257
Chapter 8—The Time Value of Money
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258 ♦ Chapter 8
Matching
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Matching
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Matching
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The Time Value of Money ♦ 259
TRUE/FALSE
1. The present value of an amount is the value of that amount on a particular date prior to the time
the amount is paid or received.
2. The present value concepts are based on the assumption that a dollar received in the future is
worth less than a dollar received now.
3. The three factors required for calculating any future or present value amount include, the amount
of the payments, the interest rate, and the time periods when payments are made.
4. Investment opportunities being evaluated by companies often require the use of present value
calculations.
5. The interest earned in one period on interest that was earned in an earlier period is known as
simple interest
6. Any investment problem can be thought of as a single amount, a series of single amounts, an
annuity, or a combination of these arrangements.
7. An annuity is a series of equal or unequal amounts received or paid over a specified number of
equal time periods.
8. If you needed to have $15,000 in 5 years, you would use a present value table to compute the
amount you would need to invest annually to accumulate $15,000.
260 ♦ Chapter 8
9. A higher interest rate will always result in a higher present value.
10. An amortization table is used to determine the present value of a series of equal annual payments
at a given interest rate.
MULTIPLE CHOICE
1. The future value of an amount is the value of that amount at
a.
the present date
b.
an unknown date
c.
a future date
d.
any given date
2. The amount earned that represents the difference between the future value and present value of a
single investment is called
a.
its cost
b.
an annuity
c.
an apportionment
d.
interest
3. Which of the following will INCREASE future value relative to present value?
a.
higher interest rate
b.
shorter period
c.
more safety
d.
less risk
4. The difference between the future value and present value of an amount is
a.
interest
b.
cash invested
c.
cash plus interest
d.
cash less interest
The Time Value of Money ♦ 261
5. Earning interest in one period on interest earned in an earlier period is known as
a.
simple interest
b.
compound interest
c.
combined interest
d.
double interest
6. A series of equal amounts received or paid over a specified number of equal time periods is known
as an
a.
investment
b.
apportionment
c.
annuity
d.
interest rate
7. Which of the following is TRUE concerning the future value of an investment?
a.
the difference between the future and present value of an investment is the annuity value
b.
the future value of an investment is expected to be larger than its present value
c.
the future value of an investment is expected to be smaller than its present value
d.
the future value of an investment is always smaller than its present value
8. If you invested $1,000 in a savings account today, how much would you have one year from now
if the bank pays 7% interest?
a.
$1,700
b.
$1,070
c.
$1,007
d.
$1,000
262 ♦ Chapter 8
9. Your daughter received a tax refund and immediately and wished to put the money into a savings
account at the local bank. She asked you how much she would accumulate if she invested the
entire amount in the bank for exactly two years. What information would you need in order to
correctly answer her question?
Amount How often bank
Interest Rate placed in savings compounds interest
a.
yes yes no
b.
yes no no
c.
yes no yes
d.
yes yes yes
10. Which of the following formulas correctly represents the calculation of the future amount of an
investment of $500 that was earning interest at 7% annually for 3 years?
a.
$500(1.07)(1.07)(1.07)
b.
$500(1.07)(3)
c.
3($500) × .07
d.
(1.07 × 3)$500
11. An annuity is a series of
a.
equal amounts paid or received over a specified number of unequal time periods
b.
unequal amounts paid or received over a specified number of equal time periods
c.
equal amounts paid or received over an unspecified number of equal time periods
d.
equal amounts paid or received over a specified number of equal time periods
12. An annuity in which amounts are paid or received at the end of each fiscal period is a(n)
a.
annuity due
b.
ordinary annuity
c.
compound annuity
d.
present value annuity
The Time Value of Money ♦ 263
13. At the end of four periods, what will be the future value of four ordinary annuity payments of
$6,000 earning 7% interest?
a.
$17,760
b.
$27,865
c.
$26,640
d.
$26,220
14. Mailer Company invested $15,000 for three years at a rate of 6.5%. By how much did the
investment grow during the third year?
a.
$3,119
b.
$1,106
c.
$1,048
d.
$975
15. The following investments are available. All cash flows occur at the end of the respective years.
I.
Pays $2,400 per year for 3 years. The rate of return expected by investors is 5%.
II.
Pays $300 the first year, zero the second year and $6,900 the third year. Investors expect a
3% rate of return.
III.
Pays $3,600 the first year, $1,800 the second year, and $1,800 the third year. Investors
expect a 10% rate of return.
Which investment opportunity has the highest present value?
a.
investment I
b.
investment II
c.
investment III
d.
investment I and III
16. Hospice Care, Inc. is seeking a bank loan to finance expanded working capital over the next two
years. The firm has budgeted $1,000 for monthly loan payments. If the firm can borrow at 1%
monthly, how large a loan can be obtained?
a.
$20,000
b.
$21,243
c.
$24,000
d.
$25,716
e.
