Principles of Finance, 6e
Besley/Brigham
Chapter 09
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1. Given some amount to be received several years in the future, if the interest rate increases, the present value of the
future amount will
a.
Be higher.
b.
Be lower.
c.
Stay the same.
d.
Cannot tell.
e.
Be variable.
ANSWER:
b
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-5 – Knowledge
Business Program-6 – Reflective Thinking
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of a Sum
2. You have determined the profitability of a planned project by finding the present value of all the cash flows form that
project. Which of the following would cause the project to look more appealing in terms of the present value of those cash
flows?
a.
The discount rate decreases.
b.
The cash flows are extended over a longer period of time, but the total amount of the cash flows remains the
same.
c.
The discount rate increases.
d.
Answers b and c above.
e.
Answers a and b above.
ANSWER:
a
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-5 – Knowledge
Business Program-6 – Reflective Thinking
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV and Discount Rate
3. As the discount rate increases without limit, the present value of the future cash inflows
a.
b.
c.
d.
e.
ANSWER:
c
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distributed with a certain product or service or otherwise on a password-protected website for classroom use.
4. Which of the following statements is false?
a.
If the discount (or interest) rate is positive, the future value of an expected series of payments will always
exceed the present value of the same series.
b.
To increase present consumption beyond present income normally requires either the payment of interest or
else an opportunity cost of interest foregone.
c.
Disregarding risk, if money has time value, it is impossible for the present value of a given sum to be greater
than its future value.
d.
Disregarding risk, if the present value of a sum is equal to its future value, either r = 0 or t = 0.
e.
Each of the above statements is true.
ANSWER:
e
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-5 – Knowledge
Business Program-6 – Reflective Thinking
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV versus FV
5. Which of the following statements is correct?
a.
The PV of an ordinary annuity will be larger than the PV of an annuity due, other things held constant.
b.
The effective annual rate will always be greater than the simple rate except in situations where the periodic
rate is equal to the simple rate.
c.
If you were borrowing money from a bank, and the simple interest rate was 10 percent, you would be better
off if the bank used daily rather than quarterly compounding.
d.
If you were borrowing money from a bank, and the simple interest rate was 10 percent, daily compounding,
you would be better off if the bank used a 365-day year rather than a 360-day year.
e.
$100 placed in a bank account which pays 6 percent will double faster if the bank pays interest annually rather
than daily.
ANSWER:
b
RATIONALE:
The effective annual rate must exceed the simple rate unless there is annual
compounding. If there is annual compounding, then m = 1, and the periodic rate is equal
to the simple rate (because rPER = rSIMPLE/1), and both are equal to the rEAR.
POINTS:
1
DIFFICULTY:
Easy
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-5 – Knowledge
Business Program-6 – Reflective Thinking
TOPICS:
PV and Discount Rate
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© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license
distributed with a certain product or service or otherwise on a password-protected website for classroom use.
8. Supposed someone offered you the choice of two equally risky annuities, each paying $10,000 per year for five years.
One is an ordinary (or deferred) annuity, the other is an annuity due. Which of the following statements is most correct?
a.
The present value of the ordinary annuity must exceed the present value of the annuity due, but the future
value of an ordinary annuity may be less than the future value of the annuity due.
b.
The present value of the annuity due exceeds the present value of the ordinary annuity, while the future value
of the ordinary annuity.
c.
The present value of the annuity due exceeds the present value of the ordinary annuity, and the future value of
the annuity due also exceeds the future value of the ordinary annuity.
d.
If interest rates increase, the difference between the present value of the ordinary annuity and the present value
of the annuity due remains the same.
e.
Both answers a and d are correct.
ANSWER:
c
RATIONALE:
By definition, an annuity due is received at the beginning of the year while an ordinary
annuity is received at the end of the year. Because the payments are received earlier,
both the present and future values of the annuity due are greater than those of the
ordinary annuity.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-5 – Knowledge
Business Program-6 – Reflective Thinking
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Annuities
9. Which of the following statements is correct?
a.
If a bank uses quarterly compounding for saving accounts, the simple rate will be greater than the effective
annual rate.
b.
The present value of a future sum increases as the simple interest rate increases or the number of discount
periods per year decreases.
c.
The present value of a future sum increases as either the simple interest rate or the number of discount periods
per year increases.
d.
The present value of a future sum decreases as either the simple interest rate or the number of discount periods
per year increases.
e.
All of the above statements are false.
ANSWER:
d
POINTS:
1
DIFFICULTY:
Moderate
TOPICS:
Annuities
Principles of Finance, 6e
Besley/Brigham
Chapter 09
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© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license
distributed with a certain product or service or otherwise on a password-protected website for classroom use.
12. A $10,000 loan is to be amortized over 5 years, with annual end-of-year payments. Given the following facts, which
of these statements is correct?
a.
The annual payments would be larger if the interest rate were lower.
b.
If the loan were amortized over 10 years rather than 5 years, and if the interest rate were the same in either
case, the first payment would include more dollars of interest under the 5-year amortization plan.
c.
The last payment would have a higher proportion of interest than the first payment.
d.
