Tuesday, January 6, 2015

Financial Management (Chapter 6: The Time Value of Money-Annuities and Other Topics)

6.1   Annuities

1) You wish to borrow $2,000 to be repaid in 12 monthly installments of $189.12. The annual interest rate is
A) 24%.
B) 8%.
C) 18%.
D) 12%.

2) If you have $20,000 in an account earning 8% annually, what constant amount could you withdraw each year and have nothing remaining at the end of five years?
A) $3,525.62
B) $5,008.76
C) $3,408.88
D) $2,465.78

3) If you invest $750 every six months at 8% compounded semi-annually, how much would you accumulate at the end of 10 years?
A) $10,065
B) $10,193
C) $22,334
D) $21,731

4) A commercial bank will loan you $7,500 for two years to buy a car. The loan must be repaid in 24 equal monthly payments. The annual interest rate on the loan is 12% of the unpaid balance. What is the amount of the monthly payments?
A) $282.43
B) $390.52
C) $369.82
D) $353.05

5) Your company has received a $50,000 loan from an industrial finance company. The annual payments are $6,202.70. If the company is paying 9% interest per year, how many loan payments must the company make?
A) 15
B) 13
C) 12
D) 19

6) ________ annuities involve depositing money at the end of the period and allowing it to grow.
A) Discount
B) Compound
C) Annuity due
D) Both B and C


7) When comparing annuity due to ordinary annuities, annuity due annuities will have higher
A) present values.
B) annuity payments.
C) future values.
D) both A and C.
E) all of the above.

8) Gina Dare, who wants to be a millionaire, plans to retire at the end of 40 years. Gina's plan is to invest her money by depositing into an IRA at the end of every year. What is the amount that she needs to deposit annually in order to accumulate $1,000,000? Assume that the account will earn an annual rate of 11.5%. Round off to the nearest $1.
A) $1,497
B) $5,281
C) $75
D) $3,622

9) Francis Peabody just won the $89,000,000 California State Lottery. The lottery offers the winner a choice of receiving the winnings in a lump sum or in 26 equal annual installments to be made at the beginning of each year. Assume that funds would be invested at 7.65%. Francis is trying to decide whether to take the lump sum or the annual installments. What is the amount of the lump sum that would be exactly equal to the present value of the annual installments? Round off to the nearest $1.
A) $89,000,000
B) $38,163,612
C) $13,092,576
D) $41,083,128

10) As time increases for an amortized loan, the ________ decreases.
A) interest paid per payment
B) principal paid per payment
C) the outstanding loan balance
D) both A and C
Answer:  D

11) What is the present value of an annuity of $27 received at the beginning of each year for the next six years? The first payment will be received today, and the discount rate is 10% (round to nearest $10).
A) $120
B) $130
C) $100
D) $110

12) What is the present value of $150 received at the beginning of each year for 16 years? The first payment is received today. Use a discount rate of 9%, and round your answer to the nearest $10.
A) $1,360
B) $1,480
C) $1,250
D) $1,210


13) What is the present value of $250 received at the beginning of each year for 21 years? Assume that the first payment is received today. Use a discount rate of 12%, and round your answer to the nearest $10.
A) $1,870
B) $2,090
C) $2,117
D) $3,243

14) What is the present value of an annuity of $12 received at the end of each year for seven years? Assume a discount rate of 11%. The first payment will be received one year from today (round to the nearest $1).
A) $25
B) $40
C) $57
D) $118

15) What is the present value of an annuity of $100 received at the end of each year for seven years? The first payment will be received one year from today (round to nearest $10). The discount rate is 13%.  To solve this problem with a financial calculator, the correct choice is
A) N=7, i=13, PMT= 100, FV=0, solve for PV
B) N=7, i=13, PV= 100, FV=0, solve for FV
C) N=7, i=13, PMT= 100, FV=100, solve for PV
D) N=7, i=.13, PMT= 100, FV=0, solve for PV


16) What is the present value of $27 received at the end of each year for five years? Assume a discount rate of 9%. The first payment will be received one year from today (round to the nearest $1).
A) $42
B) $114
C) $88
D) $105

