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CHAPTER 6Discounted Cash Flow ValuationI. DEFINITIONSANNUITYa 1. An annuity stream of cash flow payments is a set of:a. level cash flows occurring each time period for a fixed length of time.b. level cash flows occurring each time period forever.c. increasing cash flows occurring each time period for a fixed length of time.d. increasing cash flows occurring each time period forever.e. arbitrary cash flows occurring each time period for no more than 10 years.PRESENT VALUE FACTOR FOR ANNUITIESb 2. The present value factor for annuities is calculated as:a. (1 + present value factor) r.b. (1 -prese nt value factor) r.c. present value factor + (1 r).d. (present value factor r) + (1 r).e. r (1 + present value factor).FUTURE VALUE FACTOR FOR ANNUITIESd 3. The future value factor for annuities is calculated as the:a. future value factor + r.b. (1 r) + (future value factor r).c. (1 r) + future value factor.d. (future value factor -1) r.e. (future value factor + 1) r.ANNUITIES DUEe 4. Annuities where the payments occur at the end of each time period are called____ , whereas ____ refer to annuity streams with payments occurring at thebeginning of each time period.a. ordinary annuities; early annuitiesb. late annuities; straight annuitiesc. straight annuities; late annuitiesd. annuities due; ordinary annuitiese. ordinary annuities; annuities duePERPETUITYc 5. An annuity stream where the payments occur forever is called a(n):a. annuity due.b. indemnity.c. perpetuity.d. amortized cash flow stream.e. amortization table.STATED INTEREST RATESa 6. The interest rate expressed in terms of the interest payment made each period is calledthe _________ rate.a. stated interestb. compound interestc. effective annuald. periodic intereste. daily interestEFFECTIVE ANNUALRATEc 7. The interest rate expressed as if it were compounded once per year is called the rate.a. stated interestb. compound interestc. effective annuald. periodic intereste. daily interestANNUAL PERCENTAGE RATEb 8. The interest rate charged per period multiplied by the number of periods per year is calledthe _________ rate.a. effective annualb. annual percentagec. periodic interestd. compound intereste. daily interestPURE DISCOUNT LOANd 9. A loan where the borrower receives money today and repays a single lump sum at sometime in the future is called a(n) _________ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyINTEREST-ONLY LOANe 10. A loan where the borrower pays interest each period and repays the entire principal ofthe loan at some point in the future is called a(n) _____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyAMORTIZED LOANa 11. A loan where the borrower pays interest each period, and repays some or all of theprincipal of the loan over time is called a(n) ____ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyBALLOON LOANc 12. A loan where the borrower pays interest each period, repays part of the principal of theloan over time, and repays the remainder of the principal at the end of the loan, iscalled a(n) ______ loan.a. amortizedb. continuousc. balloond. pure discounte. interest-onlyII. CONCEPTSORDINARY ANNUITY VERSUS ANNUITY DUEc 13. You are comparing two annuities which offer monthly payments for ten years. Both annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity B pays on the last day of each month. Which one ofthe following statements is correct concerning these two annuities?a. Both annuities are of equal value today.b. Annuity B is an annuity due.c. Annuity A has a higher future value than annuity B.d. Annuity B has a higher present value than annuity A.e. Both annuities have the same future value as of ten years from today.UNEVENCASH FLOWS ANDPRESENT VALUEb 14. You are comparing two investment options. The cost to invest in either option is thesame today. Both options will provide you with $20,000 of income. Option A pays fiveannual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of thefollowing statements is correct given these two investment options?a. Both options are of equal value given that they both provide $20,000 of income.b. Option A is the better choice of the two given any positive rate of return.c. Option B has a higher present value than option A given a positive rate of return.d. Option B has a lower future value at year 5 than option A given a zero rate of return.e. Option A is preferable because it is an annuity due.UNEVENCASH FLOWS ANDFUTURE VALUEa 15. You are considering two projects with the following cash flows:Project A Project BYear 1 $2,500 $4,000Year 2 3,000 3,500Year 3 3,500 3,000Year 4 4,000 2,500Which of the follow ing stateme nts are true concerning these two projects?I. Both projects have the same future value at the end of year 4, give n a positive rateof return.II. Both projects have the same future value give n a zero rate of retur n.III. Both projects have the same