The proportion of interest versus principal repayment would be the same for each of the 5 payments.
e.
The proportion of each payment that represents interest as opposed to repayment of principal would be higher
if the interest rate were higher.
ANSWER:
e
RATIONALE:
If the interest rate were higher, the payments would all be higher, and all of the increase
would be attributable to interest. So, the proportion of each payment that represents
interest would be higher. Note that statement b is false because interest during Year 1
would be the interest rate times the beginning balance, which is $10,000. With the same
interest rate and the same beginning balance, the Year 1 interest charge will be the
same, regardless of whether the loan is amortized over 5 or 10 years.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Time Value Concepts
13. Which of the following statements is correct?
a.
Simple rates can’t be used in present value or future value calculations because they fail to account for
compounding effects.
b.
The periodic interest rate can be used directly in calculations as long as the number of payments per year is
greater than or equal to the number of compounding periods per year.
c.
In all cases where interest is added or payments are made more frequently than annually, the periodic rate is
less than the annual rate.
d.
Generally, the APR is greater than the EAR as a result of compounding effects.
e.
If the compounding period is semiannual then the periodic rate will equal the effective annual rate divided by
two.
ANSWER:
c
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Types of Interest Rates
Principles of Finance, 6e
Besley/Brigham
Chapter 09
Cengage Learning Testing, Powered by Cognero
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© 2015 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part, except for use as permitted in a license
distributed with a certain product or service or otherwise on a password-protected website for classroom use.
14. Which of the following statements is most correct?
a.
The first payment under a 3-year, annual payment, amortized loan for $1,000 will include a smaller percentage
(or fraction) of interest if the interest rate is 5 percent than if it is 10 percent.
b.
If you are lending money, then, based on effective interest rates, you should prefer to lend at a 10 percent
simple, or quoted, rate but with semiannual payments, rather than at a 10.1 percent simple rate with annual
payments. However, as a borrower you should prefer the annual payment loan.
c.
The value of a perpetuity (say for $100 per year) will approach infinity as the interest rate used to evaluate the
perpetuity approaches zero.
d.
Statements a, b, and c are all true.
e.
Only statements b and c are true.
ANSWER:
d
POINTS:
1
DIFFICULTY:
Hard
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Time Value Concepts
15. A recent advertisement in the financial section of a magazine carried the following claim: “Invest your money with us
at 14 percent, compounded annually, and we guarantee to double your money sooner than you imagine.” Ignoring taxes,
how long would it take to double your money at a simple rate of 14 percent, compounded annually?
a.
Approximately 3.5 years
b.
Approximately 5 years
c.
Exactly 7 years
d.
Approximately 10 years
e.
Exactly 14 years
ANSWER:
b
RATIONALE:
Cash flow time line:
Equation solution: Use of the financial calculator solution for this problem is preferred
because the equation solution for this problem is quite complex involving the use of
logarithms (a method not used in the text). Use of the Rule of 72 (also not used in text)
offers a simple equation approximation if students have been taught this method. Time to
Double ≈ 72/14 ≈ 5.14 years Financial calculator solution: Inputs: I = 14; PV = −1; FV = 2.
Output: N = 5.29 years.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
Principles of Finance, 6e
Besley/Brigham
Chapter 09
TOPICS:
RATIONALE:
Cash flow time line:
Equation solution: Financial calculator
solution: Inputs: N = 5; I = 15; PMT = −200. Output: FV = $1,348.48.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
FV of an Annuity
20. What is the present value of a 5-year ordinary annuity with annual payments of $200, evaluated at a 15 percent interest
rate?
a.
$670.43
b.
$842.91
c.
$1,169.56
d.
$1,348.48
e.
$1,522.64
ANSWER:
a
RATIONALE:
Cash flow time line:
Equation
solution: Financial calculator solution: Inputs:
N = 5; I = 15; PMT = 200. Output: PV = −$670.43.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
23. An investor is considering the purchase of 20 acres of land. An analysis indicates that if the land is used for cattle
grazing, it will produce a cash flow of $1,000 per year indefinitely. If the investor requires a return of 10 percent on
investments of this type, what is the most he or she should be willing to pay for the land?
a.
$1,000
b.
$10,000
c.
$100,000
d.
$150,000
e.
$1,000,000
ANSWER:
b
RATIONALE:
V = PMT/I = $1,000/0.10 = $10,000.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
PV of a Perpetuity
24. Assume that you will receive $2,000 a year in Years 1 through 5, $3,000 a year in Years 6 through 8, and $4,000 in
Year 9, with all cash flows to be received at the end of the year. If you require a 14 percent rate of return, what is the
present value of these cash flows?
a.
$9,851
b.
$13,250
c.
$11,714
d.
$15,129
e.
$17,353
ANSWER:
c
RATIONALE:
Cash flow time line:
Financial solution:
TOPICS:
PV of a Perpetuity
Principles of Finance, 6e
Besley/Brigham
Chapter 09
TOPICS:
Growth Rate
e.
