solving for the number of compounding period, n
Corporate Finance - Berk DeMarzo- Test Bank Chapter 4
Corporate Finance, 3e (Berk/DeMarzo)Chapter 4 The Time Value of Money4.1 The TimelineUse the figure for the question(s) below.1) Which of the following statements regarding timelines is FALSE?A) Timelines are an important first step in organizing and then solving a financial problem.B) We refer to a series of cash flows lasting several periods as a stream of cash flows.C) Not every stream of cash flows can be represented on a timeline.D) A timeline is a linear representation of the timing of the (expected) cash flows.Answer: CDiff: 1Section: 4.1 The TimelineSkill: Conceptual2) Which of the following statements regarding the timeline is FALSE?A) Date 1 is one year from now.B) The $5000 below date 1 is the payment you will receive at the end of the first year.C) The $5000 below date 2 is the payment you will receive at the beginning of the second year.D) Date 0 represents today.Answer: CDiff: 2Section: 4.1 The TimelineSkill: Definition3) Which of the following statements regarding the timeline is FALSE?A) Date 1 is the end of the first year.B) Date 0 is the beginning of the first year.C) The space between date 0 and date 1 represents the time period between two specific dates.D) You will find the timeline most useful in tracking cash flows if you interpret each point on the timeline as a period or interval of time.Answer: DDiff: 2Section: 4.1 The TimelineSkill: DefinitionUse the information for the question(s) below.Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has been offered an immediate payment of $100,000. Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years. The current market rate of interest for Joe is 6%.4) Draw a timeline detailing Joe's cash flows from the sale of the family business.Answer:Diff: 2Section: 4.1 The TimelineSkill: Conceptual5) You have been offered the following investment opportunity, if you pay $2500 today, you will receive $1000 at the end of each of the next three years. Draw a timeline detailing this investment opportunity.Answer:Diff: 1Section: 4.1 The TimelineSkill: ConceptualUse the table for the question(s) below.Year A B0 -$150 -$2251 40 1752 80 1253 100 -506) Draw a timeline detailing the cash flows from investment "A." Answer:Diff: 1Section: 4.1 The TimelineSkill: Conceptual7) Draw a timeline detailing the cash flows from investment "B." Answer:Diff: 1Section: 4.1 The TimelineSkill: ConceptualUse the information for the question(s) below.Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs, average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year.8) Assume that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest. Draw a timeline that details the amount of money she will need to have in the future four each of her four years of her undergraduate education.Answer:18 19 20 2125,322.71 $25,322.71(1.)1$25,322.71(1.04)2$25,322.71(1.04)3Note that the tuition for the first year is calculated as: $12,500(1.04)18 = $25,322.71Diff: 2Section: 4.1 The TimelineSkill: Conceptual9) Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to make deposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Draw a timeline that details the amount that would be available for the daughter's college expenses on her 18th birthday.Answer:Diff: 2Section: 4.1 The TimelineSkill: Analytical4.2 The Three Rules of Time Travel1) Which of the following statements is FALSE?A) The process of moving a value or cash flow forward in time is known as compounding.B) The effect of earning interest on interest is known as compound interest.C) It is only possible to compare or combine values at the same point in time.D) A dollar in the future is worth more than a dollar today.Answer: DExplanation: D) A dollar in the future is worth less than a dollar today.Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: Conceptual2) Which of the following statements is FALSE?A) Finding the present value and compounding are the same.B) A dollar today and a dollar in one year are not equivalent.C) If you want to compare or combine cash flows that occur at different points in time, you first need to convert the cash flows into the same units or move them to the same point in time.D) The equivalent value of two cash flows at two different points in time is sometimes referred to as the time value of money.Answer: AExplanation: A) Finding the present value and discounting are the same.Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: Conceptual3) At an annual interest rate of 7%, the future value of $5,000 in five years is closest to:A) $3,565B) $6,750C) $7,015D) $7,035Answer: CExplanation: C) FV = PV(1 + i)N = 5000(1.07)5 = 7,012.76Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: Analytical4) At an annual interest rate of 7%, the present value of $5,000 received in five years is closest to:A) $3,565B) $6,750C) $7,015D) $7,035Answer: AExplanation: A) PV = FV/(1 + i)N = 5000(/1.07)5 = 3,564.93Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: AnalyticalUse the following information to answer the question(s) below.Consider the following four alternatives:1. $132 received in two years.2. $160 received in five years.3. $200 received in eight years.4. $220 received in ten years.5) The ranking of the four alternatives from most valuable to least valuable if the interest rate is 7% per year would be:A) 1, 2, 3, 4B) 4, 3, 2, 1C) 3, 4, 2, 1D) 3, 1, 2, 4Answer: DSection: 4.2 The Three Rules of Time TravelSkill: Analytical6) The ranking of the four alternatives from most valuable to least valuable if the interest rate is 6% per year would be:A) 1, 2, 3, 4B) 1, 3, 2, 4C) 4, 3, 1, 2D) 3, 4, 2, 1Answer: DSection: 4.2 The Three Rules of Time TravelSkill: AnalyticalUse the following information to answer the question(s) below.Your great aunt Matilda put some money in an account for you on the day you were born. This account pays 8% interest per year. On your 21st birthday the account balance was $5,033.83.7) The amount of money that your great aunt Matilda originally put in the account is closest to:A) $600B) $800C) $1,000D) $1,200Answer: CExplanation: C) PV = FV/(1 + i)N = 5033.83(/1.08)21 = 1,000Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: Analytical8) The amount of money that would be in the account if you left the money there until your 65th birthday is closest to:A) $29,556B) $148,780C) $168,824D) $748,932Answer: BExplanation: B) FV = PV(1 + i)N = 5033.83(1.08)(65 - 21) = $148,779.85Diff: 2Section: 4.2 