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Chapter 04 - Discounted Cash Flow ValuationChapter 04 Discounted Cash Flow Valuation Answer Key Multiple Choice Questions1.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.Difficulty level: EasyTopic: ANNUITYType: DEFINITIONS2.Annuities where the payments occur at the end of each time period are called _, whereas _ refer to annuity streams with payments occurring at the beginning of each time period.A.ordinary annuities; early annuitiesB.late annuities; straight annuitiesC.straight annuities; late annuitiesD.annuities due; ordinary annuitiesE.ordinary annuities; annuities dueDifficulty level: EasyTopic: ANNUITIES DUEType: DEFINITIONS3.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.Difficulty level: EasyTopic: PERPETUITYType: DEFINITIONS4.The interest rate expressed in terms of the interest payment made each period is called the _ rate.A.stated annual interestB.compound annual interestC.effective annual interestD.periodic interestE.daily interestDifficulty level: EasyTopic: STATED INTEREST RATESType: DEFINITIONS5.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 interestDifficulty level: EasyTopic: EFFECTIVE ANNUAL RATEType: DEFINITIONS6.The interest rate charged per period multiplied by the number of periods per year is called the _ rate.A.effective annualB.annual percentageC.periodic interestD.compound interestE.daily interestDifficulty level: EasyTopic: ANNUAL PERCENTAGE RATEType: DEFINITIONS7.Paying off long-term debt by making installment payments is called:A.foreclosing on the debt.B.amortizing the debt.C.funding the debt.D.calling the debt.E.None of the above.Difficulty level: EasyTopic: AMORTIZATIONType: DEFINITIONS8.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 of the 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.Difficulty level: MediumTopic: ORDINARY ANNUITY VERSUS ANNUITY DUEType: CONCEPTS9.You are comparing two investment options. The cost to invest in either option is the same today. Both options will provide you with $20,000 of income. Option A pays five annual 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 the following 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.Difficulty level: MediumTopic: UNEVEN CASH FLOWS AND PRESENT VALUEType: CONCEPTS10.You are considering two projects with the following cash flows:Which of the following statements are true concerning these two projects?I. Both projects have the same future value at the end of year 4, given a positive rate of return.II. Both projects have the same future value given a zero rate of return.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 than project B, given a positive rate of return.A.II onlyB.IV onlyC.I and III onlyD.II and IV onlyE.I, II, and III onlyDifficulty level: MediumTopic: UNEVEN CASH FLOWS AND FUTURE VALUEType: CONCEPTS11.A perpetuity differs from an annuity because:A.perpetuity payments vary with the rate of inflation.B.perpetuity payments vary with the market rate of interest.C.perpetuity payments are variable while annuity payments are constant.D.perpetuity payments never cease.E.annuity payments never cease.Difficulty level: EasyTopic: PERPETUITY VERSUS ANNUITYType: CONCEPTS12.Which one of the following statements concerning the annual percentage rate is correct?A.The annual percentage rate considers interest on interest.B.The rate of interest you actually pay on a loan is called the annual percentage rate.C.The effective annual rate is lower than the annual percentage rate when an interest rate is compounded quarterly.D.When firms advertise the annual percentage rate they are violating U.S. truth-in-lending laws.E.The annual percentage rate equals the effective annual rate when the rate on an account is designated as simple interest.Difficulty level: MediumTopic: ANNUAL PERCENTAGE RATEType: CONCEPTS13.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 year increases.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 annual percentage rate.Difficulty level: MediumTopic: INTEREST RATESType: CONCEPTS14.Which of the following statements concerning the effective annual rate are correct?I. When making financial decisions, you should compare effective annual rates rather than annual percentage rates.II. The more frequently interest is compounded, the higher the effective annual rate.III. A quoted rate of 6% compounded continuously has a higher effective annual rate than if the rate were compounded daily.IV. When borrowing and 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 IVDifficulty level: MediumTopic: EFFECTIVE ANNUAL RATEType: CONCEPTS15.The highest effective annual rate that can be derived from an annual percentage rate of 9% is computed as:A.09e - 1.B.e.09 q.C.e (1 + .09).D.e.09 - 1.E.