17) What is the present value of $300 received at the beginning of each year for five years? Assume that the first payment is not received until the beginning of the third year (thus the last payment is received at the beginning of the seventh year). Use a 10% discount rate, and round your answer to the nearest $100.
A) $1,100
B) $1,000
C) $900
D) $1,200

18) Ingrid Birdman can earn a nominal annual rate of return of 12%, compounded semiannually. If Ingrid made 40 consecutive semiannual deposits of $500 each, with the first deposit being made today, how much will she accumulate at the end of Year 20? Round off to the nearest $1.
A) $52,821
B) $57,901
C) $82,024
D) $64,132


19) Charlie Stone wants to retire in 30 years, and he wants to have an annuity of $1,000 a year for 20 years after retirement. Charlie wants to receive the first annuity payment at the end of the 30th year. Using an interest rate of 10%, how much must Charlie invest today in order to have his retirement annuity (round to the nearest $10)?
A) $500
B) $490
C) $540
D) $570

20) It is January 1st and Darwin Davis has just established an IRA (Individual Retirement Account). Darwin will put $1,000 into the account on December 31st of this year and at the end of each year for the following 39 years (40 years total). How much money will Darwin have in his account at the beginning of the 41st year? Assume that the account pays 12% interest compounded annually, and round to the nearest $1,000.
A) $93,000
B) $766,000
C) $767,000
D) $850,000

21) If you put $510 in a savings account at the beginning of each year for 30 years, how much money will be in the account at the end of the 30th year? Assume that the account earns 5%, and round to the nearest $100.
A) $33,300
B) $32,300
C) $33,900
D) None of the above

22) If you put $10 in a savings account at the beginning of each year for 11 years, how much money will be in the account at the end of the 11th year? Assume that the account earns 11%, and round to the nearest $100.
A) $220
B) $200
C) $190
D) $180

23) To find the present value of an annuity due, one could
A) find the present value of an ordinary annuity and add one extra payment.
B) find the present value of an ordinary annuity but N = 1 for the number of periods.
C) find the present value of an ordinary annuity and divide by 1 + i.
D) find the present value of an ordinary annuity and multiply by 1 + i.

24) How much money must you pay into an account at the beginning of each of 30 years in order to have $10,000 at the end of the 30th year? Assume that the account pays 11% per annum, and round to the nearest $1.
A) $39
B) $46
C) $50
D) None of the above


25) How much money must you pay into an account at the beginning of each of 20 years in order to have $10,000 at the end of the 20th year? Assume that the account pays 12% per annum, and round to the nearest $1.
A) $1,195
B) $111
C) $124
D) $139

26) How much money must you pay into an account at the beginning of each of five years in order to have $5,000 at the end of the fifth year? Assume that the account pays 12% per year, and round to the nearest $10.
A) $700
B) $1,390
C) $1,550
D) $790

27) How much money must you pay into an account at the beginning of each of 11 years in order to have $5,000 at the end of the 11th year? Assume that the account pays 8% per year, and round to the nearest $1.
A) $700
B) $257
C) $300
D) $278


Use the following information in solving the following question(s).

You are going to pay $100 into an account at the beginning of each of the next 40 years. At the beginning of the 41st year, you buy a 30-year annuity whose first payment comes at the end of the 41st year (the account pays 12%).

28) How much money will be in the account at the end of year 40 (round to the nearest $1,000)?
A) $77,000
B) $86,000
C) $69,000
D) $93,000


29) How much will you receive at the end of the 41st year (i.e., the first annuity payment)? Round to the nearest $100.
A) $93,000
B) $7,800
C) $11,400
D) $10,700


30) A retirement plan guarantees to pay you or your estate a fixed amount for 20 years. At the time of retirement, you will have $31,360 to your credit in the plan. The plan anticipates earning 8% interest annually over the period you receive benefits. How much will your annual benefits be, assuming the first payment occurs one year from your retirement date?
A) $682
B) $6,272
C) $2,000
D) $3,194

