
Accumulation of an amount with interest.
___
Answer:
TERM
PHRASE
NUMBER
1. Future value
A dollar now is worth more than a dollar later.
2. Future value of an
annuity due
A series of equal periodic payments.
3. Annuity
Accumulation of a series of equal payments with the last
payment accruing interest.
4. Future value of an
ordinary annuity
Accumulation of a series of equal payments with the last
payment accruing no interest.
5. Time value of money
Accumulation of an amount with interest.
Chapter 6 Time Value of Money Concepts
76. Listed below are 5 terms followed by a list of phrases that describe or characterize each of the
terms. Match each phrase with the number for the correct term.
TERM
PHRASE
NUMBER
1. Monetary asset
Amount today equivalent to a specified future
amount.
____
2. Present value of an annuity
due
Its amount is not fixed or determinable.
____
3. Present value of a single
amount
Based on initial principal only.
____
4. Simple interest
Claim to a fixed amount of cash.
____
5. Nonmonetary asset
Current worth of a series of equal payments
received at the beginning of a period.
____
TERM
PHRASE
1. Monetary asset
Amount today equivalent to a specified future
amount.
2. Present value of an annuity
Its amount is not fixed or determinable.
3. Present value of a single
amount
Based on initial principal only.
4. Simple interest
Claim to a fixed amount of cash.
5. Nonmonetary asset
Current worth of a series of equal payments
received at the beginning of a period.
Chapter 6 Time Value of Money Concepts
77. Listed below are 5 terms followed by a list of phrases that describe or characterize each of the
terms. Match each phrase with the number for the correct term.
TERM
PHRASE
NUMBER
1. Present value of an ordinary
annuity
Current worth of a series of equal payments
received at the end of a period.
____
2. Effective yield
Current worth of future cash flow(s).
____
3. Monetary liability
Fixed obligation to pay an amount in cash.
____
4. Compound interest
Interest accumulates on interest.
____
5. Present value
The rate at which money will actually grow.
____
TERM
PHRASE
NUMBER
annuity
received at the end of a period.
2. Effective yield
Current worth of future cash flow(s).
3. Monetary liability
Fixed obligation to pay an amount in cash.
4. Compound interest
Interest accumulates on interest.
5. Present value
The rate at which money will actually grow.
Chapter 6 Time Value of Money Concepts
78. Listed below are 5 terms followed by a list of phrases that describe or characterize each of
the terms. Match each phrase with the number for the correct term.
TERM
PHRASE
NUMBER
1. Future value of a single
amount
Rent for the use of money.
____
2. Annuity due
Series of equal cash payments received at the
beginning of each period.
____
3. Interest
Series of equal cash payments received at the end of
each period.
____
4. Ordinary annuity
Series of equal cash payments with the first cash
payment more than one period after the contract date.
____
5. Deferred annuity
The money to which an amount invested will grow
over time.
____
Answer:
TERM
1. Future value of a single
amount
Rent for the use of money.
2. Annuity due
Series of equal cash payments received at the beginning
of each period.
3. Interest
Series of equal cash payments received at the end of
each period.
5. Deferred annuity
The money to which an amount invested will grow over
time.
Chapter 6 Time Value of Money Concepts
79. Listed below are columns of time value of money tables for the 9% rate, followed by labels
for five of the columns. Match the columns with their appropriate labels by placing the letter
designating the column in the space provided by the label.
A
B
C
D
E
F
1
1.090
0.917
1.000
0.917
1.000
1.090
2
1.188
1.759
1.917
0.842
2.090
2.278
3
1.295
2.531
2.759
0.772
3.278
3.573
_____ Present value of an annuity due of $1
_____ Future value of an annuity due of $1
_____ Present value of $1
_____ Future value of $1
_____ Present value of an ordinary annuity of $1
Chapter 6 Time Value of Money Concepts
80. Listed below are 10 terms followed by a list of phrases that describe or characterize the terms.
Match each phrase with the number for the correct term.
TERM
PHRASE
NUMBER
1. Deferred annuity
Amount of money required today that is
equivalent to a given future amount.
____
2. Future value of an annuity due
The amount of money that a dollar will grow
to.
____
3. Annuity
First cash flow occurs on the first day of the
agreement.
____
4. Monetary asset
Claim to a fixed amount of cash.
