## financial management: theory & practice, 13th edition by eugene f. brigham, michael c. ehrhardt solutions manual and test bank

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## financial management: theory & practice, 14th edition by eugene f. brigham, michael c. ehrhardt solutions manual and test bank

## http://www.mediafire.com/view/tqkoxuif15of2px/FM14e_TB_Ch04.rtf

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##
CHAPTER 4
TIME VALUE OF
MONEY |

**(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)**

Please see the preface for information on the AACSB letter indicators
(F, M, etc.) on the subject lines.

######
Multiple Choice: True/False

**(4.2) Compounding F J Answer: a EASY**

[1]. Starting to invest
early for retirement increases the benefits of compound interest.

a. True

b. False

**(4.2) Compounding F J Answer: b EASY**

[2]. Starting to invest early for retirement reduces the benefits of
compound interest.

a. True

b. False

**(4.2) Compounding F J Answer: a EASY**

[3]. A time line is meaningful
even if all cash flows do not occur annually.

a. True

b. False

**(4.2) Compounding F J Answer: b EASY**

[4]. A time line is not meaningful
unless all cash flows occur annually.

a. True

b. False

**(4.2) Compounding F J Answer: a EASY**

[5]. Time lines can be constructed in situations where some of the
cash flows occur annually but others occur quarterly.

a. True

b. False

**(4.2) Compounding F J Answer: b EASY**

[6]. Time lines cannot be constructed in situations where some of the
cash flows occur annually but others occur quarterly.

a. True

b. False

**(4.2) Compounding F J Answer: a EASY**

[7]. Time lines can be constructed for annuities where the payments
occur at either the beginning or the end of the periods.

a. True

b. False

**(4.2) Compounding F J Answer: b EASY**

[8]. Time lines cannot be constructed for annuities unless all the
payments occur at the end of the periods.

a. True

b. False

**(4.2) Compounding F J Answer: a EASY**

[9]. Some of the cash flows shown on a time line can be in the form of
annuity payments while others can be uneven amounts.

a. True

b. False

**(4.2) Compounding F J Answer: b EASY**

[10]. Some of the cash flows shown on a time line can be in the form of
annuity payments but none can be uneven amounts.

a. True

b. False

**(4.3) PV versus FV C J Answer: b EASY**

[11]. If the discount (or interest) rate is
positive, the present value of an expected series of payments will always
exceed the future value of the same series.

a. True

b. False

**(4.3) PV versus FV C J Answer: a EASY**

[12]. 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.

a. True

b. False

**(4.3) PV versus FV C J Answer: a EASY**

[13]. Disregarding risk, if money has time value, it is impossible for
the present value of a given sum to exceed its future value.

a. True

b. False

**(4.3) PV versus FV C J Answer: b EASY**

[14]. Disregarding risk, if money has time value, it is impossible for the future value of a
given sum to exceed its present value.

a. True

b. False

**(4.15) Effective annual rate C J Answer: b EASY**

[15]. If a bank compounds savings accounts quarterly, the nominal rate will exceed the effective annual
rate.

a. True

b. False

**(4.15) Effective annual rate C J Answer: a EASY**

[16]. If a bank compounds savings accounts quarterly, the effective annual rate will exceed the nominal
rate.

a. True

b. False

**(4.18) Growing annuity C J Answer: a EASY**

[17]. A “growing annuity” is a cash flow stream that grows at a constant
rate for a specified number of periods.

a. True

b. False

**(4.18) Growing annuity C J Answer: b EASY**

[18]. A “growing annuity” is any cash flow stream that grows over time.

a. True

b. False

**(4.2) Compounding C J Answer: b MEDIUM**

[19]. The greater the number of compounding periods within a year, then
(1) the greater the future value of a lump sum investment at Time 0

__and__(2) the greater the present value of a given lump sum to be received at some future date.
a. True

b. False

**(4.2) Compounding C J Answer: a MEDIUM**

[20]. The greater the number of compounding periods within a year, then
(1) the greater the future value of a lump sum investment at Time 0