The Three Rules of Time TravelSkill: Analytical9) Which of the following statements is FALSE?A) The process of moving a value or cash flow backward in time is known as discounting.B) FV =C) The process of moving a value or cash flow forward in time is known as compounding.D) The value of a cash flow that is moved forward in time is known as its future value. Answer: BExplanation: B) FV = C(1 + r)nDiff: 1Section: 4.2 The Three Rules of Time TravelSkill: Conceptual10) Consider the following time line:If the current market rate of interest is 8%, then the present value of this timeline is closest to:A) $1000B) $857C) $860D) $926Answer: BExplanation: B) PV = FV/(1 + r)n = 1000/(1.08)2 = 857.34 or approximately $857Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: AnalyticalIf the current market rate of interest is 10%, then the future value of this timeline is closest to:A) $666B) $500C) $605D) $650Answer: AExplanation: A) FV = PV(1 + r)n = 500(1.10)3 = 665.50 which is approximately $666 Diff: 1Section: 4.2 The Three Rules of Time TravelSkill: Analytical12) Consider the following timeline:If the current market rate of interest is 7%, then the future value of this timeline as of year 3 is closest to:A) $1720B) $1500C) $1404D) $1717Answer: AExplanation: A) FV = PV(1 + r)nFV = 500(1.07)3 + 500(1.07)2 + 500(1.07)1 = $1719.97 or approximately $1720Diff: 3Section: 4.2 The Three Rules of Time TravelSkill: AnalyticalIf the current market rate of interest is 9%, then the present value of this timeline as of year 0 is closest to:A) $492B) $637C) $600D) $400Answer: AExplanation: A) PV = FV(1 + r)n100/(1.09)1 = 91.74200/(1.09)2 = 168.34300/(1.09)3 = 231.66Sum = 491.74 which is approximately $492Diff: 3Section: 4.2 The Three Rules of Time TravelSkill: Analytical14) Consider the following timeline:If the current market rate of interest is 8%, then the value as of year 1 is closest to:A) $0B) $1003C) $540D) $77Answer: DExplanation: D) Two part problem:FV = PV(1 + r)n = 500(1.08)1 = $540PV = FV/(1 + r)n = -500/(1.08)1 = -$463So the answer is $540 + -$463 = $77Diff: 2Section: 4.2 The Three Rules of Time TravelSkill: Analytical4.3 Valuing a Stream of Cash Flows1) Consider the following timeline detailing a stream of cash flows:If the current market rate of interest is 8%, then the present value of this stream of cash flows is closest to:A) $22,871B) $21,211C) $24,074D) $26,000Answer: BExplanation: B) PV = 5000/(1.07)1 + 6000/(1.07)2 + 7000/(1.07)3 + 8000/(1.07)4 =$21,210.72Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical2) Which of the following statements is FALSE?A) FV =B) PV =C) FV = C n × (1 + r)nD) Most investment opportunities have multiple cash flows that occur at different points in time. Answer: ADiff: 1Section: 4.3 Valuing a Stream of Cash FlowsSkill: Conceptual3) Consider the following timeline detailing a stream of cash flows:If the current market rate of interest is 8%, then the future value of this stream of cash flows is closest to:A) $11,699B) $10,832C) $12,635D) $10,339Answer: AExplanation: A) FV = 1000(1.08)4 + 2000(1.08)3 + 3000(1.08)2 + 4000(1.08)1 = $11,699 Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical4) Consider the following timeline detailing a stream of cash flows:If the current market rate of interest is 10%, then the present value of this stream of cash flows is closest to:A) $674B) $600C) $460D) $287Answer: CExplanation: C) PV = 100/(1.10)1 + 100/(1.10)2 + 200/(1.10)3 + 200/(1.10)4 = $460Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical5) Consider the following timeline detailing a stream of cashflows:If the current market rate of interest is 6%, then the future value of this stream of cash flows is closest to:A) $1,723B) $1,500C) $1,626D) $1,288Answer: AExplanation: A) FV = 100(1.06)5 + 200(1.06)4 + 300(1.06)3 + 400(1.06)2 + 500(1.06)1 = $1723Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: AnalyticalUse the following timeline to answer the question(s) below.0 1 2 3$600 $1,200 $1,8006) At an annual interest rate of 7%, the future value of this timeline in year 3 is closest to:A) $3,295B) $3,600C) $3,770D) $4,035Answer: CExplanation: C) FV = PV(1 + i)N = $600(1.07)2 + 1,200(1.07)1 + 1,800 = 3,770.94Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical7) At an annual interest rate of 7%, the present value of this timeline in year 0 is closest to:A) $3,080B) $3,600C) $3,770D) $4,035Answer: AExplanation: A) PV = FV/(1 + i)N = $600/(1.07)1 + 1,200/(1.07)2 + 1,800/(1.07)3 = 3,078.21 Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical8) At an annual interest rate of 7%, the future value of this timeline in year 2 is closest to:A) $3,080B) $3,525C) $3,770D) $4,035Answer: BExplanation: B) FV year 2 = $600(1.07)1 + 1,200 + 1,800/(1.07)1 = 3,524.24Diff: 3Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical9) Taggart Transcontinental currently has a bank loan outstanding that requires it to make three annual payments at the end of the next three years of $1,000,000 each. The bank has offered to allow Taggart Transcontinental to skip making the next two payments in lieu of making one large payment at the end of the loan's term in three years. If the interest rate on the loan is 6%, then the final payment that the bank will require to make Taggart Transcontinental indifferent between the two forms of payments is closest to:A) $2,673,000B) $3,000,000C) $3,184,000D) $3,375,000Answer: CExplanation: C) FV = PV(1 + i)N = $1,000,000(1.06)2 + 1,000,000(1.06)1 + 1,000,000 = 3,183,600Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: AnalyticalUse the information for the question(s) below.Joe just inherited the family business, and having no desire to run the family business, he has decided to sell it to an entrepreneur. In exchange for the family business, Joe has been offered an immediate payment of $100,000. Joe will also receive payments of $50,000 in one year, $50,000 in two years, and $75,000 in three years. The current market rate of interest for Joe is 6%.10) In terms of present value, how much will Joe receive for selling the family business? Answer: PV = $100,000 + $50,000/(1.06)1 + $50,000/(1.06)2 + $75,000/(1.06)3 = $254,641 Diff: 2Section: 4.3 Valuing a Stream of Cash FlowsSkill: Analytical4.4 Calculating the Net Present ValueUse the following information to answer the question(s) below.Nielson Motors is considering an opportunity that requires an investment of $1,000,000 today and will provide $250,000 one year from now, $450,000 two years from now, and $650,000 three years from now.1) If the appropriate interest rate is 10%, then the NPV of this opportunity is closest to:A) ($88,000)B) $88,000C) $300,000D) $1,300,000Answer: BExplanation: B) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17Diff: 2Section: 4.4 Calculating the Net Present ValueSkill: Analytical2) If the appropriate interest rate is 10%, then Nielson Motors should:A) invest in this opportunity since the NPV is positive.B) not invest in this opportunity since the NPV is positive.C) invest in this opportunity since the NPV is negative.D) not invest in this opportunity since the NPV is negative.Answer: AExplanation: A) NPV = -1,000,000 + 250,000/(1.10)1 + 450,000/(1.10)2 + 650,000/(1.10)3 = 87,528.17Invest since positive NPVDiff: 2Section: 4.4 Calculating the Net Present ValueSkill: Analytical3) If the appropriate interest rate is 15%, then Nielson Motors should:A) invest in this opportunity since the NPV is positive.B) not invest in this opportunity since the NPV is positive.C) invest in this opportunity since the NPV is negative.D) not invest in this opportunity since the NPV is negative.Answer: DExplanation: D) NPV = -1,000,000 + 250,000/(1.15)1 + 450,000/(1.15)2 + 650,000/(1.15)3 = -14,958.49Do Not Invest since negative NPVDiff: 2Section: 4.4 Calculating the Net Present ValueSkill: Analytical4) Kampgrounds Inc. is considering purchasing a parcel of wilderness land near a popular historic site. Although this land will cost Kampgrounds $400,000 today, by renting out wilderness campsites on this land, Kampgrounds expects to make $35,000 at the end of every year indefinitely. If the appropriate discount rate is 8%, then the NPV of this new wilderness campsite is closest to:A) -$50,000B) -$37,500C) $37,500D) $50,000Answer: CExplanation: C) NPV = -400,000 + $35,000/.08 = 37,500Diff: 1Section: 4.4 Calculating the Net Present ValueSkill: Analytical5) Wyatt oil is considering drilling a new self sustaining oil well at a cost of $1,000,000. This well will produce $100,000 worth of oil during the first year, but as oil is removed from the well the amount of oil produced will decline by 2%, per year forever. If the Wyatt oil's appropriate interest rate is 8%, then the NPV of this oil well is closest to:A) -$250,000B) $0C) $250,000D) $1,000,000Answer: BExplanation: B) NPV = -1,000,000 + $100,000/(.08 - (-.02)) = $0Diff: 2Section: 4.4 Calculating the Net Present ValueSkill: Analytical4.5 Perpetuities and Annuities1) Which of the following statements regarding perpetuities is FALSE?A) To find the value of a perpetuity one cash flow at a time would take forever.B) A perpetuity is a stream of equal cash flows that occurs at regular intervals and lasts forever.C) PV of a perpetuity =D) One example of a perpetuity is the British government bond called a consol.Answer: CExplanation: C) PV of a perpetuity =Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Conceptual2) Which of the following statements regarding annuities is FALSE?A) PV of an annuity = C ×B) The difference between an annuity and a perpetuity is that a perpetuity ends after some fixed number of payments.C) An annuity is a stream of N equal cash flows paid at regular intervals.D) Most car loans, mortgages, and some bonds are annuities.Answer: BExplanation: B) A perpetuity never ends.Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Conceptual3) Which of the following statements regarding growing perpetuities is FALSE?A) We assume that r < g for a growing perpetuity.B) PV of a growing perpetuity =C) To find the value of a growing perpetuity one cash flow at a time would take forever.D) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.Answer: ADiff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical4) Which of the following statements regarding growing annuities is FALSE?A) A growing annuity is a stream of N growing cash flows, paid at regular intervals.B) We assume that g < r when using the growing annuity formula.C) PV of a growing annuity = C ×D) A growing annuity is like a growing perpetuity that never comes to an end.Answer: DExplanation: D) An annuity does end.Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Conceptual5) Which of the following statements is FALSE?A) The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments.B) Most car loans, mortgages, and some bonds are annuities.C) A growing perpetuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever.D) An annuity is a stream of N equal cash flows paid at irregular intervals.Answer: DExplanation: D) annuities are paid at regular intervals.Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Conceptual6) Which of the following formulas is INCORRECT?A) PV of a growing annuity = C ×B) PV of an annuity = C ×C) PV of a growing perpetuity =D) PV of a perpetuity =Answer: AExplanation: A) PV of a growing annuity = C ×Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: ConceptualUse the information for the question(s) below.Suppose that a young couple has just had their first baby and they wish to ensure that enough money will be available to pay for their child's college education. Currently, college tuition, books, fees, and other costs, average $12,500 per year. On average, tuition and other costs have historically increased at a rate of 4% per year.7) Assuming that costs continue to increase an average of 4% per year, tuition and other costs for one year for this student in 18 years when she enters college will be closest to:A) $12,500B) $21,500C) $320,568D) $25,323Answer: DExplanation: D) FV = PV (1 + i )N = $12,500(1.04)18 = $25,322.71Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical8) Assuming that college costs continue to increase an average of 4% per year and that all her college savings are invested in an account paying 7% interest, then the amount of money she will need to have available at age 18 to pay for all four years of her undergraduate education is closest to:A) $97,110B) $107,532C) $101,291D) $50,000Answer: AExplanation: A) This is a two step problem.Step #1 determine the cost of the first year of college.FV = PV (1 + i )N = $12,500(1.04)18 = $25,322.71Step #2 figure out the value for four years of college.PV of a growing annuity due = C ×(1 + r ) = $25,322.71 × ⎪⎪⎪⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛++07.104.141(1 + .07) = $97,110.01 Diff: 3Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical9) The British government has a consol bond outstanding that pays ₤100 in interest each year. Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment one year from now, then the value of the consol bond is closest to:A) ₤1000B) ₤1100C) ₤2100D) ₤2000Answer: DExplanation: D) PVP = C/r = 100/.05 = 2000Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical10) The British government has a consol bond outstanding that pays ₤100 in interest each year. Assuming that the current interest rate in Great Britain is 5% and that you will receive your first interest payment immediately upon purchasing the consol bond, then the value of the consol bond is closest to:A) ₤2000B) ₤2100C) ₤1000D) ₤1100Answer: BExplanation: B) PVP = C/r= 100/.05 = 2000 + 100 immediate interest payment = ₤2100 Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical11) If the current rate of interest is 8%, then the present value of an investment that pays $1000 per year and lasts 20 years is closest to:A) $18,519B) $45,761C) $9,818D) $20,000Answer: CExplanation: C) PV = C/r (1 - (1 + r)-N) = 1000/.08 (1 - (1 + 0.08)-20)PV = $9,818Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical12) If the current rate of interest is 8%, then the future value 20 years from now of an investment that pays $1000 per year and lasts 20 years is closest to:A) $45,762B) $36,725C) $9,818D) $93,219Answer: AExplanation: A) FV = C/r((1+r)N -1) = 1000/0.08((1+0.08)20 - 1)FV = $45,762Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical13) Suppose that a young couple has just had their first baby and they wish to insure that enough money will be available to pay for their child's college education. They decide to makedeposits into an educational savings account on each of their daughter's birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The parents deposit $2000 on their daughter's first birthday and plan to increase the size of their deposits by 5% each year. Assuming that the parents have already made the deposit for their daughter's 18th birthday, then the amount available for the daughter's college expenses on her 18th birthday is closest to:A) $42,825B) $97,331C) $67,998D) $103,063Answer: BExplanation: B) FV of a growing annuity$2,000 × ⎪⎪⎪⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛++07.105.1181(1.07)18 = $97,331 Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical14) Since your first birthday, your grandparents have been depositing $1000 into a savings account on every one of your birthdays. The account pays 4% interest annually. Immediately after your grandparents make the deposit on your 18th birthday, the amount of money in your savings account will be closest to:A) $25,645B) $36,465C) $12,659D) $18,000Answer: AExplanation: A) FV = C/r((1+r)N -1) = 1000/0.04((1+0.04)18 - 1)FV = $25,645Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical15) Consider a growing perpetuity that will pay $100 in one year. Each year after that, you will receive a payment on the anniversary of the last payment that is 6% larger than the last payment. This pattern of payments will continue forever. If the interest rate is 11%, then the value of this perpetuity is closest to:A) $1,667B) $588C) $2,000D) $909Answer: CExplanation: C) PV growing Perpetuity = C/r - g = 100/(.11 - .06) = $2000Diff: 1Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical16) You are thinking about investing in a mine that will produce $10,000 worth of ore in the first year. As the ore closest to the surface is removed it will become more difficult to extract the ore. Therefore, the value of the ore that you mine will decline at a rate of 8% per year forever. If the appropriate interest rate is 6%, then the value of this mining operation is closest to:A) $71,429B) $500,000C) $166,667D) This problem cannot be solved.Answer: AExplanation: A) PVP = C/r - g = 10,000/(.06 - -.08) = 10,000/.14 = $71,429Diff: 3Section: 4.5 Perpetuities and AnnuitiesSkill: AnalyticalUse the information for the question(s) below.Assume that you are 30 years old today, and that you are planning on retirement at age 65. Your current salary is $45,000 and you expect your salary to increase at a rate of 5% per year as long as you work. To save for your retirement, you plan on making annual contributions to a retirement account. Your first contribution will be made on your 31st birthday and will be 8% of this year's salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. Assume that the rate of interest is 7%.17) The present value (at age 30) of your retirement savings is closest to:A) $87,000B) $108,000C) $46,600D) $75,230Answer: AExplanation: A) First deposit = .08 × $45,000 = $3,600$3,600 × ⎪⎪⎪⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛++07.105.1351 = $87,003Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical18) The future value at retirement (age 65) of your savings is closest to:A) $497,530B) $928,895C) $1,263,236D) $108,000Answer: BExplanation: B) First deposit = .08 × $45,000 = $3,600$3,600 × ⎪⎪⎪⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛++07.105.1351(1.07)35 = $928,895 or PVA (growing) = $3,600 × ⎪⎪⎪⎪⎭⎫ ⎝⎛-⎪⎭⎫ ⎝⎛++07.105.1351= $87,003FV = PV (1 + i )N = $87,003(1.07)35 = $928,895Diff: 2Section: 4.5 Perpetuities and AnnuitiesSkill: Analytical。
CFA考试投资分析的数量方法投资工具
第一章：货币的时间价值Chapter ⒈ The Time Value of Money§⒈解释利息率是对投资者的不同风险予以回报的实际无风险利率和风险溢价的总和利息率和折现率（Interest Rates and Discount Rates）货币时间价值概念的基础：收益率（rates of return）、利息率（interest rate）、要求的收益率（required rates of return）、折现率（discount rates）、机会成本（opportunity costs）、通货膨胀（inflation）和风险（risk）。
货币的时间价值，反映了时间、现金流量和利息率三者之间的关系。
投资者偏好现在消费。
利息率是投资者推迟现在消费的回报。
在确定世界，利息率被认为是无风险（risk-free）利率。
一般是国家的短期债券，如美国的国库券（Treasury-bills, T-bills）。
在不确定的世界，有两个因素影响利息率：①通货膨胀。
贷款者承担通货溢价（inflation premium）和推迟消费的机会成本。
因此，货币的名义成本（nominal cost of money），由实际利率（real rate）和通货溢价组成。
②风险。
贷款者还承担了不履行风险（default risk）。
因此，利息率包括：名义的无风险利率和不履行风险溢价。
利息率的意义：①收益要求率。
即促使投资者放弃现在消费所要求的收益。
②折现率（利息率和折现率可以交互使用）。
③机会成本。
即投资者按某一选择行为而放弃其他选择所失去的价值。
影响利息率最重要的因素是：资金的供求关系。
§⒉计算整笔现金的终值（FV）和现值（PV）单一现金流量的终值（The Future Value of a Single Cash Flow）整笔现金流（或lump-sum investment）的终值计算公式（N的初值为0）：基本概念：①简单利息（simple interest），即利息率乘原始本金。
财务管理专业英语-The Time Value of Money
5 years: PV = 500 / (1.1)5 = 310.46 10 years: PV = 500 / (1.1)10 = 192.77
4
Effects of Compounding
Simple interest Compound interest Consider the previous example
FV with simple interest = 1000 + 50 + 50 = 1100 FV with compound interest = 1102.50 The extra 2.50 comes from the interest of .05(50)
12
PV – One Period Example
Suppose you need $10,000 in one year for the down payment on a new car. If you can earn 7% annually, how much do you need to invest today?