31) SellUCars, Inc. offers you a car loan at an annual interest rate of 8% compounded monthly. What is the annual percentage yield of the loan?
A) 8.00%
B) 8.24%
C) 8.30%
D) 8.44%

32) George and Laura will be retiring in four years and would like to buy a lake house. They estimate that they will need $550,000 at the end of four years to buy this house. They want to make four equal annual payments into an account at the end of each year. If they can earn 8% on their money, compounded annually, over the next four years, how much must they invest at the end of each year for the next four years to have accumulated $550,000 by retirement?
A) $137,500
B) $122,056
C) $113,015
D) $131,821

33) You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in Paris, France. You will need $15,000 every six months (beginning six months from now) for the next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your education. They want to make one deposit now in a bank account earning 6% interest, compounded semiannually, so that you can withdraw $15,000 every six months for the next three years. How much must they deposit now?
A) $97,026
B) $73,760
C) $90,000
D) $81,258

34) Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing $95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make equal monthly installments over the next 20 years?
A) $1,046
B) $749
C) $1,722
D) $1,346

35) Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold's monthly payments be? Round off to the nearest $1.
A) $1,450
B) $1,788
C) $3,200
D) $1,682

36) You buy a race horse, which has a winning streak for four years, bringing in $500,000 per year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what was your annual return over this four-year period?
A) 8%
B) 33%
C) 18%
D) 12%

37) You are considering a home loan with monthly payments at an annual percentage yield of 5.116%. What is the quoted rate of interest on the loan?
A) 4.5%
B) 4.75%
C) 5%
D) 6%

38) You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made $2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will calculate your bank balance just after the last payment was deposited?
A) FV = $2,000[1.06]-1 + $2,000[1.06]-2 + $2,000[1.06]-3 
B) FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3 
C) FV = $2,000[1.06]0 + $2,000[1.06]1 + $2,000[1.06]2 
D) FV = $2,000[1.06]-0 + $2,000[1.06]-1 + $2,000[1.06]-2 + $1,000[1.06]-3 


39) Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back the principal and interest in five equal annual installments beginning one year from now. Determine the amount of Harry's annual payment.
A) $8,322
B) $9,600
C) $9,709
D) $6,720

40) Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in a mutual fund today that pays 12% per year compounded monthly. How much must you invest at the end of each month to meet your investment goal? Round to the nearest $1.
A) $245
B) $255
C) $285
D) $305
E) $315


41) You have borrowed $70,000 to buy a sports car. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the total amount of interest dollars you will pay the bank over the life of the loan. Round to the nearest dollar and assume end-of-month payments.
A) $47,451
B) $51,644
C) $54,776
D) $57,798

42) You have borrowed $70,000 to buy rental property. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the principal paid to the bank in month two of the loan. Assume end-of-period payments.
A) $184.01
B) $186.38
C) $188.46
D) $190.64
E) $192.73

43) A friend of yours plans to begin saving for retirement by depositing $2,000 at the end of each year for the next 25 years. If she can earn 10% annually on her investment, how much will she have accumulated at the end of 25 years?
A) $50,000
B) $196,692
C) $100,000
D) $216,361

44) How much must you deposit at the end of each of the next 10 years in a savings account paying 5% annually in order to have $10,000 saved by the end of the 10th year?
A) $1,000
B) $1,638
C) $1,500
D) $795

45) What is the value today of an investment that pays $500 every year at year-end during the next 15 years if the annual interest rate is 9%?
A) $4,030.50
B) $7,500.00
C) $3,500.00
D) $7,000.00

46) How much would an investor be willing to pay today for an investment that returns $1,000 every year at year-end for five years if he wants to earn a 10% annual return on the investment?
A) $1,000
B) $3,791
C) $5,000
D) $7,700


47) A friend of yours would like you to lend him $5,000 today to be paid back in 5 annual payments. What would be the equal annual end-of-year payment on this loan if you charge your friend 7% interest?
A) $869.45
B) $1,000.00
C) $1,219.51
D) $1,350.00

48) Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in equal annual payments which begin today, and will continue to be payable at the beginning of each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan payment?
A) $3,756.85
B) $4,200.00
C) $3,478.31
D) $3,000.00

49) A friend of yours borrows $19,500 from the bank at 8% annually to be repaid in 10 equal annual end-of-year installments. The interest paid on this loan in year three is
A) $1,336.01.
B) $1,560.00.
C) $2,906.11.
D) $1,947.10.