future value at any point in time, given a positive rate of return.IV. Project A has a higher future value tha n project B, give n a positive rate of return.a. II on lyb. IV onlyc. I and III onlyd. II a nd IV onlye. I, II, and III o nlyPERPETUITY VERSUS ANNUITYd 16. A perpetuity differs from an annuity because:a. perpetuity payme nts vary with the rate of in flati on.b. perpetuity payme nts vary with the market rate of in terest.c. perpetuity payme nts are variable while ann uity payme nts are con sta nt.d. perpetuity payme nts n ever cease.e. ann uity payme nts n ever cease.ANNUAL PERCENTAGE RATEe 17. Which one of the following statements concerning the annual percentage rate is correct?a. The annual perce ntage rate con siders in terest on in terest.b. The rate of in terest you actually pay on a loa n is called the annual perce ntage rate.c. The effective annual rate is lower tha n the annual perce ntage rate whe n an in terest rateis compo un ded quarterly.d. When firms advertise the annual percentage rate they are violating U.S. truth-inlending laws.e. The annual perce ntage rate equals the effective annual rate whe n the rate on an account is desig nated as simple in terest.INTEREST RATESb 18. Which one of the following statements concerning interest rates is correct?a. The stated rate is the same as the effective annual rate.b. An effective annual rate is the rate that applies if interest were charged annually.c. The annual percentage rate increases as the number of compounding periods per yearincreases.d. Banks prefer more frequent compounding on their savings accounts.e. For any positive rate of interest, the effective annual rate will always exceed the annualpercentage rate.EFFECTIVE ANNUAL RATEc 19. Which of the following statements concerning the effective annual rate are correct?I. When making financial decisions, you should compare effective annual rates rather thanannual percentage rates.II. The more frequently interest is compounded, the higher the effective annual rate.III. A quoted rate of 6 percent compounded continuously has a higher effective annual rate than if the rate were compounded daily.IV. When choosing which loan to accept, you should select the offer with the highest effective annual rate.a. I and II onlyb. I and IV onlyc. I, II, and III onlyd. II, III, and IV onlye. I, II, III,and IVCONTINUOUS COMPOUNDINGd 20. The highest effective annual rate that can be derived from an annual percentage rate of9 percent is computed as:a. .09e -1. .09b. e q.c. e (1 + .09).d. e.09-1.e. (1 + .09)q.PURE DISCOUNT LOAN a 21. A pure discount loan is a(n):a. example of a present value problem.b. loan that is interest-free.c. loan that gives you a discount if you pay your payments on time.d. loan that requires all interest to be paid at the time the loan is made.e. loan that discounts the payments if you pay them in advance.INTEREST-ONLY LOANc 22. The principle amount of an interest-only loan is:a. never repaid.b. repaid in equal increments and included in each loan payment.c. repaid in full at the end of the loan period.d. repaid in equal annual payments even when the loan interest is repaid monthly.e. repaid in increasing increments and included in each loan payment.AMORTIZED LOANb 23. An amortized loan:a. requires the principle amount to be repaid in even increments over the life of the loan.b. may have equal or increasing amounts applied to the principle from each loan payment.c. requires that all interest be repaid on a monthly basis while the principle is repaid at theend of the loan term.d. requires that all payments be equal in amount and include both principle and interest.e. is the type of loan that describes most corporate bonds.III. PROBLEMSORDINARY ANNUITY AND PRESENT VALUEd 24. Your parents are giving you $100 a month for four years while you are in college. At a6 percent discount rate, what are these payments worth to you when you first startcollege?a. $3,797.40b. $4,167.09c. $4,198.79d. $4,258.03e. $4,279.32ORDINARY ANNUITYAND PRESENT VALUEb 25. You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If youcan earn 8 percent on your money, what is this prize worth to you today?a. $87,003.69b. $87,380.23c. $87,962.77d. $88,104.26e. $90,723.76ORDINARY ANNUITYAND PRESENT VALUE b 26. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9 percent, how much can Todd afford to borrow to buy a car?a. $6,961.36b. $8,499.13c. $8,533.84d. $8,686.82e. $9,588.05ORDINARY ANNUITYAND PRESENT VALUEa 27. You are the beneficiary of a life insurance policy. The insurance company informs you thatyou have two options for receiving the insurance proceeds. You can receive a lump sumof $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5percent on your money. Which option should you take and why?a. You should accept the payments because they are worth $56,451.91 today.b. You should accept the payments because they are worth $56,523.74 today.c. You should accept the payments because they are worth $56,737.08 today.d. You should accept the $50,000 because the payments are only worth $47,757.69 today.e. You should accept the $50,000 because the payments are only worth $47,808.17 today.ORDINARY ANNUITYAND PRESENT VALUEc 28.Your employer contributes $25 a week to your retirement plan. Assume that you work foryour employer for another twenty years and that the applicable discount rate is 5 percent.Given these assumptions, what is this employee benefit worth to you today?a. b. $13,144.43 $15,920.55c. d. $16,430.54 $16,446.34e. $16,519.02ORDINARY ANNUITYAND PRESENT VALUEa 29. You have a sub-contracting job with a local manufacturing firm. Your agreement calls forannual payments of $50,000 for the next five years. At a discount rate of 12 percent, what is this job worth to you today?a. b. $180,238.81 $201,867.47c. d. $210,618.19 $223,162.58e. $224,267.10ANNUITY DUE AND PRESENT VALUEb 30. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety netfor recessionary periods. The money will be set aside in a separate savings accountwhich pays 3.25 percent interest compounded monthly. They deposit the first $1,500today. If the company had wanted to deposit an equivalent lump sum today, how muchwould they have had to deposit?a. b. $82,964.59 $83,189.29c.d.e. $83,428.87 $83,687.23 $84,998.01ANNUITY DUE AND PRESENT VALUEb 31. You need some money today and the only friend you have that has any is your‘ miserly ' friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six month. In keeping with his reputation, he requires that thefirst payment be paid today. He also charges you 1.5 percent interest per month. Howmuch money are you borrowing?a. b.c. d.e. $113.94 $115.65 $119.34 $119.63 $119.96ANNUITY DUE AND PRESENT VALUEc 32. You buy an annuity which will pay you $12,000 a year for ten years. The paymentsare paid on the first day of each year. What is the value of this annuity today at a 7percent discount rate?a. b.c. d.e. $84,282.98 $87,138.04 $90,182.79 $96,191.91 $116,916.21ORDINARY ANNUITY VERSUS ANNUITY DUEa 33. You are scheduled to receive annual payments of $10,000 for each of the next 25years. Your discount rate is 8.5 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end ofeach year?a. b. $8,699 $9,217c. d. $9,706 $10,000e. $10,850ORDINARY ANNUITY VERSUS ANNUITY DUEd 34. You are comparing two annuities with equal present values. The applicable discountrate is 7.5 percent. One annuity pays $5,000 on the first day of each year for twentyyears. How much does the second annuity pay each year for twenty years if it pays at the end of each year?a. b. c.d. e. $4,651 $5,075 $5,000 $5,375 $5,405ORDINARY ANNUITY VERSUS ANNUITY DUEa 35. Martha receives $100 on the first of each month. Stewart receives $100 on the lastday of each month. Both Martha and Stewart will receive payments for five years. Atan 8 percent discount rate, what is the difference in the present value of these twosets of payments?a. b. $32.88 $40.00c.d.e. $99.01 $108.00 $112.50ORDINARY ANNUITYAND FUTURE VALUEWhat is the future value of $1,000 a year for five years at a 6 percent rate of interest? $4,212.36 $5,075.69 $5,637.09 $6,001.38 $6,801.91c 36.a.b.c.d.e.ORDINARY ANNUITYAND FUTURE VALUE d 37. What is the future value of $2,400 a year for three years at an 8 percent rate of interest?a. $6,185.03b. $6,847.26c. $7,134.16d. $7,791.36e. $8,414.67ORDINARY ANNUITYAND FUTURE VALUEc 38. Janet plans on saving $3,000 a year and expects to earn 8.5 percent. How much willJanet have at the end of twenty-five years if she earns what she expects?a. $219,317.82b. $230,702.57c. $236,003.38d. $244,868.92e. $256,063.66ANNUITY DUE VERSUS ORDINARY ANNUITYb 39. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to hissavings on the last day of each year. They both earn a 9 percent rate of return. Whatis the difference in their savings account balances at the end of thirty years?a. $35,822.73b. $36,803.03c. $38,911.21d. $39,803.04e. $40,115.31ORDINARY ANNUITY PAYMENTSd 40. You borrow $5,600 to buy a car. The terms of the loan call for monthly payments for fouryears at a 5.9 percent rate of interest. What is the amount of each payment?a. $103.22b. $103.73c. $130.62d. $131.26e. $133.04ORDINARY ANNUITY PAYMENTS AND COST OF INTERESTc 41. You borrow $149,000 to buy a house. The mortgage rate is 7.5 percent and the loanperiod is 30 years. Payments are made monthly. If you pay for the house accordingto the loan agreement, how much total interest will you pay?a. $138,086b. $218,161c. $226,059d. $287,086e. $375,059ORDINARY ANNUITY PAYMENTS AND FUTURE VALUEd 42. The Great Giant Corp. has a management contract with their newly hired president. The contract requires a lump sum payment of $25 million be paid to the president upon the completion of her first ten years of service. The company wants to set asideanequal amount of funds each year to cover this