8
Future Values – Example 3
Suppose you had a relative deposit $10 at 5.5% interest 200 years ago. How much would the investment be worth today?
FV = 10(1.055)200 = 447,189.84
16
topic1
Topic 1: Relationship Between Risk and ReturnBUS 442 Investment Theory and Portfolio ManagementOne of the most important concepts in investment theory is the relationship between risk and return. It is this relationship that drives the theoretical foundation of many investment models (such as the Capital Asset Pricing Model). Before we begin our discussion on the development of theoretical models that attempt to “capture” the relationship between risk and return, we need to first understand how these two variables (or measurements) are determined.1. (Rate of) ReturnIn your own words, explain what rate of return represents and why it is so important to an investor?One of the measurements of return is the holding period return (HPR), which represents the return an investor received for holding an investment for a certain amount of time. The formula for determining the HPR is as follows:pricePurchase income Current gain/loss Capital price Purchase income Current price) Purchase price (Sale +=+-=HPRFrom the above formula, it is clear that the HPR is dependent on two components:(a) Capital gain/loss(b) Current incomeRefer to In-class Example 1It is important to understand that the HPR is an ex-post return, i.e. a return that has already taken place. It is sometimes known as the historical return. Another thing that you should be aware of is that the HPR is a measurement for return over a single period (i.e. 4 months, 5 years, etc.)What happen if you needed to determine the investment returns over multiple periods? In other words, what if you are interested in the average returns of an investment over a number of quarters or years? There are three different measures for average returns: (a) arithmetic average, (b) geometric average, and (c) dollar-weighted average return. It is important for you to understand the advantages and disadvantages for each of the three return measurements.(a)Arithmetic average(i)Advantage(ii)Disadvantage(b)Geometric average(i)Advantage(ii)Disadvantage(c)Dollar-weighted average return(i)Advantage(ii)DisadvantageRefer to In-class Example 2In order to compare the performances among different investments, it is important to make sure that you are doing so on equal terms. In other words, you need to “compare apples with apples”. One way to do this is to annualize all your returns before making the comparisons. There are two common annualized returns: (a) annual percentage rates (APR) and (b) effective annual rate (EAR).(a) Annual percentage rate (APR)Explain how the APR of an investment is determined. What does this measurement ignored?(b) Effective annual rate (EAR)Explain the difference between APR and EAR.The relationship between the EAR and the APR of an investment can be expressed with the formula as follows:nn APR EAR ⎪⎭⎫ ⎝⎛+=+11where n = number of compounding period per year.Keep in mind that the formula has to be “modified” when you are dealing with continuous compounding. In this case, the relationship between EAR and APR is determined by the formula as follows:1-=APR e EARRefer to In-class Example 32. Uncertainty and its Impact on ReturnWhen it comes to investments, there are always some levels of uncertainty associated with future holding period returns. Such uncertainty is commonly known as the risk of the investment.What cause s the uncertainty (or volatility) of an investment’s returns? The answer depends on the nature of the investment, the performance of the economy, and other factors. In other words, when you “dissect” the uncertainty of an investment’s return, you will real ize that it is made up of different components. The following are some of the components:(a) Business risk : This is the uncertainty regarding the earnings (or profitability) of a firm as a result ofchanges in demand, input prices, and technological obsolescence.(b) Default risk : This is the uncertainty regarding an issuing firm’s ability to pay interest, principal, etc. on itsdebt instruments.(c) Inflation risk : This is the uncertainty over future rates of inflation. If the return from an investment is barelykee ping up with the rate of inflation, an investor’s purchasing power will be eroded as time goes on. In other words, the investor will receive a lesser amount of purchasing power than what was originally invested because the cost of buying everything has gone up. Inflation risk is also known as purchasing power risk .(d) Market risk : This represents the changes in an investment’s price (or market value) as a result of an eventthat affects the entire market. An example is the impact of a market correction or a market crash on an investment’s return.(e) Interest rate risk : This represents the fluctuation in the value of an investment when market interest ratechanges. This has a big impact on interest-paying investments because as market interest rate rises (falls), a n investor’s money is tied up in a bond that pay less (more) than the going rate, and hence the value of the investor’s bond decreases (increases).(f) Liquidity risk : This is the risk of not being able to sell an investment immediately with a reasonable price. (g) Political risk : This is caused by changes in the political environment that affect an investment’s marketvalue. Political risk can be classified as either domestic or foreign political risk. An example of domestic political risk is a change in the tax laws, and an example of foreign political risk is a change in a foreign government’s policy regarding capital outflow.(h) Callability risk : This is the risk that an investment is recalled (or retired) prior to the original stated date.This type of risk is most applicable to long-term bonds and preferred stocks. This usually happens when the issuing firms find the market conditions favorable in “refinancing” such investments.(i) Exchange rate risk : This is the uncertainty regarding the changes in exchange rates that might affect thevalue of an investment. Exchange rate uncertainty has an impact on both domestic and foreign investments. Why is this the case?It is important to understand that the components of risk present and the “size” of each component differ f rom one investment to another investment. For example, certain investments have no liquidity risk while other investments have extremely high level of liquidity risk.Now that you knew more about the concept of risk, how do we measure it? We can determine the risk of an investment using the scenario analysis approach. This approach is based on an investment’s expected return rather than its historical return.In your own words, explain what the expected return represents (or measures).The expected return of an investment can be determined using the following formula:)(...)