50) If a loan of $10,000 is paid back in equal annual end-of-year payments of $2,570.69 during the next five years, what is the annual interest rate on the loan?
A) 2%
B) 5%
C) 9%
D) 12%

51) What is the present value of an investment that pays $10,000 every year at year-end for the next five years and $15,000 every year at year-end for years six through 10? The annual rate of interest for the investment is 9%.
A) $125,000.00
B) $97,250.00
C) $135,173.00
D) $76,827.50

52) Congratulations. You just won the California State Lottery. The amount awarded is paid in 20 equal annual installments, at the beginning of each year. You can invest your money at 6.6%, compounded annually. You have calculated that the lottery is worth $20,975,400 today. How much was the amount awarded?
A) $75,310,294
B) $36,000,000
C) $81,047,770
D) $42,000,000


53) If you have $375,000 in an account earning 9% annually, what constant amount could you withdraw each year and have nothing remaining at the end of 20 years?
A) $7,500
B) $18,750
C) $66,912
D) $5,575
E) $41,080

54) You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual interest rate is
A) 10.50%.
B) 12.75%.
C) 15.25%.
D) 6.50%.
E) 8.80%.

55) You wish to purchase a condo at a cost of $175,000. You are able to make a down payment of $35,000 and will borrow $140,000 for 30 years at an interest rate of 7.25%. How much is your monthly payment? To solve this problems with an EXCEL spreadsheet, you would enter
A) =PMT(7.25/12,360,140000,0,1)
B) =PMT(.0725/12,360,140000,0,1)
C) =PMT(7.25,30,140000,0,1) /12
D) =PMT(.0725/12,360,175000,0,1)


56) Suppose that you wish to save for your child's college education by opening up an educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume that you will be able to earn 10%, compounded monthly, on your investment. How much will you have accumulated at the end of 18 years?
A) $21,600
B) $54,719
C) $33,548
D) $85,920
E) $60,056

57) Edward Johnson decided to open up a Roth IRA. He will invest $1,800 per year for the next 35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life of the IRA. How much will he have at the end of 35 years?
A) $125,250
B) $250,321
C) $363,000
D) $414,405

58) What is a series of equal payments for a finite period of time called?
A) A perpetuity
B) An axiom
C) A lump sum
D) An annuity


59) Which of the following statements is true?
A) The future value of an annuity would be greater if funds are invested at the beginning of each period instead of at the end of each period.
B) An annuity is a series of equal payments that are made, or received, forever.
C) The effective annual rate (APR) of a loan is higher the less frequently payments are made.
D) The future value of an annuity would be greater if funds are invested at the end of each period rather than at the beginning of each period.

60) What is a series of equal payments to be received at the end of each period, for a finite period of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity

61) What is a series of equal payments to be received at the beginning of each period, for a finite period of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity


62) One characteristic of an annuity is that an equal sum of money is deposited or withdrawn each period.
Answer:  TRUE

63) The present value of an annuity increases as the discount rate increases.
Answer:  FALSE

64) We can use the present value of an annuity formula to calculate constant annual loan payments.
Answer:  TRUE

65) A compound annuity involves depositing or investing a single sum of money and allowing it to grow for a certain number of years.
Answer:  FALSE

66) When repaying an amortized loan, the interest payments increase over time.
Answer:  FALSE

67) An amortized loan is a loan paid in unequal installments.
Answer:  FALSE

68) A loan amortization schedule provides a breakdown of loan payments into principal and interest payments.
Answer:  TRUE

69) Holding all other variables constant, payment per period for an annuity due will be higher than an ordinary annuity.
Answer:  FALSE

