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*Financial Management, 12e ***(Titman/Keown/Martin)**

**Time Value of Money-The Basics**

**5.1 Using Timelines to Visualize Cash Flows**

1) Financial managers use the time value of money to

- make business decisions.
- compare cash flows of different projects.
- determine the price of common stock.
- both A and B.
- all of the above.

**Answer: D**

2) The time value of money is created by

- the existence of profitable investment alternatives and interest rates.
- the fact that the passing of time increases the value of money.
- the elimination of the opportunity cost as a consideration.
- the fact that the value of saving money for tomorrow could be more or less than spending it today.

**Answer: A**

3) Which of the following statements is FALSE?

- A dollar received one year from now will be worth more than a dollar received today.
- On monthly compounding loans, the annual percentage yield will be less than the nominal or quoted rate of interest.
- Compounding essentially means earning interest on interest on an initial balance.
- Perpetuities pay an equal payment forever.

**Answer: A**

4) An investor will invest $1,000 now and expect to receive $10 for each of the next 10 years plus $1,000 at the end of the 10th year. Her cash flow at time period 0 is

- $1,000
- -$1,000
- $-990
- $1,010

**Answer: B**

5) An investor will invest $1,000 now and expect to receive $10 for each of the next 10 years plus $1,000 at the end of the 10th year. Her cash at time period 10 is

- $10
- $1,000
- $-990
- $1,010

**Answer: D**

6) Should you prefer to receive $100,000 right now or $10,000 at the end of each of the next 12 years?

- $100,000 now
- $10,000 at the end of each of the next 12 years
- The answer depends on the time value of money.
- Either alternative is equally valuable.

**Answer: C**

7) Money has a greater time value time value

- when rates of return are higher.
- when rates of return are lower.
- when the future is uncertain.
- when investors are willing to assume greater risks.

**Answer: A**

8) A diagram for visualizing future cash flows is known as

- a future value vector.
- a cash flow chart.
- an FV/PV plot.
- a timeline.

**Answer: D**

9) On timeline, the present is represented as

- time sub n
- time zero
- time sub i
- time 1

**Answer: B**

10) A timeline typically represents cash flows as an exponential growth curve.

**Answer: FALSE**

11) A timeline is a linear representation of the timing of cash flows.

**Answer: TRUE**

12) A timeline represents the value of a sum invested now at the end of a series of time periods.

**Answer: FALSE**

13) The end of one time period and the beginning of the next occupy the same place on a timeline.

**Answer: TRUE**

14) Timelines are always expressed in years.

**Answer: FALSE**

15) Timelines used to visualize cash flows normally represent present values on the left and future values on the right.

**Answer: TRUE**

16) The last amount shown on a timeline represents the future value of all amounts invested up to that point.

**Answer: FALSE**

17) The first amount on a timeline represent the present value of all the future amounts at a given interest rate.

**Answer: TRUE**

18) Sketch a timeline that represents an immediate investment of $20,000 with $25,000 to be received at the end of 4 years.

**Answer: **

_0__________1__________2_________3__________4

-$20,000 $25,000

**5.2 Compounding and Future Value**

1) Which of the following is the formula for compound value?

- FVn= P(1 + i)n
- FVn= (1 + i)/P
- FVn= P/(1 + i)n
- FVn= P(1 + i)-n

**Answer: A**

2) At 8% compounded annually, how long will it take $750 to double?

- 6.5 years
- 48 months
- 9 years
- 12 years

**Answer: C**

3) At what rate must $400 be compounded annually for it to grow to $716.40 in 10 years?

- 6%
- 5%
- 7%
- 8%

**Answer: A**

4) An increase in future value can be caused by an increase in the

- annual interest rate.
- number of compounding periods.
- original amount invested.
- both A and B.