anticipated cash outflow. The companycan earn 6.5 percent on these funds. How much must the company set aside each year for this purpose?a. $1,775,042.93b. $1,798,346.17c. $1,801,033.67d. $1,852,617.25e. $1,938,018.22ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEe 43. You retire at age 60 and expect to live another 27 years. On the day you retire, you have$464,900 in your retirement savings account. You are conservative and expect toearn 4.5 percent on your money during your retirement. How much can you withdrawfrom your retirement savings each month if you plan to die on the day you spendyour last penny?a. $2,001.96b. $2,092.05c. $2,398.17d. $2,472.00e. $2,481.27ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEc 44. The McDonald Group purchased a piece of property for $1.2 million. They paid a downpayment of 20 percent in cash and financed the balance. The loan terms requiremonthly payments for 15 years at an annual percentage rate of 7.75 percentcompounded monthly. What is the amount of each mortgage payment?a. $7,440.01b. $8,978.26c. $9,036.25d. $9,399.18e. $9,413.67ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEd 45. You estimate that you will have $24,500 in student loans by the time you graduate. Theinterest rate is 6.5 percent. If you want to have this debt paid in full within five years,how much must you pay each month?a. $471.30b. $473.65$476.79$479.37$480.40c. d. e.ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEb 46. You are buying a previously owned car today at a price of $6,890. You are paying$500 down in cash and financing the balance for 36 months at 7.9 percent. What isthe amount of each loan payment?a. b.c. d.e. $198.64 $199.94 $202.02 $214.78 $215.09ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEb 47. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500per quarter for 25 years. You want to earn a minimum rate of return of 5.5 percent.What is the most you are willing to pay as a lump sum today to buy this annuity?a. b.c. d.e. $26,988.16 $27,082.94 $27,455.33 $28,450.67 $28,806.30ANNUITY DUE PAYMENTSAND PRESENT VALUEc 48. Your car dealer is willing to lease you a new car for $299 a month for 60 months.Payments are due on the first day of each month starting with the day you sign thelease contract. If your cost of money is 4.9 percent, what is the current value of thelease?a. b. $15,882.75 $15,906.14c. d. $15,947.61 $16,235.42e. $16,289.54ANNUITY DUE PAYMENTS AND PRESENT VALUEd 49. Your great-aunt left you an inheritance in the form of a trust. The trust agreementstates that you are to receive $2,500 on the first day of each year, startingimmediately and continuing for fifty years. What is the value of this inheritancetoday if the applicable discount rate is 6.35 percent?a. b. c.d. e. $36,811.30 $37,557.52 $39,204.04 $39,942.42 $40,006.09ANNUITY DUE PAYMENTS AND PRESENT VALUEe 50. You recently filed suit against a company. Today, you received three settlement optionsas follows:Option A: $10,000 on the first day of each year for 25 yearsOption B: $880 on the first day of each month for 25 yearsOption C: $119,830 as a lump sum payment todayYou can earn 7.5 percent on your investments. You do not care if you personallyreceive the funds or if they are paid to your heirs should you die within the next 25years. Which one of the following statements is correct given this information?a. Option C is clearly the best choice since you can earn 7.5 percent on the entirelump sum starting immediately.b. Option B is clearly the best choice since it offers the largest number of payments.c. Option A is clearly the best choice since it has by far the largest future value.d. Option B is clearly the best choice since it has by far the largest present value.e. You are relatively indifferent to the three options as they are all approximately equalin value to you.ANNUITY DUE PAYMENTSAND FUTURE VALUEa 51. Your firm wants to save $250,000 to buy some new equipment three years from now.The plan is to set aside an equal amount of money on the first day of each yearstarting today. The firm can earn a 4.7 percent rate of return. How much does thefirm have to save each year to achieve their goal?a. $75,966.14b. $76,896.16c. $78,004.67d. $81.414.14e. $83,333.33ANNUITY DUE PAYMENTSAND FUTURE VALUEe 52. Today is January 1. Starting today, Sam is going to contribute $140 on the first of eachmonth to his retirement account. His employer contributes an additional 50 percentof the amount contributed by Sam. If both Sam and his employer continue to dothis and Sam can earn a monthly rate of ? of 1 percent, how much will he have inhis retirement account 35 years from now?a. $199,45.944.b. $200,456.74c. $249,981.21d. $299,189.16e. $300,685.11ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUEc 53. You are considering an annuity which costs $100,000 today. The annuity pays $6,000 ayear. The rate of return is 4.5 percent. What is the length of the annuity timeperiod?a. 24.96 yearsb. 