70) If you have an opportunity cost of 10%, how much must you invest each year to have $4,000 accumulated in 10 years?
Answer:  Using a financial calculator, N=10, i=10, PV=0, FV=4000, solve for PMT=-250.98


71) You have just received an endowment of $32,976. You plan to put the entire amount in an account earning 8 percent compounded annually and to withdraw $4000 at the end of each year. How many years can you continue to make the withdrawals?
Answer:   Using a financial calculator, i=8, PV=32976, FV=0, solve for PMT=-4000, solve for N=approximately 14 years

72) To repay a $2,000 loan from your bank, you promise to make equal payments every six months for the next five years totaling $3,116.20. What annual rate of interest will you be paying?
Answer:  Using a financial calculator, N=10, i=10, PV=0, FV=4000, solve for PMT=-250.98
        Annual interest rate = (.09)(2) = .18 = 18%

73) You are saving money to buy a house. You will need $7,473.50 to make the down payment. If you can deposit $500 per month in a savings account which pays 1% per month, how long will it take you to save the $7,473.50?
Answer:   $7,473.50 = $500 FVIFA[1%, n periods]
14.947 = FVIFA[1%, n periods]
        n = 14 months


74) You have a credit card with a balance of $18,000. The annual interest rate on the card is 18% compounded monthly, and the minimum payment is $400 per month. If you pay only the minimum payment each month and do not make any new charges on the card, how many years will it take for you to pay off the $18,000 balance?
Answer:  Calculator steps:
18,000                   PV
-400                       PMT
18                           I/yr or I
N = Approximately 75 months = 6.25 years

75) You have borrowed $70,000 to buy a speed boat. You plan to make monthly payments over a 15-year period. The bank has offered you a 9% interest rate, compounded monthly. Create an amortization schedule for the first two months of the loan.
Answer:  Using a financial calculator N=180, i=9/12, PV=70000, FV=0, PMT=-709.99

MO         Beg                         PMT               Int.                 Princ.             End
1              $70,000                 $709.99         $525              $184.99         $69,815.01
2              $69,815.01           $709.99         $523.61         $186.38         $69,628.63

76) You have just purchased a car from Friendly Sam. The selling price of the car is $6,500. If you pay $500 down, then your monthly payments are $317.22. The annual interest rate is 24%. How many payments must you make?
Answer:  i=24/2, PV=6000, PMT=317.22, FV=0, n = 24 months


77) a.) If Sparco, Inc. deposits $150 at the end of each year for the next eight years in an account that pays 5% interest, how much money will Sparco have at the end of eight years?
b.) Suppose Sparco decides that they need to have $5,300 at the end of the eight years. How much will they have to deposit at the end of each year?
Answer: 
a.     n=8, i=5, PV=0, PMT=-150, FV= 1432.37
b.    n=8, i=5, PV=0, FV=5300, PMT=-555.03

6.2   Perpetuities

1) What is a series of equal payments for an infinite period of time called?
A) A perpetuity
B) An axiom
C) A cash cow
D) An annuity

2) You have just purchased a share of preferred stock for $50.00. The preferred stock pays an annual dividend of $5.50 per share forever. What is the rate of return on your investment?
A) .055
B) .010
C) .110
D) .220


3) The present value of a perpetuity decreases when the ________ decreases.
A) number of investment periods
B) annual discount rate
C) perpetuity payment
D) both B and C

4) You are going to pay $800 into an account at the beginning of each of 20 years. The account will then be left to compound for an additional 20 years. At the end of the 41st year you will begin receiving a perpetuity from the account. If the account pays 14%, how much will you receive each year from the perpetuity (round to nearest $1,000)?
A) $140,000
B) $150,000
C) $160,000
D) $170,000

5) You are considering the purchase of XYZ Company's common stock which will pay a $1.00 per share dividend one year from the date of purchase.  The dividend is expected to grow at the rate of 4% per year.  If the appropriate discount rate for this investment is 14%, what is the price of one share of this stock?
A) $7.14
B) $10.00
C) $25.00
D) Cannot be determined without maturity date