()(][)(2211n n i i p r p r p r p r r E ⨯++⨯+⨯=⨯=∑where i p = probability of a given scenario and n = the number of scenarios.The above formula should look familiar to you since you would have encountered it in statistics and introductory finance courses. Now that you are once again comfortable with the formula to calculate the expected return, lets take a look at a slightly more complex formula for calculating the standard deviation, which is a common measurement for risk.[][]22)()(r E p r i i -⨯=∑σIt is easier to understand the concept of standard deviation when we look at the distribution curve of the returns of an asset. The following graph depicts the distribution curves of the returns of two assets, A and B, which have the same expected return.Frequency Return Mean Asset AAsset BWe know the standard deviation measures how far the returns deviate from the asset’s average return. In the preceding graph, we know that the standard deviation of Asset B is greater than that of Asset A because we can visually verify that the returns of Asset B deviate more from its mean return. Another way to compare the volatility (or standard deviation) of two assets is to look at the shapes of the distribution curves. The flatter (or more spread out) the curve, the more volatile the returns; and the narrower the curve, the less volatile the returns.Refer to In-class Example 4It is important to understand that the formula above is an ex-ante formula. In other words, it tries to “predict” the volatility of a particular investment’s returns in the future. However, it is also crucial to analyze how the investment had behaved in the past. In order to accomplish this, we will need to analyze the volatility of the investment’s historical return.The concepts behind standard deviations based on expected returns and historical returns are very similar. They both look at the average deviation of the returns from the investment’s average return. The only differ ence is that one uses the expected return for the average return while the other uses average historical return for the average return (which is denoted by x ). The following is the formula for calculating the standard deviation based on historical returns:[]122--=∑n x n x sIt is important to note that most investors use a small sample of an investment’s historical returns to determine its volatility. As a result, we will be determining the standard deviation of an investment’s return based on a sample rather than the population. In other words, we are solving for the sample standard deviation, and this is usually denoted by s rather than σ (as indicated by the formula above).Refer to In-class Example 5。
cbok完整版
CANDIDATE BODY OF KNOWLEDGE TMThe CFA curriculum is grounded in the practice of the investment profession. CFA Institute periodically conducts a job analysis involving CFA charterholders around the world to determine those elements of the body of investment knowledge and skills that are important to charterholders in their practice. The most recent job analysis was completed in 2001. The survey results define the Candidate Body of Knowledge (CBOK TM) and to determine how much emphasis each of the major topic areas receives on the CFA examinations.The CBOK is organized into four major topic areas: ethical and professional standards, tools and inputs for investment valuation and management, asset valuation, and portfolio management and performance presentation.Two features of the CBOK are especially relevant to the CFA examinations. First, the curriculum for each level of the CFA Program is organized primarily around a functional area: The Level I study program emphasizes tools and inputs and includes an introduction toasset valuation and portfolio management techniques.The Level II study program emphasizes asset valuation and includes applications of the tools and inputs (including economics, financial statement analysis, and quantitativemethods) in asset valuation.The Level III study program emphasizes portfolio management and includes strategiesfor applying the tools, inputs, and asset valuation models in managing equity, fixedincome, and derivative investments for individuals and institutions.Second, because they are an integral part of the other three functional areas of investment management, ethical and professional standards are covered at all three levels of the curriculum.CFA® CANDIDATE BODY OF KNOWLEDGERevised 2001I.ETHICAL AND PROFESSIONAL STANDARDSA.Professional Standards of Practice1.The Code of Ethics2.Standards of Professional Conducta.Standard I: Fundamental responsibilitiesb.Standard II: Relationships with and responsibilities to the profession(1)Use of professional designation(2)Professional misconduct(3)Prohibition against plagiarismc.Standard III: Relationships with and responsibilities to the employer(1)Obligation to inform employer of code and standards(2)Duty to employer(3)Disclosure of conflicts to employer(4)Disclosure of additional compensation arrangements(5)Responsibilities of supervisorsd.Standard IV: Relationships with and responsibilities to clients and prospects(1)Reasonable basis and representations(2)Research reports(3)Independence and objectivity(4)Fiduciary duties(5)Portfolio investment recommendations and actions(6)Fair dealing(7)Priority of transactions(8)Preservation of confidentiality(9)Prohibition against misrepresentation(10) Disclosure of conflicts to clients and prospects(11) Disclosure of referral feese.Standard V: Relationships with and responsibilities to the investing public(1)Prohibition against use of material nonpublic information(2)Performance presentation3.Disciplinary sanctions for violationsB.Topical Issues1.Corporate governance2.Soft dollar standards3.Fiduciary duty4.Insider tradinga.Mosaic Theoryb.Selective disclosure vs. full disclosure5.Personal investingII.QUANTITATIVE METHODSA.Time Value of Money1.Future value of a single cash flowa.Calculating the future value of a single cash flowb.Frequency of compoundingc.Continuous compoundingd.Annual and effective interest rates2.Future value of a series of cash flowsa.Equal cash flows(1)Ordinary annuity(2)Annuity dueb.Unequal cash flows3.Present value of a single cash flowa.Calculating the present value of a single cash flowb.Frequency of compounding4.Present value of a series of cash flowsa.Calculating the present value of a series of equal cash flows(1)Ordinary annuity(2)Annuity dueb.Present value of a series of unequal cash flowsc.Present value of an infinite series of equal cash flows (perpetuity)5.Equivalence of present and future