____
5. Expected cash flow approach
Present value of equal-sized cash flows
beginning at the end of the period.
____
6. Present value of a single amount
The first cash flow occurs more than one
period after the date of the agreement.
____
7. Future value of a single amount
Discount rate is the credit-adjusted risk-free
rate.
____
8. Annuity due
A series of equal-sized cash flows.
____
9. Present value of an ordinary
annuity
Future value of equal-sized cash flows
starting at the beginning of the period.
____
10. Interest
Amount of money paid/received in excess of
the amount borrowed/lent.
____
Answer:
TERM
1. Deferred annuity
Amount of money required today that is
equivalent to a given future amount.
2. Future value of an annuity due
The amount of money that a dollar will grow
to.
3. Annuity
First cash flow occurs on the first day of the
agreement.
4. Monetary asset
Claim to a fixed amount of cash.
5. Expected cash flow approach
Present value of equal-sized cash flows
beginning at the end of the period.
6. Present value of a single amount
The first cash flow occurs more than one
period after the date of the agreement.
7. Future value of a single amount
Discount rate is the credit-adjusted risk-free
rate.
8. Annuity due
A series of equal-sized cash flows.
9. Present value of an ordinary
annuity
Future value of equal-sized cash flows starting
at the beginning of the period.
10. Interest
Amount of money paid/received in excess of
the amount borrowed/lent.
Chapter 6 Time Value of Money Concepts
Chapter 6 Time Value of Money Concepts
Problems
Use the following to answer questions 81–84:
The note about debt included in the financial statements of Healdsburg Company for the year ended
December 31, 2015 disclosed the following:
Debt. The following table summarizes the long-term debt of the Company at December 31, 2015. All
of the notes were issued at their face (maturity) value.
7.25% notes due 2016
$201,335,000
7.75% notes due 2023
$345,154,000
8% notes due 2030
$225,000,000
7.63% notes due 2038
$200,000,000
6.55% notes due 2017
$ 25,000,000
Required: Assuming that the notes pay interest annually and mature on December 31 of the
respective years, compute the following:
81. The total cash interest payments in 2016 for these notes.
82. Suppose that Healdsburg wants to buy back the 7.75% notes on December 31, 2016, (i.e., five
years early) when the going interest rate is 6%, thereby retiring the $345,154,000 in debt.
How much would Healdsburg have to pay for the notes (principal only)?
83. Suppose that Healdsburg renegotiates the 8% notes on December 31, 2021, when the going
interest rate is 8%. Healdsburg agrees to make 12 equal annual installments, commencing on
December 31, 2022, rather than pay the annual interest payments and the $225 million in a
lump sum at maturity. What would the annual payments be?
84. Suppose that Healdsburg enters into a sales contract with an auto manufacturer on January 1,
2016, to provide tires that cost Healdsburg $18 million to produce. The buyer offers
Healdsburg $6 million in cash and agrees to take over only the principal payment on
Healdsburg’s 6.55% debt notes. Assume that the going market interest is 7% at the time.
What would Healdsburg’s gross profit be on the sale?
85. 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
86. 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
Chapter 6 Time Value of Money Concepts
c.
$50,000
11%
10
87. DON Corp. is contemplating the purchase of a machine that will produce net after-tax cash
savings of $20,000 per year for five years. At the end of five years, the machine can be sold to
realize after-tax cash flows of $5,000. Interest is 12%. Assume the cash flows occur at the end
of each year.
Required: Calculate the total present value of the cash savings.
$74,933
88. 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. Interest is at
12%. Assume cash flows occur at the end of the year.
Required: Calculate the total present value of the cash flows.
Chapter 6 Time Value of Money Concepts
89. 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. Interest is at 12%. Assume cash flows
occur at the end of the year.
Required: Calculate the total present value of the cash flows.
90. 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 10 years and can be sold at
the end of 10 years for $10,000. Interest is at 10%. Assume the machine purchase 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.
Required: Determine if Baird should purchase the machine.
Chapter 6 Time Value of Money Concepts
91. 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. Interest is at 12%. Assume the equipment purchase 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.
Required: Determine if Dobson should purchase the machine.
92. 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. Interest is at 8%. Ignore income
taxes.
Required: Determine which option should be chosen based on present value considerations.