6) Michael Bilkman has an opportunity to buy a perpetuity that pays $24,350 annually. His required rate of return on this investment is 14.25%. At what price would Michael be indifferent to buying or not buying the investment? Round off to the nearest $1.
A) $83,470
B) $170,877
C) $95,621
D) $121,709

7) A perpetuity will grow at the rate of 5% per year.  One year from the date of purchase, it will pay $50,0000.  If the appropriate discount rate is 10%, what is the value of the perpetuity?
A) $1,000,000
B) $500,000
C) $5,000,000
D) $1,050,000

8) Your rich great, great aunt just passed away at the age of 91. She liked you more than she let on and left you in her will. You will receive 100 British bonds that pay interest forever. The amount of annual interest payments that you will receive is $5,000. If you could invest your money at 4.25%, how much are these bonds worth today?
A) $64,480
B) $197,250
C) $250,000
D) $117,647
E) $55,000


9) A bond paying interest of $120 per year forever is an example of a perpetuity.
Answer:  TRUE

10) The formula for calculating the present value of a growing perpetuity is PV = Payment period 1/(i-g)
Answer:  TRUE

11) A perpetuity is an investment that continues forever but pays a different dollar amount each year.
Answer:  FALSE

12) The present value of a $100 perpetuity discounted at 5% is $1200.
Answer:  FALSE

13) All else constant, an individual would be indifferent between receiving $2,000 today or receiving a $200 perpetuity when the discount rate is 10% annually.
Answer:  TRUE


14) If your opportunity cost is 12%, how much will you pay for a bond that pays $100 per year forever?
Answer:  PV = $100/.12 = $833.33

15) What is the present value of the following perpetuities?
a.    $600 discounted at 7%
b.    $450 discounted at 12%
c.     $1,000 discounted at 6%
d.    $880 discounted at 9%
Answer: 
a.     PV = $600/.07
        PV = $8,571.43
b.    PV = $450/.12
        PV = $3,750
c.     PV = $1,000/.06
        PV = $16,666.67
d.    PV = $880/.09
        PV = $9,777.78


6.3   Complex Cash Flow Streams

1) What is the value on 1/1/14 of the following cash flows? Use a 10% discount rate, and round your answer to the nearest $1.00.

Date Cash Received         Amount of Cash
          1/1/16                                     $100
          1/1/17                                     $200
          1/1/18                                     $300
          1/1/19                                     $400
          1/1/20                                     $500

A) $1,500
B) $880
C) $968
D) $1,065

2) Consider the following cash flows:

Date Cash Received         Amount of Cash
          1/1/15                                     $100
          1/1/16                                     $100
          1/1/17                                     $500
          1/1/18                                     $100

What is the value on 1/1/14 of the above cash flows? Use an 8% discount rate, and round your answer to the nearest $1.00.
A) $649
B) $601
C) $740
D) $800


3) If you put $200 in a savings account at the beginning of each year for 10 years and then allow the account to compound for an additional 10 years, how much will be in the account at the end of the 20th year? Assume that the account earns 10%, and round to the nearest $10.
A) $8,300
B) $9,100
C) $8,900
D) $9,700

4) An investment is expected to yield $300 in three years, $500 in five years, and $300 in seven years. What is the present value of this investment if our opportunity rate is 5%?
A) $735
B) $865
C) $885
D) $900

5) Jay Coleman just graduated. He plans to work for five years and then leave for the Australian "Outback" country. He figures that he can save $3,500 a year for the first three years and $5,000 a year for the next two years. These savings will start one year from now. In addition, his family gave him a $2,500 graduation gift. If he puts the gift, and the future savings when they start, into an account that pays 7.75% compounded annually, what will his financial "stake" be when he leaves for Australia five years from now? Round off to the nearest $1.
A) $36,082
B) $24,725
C) $30,003
D) $27,178


6) You are thinking of buying a miniature golf course. It is expected to generate cash flows of $40,000 per year in years one through four and $50,000 per year in years five through eight. If the appropriate discount rate is 10%, what is the present value of these cash flows?
A) $285,288
B) $167,943
C) $235,048
D) $828,230

7) You have been depositing money at the end of each year into an account drawing 8% interest. What is the balance in the account at the end of year four if you deposited the following amounts?

       Year            End of Year Deposit
           1                              $350
           2                              $500
           3                              $725
           4                              $400

A) $1,622
B) $2,207
C) $2,384
D) $2,687


8) You want to travel to Europe to visit relatives when you graduate from college three years from now. The trip is expected to cost a total of $10,000. Your parents have deposited $5,000 for you in a CD paying 6% interest annually, maturing three years from now. Aunt Hilda has agreed to finance the balance. If you are going to put Aunt Hilda's gift in an investment earning 10% annually over the next three years, how much must she deposit now so you can visit your relatives in three years?
A) $3,757
B) $3,039
C) $3,801
D) $3,345

9) What is the present value of the following uneven stream of cash flows? Assume a 6% discount rate and end-of-period payments. Round to the nearest whole dollar.

       Year                     Cash Flow
           1                             $3,000
           2                             $4,000
           3                             $5,000

A) $10,588
B) $11,461
C) $12,688
D) $13,591


10) As a part of your savings plan at work, you have been depositing $250 per quarter in a savings account earning 8% interest compounded quarterly for the last 10 years. You will retire in 15 years and want to increase your contribution each year from $1,000 to $2,000 per year, by increasing your contribution every four months from $250 to $500. Additionally, you have just inherited $10,000, which you plan to invest now to earn interest at 12% compounded annually for the next 15 years. How much money will you have in savings when you retire 15 years from now?
A) $126,862
B) $73,012
C) $161,307
D) $194,415

11) Ronald Slump purchased a real estate investment with the following end-of-year cash flows:

       Year                EOY Cash Flow
           1                              $200
           2                              $-350
           3                              $-430
           4                              $950

What is the present value of these cash flows if the appropriate discount rate is 20%?
A) $178
B) $160
C) $133
D) $767


12) You have just won a magazine sweepstakes and have a choice of three alternatives. You can get $100,000 now, or $10,000 per year in perpetuity, or $50,000 now and $150,000 at the end of 10 years. If the appropriate discount rate is 12%, which option should you choose?
A) $100,000 now
B) $10,000 perpetuity
C) $50,000 now and $150,000 in 10 years

13) Your parents are planning to retire in Phoenix, AZ in 20 years. Currently, the typical house that pleases your parents costs $200,000, but they expect inflation to increase the price of the house at a rate of 4% over the next 20 years. To buy a house upon retirement, what must they save each year in equal annual end-of-year deposits if they can earn 10% annually?
A) $21,910.00
B) $7,650.94
C) $10,000.00
D) $14,715.52

14) You intend to purchase a new car upon graduation in two years. It will have a cost of $29,371, including all extra features and sales tax. You just received a $3,000 pre-graduation gift from your rich uncle that you intend to deposit in a money market account that pays 6% interest, compounded monthly.  If you use the amount in the money market account for a down payment, and take out an auto loan for the remainder, how much will you need to borrow? (Round to the nearest dollar.)
A) $29,371
B) $25,880
C) $26,371
D) $26,000


15) Assume that two investments have a three-year life and generate the cash flows shown below. Which of the two would you prefer?

       Year                  Investment A         Investment B
           1                            $5,000                       $8,000
           2                            $5,000                       $5,000
           3                            $5,000                       $2,000

A) Investment A, since it has the most even cash flows
B) Investment B, since it gives you the largest cash flows in earlier years
C) Neither, since they both have equal lives
D) Both investments are equally attractive

16) You have just purchased an investment that generates the cash flows that are shown below. You are able to invest your money at 5.75%, compounded annually. How much is this investment worth today?