$29,052
264 ♦ Chapter 8
17. Which of the following best expresses the concept of compound interest?
a.
calculating interest on an annuity
b.
earning interest on interest already earned
c.
making complicated interest calculations
d.
making more than one interest payment
18. Determining the amount a series of equal deposits necessary to accumulate $40,000 in five years
involves which of the following concepts?
a.
present value of an annuity
b.
present value of a single amount
c.
future value of an annuity
d.
future value of a single amount
19. The ______ value of an amount is the value of that amount on a particular date prior to the time
the amount is paid or received.
a.
present
b.
current
c.
future
d.
investment
20. Determining the monthly payments required to pay off a 5-year auto loan involves which of the
following concepts?
a.
present value of an annuity
b.
present value of a single amount
c.
present value of an apportionment
d.
future value of an annuity
21. Which of the following is TRUE concerning the present value of an investment?
a.
the difference between the future and present value of an investment is the annuity
b.
the present value of an investment is expected to be larger than its future value
c.
the present value of an investment is expected to be smaller than its future value
d.
the present value of an investment is always larger than its future value
The Time Value of Money ♦ 265
22. A company borrowed $85,356 via an 8%, 3-year loan requiring equal-sized payments at the end of
every quarter (every three months). All required payments were made during the first year. What
amount of interest expense did the company incur during the first 6 months of the loan and how
much principal did it repay?
Loan Interest Principal Repayment
a.
$3,414 $12,758
b.
$3,287 $12,855
c.
$2,581 $10,177
d.
$1,707 $6,364
23. When a borrower obtains a bank loan at 8% interest, the rate of return earned by the bank on this
loan
a.
is exactly 8%
b.
is more than 8%
c.
is less than 8%
d.
cannot be determined without more information
24. Summerville Dental Clinic is considering acquisition of sophisticated new x-ray equipment
costing $100,000. The present value of expected net cash flows (except for purchase cost) from
this equipment is $120,000 when discounted at 10%. From this information, we can conclude that
the
a.
company should reject this investment
b.
expected rate of return is greater than 10%
c.
life of the equipment is less than 6 years
d.
net cash flows will occur evenly over the equipment’s life
25. The Gold Ore Mining Company is contemplating purchase of new equipment. The machinery is
expected to generate increased sales of $50,000 per year over its 5 year life. Excluding the cost of
the machinery, additional operating costs are expected to be $15,000 per year. If the firm requires
a minimum 12% return on its investment, what is the maximum price the company can pay for
this equipment?
a.
$180,239
b.
$175,000
c.
$126,167
d.
$ 54,072
266 ♦ Chapter 8
26. The Turbo Speedboat Company has just acquired new manufacturing equipment. No down
payment was made, but four year-end payments of $2,400 will be required to pay for the machine.
If 8% is the appropriate rate, at what amount should Turbo Speedboat Company record the new
equipment on its books?
a.
$7,056
b.
$7,949
c.
$10,814
d.
$13,060
27. You have an opportunity to purchase the Waiting Line Cafe, a busy shop near your office. The
owner is asking $80,000. After satisfying yourself as to the accuracy of the firm’s past financial
statements, you note that it generated $12,000 per year in net cash flow. You believe you could
operate the business for 4 years and sell it for $50,000. What is the maximum amount you would
be willing to pay for the business if you wish to earn at least a 10% return on your investment?
a.
$54,641
b.
$72,189
c.
$80,000
d.
$38,034
28. The Holiday Family Fun Center is for sale at an asking price of $400,000. The audited financial
statements show that the business generates approximately $43,000 per year in net cash flow. You
believe you could operate the business for 3 years and sell it for $500,000. What is the maximum
amount you would be willing to pay for the business if you wish to earn at least a 10% return on
your investment?
a.
$629,000
b.
$500,000
c.
$482,590
d.
$375,655
29. A business is for sale at $100,000. Discounting the expected cash inflows and expected cash
outflows (except purchase price) at 12% yields an amount of $94,741. Based on this information,
a.
the minimum price you should pay for the business is $94,741
b.
at a purchase price of $100,000, the business is projected to earn just a little more than
12%
c.
a higher discount rate would make this business opportunity more attractive
d.
the investment opportunity should be rejected if a 12% return is required
The Time Value of Money ♦ 267
30. A $10,000 loan was obtained from a bank at 12% annual interest. The loan is to be repaid in four
equal year-end installments. What amount of interest revenue should be recognized by the bank
for the second year of the loan?
a.
$2,500
b.
$1,200
c.
$949
d.
$668
31. Tiger Tail, Inc. borrowed $150,000 from a bank at 10% and promised to repay the loan in 3 equal
year-end payments. How much total interest expense will the company incur over the three year
period?
a.
$30,952
b.
$37,302
c.
$45,000
d.
$112,696
32. How much would you have to invest today at 6% interest to have $30,000 at the end of five
periods?
a.
$3,600
b.
$9,000
c.
$22,418
d.
$28,302
33. What amount must be invested at 10% to amount to $1,000 at the end of 15 periods?
a.
$315
b.
$667
c.
$334
d.