(1 + .09)q.Difficulty level: MediumTopic: CONTINUOUS COMPOUNDINGType: CONCEPTS16.The time value of money concept can be defined as:A.the relationship between the supply and demand of money.B.the relationship between money spent versus money received.C.the relationship between a dollar to be received in the future and a dollar today.D.the relationship between interest rate stated and amount paid.E.None of the above.Difficulty level: EasyTopic: TIME VALUEType: CONCEPTS17.Discounting cash flows involves:A.discounting only those cash flows that occur at least 10 years in the future.B.estimating only the cash flows that occur in the first 4 years of a project.C.multiplying expected future cash flows by the cost of capital.D.discounting all expected future cash flows to reflect the time value of money.E.taking the cash discount offered on trade merchandise.Difficulty level: EasyTopic: CASH FLOWSType: CONCEPTS18.Compound interest:A.allows for the reinvestment of interest payments.B.does not allow for the reinvestment of interest payments.C.is the same as simple interest.D.provides a value that is less than simple interest.E.Both A and D.Difficulty level: EasyTopic: INTERESTType: CONCEPTS19.An annuity:A.is a debt instrument that pays no interest.B.is a stream of payments that varies with current market interest rates.C.is a level stream of equal payments through time.D.has no value.E.None of the above.Difficulty level: EasyTopic: ANNUITYType: CONCEPTS20.The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest?A.annual compoundingB.monthly compoundingC.daily compoundingD.continuous compoundingE.It is impossible to tell without knowing the term of the loan.Difficulty level: EasyTopic: COMPOUNDINGType: CONCEPTS21.The present value of future cash flows minus initial cost is called:A.the future value of the project.B.the net present value of the project.C.the equivalent sum of the investment.D.the initial investment risk equivalent value.E.None of the above.Difficulty level: EasyTopic: PRESENT VALUEType: CONCEPTS22.Find the present value of $5,325 to be received in one period if the rate is 6.5%.A.$5,000.00B.$5,023.58C.$5,644.50D.$5,671.13E.None of the above.Difficulty level: EasyTopic: PRESENT VALUE - SINGLE SUMType: PROBLEMS23.If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compounded interest at 7.5% for three years which one will pay more and by how much?A.Simple interest by $50.00B.Compound interest by $22.97C.Compound interest by $150.75D.Compound interest by $150.00E.None of the above.Simple Interest = $10,000 (.08)(3) = $2,400;Compound Interest = $10,000(1.075)3 - 1) = $2,422.97;Difference = $2,422.97 - $2,400 = $22.97Difficulty level: EasyTopic: SIMPLE & COMPOUND INTERESTType: PROBLEMS24.Bradley Snapp has deposited $7,000 in a guaranteed investment account with a promised rate of 6% compounded annually. He plans to leave it there for 4 full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make?A.$1,960.00B.$2,175.57C.$8,960.00D.$8,837.34E.$9,175.57$7,000 (1.06)4 = $8,837.34Difficulty level: EasyTopic: FUTURE VALUE - SINGLE SUMType: PROBLEMS25.Your parents are giving you $100 a month for four years while you are in college. At a 6% discount rate, what are these payments worth to you when you first start college?A.$3,797.40B.$4,167.09C.$4,198.79D.$4,258.03E.$4,279.32Difficulty level: EasyTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS26.You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today?A.$87,003.69B.$87,380.23C.$87,962.77D.$88,104.26E.$90,723.76Difficulty level: EasyTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS27.Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9%, how much can Todd afford to borrow to buy a car?A.$6,961.36B.$8,499.13C.$8,533.84D.$8,686.82E.$9,588.05Difficulty level: EasyTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS28.You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5% 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.Difficulty level: MediumTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS29.Your employer contributes $25 a week to your retirement plan. Assume that you work for your employer for another twenty years and that the applicable discount rate is 5%. Given these assumptions, what is this employee benefit worth to you today?A.$13,144.43B.$15,920.55C.$16,430.54D.$16,446.34E.$16,519.02Difficulty level: MediumTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS30.You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12%, what is this job worth to you today?A.$180,238.81B.$201,867.47C.$210,618.19D.