       Year                       Amount
           0                                $0
           1                            $1,250
           2                            $1,585
           3                            $1,750
           4                            $2,225
           5                            $3,450

A) $7,758
B) $4,521
C) $10,260
D) $8,467


17) To evaluate and compare investment proposals, we must adjust all cash flows to a common date.
Answer:  TRUE

18) Consider an investment that has cash flows of $500 the first year and $400 for the next four years. If your opportunity cost is 10%, you should be willing to pay $1,607.22 for this investment.
Answer:  TRUE

19) You believe WSU stock will pay dividends of $1.00, $1.25, and $1.50 at the end of each of the next 3 years.  Immediately after receiving the third dividend, you will sell the stock for $28.50.  If the appropriate discount rate is 12%, you should be willing to pay $20.75 for this stock.
Answer:  FALSE

20) The present value of a complex cash flow stream is equal to the sum of the present values of each of the cash flows.
Answer:  TRUE


21) You are considering purchasing common stock in AMZ Corporation. You anticipate that the company will pay dividends of $5.00 per share next year and $7.50 per share in the following year. You also believe that you can sell the common stock two years from now for $30.00 per share. If you require a 14% rate of return on this investment, what is the maximum price that you would be willing to pay for a share of AMZ common stock?
Answer: 
PV  = $5.00 /(1.14)1 + ($7.50 + $30.00)/(1.14)2
        = $33.24

22) You have decided to invest $500 in a mutual fund today and make $500 end-of-the-year investments in the fund each year until you retire for 40 years. Assuming an opportunity cost of 12%, what do you estimate that you will have in this account at retirement?
Answer: 
Calculator steps:
-500               PV
-500               PMT
    40               N
    12               I/yr or I
FV = $430,071

23) You are planning to deposit $10,000 today into a bank account. Five years from today you expect to withdraw $7,500. If the account pays 5% interest per year, how much will remain in the account eight years from today? Round to the nearest dollar.
Answer: 
FV  = $10,000(1.05)5 
         = $12,760
             Amount to invest in remaining three years = $12,760 - $7,500 = $5,260
FV  = $5,260 (1.05)3 
         = $6,089


24) Suppose you are 40 years old and plan to retire in exactly 20 years. 21 years from now you will need to withdraw $5,000 per year from a retirement fund to supplement your social security payments. You expect to live to the age of 85. How much money should you place in the retirement fund each year for the next 20 years to reach your retirement goal if you can earn 12% interest per year from the fund?
Answer:  Using a financial calculator N=25, i=12, PMT=5000, PV=39,215.70=s the amount in fund at age 60.
To find the annual contribution, n=20, i=12,PV=0, FV=39215.70, solve for PMT=-544.27, so 
Annual contribution = $544.27

25) An investment will pay $500 in three years, $700 in five years, and $1,000 in nine years. If the opportunity rate is 6%, what is the present value of this investment?
Answer: 
PV = $500(1/(1.06)3) + $700(1/1.06)5) + $1000(1/(1.06)9)
PV = $500(.840) + $700(.747) + $1000(.592)
       = $420.00 + $522.90 + $592.00
       = $1,534.90

26) What is the value (price) of a bond that pays $400 semiannually for 10 years and returns $10,000 at the end of 10 years? The market discount rate is 10% paid semiannually.
Answer:  Using a financial calculator N=20, i=5, PMT=400, FV=10000, solve for PV=-5361.77 or $5,361.77


27) The expected after-tax cash flow from an investment property that you are considering is
Year 1   $25,000
Year 2   $27,500
Year 3   $30,250
At the end of year 3 you expect to sell the property for $400,000.  If the appropriate discount rate is 12%, what is the most you should pay for this property?
Answer:  [25000/(1.12)1 + 27500/(1.12)2 + 302500/(1.12)3 + 400000/(1.12)3] = $350,487.71

28) In order to send your oldest child to law school when the time comes, you want to accumulate $40,000 at the end of 18 years. Assuming that your savings account will pay 6% compounded annually, how much would you have to deposit if:
a. you want to deposit an amount annually at the end of each year?
b. you want to deposit one large lump sum today?
Answer: 
a. PMT = $1,294.26
b. PMT = $14,013.75

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