$117.48
ANSWER:
a
RATIONALE:
Cash flow time line:
Equation solution: FV = $100(1 + 0.01)20 = $122.02. Financial calculator solution: Inputs: N
= 20; I = 1; PV = −100. Output: FV = $122.02.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARD
S:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Quarterly Compounding
27. In 1981 the average tuition for one year at a certain state school was $1,800. Thirty years later, in 2011, the average
cost was $13,700. What was the growth rate in tuition over the 30-year period?
a.
12%
b.
9%
c.
6%
d.
7%
e.
8%
ANSWER:
d
RATIONALE:
Cash flow time line: Equation
solution: Financial calculator
solution: Inputs: N = 30; PV = −1,800; FV = 13,700. Output: I = 7.0%.
POINTS:
1
DIFFICULTY:
Easy
28. At an inflation rate of 9 percent, the purchasing power of $1 would be cut in half in 8.04 years. How long to the
nearest year would it take the purchasing power of $1 to be cut in half if the inflation rate were only 4%?
a.
12 years
b.
15 years
c.
18 years
d.
20 years
e.
23 years
ANSWER:
c
RATIONALE:
Cash flow time line:
Equation solution: Use of the financial calculator solution for this problem is preferred
because the equation solution for this problem is quite complex involving the use of
logarithms (a method not used in the text). Use of the Rule of 72 (also not used in text)
offers a simple equation approximation if students have been taught this method. Time to
half ≈ 72/4 ≈ 18 years Although a financial calculator or interpolation might be used to
solve precisely, Response c is clearly the closest and best answer of those given.
Financial calculator solution: Inputs: I = 4; PV = 1; PV = −0.50. Output: N = −17.67 = 18
years.
POINTS:
1
DIFFICULTY:
Easy
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
Effect of Inflation
29. South Penn Trucking is financing a new truck with a loan of $10,000 to be repaid in 5 annual end-of-year installments
of $2,504.56. What annual interest rate is the company paying?
a.
7%
b.
8%
c.
9%
d.
10%
e.
11%
ANSWER:
b
RATIONALE:
Cash flow time line:
Principles of Finance, 6e
Besley/Brigham
Chapter 09
c.
$7,922.33
d.
$8,591.00
e.
$6,752.46
ANSWER:
b
d.
$62,527.47
e.
$64,131.50
ANSWER:
d
RATIONALE:
Cash flow time line: Equation
solution: First, calculate the FV as of Year 10
Calculate FV as of
Year 20 using FV10 as the PV FV = $19,496.36(1 + 0.06)20 = $62,527.47. Financial
calculator solution: Calculate the FV as of Year 10 BEGIN mode. Inputs: N = 20; I = 6;
PMT = −500. Output: FV = $19,496.36. Calculate the FV as of Year 20 using FV10 as the
PV END mode. Inputs: N = 20; I = 6; PMT = −19,496.36. Output: FV = $62,527.47. Note:
Tabular solution differs from calculator solution due to interest factor rounding.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
FV under Semiannual Compounding
32. Assume you are to receive a 20-year annuity with annual payments of $50. The first payment will be received at the
end of Year 1, and the last payment will be received at the end of Year 20. You will invest each payment in an account
that pays 10 percent. What will be the value in your account at the end of Year 30?
a.
$6,354.81
b.
$7,427.83
Principles of Finance, 6e
Besley/Brigham
Chapter 09
e.
$3,438
ANSWER:
c
RATIONALE:
Cash flow time line:
Equation
solution: One possible way to solve this problem is to consider the FV of the three
deposits separately and then add them together. FV1 = $1,000(1 + 0.05)4 = $1,215.50
FV2 = $1,000(1 + 0.05)2 = $1,102.50 FV3 = $1,000 FV = $1,215.50 + $1,102.50 + $1,000
= $3,318. Financial calculator solution: Convert rSIMPLE to rEAR using interest rate
conversion Inputs: P/YR = 2; NOM% = 10. Output: EFF% = rEAR = 10.25%. Solve for FV
on annual basis using rEAR Inputs: N = 3; I = 10.25; PMT = −1,000. Output: FV =
$3,318.006 ≈ $3,318.00.
POINTS:
1
DIFFICULTY:
Moderate
ACCREDITING STANDARDS:
Blooms Taxonomy-2 – Application
Business Program-3 – Analytic
DISC-FIN-05 – Financial Analysis and Cash Flows
DISC-FIN-09 – Investments
Time Estimate-a – 5 min.
TOPICS:
FV of an Annuity
35. You just graduated, and you plan to work for 10 years and then to leave for the Australian “Outback” bush country.
You figure you can save $1,000 a year for the first 5 years and $2,000 a year for the next 5 years. These savings cash
flows will start one year from now. In addition, your family has just given you a $5,000 graduation gift. If you put the gift
now, and your future savings when they start, into an account which pays 8 percent compounded annually, what will your
financial “stake” be when you leave for Australia 10 years from now?
a.
$21,432
b.
$28,393
c.
$16,651
d.
$31,148
e.
$20,000
ANSWER:
d
RATIONALE:
Cash flow time line:
Equation solution: