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

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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

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.

[1].    (4.2) Compounding                  F J                Answer: a  EASY
[2].    (4.2) Compounding                  F J                Answer: b  EASY
[3].    (4.2) Compounding                  F J                Answer: a  EASY
[4].    (4.2) Compounding                  F J                Answer: b  EASY
[5].    (4.2) Compounding                  F J                Answer: a  EASY
[6].    (4.2) Compounding                  F J                Answer: b  EASY
[7].    (4.2) Compounding                  F J                Answer: a  EASY
[8].    (4.2) Compounding                  F J                Answer: b  EASY
[9].    (4.2) Compounding                  F J                Answer: a  EASY
[10].   (4.2) Compounding                  F J                Answer: b  EASY
[11].   (4.3) PV versus FV                 C J                Answer: b  EASY
[12].   (4.3) PV versus FV                 C J                Answer: a  EASY
[13].   (4.3) PV versus FV                 C J                Answer: a  EASY
[14].   (4.3) PV versus FV                 C J                Answer: b  EASY
[15].   (4.15) Effective annual rate       C J                Answer: b  EASY
[16].   (4.15) Effective annual rate       C J                Answer: a  EASY
[17].   (4.18) Growing annuity             C J                Answer: a  EASY
[18].   (4.18) Growing annuity             C J                Answer: b  EASY
[19].   (4.2) Compounding                  C J              Answer: b  MEDIUM
[20].   (4.2) Compounding                  C J              Answer: a  MEDIUM
[21].   (4.2) Comparative compounding      C J              Answer: a  MEDIUM
Work out the numbers with a calculator:
PV                               1000               FVA =         \$1,710.34
Rate on A                      5%               2 × FVA =  \$3,420.68
Rate on B                    12%               FVB =         \$3,478.55
Years                              11               FVB > 2 × FVA, so TRUE

[22].   (4.2) Comparative compounding      C J              Answer: b  MEDIUM
Work out the numbers with a calculator:
PV                               1000               FVA =         \$1,710.34
Rate on A                      5%               2 × FVA =  \$3,420.68
Rate on B                    12%               FVB =         \$3,478.55
Years                              11               FVB > 2 × FVA, so FALSE

[23].   (4.3) PV of a dollar               C J              Answer: a  MEDIUM
[24].   (4.3) PV of a sum                  C J              Answer: b  MEDIUM
[25].   (4.9) PV of an annuity             C J              Answer: a  MEDIUM
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.

[26].   (4.9) PV of an annuity             C J              Answer: b  MEDIUM
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.

[27].   (4.15) Periodic and nominal rates  C J              Answer: a  MEDIUM
[28].   (4.15) Periodic and nominal rates  C J              Answer: b  MEDIUM
[29].   (4.15) Effective and nominal rates    C J              Answer: a  MEDIUM
[30].   (4.15) Effective and nominal rates    C J              Answer: b  MEDIUM
[31].   (4.17) Amortization                C J              Answer: b  MEDIUM
[32].   (4.17) Amortization                C J              Answer: a  MEDIUM
[33].   (4.17) Amortization                C J              Answer: a  MEDIUM
[34].   (4.17) Amortization                C J              Answer: b  MEDIUM

[35].   (4.17) Amortization                C J                Answer: b  HARD
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

[36].   (4.17) Amortization                C J                Answer: a  HARD
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

[37].   (4.1) Time lines                   F J              Answer: b  MEDIUM

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