$240
268 ♦ Chapter 8
34. William has recently made an investment that is expected to grow large enough for him to
withdraw $20,000 per year for several years upon his retirement 20 years from now. The value of
his current investment is expected to grow by
a.
the same amount each year
b.
an increasing amount each year
c.
a decreasing amount each year
d.
an increasing number of dollars and at an increasing rate
35. Manny is buying a vacation home. Manny makes a down payment of $45,000 and borrows the
remainder of the cost to complete the purchase. Manny’s mortgage requires him to pay $12,500
per period for 20 periods at an interest rate of 12%. What is the approximate present value of the
amount borrowed?
a.
$250,000
b.
$205,000
c.
$120,575
d.
$93,368
36. The Sporting Goods Depot borrowed $106,000 via 3-year, 8% note payable. The note is to be
repaid in three equal year-end installments. How much interest expense will the firm incur for the
first year of the note?
a.
$5,798
b.
$6,982
c.
$8,480
d.
$9,340
37. How much must be invested today at 9% per period to amount to $175,000 in 15 periods?
a.
$15,750
b.
$11,667
c.
$48,045
d.
$16,445
The Time Value of Money ♦ 269
38. What amount would accumulate if you invested $1,000 at the end of each period for 21 periods at
10%?
a.
$22,000
b.
$25,959
c.
$64,003
d.
$134,540
39. What is the present value of an ordinary annuity requiring payments of $10,000 to be made over
16 periods at 10%?
a.
$16,000
b.
$22,469
c.
$34,880
d.
$78,240
40. What is the amount of each periodic payment that a worker must make at the end of each period
for eight periods to accumulate a savings account of $100,000 by the end of the eighth period to
help pay his retirement, assuming the bank pays 5% interest?
a.
$12,500
b.
$ 8,338
c.
$15,472
d.
$10,472
41. You receive a windfall of $10,000. Your debt from student loans is $17,720. If you invest the
entire amount today at 10% interest, how long will it take to accumulate enough to cover your
debt for student loans?
a.
8 years
b.
7 years
c.
6 years
d.
not enough information to determine
270 ♦ Chapter 8
42. Determining the monthly payments necessary to pay off a car loan of $25,000 in 5 years involves
which of the following concepts?
a.
present value of a single amount
b.
present value of an annuity
c.
future value of an annuity
d.
future value of a single amount
43. If you invest $4,000 for five years at 8% interest, what would be the total amount of interest
earned by the investment?
a.
$5,877
b.
$1,039
c.
$1,877
d.
$4,654
44. George has five years to save for his freshman year tuition of $15,000, how much money must
George deposit into a 6% savings account every year?
a.
$3,000
b.
$2,661
c.
$2,150
d.
$2,205
45. Which of the following combinations of interest rate and number of periods is needed for
calculating the present value of an investment that involves an annual interest rate of 12% for three
years with monthly compounding?
Number of periods Interest rate
a.
3 12%
b.
6 6%
c.
12 3%
d.
36 1%
The Time Value of Money ♦ 271
46. Mondo Cano Enterprises, borrowed $100,000 from a bank at 12% annual interest and arranged to
repay it over two years with monthly payments. How much is the payment?
a.
$4,707
b.
$4,167
c.
$4,541
d.
$4,889
47. If $69,840 is invested today at 7% per year, how many years will it take to be worth $120,000?
a.
7 years
b.
8 years
c.
9 years
d.
10 years
48. Under a loan amortization payment schedule, the amount of interest expense per period will
a.
increase as a percentage of the loan payment as the loan is repaid
b.
decrease as a percentage of the loan payment as the loan is repaid
c.
be constant through the life of the loan
d.
be equal to one-half the loan payment each period
49. Bollinger Enterprises borrowed $10,000 for 2 years at a 12% annual rate. If payments of $471 are
made monthly, what is the interest expense for the second month?
a.
$100
b.
$96
c.
$93
d.
$89
272 ♦ Chapter 8
MATCHING
Match each term with the correct definition.
a.
Compound interest
b.
Future value
c.
Present value
d.
Simple interest
e.
Annuity
f.
Interest
1. An amount that must be invested now to result in a given future value.
2. A series of equal amounts received or paid over a specified number of equal time periods.
3. The amount an investment will be worth at a later date.
4. The difference between future value and present value.
5. Interest computed without considering interest earned in a previous period.
6. Interest earned in one period on interest earned in an earlier period.
For each of the following items, select the letter of the table that would be used to solve the
problem. Assume compound interest in all situations. Letters may be used more than once.
a.
Future value of a single amount
b.
Future value of an annuity
c.
Present value of a single amount
d.
Present value of an annuity
7. Amount on hand at end of 5 years if equal sum invested each year.
8. Single amount that must be invested today to have $100,000 in 10 years.
9. Amount that must be invested today to achieve a desired balance in 10 years.
10. Amount required today to fund future equal monthly retirement benefits.
11. The monthly payments necessary to pay off a car loan.
12. Amount on hand at end of 10 years based on a one-time investment today.