Financial Management (Chapter 5: Time Value of Money-The Basics)

5.1    Using Timelines to Visualize Cash Flows

1) Financial managers use the time value of money to

A) make business decisions.

B) compare cash flows of different projects.

C) determine the price of common stock.

D) both A and B.

E) all of the above.

2) The time value of money is created by

A) the existence of profitable investment alternatives and interest rates.

B) the fact that the passing of time increases the value of money.

C) the elimination of the opportunity cost as a consideration.

D) the fact that the value of saving money for tomorrow could be more or less than spending it today. 

3) Which of the following statements is FALSE?

A) A dollar received one year from now will be worth more than a dollar received today.

B) On monthly compounding loans, the annual percentage yield will be less than the nominal or quoted rate of interest.

C) Compounding essentially means earning interest on interest on an initial balance.

D) Perpetuities pay an equal payment forever.

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

A) $1,000

B) -$1,000

C) $-990

D) $1,010

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

A) $10

B) $1,000

C) $-990

D) $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?

A) $100,000 now

B) $10,000 at the end of each of the next 12 years

C) The answer depends on the time value of money.

D) Either alternative is equally valuable.

7) Money has a greater time value time value

A) when rates of return are higher.

B) when rates of return are lower.

C) when the future is uncertain.

D) when investors are willing to assume greater risks.

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

A) a future value vector.

B) a cash flow chart.

C) an FV/PV plot.

D) a timeline.

Answer:  D

9) On timeline, the present is represented as

A) time sub n

B) time zero

C) time sub i

D) time 1

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?

A) FVn = P(1 + i)n 

B) FVn = (1 + i)/P

C) FVn = P/(1 + i)n 

D) FVn = P(1 + i)-n 

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

A) 6.5 years

B) 48 months

C) 9 years

D) 12 years

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

A) 6%

B) 5%

C) 7%

D) 8%

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

A) annual interest rate.

B) number of compounding periods.

C) original amount invested.

D) both A and B.

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.

A) $1,444

B) $1,604

C) $1,764

D) $1,283

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?

A) $25,000

B) $31,060

C) $38,720

D) $34,310

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)?

A) $72

B) $70

C) $71

D) $57

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)?

A) $827

B) $833

C) $828

D) $1,176

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)?

A) $648

B) $635

C) $634

D) $645

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

A) 500(1 + .08)5 

B) 500(1 + .08)20 

C) 500(1 + .02)5 

D) 500(1 + .02)20 

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

A) $1,048

B) $1,010

C) $1,038

D) $808

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)?

A) 73 months

B) 75 months

C) 77 months

D) 79 months

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.

A) 10,000/(1 + .05)10 

B) 10,000/(1 + .005)120 

C) 10,000/(1 + .06)10 

D) 10,000/(1 + .006)120 

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%.

A) 15.5%

B) 4.2%

C) 9.8%

D) 10.6%

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).

A) $1,120

B) $1,130

C) $1,110

D) $1,140

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).

A) $64

B) $65

C) $66

D) $71

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)?

A) $237

B) $191

C) $187

D) $179

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).

A) $910

B) $890

C) $880

D) $860

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?

A) $2,800

B) $3,100

C) $3,111

D) $3,148

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

A) $3,100

B) $3,188

C) $3,240

D) $3,290

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

A) 17

B) 19

C) 21

D) 25

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?

A) 47%

B) 4.7%

C) 19%

D) 12.8%

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?

A) $7,401

B) $5,523

C) $7,128

D) $6,720

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?

A) 1,560,000

B) 2,220,366

C) 2,100,000

D) 1,824,979

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?

A) 8 years

B) 10 years

C) 11 years

D) 13 years

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% ?

A) N=4, i=.03, PV=-200, PMT=0, solve for FV

B) N=4, i=3, PV=-200, PMT=0, solve for FV

C) N=4, i=3, PV=0, PMT = $200, solve for FV

D) N=4, i=3, FV=200, PMT=0, solve for PV

27) The future value of a single sum:

A) increases as the compound rate decreases.

B) decreases as the compound rate increases.

C) increases as the number of compound periods decreases.

D) increases as the compound rate increases.