**Answer: D**

5) A friend plans to buy a big-screen TV/entertainment system and can afford to set aside $1,320 toward the purchase today. If your friend can earn 5.0%, compounded yearly, how much can your friend spend in four years on the purchase? Round off to the nearest $1.

- $1,444
- $1,604
- $1,764
- $1,283

**Answer: B**

6) You just purchased a parcel of land for $10,000. If you expect a 12% annual rate of return on your investment, how much will you sell the land for in 10 years?

- $25,000
- $31,060
- $38,720
- $34,310

**Answer: B**

7) If you place $50 in a savings account with an interest rate of 7% compounded weekly, what will the investment be worth at the end of five years (round to the nearest dollar)?

- $72
- $70
- $71
- $57

**Answer: C**

8) If you put $700 in a savings account with a 10% nominal rate of interest compounded monthly, what will the investment be worth in 21 months (round to the nearest dollar)?

- $827
- $833
- $828
- $1,176

**Answer: B**

9) If you put $600 in a savings account that yields an 8% rate of interest compounded weekly, what will the investment be worth in 37 weeks (round to the nearest dollar)?

- $648
- $635
- $634
- $645

**Answer: B**

10) Which of the following formulas represents the future value of $500 invested at 8% compounded quarterly for five years?

- 500(1 + .08)5
- 500(1 + .08)20
- 500(1 + .02)5
- 500(1 + .02)20

**Answer: D**

11) What is the value of $750 invested at 7.5% compounded quarterly for 4.5 years (round to the nearest $1)?

- $1,048
- $1,010
- $1,038
- $808

Answer: A

12) Shorty Jones wants to buy a one-way bus ticket to Mule-Snort, Pennsylvania. The ticket costs $142, but Mr. Jones has only $80. If Shorty puts the money in an account that pays 9% interest compounded monthly, how many months must Shorty wait until he has $142 (round to the nearest month)?

- 73 months
- 75 months
- 77 months
- 79 months

**Answer: C**

13) If you want to have $10,000 in 10 years, which of the following formulas represents how much money you must put in a savings account today? Assume that the savings account pays 6% and it is compounded monthly.

- 10,000/(1 + .05)10
- 10,000/(1 + .005)120
- 10,000/(1 + .06)10
- 10,000/(1 + .006)120

**Answer: B**

14) Dawn Swift discovered that 20 years ago, the average tuition for one year at an Ivy League school was $4,500. Today, the average cost is $29,000. What is the growth rate in tuition cost over this 20-year period? Round off to the nearest 0.1%.

- 15.5%
- 4.2%
- 9.8%
- 10.6%

**Answer: C**

15) If you want to have $1,700 in seven years, how much money must you put in a savings account today? Assume that the savings account pays 6% and it is compounded quarterly (round to the nearest $10).

- $1,120
- $1,130
- $1,110
- $1,140

**Answer: A**

16) If you want to have $90 in four years, how much money must you put in a savings account today? Assume that the savings account pays 8.5% and it is compounded monthly (round to the nearest $1).

- $64
- $65
- $66
- $71

**Answer: A**

17) How much money must be put into a bank account yielding 5.5% (compounded annually) in order to have $250 at the end of five years (round to nearest $1)?

- $237
- $191
- $187
- $179

**Answer: B**

18) If you want to have $1,200 in 27 months, how much money must you put in a savings account today? Assume that the savings account pays 14% and it is compounded monthly (round to the nearest $10).

- $910
- $890
- $880
- $860

**Answer: C**

*Use the following information to answer the following question(s).*

A Max, Inc. deposited $2,000 in a bank account that pays 12% interest annually.

19) What will the dollar amount be in four years, assuming that interest is paid annually?

- $2,800
- $3,100
- $3,111
- $3,148

**Answer: D**

20) What will the dollar amount be if the interest is compounded semiannually for those four years?

- $3,100
- $3,188
- $3,240
- $3,290

**Answer: B**

21) How many periods would it take for the deposit to grow to $6,798 if the interest is compounded semiannually?