__and__(2) the smaller the present value of a given lump sum to be received at some future date.
a. True

b. False

**(4.2) Comparative compounding C J Answer: a MEDIUM**

[21]. Suppose Sally Smith plans to invest $1,000. She can earn an effective annual rate of 5%
on Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of
Security B should be more than twice the compounded value of Security A. (Ignore risk, and assume that compounding
occurs annually.)

a. True

b. False

**(4.2) Comparative compounding C J Answer: b MEDIUM**

[22]. Suppose Randy Jones plans to invest $1,000. He can earn an effective annual rate of 5% on
Security A, while Security B has an effective annual rate of 12%. After 11 years, the compounded value of Security B should be somewhat less
than twice the compounded value of Security A. (Ignore risk, and assume that
compounding occurs annually.)

a. True

b. False

**(4.3) PV of a dollar C J Answer: a MEDIUM**

[23]. The present value of a future sum

__decreases__as either the discount rate or the number of periods per year increases, other things held constant.
a. True

b. False

**(4.3) PV of a sum C J Answer: b MEDIUM**

[24]. The present value of a future sum

__increases__as either the discount rate or the number of periods per year increases, other things held constant.
a. True

b. False

**(4.9) PV of an annuity C J Answer: a MEDIUM**

[25]. All other things held constant, the present value of a given
annual annuity

__decreases__as the number of periods per year increases.
a. True

b. False

**(4.9) PV of an annuity C J Answer: b MEDIUM**

[26]. All other things held constant, the
present value of a given annual annuity

__increases__as the number of periods per year increases.
a. True

b. False

**(4.15) Periodic and nominal rates C J Answer: a MEDIUM**

[27]. If we are given a periodic interest rate, say a monthly rate, we
can find the nominal annual rate by multiplying the periodic rate by the number
of periods per year.

a. True

b. False

**(4.15) Periodic and nominal rates C J Answer: b MEDIUM**

[28]. If we are given a periodic interest rate, say a monthly rate, we can find the nominal
annual rate by dividing the periodic rate by the number of periods per year.

a. True

b. False

**(4.15) Effective and nominal rates C J Answer: a MEDIUM**

[29]. As a result of compounding, the effective annual rate on a bank
deposit (or a loan) is always equal to or greater than the nominal rate on the
deposit (or loan).

a. True

b. False

**(4.15) Effective and nominal rates C J Answer: b MEDIUM**

[30]. As a result of compounding, the effective annual rate on a bank
deposit (or a loan) is always equal to or less than the nominal rate on the
deposit (or loan).

a. True

b. False

**(4.17) Amortization C J Answer: b MEDIUM**

[31]. When a loan is amortized, a relatively high percentage of the
payment goes to reduce the outstanding principal in the early years, and the
principal repayment's percentage declines in the loan's later years.

a. True

b. False

**(4.17) Amortization C J Answer: a MEDIUM**

[32]. When a loan is amortized, a relatively low percentage of the
payment goes to reduce the outstanding principal in the early years, and the
principal repayment's percentage increases in the loan's later years.

a. True

b. False

**(4.17) Amortization C J Answer: a MEDIUM**

[33]. The payment made each period on an amortized loan is constant, and
it consists of some interest and some principal. The closer we are to the end of the loan's
life, the greater the percentage of the payment that will be a repayment of
principal.

a. True

b. False

**(4.17) Amortization C J Answer: b MEDIUM**

[34]. The payment made each period on an amortized loan is constant, and
it consists of some interest and some principal. The closer we
are to the end of the loan's life, the smaller the percentage of the payment
that will be a repayment of principal.

a. True

b. False

**(4.17) Amortization C J Answer: b HARD**

[35]. Midway through the life of an amortized loan, the percentage of
the payment that represents interest must be equal to the percentage that represents repayment of
principal. This is true regardless of
the original life of the loan or the interest rate on the loan.