value6.Other applications of the time value of moneya.Solving for interest rates and growth ratesb.Solving for the number of periodsc.Solving for the size of annuity payments7.Discounted cash flow analysis present value ruleb.Internal rate of return rulec.Problems with the internal rate of return rule8.Simple interest and money-market conventionsa.Bank-discount yieldb.Periodic yieldc.Bond-equivalent yieldd.Effective annual yielde.CD-equivalent yield9.Investment measures of returna.Dollar-weighted rate of returnb.Time-weighted rate of returnB.Basic Statistical Concepts1.Nature of statisticsa.Populations and samplesb.Types of statistical data(1)Nominal data(2)Ordinal data(3)Interval data(4)Ratio data2.Frequency distributions3.Measures of central tendencya.Population meanb.Sample meanc.Mediand.Modee.Quartiles, quintiles, deciles, and percentilesf.Weighted meang.Geometric mean(1)Geometric mean return(2)Relationship to arithmetic mean return4.Measures of dispersiona.Measures of absolute dispersion(1)Range(2)Mean absolute deviation(3)Variance and standard deviation(a)Population variance and standard deviation(b)Sample variance and standard deviationb.Relative dispersion5.Measures of skewness6.Measures of kurtosisC.Probability Concepts and Random Variables1.Probability conceptsa.Definitions, including outcome, event, sample space, and mutually exclusiveb.Objective probability(1)Classical probability(2)Empirical concept(3)Subjective probability2.Methods of countinga.Multiplication rule of countingb.Factorial rulec.Permutation rulebination rule3.Random variables and probabilitya.Random variableb.Univariate probability distributionc.Discrete versus continuous random variablesd.Probability density functione.Cumulative density function4.Probability theorems/axiomsa.The complement ruleb.The special rule of additionc.General rule of additiond.Rule of multiplication(1)Independent events(2)Dependent events(3)Decision trees(4)Bayes’ Theorem5.Expected value, variance, and covariance/correlationa.Expected value(1)Random variable(2)Constant times a random variable(3)Sum of random variables(4)Weighted sumb.Multivariate probability distributionc.Variance(1)Random variable(2)Constant times a random variable(3)Random variable plus a constantd.Covariance(1)Between two random variables(2)Constant times a random variablee.Correlation coefficient between two random variablesf.Covariance among more than two random variables6.Standardized random variablesmon Probability Distributions1.Discrete random variablesa.Discrete uniform distributionb.Binomial distributionc.Expected value and variance of a binomial random variable2.Continuous probability distributionsa.Uniform distributionb.Normal distributionc.Standard normal distributiond.Cumulative density for the standard normal distributione.Finding standard normal distribution areasf.Confidence intervalsg.Mean-variance portfolio selectionh.Monte Carlo simulation3.Lognormal distributiona.Lognormal stock pricesb.Price relativesE.Sampling and Estimation1.Random samplesa.Sampling in investment analysisb.Time series and cross-sectional datac.Data-snooping biasd.Sample selection bias(1)Survivorship bias(2)Delisting bias2.Distribution of the sample mean3.Point and interval estimates of the population meana.Point estimatorsb.Confidence intervals when sampling from a normal distribution with knownvariancec.Confidence intervals when sampling from a normal distribution with unknownvarianceing t distribution tablese.Confidence intervals when sampling from a non-normal populationF.Statistical Inference and Hypothesis Testing1.Establishing hypothesesa.Null hypothesisb.Alternative hypothesis2.Testing hypothesesa.Test criterionb.Two-tail testsc.One-tail testsd.Type I error (rejecting a true null hypothesis)e.Type II error (failing to reject a false null hypothesis)3.Types of hypothesis testinga.Testing the mean of a single sample when the population standard deviation is notknownb.Testing the difference between the population means of two samples(1)Population variances are known(2)Population variances are not known but assumed equal(3)Dependent samples: paired datac.Testing the proportion of a single sample: significance tests with small samplesd.Significance tests and confidence intervals for a single variance(1)Confidence interval for the sample variance(2)Hypothesis test about a single population variance(3)Testing the equality of two variances: the F-distribution4.Analysis of variance (ANOVA)a.Single-Factor analysis of varianceb.F-test for equality of factor-level meansputing sums of squaresd.Degrees of freedomG.Correlation Analysis and Linear Regression1.Correlation analysisa.Scatter plots and correlation analysisputing the correlation coefficientc.Testing the significance of the correlation coefficient2.Linear regressiona.Linear regression with one independent variableb.Assumptions of the linear regression modelc.Standard error of estimated.Coefficient of determinatione.Confidence intervals and testing hypotheses(1)Significance level(2)Standard error of the estimated coefficient(3)Critical value for rejecting the null hypothesisf.Prediction intervalsg.Limitations to regression analysisH.Multivariate Regression1.Multiple linear regressiona.Assumptions of the multiple linear regression modelb.Standard error of estimate in multiple linear regressionc.Predicting the dependent variable in a multiple regression modeld.Testing whether all the regression coefficients are equal to zeroing dummy variables in regressions3.Heteroskedasticitya.Types of heteroskedasticityb.Tests that evaluate heteroskedasticityc.Correcting for heteroskedasticity4.Serial correlation and Durbin-Watson testa.Consequences of serial correlationb.Durbin-Watson statistic to test for serial correlationc.Correcting for serial correlationd.Generalized least squares5.Multicollinearity6.Models with qualitative dependent variablesI.Time Series Analysis1.Trends2.Limitations to trends3.Fundamental issues in time series4.Autoregressive time series modelsa.Mean reversionb.Multiperiod forecastsc.Instability of regression coefficients5.Random walks and unit roots6.Moving-average time series modelsa.Smoothing past values with a moving averageb.Moving average models for forecasting7.Seasonality in time-series modelsJ.Portfolio Concepts1.Optimal portfolios with three assets2.Minimum Variance Frontier for many assets3.Instability in the Minimum Variance Frontier4.Diversification and portfolio size5.Risk free assets and the trade-off between risk and return6.The Capital Allocation Line7.The Capital Asset Pricing Model (CAPM)8.Estimates based on historical means, variances and covariances9.The Market Model10.Adjusted-beta Market Models11.The structure of factor models12.Arbitrage Pricing