- 17
- 19
- 21
- 25

**Answer: C**

22) You bought a painting 10 years ago as an investment. You originally paid $85,000 for it. If you sold it for $484,050, what was your annual return on investment?

- 47%
- 4.7%
- 19%
- 12.8%

**Answer: C**

23) You deposit $5,000 today in an account drawing 12% compounded quarterly. How much will you have in the account at the end of 2 1/2 years?

- $7,401
- $5,523
- $7,128
- $6,720

**Answer: D**

24) Middletown, USA currently has a population of 1.5 million people. It has been one of the fastest growing cities in the nation, growing by an average of 4% per year for the last five years. If this city's population continues to grow at 4% per year, what will the population be 10 years from now?

- 1,560,000
- 2,220,366
- 2,100,000
- 1,824,979

**Answer: B**

25) How many years will it take for an initial investment of $200 to grow to $544 if it is invested today at 8% compounded annually?

- 8 years
- 10 years
- 11 years
- 13 years

**Answer: D**

26) When using a financial calculator, which of the following is the correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 3% ?

- N=4, i=.03, PV=-200, PMT=0, solve for FV
- N=4, i=3, PV=-200, PMT=0, solve for FV
- N=4, i=3, PV=0, PMT = $200, solve for FV
- N=4, i=3, FV=200, PMT=0, solve for PV

**Answer: B**

27) The future value of a single sum:

- increases as the compound rate decreases.
- decreases as the compound rate increases.
- increases as the number of compound periods decreases.
- increases as the compound rate increases.

**Answer: D**

28) When using a financial calculator, which of the following is a correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 2% compounded quarterly?

- N=16, i=.005, PV=200, PMT=0, solve for FV
- N=4, i=.5, PV=200, PMT=0, solve for FV
- N=16, i=.5, PV=-200, PMT=0, solve for FV
- N=16, i=.03, FV=-200, PMT=0, solve for PV

**Answer: C**

29) When using EXCEL to find the future value of $2,000 invested in an account that would earn interest of 7.5% for 18 years, the correct entry would be

- =FV(7.5,18,0,-1,000)
- =PV(.075,18,0,-1,000)
- =FV(7.5,18,0,1,000)
- =FV(.075,18,0,-1,000)

**Answer: D**

30) When using a financial calculator, which of the following is a correct way to find the future value of $200 deposited today in an account for four years paying annual interest of 2% compounded quarterly?

- N=16, i=.005, PV=-200, PMT=0, solve for FV
- N=4, i=.5, PV=$200, PMT=0, solve for FV
- N=16, i=.5, PV=-200, PMT=0, solve for FV
- N=16, i=.03, FV=200, PMT=0, solve for PV

**Answer: C**

31) If you purchased a share of Mico.com stock on March 1, 1993 for $45 and you sold the stock at $168 on February 28, 1998, what was your annual rate of return on the stock?

- 83%
- 75%
- 20%
- 30%
- 50%

**Answer: D**

32) At 8%, compounded annually, how long will it take $750 to double?

- 9 years
- 8 years
- 12 years
- 4 years
- 6 years

**Answer: A**

33) The future value of a lump sum deposited today increases as the number of years of compounding at a positive rate of interest declines.

**Answer: FALSE**

34) If we invest money for 10 years at 8% interest, compounded semi-annually, we are really investing money for 20 six-month periods, during which we receive 4% interest each period.

**Answer: TRUE**

35) Determining the specified amount of money that you will receive at the maturity of an investment is an example of a future value equation.

**Answer: TRUE**

36) When performing time value of money computations with a financial calculator or EXCEL, PV and FV must have opposite signs.

**Answer: TRUE**

37) Assuming equal annual rates, the more frequent the compounding periods in a year, the higher the future value.

**Answer: TRUE**

38) Briefly discuss how non-annual compounding (more than one compounding period per year) is preferable to annual compounding if you are an investor.