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?

A) N=16, i=.005, PV=200, PMT=0, solve for FV

B) N=4, i=.5, PV=200, PMT=0, solve for FV

C) N=16, i=.5, PV=-200, PMT=0, solve for FV

D) N=16, i=.03, FV=-200, PMT=0, solve for PV

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

A) =FV(7.5,18,0,-1,000)

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

C) =FV(7.5,18,0,1,000)

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

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?

A) N=16, i=.005, PV=-200, PMT=0, solve for FV

B) N=4, i=.5, PV=$200, PMT=0, solve for FV

C) N=16, i=.5, PV=-200, PMT=0, solve for FV

D) N=16, i=.03, FV=200, PMT=0, solve for PV

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?

A) 83%

B) 75%

C) 20%

D) 30%

E) 50%

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

A) 9 years

B) 8 years

C) 12 years

D) 4 years

E) 6 years

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

A) increases as the number of discount periods increases.

B) is generally larger than the future sum.

C) depends upon the number of discount periods.

D) increases as the discount rate increases.

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

A) the investment with large cash flow early.

B) the investment with large cash flow late.

C) the investment with even cash flow.

D) neither investment since they have equal lives.

3) High discount rates favor

A) neither long-term nor short-term investments.

B) both long-term and short-term investments.

C) long-term investments.

D) short-term investments.

4) An increase in ________ will decrease present value.

A) the discount rate per period

B) the original amount invested

C) the number of periods

D) both A and C

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).

A) $893

B) $3,106

C) $429

D) $833

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.

A) $5,790

B) $11,574

C) $9,210

D) $17,010

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.

A) $1,250

B) $900

C) $1,866

D) $3,775

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).

A) $630

B) $570

C) $650

D) $660

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

A) FVn = P(1 + i)n 

B) FVn = (1 + i)/P

C) FVn = P/(1 + i)n 

D) FVn = P(1 + i)-n 

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

A) the investment is discounted at a higher interest rate. 

B) the investment is discounted for fewer years.

C) the investment is discounted at a lower interest rate.

D) 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

A) N=20, i=.08,PMT = 0, FV=1000 solve for PV

B) N=20, i=8,PMT = 0, FV=1000 solve for PMT

C) N=20, i=.08,PMT = 0, PV=1000 solve for FV

D) N=20, i=8,PMT = 0, FV=1000 solve for PV

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.

A) Approximately two years

B) Approximately four years

C) Approximately six years

D) Approximately eight years

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%?

A) i=5, PV=-1, PMT = 0, FV=3, solve for N

B) i=5, PV=1, PMT = 0, FV=3, solve for N

C) i=.05, PV=-1, PMT = 0, FV=3, solve for N

D) Financial calculators cannot be used to solve this problem.

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?

A) 6.00%

B) 16.67%

C) 15.00%

D) 11.44%

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?

A) =PV(25,i,-100,1500)

B) =rate(25,0,100,1500)

C) =rate(25,0,-100,1500)

D) =rate(0,-100,1500,25)

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

A) $400.00.

B) $248.40.

C) $313.60.

D) $245.60.

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

A) $621.

B) $784.

C) $614.

D) $500.

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%?

A) $1,100.00

B) $675.30

C) $775.40

D) $424.60

19) The present value of a single sum

A) increases as the discount rate decreases.

B) decreases as the discount rate decreases.

C) increases as the number of discount periods increases.

D) increases as the discount rate increases.

E) none of the above.

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?

A) 10% compounded annually

B) 9.5% compounded monthly

C) 9% compounded quarterly

D) 8.5% compounded daily

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

A) number of compounding periods in a year

B) number of years invested

C) quoted rate

D) both A and C

E) all of the above

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%)?

A) 51.7%

B) 6.7%

C) 10.9%

D) 6.1%

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.

A) 19.875%

B) 10%

C) 10.38%

D) 10.125%

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

A) Interest rate per period x compounding periods per year

B) (1+quoted annual rate/compounding periods per year)compounding periods per year-1

C) Interest rate per period / compounding periods per year

D) 1+quoted annual rate/compounding periods per year)1/compounding periods per year-1

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