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CHAPTER 6
ACCOUNTING AND THE TIME VALUE OF MONEY
TRUEFALSE—Conceptual
1. The
time value of money refers to the fact that a dollar received today is worth
less than a dollar promised at some time in the future.
2. Interest
is the excess cash received or repaid over and above the amount lent or
borrowed.
3. Simple
interest is computed on principal and on any interest earned that has not been
withdrawn.
4. Compound
interest, rather than simple interest, must be used to properly evaluate long
term investment proposals.
5. Compound
interest uses the accumulated balance at each year end to compute interest in
the succeeding year.
6. The
future value of an ordinary annuity table is used when payments are invested at
the beginning of each period.
7. The
present value of an annuity due table is used when payments are made at the end
of each period.
8. If
the compounding period is less than one year, the annual interest rate must be
converted to the compounding period interest rate by dividing the annual rate
by the number of compounding periods per year.
9. Present
value is the value now of a future sum or sums discounted assuming compound
interest.
10. The
future value of a single sum is determined by multiplying the future value
factor by its present value.
11. In
determining present value, a company moves backward in time using a process of
accumulation.
12. The
unknown present value is always a larger amount than the known future value
because dollars received currently are worth more than dollars to be received
in the future.
13. The
rents that comprise an annuity due earn no interest during the period in which
they are originally deposited.
14. If
two annuities have the same number of rents with the same dollar amount, but
one is an annuity due and one is an ordinary annuity, the future value of the
annuity due will be greater than the future value of the ordinary annuity.
15. If
two annuities have the same number of rents with the same dollar amount, but
one is an annuity due and one is an ordinary annuity, the present value of the
annuity due will be greater than the present value of the ordinary annuity.
16. The
number of compounding periods will always be one less than the number of rents
when computing the future value of an ordinary annuity.
17. The
future value of an annuity due factor is found by multiplying the future value
of an ordinary annuity factor by 1 minus the interest rate.
18. The
present value of an ordinary annuity is the present value of a series of equal
rents withdrawn at equal intervals.
19. The
future value of a deferred annuity is less than the future value of an annuity
not deferred.
20. The
expected cash flow approach uses a range of cash flows and incorporates the
probabilities of those cash flows to provide a more relevant present value
measurement.
MULTIPLE CHOICE—Conceptual
21. Which of the following
transactions would require the use of the present value of an annuity due concept in order to
calculate the present value of the asset obtained or liability owed at the date
of incurrence?
a. A
capital lease is entered into with the initial lease payment due upon the
signing of the lease agreement.
b. A
capital lease is entered into with the initial lease payment due one month
subsequent to the signing of the lease agreement.
c. A
tenyear 8% bond is issued on January 2 with interest payable semiannually on
July 1 and January 1 yielding 7%.
d. A
tenyear 8% bond is issued on January 2 with interest payable semiannually on
July 1 and January 1 yielding 9%.
22. What best describes the time value of
money?
a. The
interest rate charged on a loan.
b. Accounts
receivable that are determined uncollectible.
c. An
investment in a checking account.
d. The
relationship between time and money.
23. Which of the following situations does not base
an accounting measure on present values?
a. Pensions.
b. Prepaid
insurance.
c. Leases.
d. Sinking
funds.
24. What is interest?
a. Payment
for the use of money.
b. An
equity investment.
c. Return
on capital.
d. Loan.
25. What is not a variable that is considered in interest computations?
a. Principal.
b. Interest
rate.
c. Assets.
d. Time.
26. If you invest $50,000 to earn 8% interest,
which of the following compounding approaches would return the lowest amount
after one year?
a. Daily.
b. Monthly.
c. Quarterly.
d. Annually.
27. Which factor would be greater — the present value of $1 for 10
periods at 8% per period or the future value of $1 for 10 periods at 8% per
period?
a. Present
value of $1 for 10 periods at 8% per period.
b. Future
value of $1 for 10 periods at 8% per period.
c. The
factors are the same.
d. Need
more information.
28. Which of the following tables would show
the smallest value for an interest rate of 5% for six periods?
a. Future
value of 1
b. Present
value of 1
c. Future
value of an ordinary annuity of 1
d. Present
value of an ordinary annuity of 1
29. Which table would you use to determine how
much you would need to have deposited three years ago at 10% compounded
annually in order to have $1,000 today?
a. Future
value of 1 or present value of 1
b. Future
value of an annuity due of 1
c. Future
value of an ordinary annuity of 1
d. Present
value of an ordinary annuity of 1
30. Which table would you use to determine how
much must be deposited now in order to provide for 5 annual withdrawals at the
beginning of each year, starting one year hence?
a. Future
value of an ordinary annuity of 1
b. Future
value of an annuity due of 1
c. Present
value of an annuity due of 1
d. None
of these answer choices are correct.