29.48 yearsc. 31.49 yearsd. 33.08 yearse. 38.00 yearsORDINARY ANNUITY TIME PERIODS AND PRESENT VALUEd 54. Today, you signed loan papers agreeing to borrow $4,954.85 at 9 percentcompounded monthly. The loan payment is $143.84 a month. How many loanpayments must you make before the loan is paid in full?a. b.c. d.e. 29.89 36.00 38.8840.0041.03ORDINARY ANNUITY TIME PERIODS AND FUTURE VALUEa 55. Winston Enterprises would like to buy some additional land and build a new factory.The anticipated total cost is $136 million. The owner of the firm is quite conservativeand will only do this when the company has sufficient funds to pay cash for the entireexpansion project. Management has decided to save $450,000 a month for thispurpose. The firm earns 6 percent compounded monthly on the funds it saves. Howlong does the company have to wait before expanding its operations?a. b. 184.61 months 199.97 monthsc.d.e. 234.34 months 284.61 months 299.97 monthsANNUITY DUE TIME PERIODS AND PRESENT VALUEb 56. Today, you are retiring. You have a total of $413,926 in your retirement savings andhave the funds invested such that you expect to earn an average of 3 percent,compounded monthly, on this money throughout your retirement years. You want towithdraw $2,500 at the beginning of every month, starting today. How long will it beuntil you run out of money?a. b.c. d.e. 185.00 months 213.29 months 227.08 months 236.84 months 249.69 monthsANNUITY DUE TIME PERIODSc 57. The Bad Guys Co. is notoriously known as a slow-payer. They currently need toborrow $25,000 and only one company will even deal with them. The terms of theloancall for daily payments of $30.76. The first payment is due today. The interest rate is21 percent compounded daily. What is the time period of this loan?a. b. c. 2.88 years2.94 years3.00 yearsd. 3.13 yearse. 3.25 yearsORDINARY ANNUITY INTEREST RATEc 58. The Robertson Firm is considering a project which costs $123,900 to undertake. The project will yieldcash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project?a. 12.53 percentb. 13.44 percentc. 13.59 percentd. 14.02 percente. 14.59 percentORDINARY ANNUITY INTEREST RATEa 59. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 amonth for the next 40 years. What is the rate of return on this investment?a. 3.45 percentb. 3.47 percentc. 3.50 percentd. 3.52 percente. 3.55 percentORDINARY ANNUITY INTEREST RATEe 60. You have been investing $120 a month for the last 15 years. Today, your investment account is worth$47,341.19. What is your average rate of return on your investments?a. 9.34 percentb. 9.37 percentc. 9.40 percentd. 9.42 percente. 9.46 percentORDINARY ANNUITY INTEREST RATEc 61. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business venture. Today,Brinker sold that venture for $685,000. What is their rate of return on this venture?a. 9.43 percentb. 11.06 percentc. 15.59 percentd. 16.67 percente. 18.71 percentANNUITY DUE INTEREST RATEb 62. Your mother helped you start saving $25 a month beginning on your 10 th birthday.She always made you make your deposit on the first day of each month just to“ start the month out right ” . Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings?a. b.c. d.e. 5.25 percent 5.29 percent 5.33 percent 5.36 percent 5.50 percentANNUITY DUE INTERESTRATEa 63. Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In anattempt to reach this goal, you decide to save $25 a day, every day until you turn 40. You openan investment account and deposit your first $25 today. What rate of return must you earn toachieve your goal?a. b.c. d. 15.07 percent 15.13 percent 15.17 percent 15.20 percente. 15.24 percentUNEVENCASH FLOWS ANDPRESENT VALUEb 64.Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generatecash flows of $5,000, $9,000, and $15,000 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a 14 percent rate of return is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.?a. b. $19,201.76 $21,435.74c. d. $23,457.96 $27,808.17e. $31,758.00UNEVEN CASH FLOWS ANDPRESENT VALUEa 65.You are considering two savings options. Both options offer a 4 percent rate of return. The firstoption is to save $1,200, $1,500, and $2,000 a year over the next three years, respectively. Theother option is to save one lump sum amount today. If you want to have the same balance in your savings at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option?a. b. c.d. $4,318.67 $4,491.42 $4,551.78 $4,607.23e. $4,857.92UNEVEN CASH FLOWS ANDPRESENT VALUEYou are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively.The other offer is the payment of one lump sum amount today. You are trying todecide which offer to accept given the fact that your discount rate is 5 percent. Whatis the minimum amount that you will accept today if you are to select the lump sumoffer?$19,877.67$20,203.00$21,213.15$23,387.50$24,556.88b 66.a. b. c. d. e.。