$223,162.58E.$224,267.10Difficulty level: MediumTopic: ORDINARY ANNUITY AND PRESENT VALUEType: PROBLEMS31.The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. It deposits the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today, how much would it have had to deposit?A.$82,964.59B.$83,189.29C.$83,428.87D.$83,687.23E.$84,998.01Difficulty level: MediumTopic: ANNUITY DUE AND PRESENT VALUEType: PROBLEMS32.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 months. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing?A.$113.94B.$115.65C.$119.34D.$119.63E.$119.96Difficulty level: MediumTopic: ANNUITY DUE AND PRESENT VALUEType: PROBLEMS33.You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the first day of each year. What is the value of this annuity today at a 7% discount rate?A.$84,282.98B.$87,138.04C.$90,182.79D.$96,191.91E.$116,916.21Difficulty level: MediumTopic: ANNUITY DUE AND PRESENT VALUEType: PROBLEMS34.You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Your discount rate is 8.5%. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year?A.$8,699B.$9,217C.$9,706D.$10,000E.$10,850Difference = $111,040.97 - $102,341.91 = $8,699.06 = $8,699 (rounded)Note: The difference = .085 $102,341.91 = $8,699.06Difficulty level: MediumTopic: ORDINARY ANNUITY VERSUS ANNUITY DUEType: PROBLEMS35.You are comparing two annuities with equal present values. The applicable discount rate is 7.5%. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year?A.$4,651B.$5,075C.$5,000D.$5,375E.$5,405Because each payment is received one year later, then the cash flow has to equal: $5,000 (1 + .075) = $5,375Difficulty level: MediumTopic: ORDINARY ANNUITY VERSUS ANNUITY DUEType: PROBLEMS36.Martha receives $100 on the first of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for five years. At an 8% discount rate, what is the difference in the present value of these two sets of payments?A.$32.88B.$40.00C.$99.01D.$108.00E.$112.50Difference = $4,964.72 - $4,931.84 = $32.88Difficulty level: MediumTopic: ORDINARY ANNUITY VERSUS ANNUITY DUEType: PROBLEMS37.What is the future value of $1,000 a year for five years at a 6% rate of interest?A.$4,212.36B.$5,075.69C.$5,637.09D.$6,001.38E.$6,801.91Difficulty level: EasyTopic: ORDINARY ANNUITY AND FUTURE VALUEType: PROBLEMS38.What is the future value of $2,400 a year for three years at an 8% rate of interest?A.$6,185.03B.$6,847.26C.$7,134.16D.$7,791.36E.$8,414.67Difficulty level: EasyTopic: ORDINARY ANNUITY AND FUTURE VALUEType: PROBLEMS39.Janet plans on saving $3,000 a year and expects to earn 8.5%. How much will Janet 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.$256,063.66Difficulty level: EasyTopic: ORDINARY ANNUITY AND FUTURE VALUEType: PROBLEMS40.Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings on the last day of each year. They both earn a 9% rate of return. What is 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.$40,115.31Difference = $445,725.65 - $408,922.62 = $36,803.03Note: Difference = $408,922.62 .09 = $36,803.03Difficulty level: MediumTopic: ANNUITY DUE VERSUS ORDINARY ANNUITYType: PROBLEMS41.You borrow $5,600 to buy a car. The terms of the loan call for monthly payments for four years at a 5.9% rate of interest. What is the amount of each payment?A.$103.22B.$103.73C.$130.62D.$131.26E.$133.04Difficulty level: EasyTopic: ORDINARY ANNUITY PAYMENTSType: PROBLEMS42.You borrow $149,000 to buy a house. The mortgage rate is 7.5% and the loan period is 30 years. Payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay?A.$138,086B.$218,161C.$226,059D.$287,086E.$375,059Total interest = ($1,041.83 30 12) - $149,000 = $226,058.80 = $226,059 (rounded)Difficulty level: MediumTopic: ORDINARY ANNUITY PAYMENTS AND COST OF INTERESTType: PROBLEMS43.The Great Giant Corp. has a management contract with its 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 aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 6.5% 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.$1,938,018.22Difficulty level: EasyTopic: ORDINARY ANNUITY PAYMENTS AND FUTURE VALUEType: PROBLEMS44.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 to earn 4.5% on your money during your retirement. How much can you withdraw from your retirement savings each month if you plan to die on the day you spend your last penny?A.$2,001.96B.$2,092.05C.$2,398.17D.$2,472.00E.$2,481.27Difficulty level: MediumTopic: ORDINARY ANNUITY PAYMENTS AND PRESENT VALUEType: PROBLEMS45.The McDonald Group purchased a piece of property for $1.2 million. It paid a down payment of 20% in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75% com
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