31. Which table has a factor of 1.00000 for 1
period at every interest rate?
a. Future
value of 1
b. Present
value of 1
c. Future
value of an ordinary annuity of 1
d. Present
value of an ordinary annuity of 1
32. Which table would show the largest factor
for an interest rate of 8% for five periods?
a. Future
value of an ordinary annuity of 1
b. Present
value of an ordinary annuity of 1
c. Future
value of an annuity due of 1
d. Present
value of an annuity due of 1
33. Which of the following tables would show
the smallest factor for an interest rate of 10% for six periods?
a. Future
value of an ordinary annuity of 1
b. Present
value of an ordinary annuity of 1
c. Future
value of an annuity due of 1
d. Present
value of an annuity due of 1
34. The figure .94232 is taken from the column
marked 2% and the row marked three periods in a certain interest table. From
what interest table is this figure taken?
a. Future
value of 1
b. Future
value of annuity of 1
c. Present
value of 1
d. Present
value of annuity of 1
^{S}35. Which
of the following tables would show the largest value for an interest rate of
10% for 8 periods?
a. Future
amount of 1 table.
b. Present
value of 1 table.
c. Future
amount of an ordinary annuity of 1 table.
d. Present
value of an ordinary annuity of 1 table.
^{S}36. On
June 1, 2014, Pitts Company sold some equipment to Gannon Company. The two
companies entered into an installment sales contract at a rate of 8%. The
contract required 8 equal annual payments with the first payment due on June 1,
2014. What type of compound interest table is appropriate for this situation?
a. Present
value of an annuity due of 1 table.
b. Present
value of an ordinary annuity of 1 table.
c. Future
amount of an ordinary annuity of 1 table.
d. Future
amount of 1 table.
^{S}37.
Which of the following transactions would best use the present value of an
annuity due of 1 table?
a. Fernetti,
Inc. rents a truck for 5 years with annual rental payments of $20,000 to be
made at the beginning of each year.
b. Edmiston
Co. rents a warehouse for 7 years with annual rental payments of $120,000 to be
made at the end of each year.
c. Durant,
Inc. borrows $20,000 and has agreed to pay back the principal plus interest in
three years.
d. Babbitt,
Inc. wants to deposit a lump sum to accumulate $50,000 for the construction of
a new parking lot in 4 years.
^{P}38. A series of equal
receipts at equal intervals of time when each receipt is received at the
beginning of each time period is called an
a. ordinary
annuity.
b. annuity
in arrears.
c. annuity
due.
d. unearned
receipt.
^{P}39. In the time diagram below, which concept is
being depicted?
0

1
$1

2
$1

3
$1

4
$1


a. Present
value of an ordinary annuity
b. Present
value of an annuity due
c. Future
value of an ordinary annuity
d. Future
value of an annuity due
^{P}40. On December 1, 2014, Richards Company sold
some machinery to Fleming Company. The two companies entered into an
installment sales contract at a predetermined interest rate. The contract
required four equal annual payments with the first payment due on December 1, 2014,
the date of the sale. What present value concept is appropriate for this situation?
a. Future
amount of an annuity of 1 for four periods
b. Future
amount of 1 for four periods
c. Present
value of an ordinary annuity of 1 for four periods
d. Present
value of an annuity due of 1 for four periods.
41. An amount is deposited
for eight years at 8%. If compounding occurs quarterly, then the table value is
found at
a. 8%
for eight periods.
b. 2%
for eight periods.
c. 8% for 32 periods.
d. 2% for 32 periods.
42. If the number of periods is
known, the interest rate is determined by
a. dividing
the future value by the present value and looking for the quotient in the
future value of 1 table.
b. dividing
the future value by the present value and looking for the quotient in the
present value of 1 table.
c. dividing
the present value by the future value and looking for the quotient in the
future value of 1 table.
d. multiplying
the present value by the future value and looking for the product in the
present value of 1 table.
43. Present value is
a. The
value now of a future amount.
b. The
amount that must be invested now to produce a known future value.
c. Always
smaller than the future value.
d. All
of these answer choices are correct.
^{P}44. Which
of the following statements is true?
a. The
higher the discount rate, the higher the present value.
b. The
process of accumulating interest on interest is referred to as discounting.
c. If
money is worth 10% compounded annually, $1,100 due one year from today is
equivalent to $1,000 today.
d. If
a single sum is due on December 31, 2014, the present value of that sum
decreases as the date draws closer to December 31, 2014.