a. True

b. False

**(4.17) Amortization C J Answer: a HARD**

[36]. Midway through the life of an amortized loan, the percentage of
the payment that represents interest could be equal to, less than, or greater than to the percentage that
represents repayment of principal. The
proportions depend on the original life of the loan and the interest rate.

a. True

b. False

######
Multiple Choice: Conceptual

*The correct answers to most of these questions can be determined without doing any calculations. However, calculations are required for a few of them, and calculations are useful to confirm the answers to several others. You can see from the answer where calculations are required. Those questions generally take students longer to answer.*

**(4.1) Time lines F J Answer: b MEDIUM**

[37]. Which of the following statements is CORRECT?

a. A time line
is not meaningful unless all cash flows occur annually.

b. Time lines
are useful for visualizing complex problems prior to doing actual calculations.

c. Time lines
cannot be constructed in situations where some of the cash flows occur annually
but others occur quarterly.

d. Time lines
cannot be constructed for annuities where the payments occur at the beginning
of the periods.

e. Some of the cash flows shown on a time line can
be in the form of annuity payments, but none can be uneven amounts.

Work out the numbers with a
calculator:

PV 1000 FV

_{A}= $1,710.34
Rate on A 5% 2 × FV

_{A}= $3,420.68
Rate on B 12% FV

_{B}= $3,478.55
Years 11 FV

_{B}> 2 × FV_{A}, so TRUE
Work out the numbers with a
calculator:

PV 1000 FV

_{A}= $1,710.34
Rate on A 5% 2 × FV

_{A}= $3,420.68
Rate on B 12% FV

_{B}= $3,478.55
Years 11 FV

_{B}> 2 × FV_{A}, so FALSE
One could
make up an example and see that the statement is true. Alternatively, one could simply recognize
that the PV of an annuity declines as the discount rate increases and recognize
that more frequent compounding increases the effective rate.

One could
make up an example and see that the statement is false. Alternatively, one could simply recognize
that the PV of an annuity declines as the discount rate increases and recognize
that more frequent compounding increases the effective rate.

There is no
reason to think that this statement would always be true. The portion of the payment representing
interest declines, while the portion representing principal repayment
increases. Therefore, the statement is
false. We could also work out some
numbers to prove this point. Here's an
example for a 3‑year loan at a 10% and a 41.45% annual interest rate. The interest component is not equal to the
principal repayment component except at the high interest rate.

Original loan $1,000 Original loan $1,000

Rate 10% Rate 41.45%

Life 3 Life 3

Payment $402.11 Payment $640.98

__Beg. Balance Interest Principal End. Bal.__

__Beg. Balance Interest Principal End. Bal.__

1 $1,000.00 $100.00 $302.11 $697.89 1 $1,000.00 $414.50 $226.48 $773.52

2 $697.89 $69.79 $332.33 $365.56 2 $773.52 $320.62 $320.36 $453.15

3 $365.56 $36.56 $365.56 $0.00 3 $453.15 $187.83 $453.15 $0.00

This statement
is true. The portion of the payment
representing interest declines, while the portion representing principal
repayment increases. The interest
portion could be equal to, greater than, or less than the principal
portion. We can work out some numbers to
prove this point. Here's an example for
a 3-year loan at a 10% and a 41.45% annual interest rate. The interest component is less than the
principal at 10%, equal at about 41.45%, and greater at rates above 41.45%.

Original loan $1,000 Original
loan $1,000

Rate 10% Rate 41.45%

Life 3 Life 3

Payment $402.11 Payment $640.98

__Beg. Balance Interest Principal End. Bal.__

__Beg. Balance Interest Principal End. Bal.__

1 $1,000.00 $100.00 $302.11 $697.89 1 $1,000.00 $414.50 $226.48 $773.52

2 $697.89 $69.79 $332.33 $365.56 2 $773.52 $320.62 $320.36 $453.15

3 $365.56 $36.56 $365.56 $0.00 3 $453.15 $187.83 $453.15 $0.00

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