**Answer:** Non-annual compounding is preferable to annual compounding because with non-annual compounding, interest is compounded more frequently within a year period. This means that more interest on interest would be generated on a given investment.

39) If you deposit $1,000 each year in a savings account earning 4%, compounded annually, how much will you have in 10 years?

**Answer: FV[10] = $1,000(12.006) = $12,006**

40) Your bank has agreed to loan you $3,000 if you agree to pay a lump sum of $5,775 in five years. What annual rate of interest will you be paying?

**Answer:** FVIF[? %, 5 yr] $3,000 = $5,775

FVIF[? %, 5 yr] = $1.925

i = 14%

41) Earnings per share for XYZ, Inc. grew constantly from $7.99 in 1974 to $12.68 in 1980. What was the compound annual growth rate in earnings-per-share over the period?

**Answer: ** $12.68 = $7.99 FVIF[? %, 6 yr]

1.587 = FVIF[? %, 6 yr]

g = 8%

42) If you invest $450 today and it increases to $6,185 at the end of 20 years, what rate of return have you earned?

**Answer: ** $6,185 = $450 FVIF[? %, 20 yr]

13.743 = FVIF[? %, 20 yr]

i = 14%

**5.3 Discounting and Present Value**

1) The present value of a single future sum

- increases as the number of discount periods increases.
- is generally larger than the future sum.
- depends upon the number of discount periods.
- increases as the discount rate increases.

**Answer: C**

2) Assuming two investments have equal lives, a high discount rate tends to favor

- the investment with large cash flow early.
- the investment with large cash flow late.
- the investment with even cash flow.
- neither investment since they have equal lives.

**Answer: A**

3) High discount rates favor

- neither long-term nor short-term investments.
- both long-term and short-term investments.
- long-term investments.
- short-term investments.

**Answer: D**

4) An increase in ________ will decrease present value.

- the discount rate per period
- the original amount invested
- the number of periods
- both A and C

**Answer: D**

5) What is the present value of $1,000 to be received 10 years from today? Assume that the investment pays 8.5% and it is compounded monthly (round to the nearest $1).

- $893
- $3,106
- $429
- $833

**Answer: C**

6) What is the present value of $12,500 to be received 10 years from today? Assume a discount rate of 8% compounded annually and round to the nearest $10.

- $5,790
- $11,574
- $9,210
- $17,010

**Answer: A**

7) Three years from now, Barbara Waters will purchase a laptop computer that will cost $2,250. Assume that Barbara can earn 6.25% (compounded monthly) on her money. How much should she set aside today for the purchase? Round off to the nearest $1.

- $1,250
- $900
- $1,866
- $3,775

**Answer: C**

8) If you want to have $875 in 32 months, how much money must you put in a savings account today? Assume that the savings account pays 16% and it is compounded monthly (round to the nearest $10).

- $630
- $570
- $650
- $660

**Answer: B**

9) Which of the following is the formula for present value?

- FVn= P(1 + i)n
- FVn= (1 + i)/P
- FVn= P/(1 + i)n
- FVn= P(1 + i)-n

**Answer: C**

10) All else constant, the present value of an investment will increase if

- the investment is discounted at a higher interest rate.
- the investment is discounted for fewer years.
- the investment is discounted at a lower interest rate.
- both B and C.

**Answer: D**

11) To find the present value of $1000 discounted for 20 years at 8%, when using a financial calculator, the correct entry is

- N=20, i=.08,PMT = 0, FV=1000 solve for PV
- N=20, i=8,PMT = 0, FV=1000 solve for PMT
- N=20, i=.08,PMT = 0, PV=1000 solve for FV
- N=20, i=8,PMT = 0, FV=1000 solve for PV

**Answer: D**

12) California Investors recently advertised the following claim: Invest your money with us at 21%, 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 nominal rate of 21%, compounded annually? Round off to the nearest year.