45. What is the primary difference between an
ordinary annuity and an annuity due?
a. The
timing of the periodic payment.
b. The
interest rate.
c. Annuity
due only relates to present values.
d. Ordinary
annuity only relates to present values.
46. What is the relationship between the future
value of one and the present value of one?
a. The
present value of one equals the future value of one plus one.
b. The
present value of one equals one plus future value factor for n1 periods.
c. The
present value of one equals one divided by the future value of one.
d. The
present value of one equals one plus the future value factor for n+1 value
47. Peter invests $100,000 in a 3year certificate
of deposit earning 3.5% at his local bank. Which time value concept would be
used to determine the maturity value of the certificate?
a. Present
value of one.
b. Future
value of one.
c. Present
value of an annuity due.
d. Future
value of an ordinary annuity.
48. Jerry recently was offered a position with
a major accounting firm. The firm offered Jerry either a signing bonus of
$23,000 payable on the first day of work or a signing bonus of $26,000 payable
after one year of employment. Assuming that the relevant interest rate is 10%,
which option should Jerry choose?
a. The
options are equivalent.
b. Insufficient
information to determine.
c. The
signing bonus of $23,000 payable on the first day of work.
d. The
signing bonus of $26,000 payable after one year of employment.
49. If Jethro wanted to save a set amount each
month in order to buy a new pickup truck when the new models are next
available, which time value concept would be used to determine the monthly
payment?
a. Present
value of one.
b. Future
value of one.
c. Present
value of an annuity due.
d. Future
value of an ordinary annuity.
50. Betty wants to know how much she should
begin saving each month to fund her retirement. What kind of problem is this?
a. Present
value of one.
b. Future
value of an ordinary annuity.
c. Present
value of an ordinary.
d. Future
value of one.
^{P}51 If
the interest rate is 10%, the factor for the future value of annuity due of 1
for n = 5, i = 10% is equal to the factor for the future value of an ordinary annuity
of 1 for n = 5, i = 10%
a. plus 1.10.
b. minus 1.10.
c. multiplied
by 1.10.
d. divided
by 1.10.
52. Which of the following is true?
a. Rents
occur at the beginning of each period of an ordinary annuity.
b. Rents
occur at the end of each period of an annuity due.
c. Rents
occur at the beginning of each period of an annuity due.
d. None
of these answer choices are correct.
53. Which of the following statements is false?
a. The
factor for the future value of an annuity due is found by multiplying the
ordinary annuity table value by one plus the interest rate.
b. The
factor for the present value of an annuity due is found by multiplying the
ordinary annuity table value by one minus the interest rate.
c. The
factor for the future value of an annuity due is found by subtracting from the
ordinary annuity table value for one more period.
d. The
factor for the present value of an annuity due is found by adding to the
ordinary annuity table value for one less period.
54. Al Darby wants to withdraw $20,000 (including
principal) from an investment fund at the end of each year for five years. How
should he compute his required initial investment at the beginning of the first
year if the fund earns 10% compounded annually?
a. $20,000
times the future value of a 5year, 10% ordinary annuity of 1.
b. $20,000
divided by the future value of a 5year, 10% ordinary annuity of 1.
c. $20,000
times the present value of a 5year, 10% ordinary annuity of 1.
d. $20,000
divided by the present value of a 5year, 10% ordinary annuity of 1.
55. Sue Gray wants to invest a certain sum of
money at the end of each year for five years. The investment will earn 6%
compounded annually. At the end of five years, she will need a total of $40,000
accumulated. How should she compute her required annual investment?
a. $40,000
times the future value of a 5year, 6% ordinary annuity of 1.
b. $40,000
divided by the future value of a 5year, 6% ordinary annuity of 1.
c. $40,000
times the present value of a 5year, 6% ordinary annuity of 1.
d. $40,000
divided by the present value of a 5year, 6% ordinary annuity of 1.
56. An accountant wishes to find the present value
of an annuity of $1 payable at the beginning of each period at 10% for eight
periods. The accountant has only one present value table which shows the
present value of an annuity of $1 payable at the end of each period. To compute
the present value, the accountant would use the present value factor in the 10%
column for
a. seven
periods.
b. eight
periods and multiply by (1 + .10).
c. eight
periods.
d. nine
periods and multiply by (1 – .10).
57. If an annuity due and an ordinary annuity
have the same number of equal payments and the same interest rates, then
a. the
present value of the annuity due is less than the present value of the ordinary
annuity.
b. the
present value of the annuity due is greater than the present value of the
ordinary annuity.
c. the
future value of the annuity due is equal to the future value of the ordinary
annuity.
d. the
future value of the annuity due is less than the future value of the ordinary
annuity.
58. What is the relationship between the
present value factor of an ordinary annuity and the present value factor of an
annuity due for the same interest rate?
a. The
ordinary annuity factor is not related to the annuity due factor.
b. The
annuity due factor equals one plus the ordinary annuity factor for n1 periods.
c. The
ordinary annuity factor equals one plus the annuity due factor for n+1 periods.
d. The
annuity due factor equals the ordinary annuity factor for n+1 periods minus
one.
59. Paula purchased a house for $300,000. After
providing a 20% down payment, she borrowed the balance from the local savings
and loan under a 30year 6% mortgage loan requiring equal monthly installments
at the end of each month. Which time value concept would be used to determine
the monthly payment?
a. Present
value of one.
b. Future
value of one.
c. Present
value of an ordinary annuity.
d. Future
value of an ordinary annuity.
60. Stemway Company requires a new manufacturing
facility. It found three locations; all of which would provide the needed
capacity, the only difference is the price. Location A may be purchased for
$500,000. Location B may be acquired with a down payment of $100,000 and annual
payments at the end of each of the next twenty years of $50,000. Location C
requires $40,000 payments at the beginning of each of the next twentyfive
years. Assuming Stemway's borrowing costs are 8% per annum, which option is the
least costly to the company?
a. Location A.
b. Location B.
c. Location C.
d. Location
A and Location B.
61. Which of the following is false?
a. The
future value of a deferred annuity is the same as the future value of an
annuity not deferred.
b. A deferred annuity is an annuity in which the
rents begin after a specified number of periods.
c. To
compute the present value of a deferred annuity, we compute the present value
of an ordinary annuity of 1 for the entire period and subtract the present
value of the rents which were not received during the deferral period.
d. If
the first rent is received at the end of the sixth period, it means the
ordinary annuity is deferred for six periods.
Multiple Choice—Computational
62. Assume ABC Company deposits $70,000 with
First National Bank in an account earning interest at 6% per annum, compounded
semiannually. How much will ABC have in the account after five years if
interest is reinvested?
a. $94,074.
b. $70,000.
c. $91,000.
d. $93,677.
63. Charlie Corp. is purchasing new equipment
with a cash cost of $250,000 for an assembly line. The manufacturer has offered
to accept $57,400 payment at the end of each of the next six years. How much
interest will Charlie Corp. pay over the term of the loan?
a. $57,400.
b. $250,000.
c. $307,400.
d. $94,400.
64. If a savings account pays interest at 4%
compounded quarterly, then the amount of $1 left on deposit for 5 years would
be found in a table using
a. 5 periods at 4%.
b. 5 periods at 1%.
c. 20 periods at 4%.
d. 20 periods at 1%.
Items 65 through 68 apply to the
appropriate use of interest tables. Given below are the future value factors
for 1 at 8% for one to five periods. Each of the items 65 to 68 is based on 8%
interest compounded annually.
Periods Future Value of 1 at 8%
1 1.080
2 1.166
3 1.260
4 1.360
5 1.469
65. What amount should be deposited in a bank
account today to grow to $15,000 three years from today?
a. $15,000
× 1.260
b. $15,000
× 1.260 × 3
c. $15,000
÷ 1.260
d. $15,000
÷ 1.080 × 3
66. If $5,000 is deposited in a savings account
today, what amount will be available three years from today?
a. $5,000
÷ 1.260
b. $5,000
× 1.260
c. $5,000
× 1.080 × 3
d. ($5,000
× 1.080) + ($5,000 × 1.166) + ($5,000 × 1.260)
67. What amount will be in a bank account three
years from now if $8,000 is invested each year for four years with the first
investment to be made today?
a. ($8,000
× 1.260) + ($8,000 × 1.166) + ($8,000 × 1.080) + $8,000
b. $8,000
× 1.360 × 4
c. ($8,000
× 1.080) + ($8,000 × 1.166) + ($8,000 × 1.260) + ($8,000 × 1.360)
d. $8,000
× 1.080 × 4
68. If $6,000 is deposited in a savings account
today, what amount will be available six years from now?
a. $6,000
× 1.080 × 6
b. $6,000
× 1.080 × 1.469
c. $6,000
× 1.166 × 3
d. $6,000
× 1.260 × 2
Items 69 through 72 apply to the appropriate use of present value tables.
Given below are the present value factors for $1.00 discounted at 10% for one
to five periods. Each of the items 69 to 72 is based on 10% interest compounded
annually.
Present
Value of $1
Periods Discounted at 10% per
Period
1 0.909
2 0.826
3 0.751
4 0.683
5 0.621