- Approximately two years
- Approximately four years
- Approximately six years
- Approximately eight years

**Answer: B**

13) Using a financial calculator, which of the following would be a correct way to find how long it would take for a sum to triple at a rate of 3%?

- i=5, PV=-1, PMT = 0, FV=3, solve for N
- i=5, PV=1, PMT = 0, FV=3, solve for N
- i=.05, PV=-1, PMT = 0, FV=3, solve for N
- Financial calculators cannot be used to solve this problem.

**Answer: A**

14) Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500. What was the average rate of return on the account?

- 6.00%
- 16.67%
- 15.00%
- 11.44%

**Answer: D**

15) Stephen's grandmother deposited $100 in an investment account for him when he was born, 25 years ago. The account is now worth $1,500. What was the average rate of return on the account? Which of the following is a correct way to solve this problem using EXCEL?

- =PV(25,i,-100,1500)
- =rate(25,0,100,1500)
- =rate(25,0,-100,1500)
- =rate(0,-100,1500,25)

**Answer: C**

16) The present value of $400 to be received at the end of 10 years, if the discount rate is 5%, is

- $400.00.
- $248.40.
- $313.60.
- $245.60.

**Answer: D**

17) The present value of $1,000 to be received at the end of five years, if the discount rate is 10%, is

- $621.
- $784.
- $614.
- $500.

**Answer: A**

18) What is the present value of an investment that pays $400 at the end of three years and $700 at the end of 10 years if the discount rate is 5%?

- $1,100.00
- $675.30
- $775.40
- $424.60

**Answer: C**

19) The present value of a single sum

- increases as the discount rate decreases.
- decreases as the discount rate decreases.
- increases as the number of discount periods increases.
- increases as the discount rate increases.
- none of the above.

**Answer: A**

20) As the discount rate increases, the present value of future cash flows increases.

**Answer: FALSE**

21) As the compound interest rate increases, the present value of future cash flows decreases.

**Answer: TRUE**

22) The present value of a future sum of money increases as the number of years before the payment is received increases.

**Answer: FALSE**

23) When calculating either discount rates or the number of periods using a financial calculator, the PV and FV must have opposite signs.

**Answer: TRUE**

**5.4 Making Interest Rates Comparable**

1) Which of the following provides the greatest annual interest?

- 10% compounded annually
- 9.5% compounded monthly
- 9% compounded quarterly
- 8.5% compounded daily

**Answer: A**

2) The effective annual rate increases when the ________ increases.

- number of compounding periods in a year
- number of years invested
- quoted rate
- both A and C
- all of the above

**Answer: D**

3) What is the annual compounded interest rate of an investment with a stated interest rate of 6% compounded quarterly for seven years (round to the nearest .1%)?

- 51.7%
- 6.7%
- 10.9%
- 6.1%

**Answer: D**

4) You are considering two investments. Investment A yields 10% compounded quarterly. Investment B yields r% compounded semiannually. Both investments have equal annual yields. Find r.

- 19.875%
- 10%
- 10.38%
- 10.125%

**Answer: D**

5) The annual percentage rate (APR) is calculated as which of the following?

- Interest rate per period x compounding periods per year
- (1+quoted annual rate/compounding periods per year)compounding periods per year-1
- Interest rate per period / compounding periods per year
- 1+quoted annual rate/compounding periods per year)1/compounding periods per year-1

**Answer: A**

6) For any number of compounding periods per year greater than 1, EAR will always be greater than the APR.

**Answer: TRUE**

7) As the number of compounding periods per year increase, the annual percentage rate of interest increases.

**Answer: FALSE**

8) A monthly credit card interest rate of 1.5% is equal to and effective annual rate of 19.56%

**Answer: TRUE**

9) The annual percentage rate on two different investments will equal the effective annual rate on the two investments only if interest on both investments is compounded annually.

**Answer: TRUE**

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