Theory (APT) and the factor model13.Multifactor models in current practiceIII.E CONOMICSA.Market Forces of Supply and Demand1.Determinants of individual demand2.Determinants of individual supply3.Equilibrium price4.Analyzing changes in equilibrium5.How prices allocate resourcesB.Elasticity1.Determinants of price elasticity of demand2.Determinants of price elasticity of supply3.Microeconomic government policies4.Analysis of price ceilings5.Analysis of price floors6.Tax incidence7.Market efficiencyC.The Firm and Industry Organizationanization of the business firma.Basic types of business firmsb.The principal-agent problem2.Costs of productiona.Opportunity cost, explicit cost, and implicit costb.Accounting cost versus opportunity costc.The production functiond.Fixed and variable costse.Average and marginal costf.Cost curves and their shapesg.Diminishing returns and cost curvesh.Output and costs in the long run3.Firms in competitive marketsa.Definition of competitionb.Revenue of a competitive firmc.Profit maximization for the competitive firmd.Accounting profit and economic profite.The competitive firm’s supply curvef.The supply curve in a competitive market4.Monopolya.Barriers to entry (e.g., economics of scale, government licensing, patents, controlof essential resources)b.How monopolies make production and pricing decisionsc.Public policy and monopolies5.Oligopolya.Duopolyb.Equilibrium for an oligopolyc.Game theory and the economics of cooperationd.Public policy when entry barriers are high6.Monopolistic competitiona.Price and output in competitive markets with differentiated productsb.Allocative efficiency in monopolistic competitionD.Supply and Demand for Productive Resources1.Demand for resourcesa.Marginal productivity and the firm’s hiring decisionb.Supply, demand, and resource prices2.Capital marketsa.Interest ratesb.Determination of interest ratesc.Money rate versus real rate of interestd.Interest rates and riskE.Measuring National Income1.Gross Domestic Product (GDP)ponents of GDP3.Real versus nominal GDPa.GDP deflatoring the GDP deflator to derive real GDPc.The consumer price index4.Problems with GDP as a measure of national productF.Economic Fluctuations and Unemployment1.Descriptive terms in business cycle analysis2.Index of leading economic indicators3.Types of unemployment4.Problems of measuring unemploymentG.The Monetary System1.Role of a central bank2.Tools of monetary controla.Open-market operationsb.Reserve requirementsc.Discount rateH.Inflation: Causes and Consequences1.Causes of inflation2.Quantity theory of money3.Equation of exchange4.Deflation/stagflationI.International Trade1.Gains from specialization and trade2.Economics of trade restrictionsa.Economics of tariffsb.Economics of quotasc.Other nontariff barriers to traded.Exchange-rate controls as a trade restrictionJ.International Finance1.Foreign exchange marketanization of the foreign exchange marketb.The spot marketc.The forward marketd.Interest rate parity theory2.Determination of exchange ratesa.Nominal exchange ratesb.Real exchange ratesc.Purchasing-power parity3.Balance of paymentsa.Current-account transactionsb.Capital-account transactionsc.Official reserve accountK.The Macroeconomics of an Open Economy1.Supply and demand for loanable funds and for foreign-currency exchangea.The market for loanable fundsb.The market for foreign-currency exchange2.Equilibrium in the open economy foreign investment flowsernment budget deficitsc.Trade policyd.Political instability and capital flightL.Aggregate Demand and Aggregate Supply1.The aggregate demand curvea.Reasons for downward sloping aggregate demand curve (e.g., wealth effect,interest rate effect, exchange rate effect)b.Shifts in the aggregate demand curve2.The aggregate supply curvea.Short-run aggregate supply curveb.Long-run aggregate supply curvec.Shifts in the short-run aggregate supply curve3.The influence of monetary policy on aggregate demanda.Money supply and money demandb.Transmission of monetary policyc.Unanticipated expansionary monetary policyd.Unanticipated restrictive monetary policye.Timing of monetary policyf.Anticipated monetary policy4.The influence of fiscal policy on aggregate demanda.Fiscal policy and the crowding-out effectb.Problems of proper timing of fiscal policyc.Fiscal policy as a stabilization toold.Supply-side effects of fiscal policy5.Expectations and economic policya.Adaptive expectations hypothesisb.Rational expectations hypothesisc.The differences between adaptive and rational expectationsd.The implications of adaptive and rational expectationse.Activist versus nonactivist stabilization policyM.Sources of Economic Growth1.Physical capital2.Human capital3.Technological progress4.Institutional environment (e.g., property rights, political stability, competitivemarkets, stable money and price, an open economy, moderate marginal tax rates) ernment Regulation1.Regulation of business2.Costs of regulationO.Natural Resource MarketsP.Relationship of Economic Activity to the Investment ProcessIV.FINANCIAL STATEMENT ANALYSISA.Financial Reporting System1.General concepts and rules2.U.S. Generally Accepted Accounting Principles (GAAP)3.International Accounting Standards (IAS)B.Principal Financial Statements1.Balance sheeta.Format and classification (e.g., assets, liabilities, stockholders’ equity)b.Measurement of assets and liabilitieses of the balance sheet2.Income statementa.Format and classificationb.The accrual concept of incomec.Revenue and expense recognition(1)General principles(2)Percentage-of-completion method(3)Completed contract method(4)Installment method(5)Cost recovery methodd.Nonrecurring items (e.g., extraordinary items, unusual items, restructuringcharges, discontinued operations, changes in accounting standards, disclosure ofnonrecurring items, analysis of nonrecurring items)e.Earnings qualityf.Earnings per share3.Statement of cash flowsa.Direct and indirect method cash flow statementsb.Preparing a direct method statement of cash flows (e.g., cash flow fromoperations, investing cash flow, financing cash flow)c.Indirect methodd.Reported versus observed changes in assets and liabilities (e.g., acquisitions anddivestitures, translation of foreign subsidiaries)e.Analysis of cash flow information4.Statement of stockholders’ equitya.Format, classification, and usesb.Other comprehensive income5.Other sources of financial informationa.Letter to shareholdersb.Footnotesc.Management discussion and analysisd.Segment/disaggregated informatione.Operating and performance dataf.Forward looking information/plansg.Role of the auditorh.Annual report to regulators (e.g., Form 10K in U.S.)i.Proxy statementj.Change in material status report (e.g., Form 8K in U.S.)k.Quarterly reportsl.News releasesC.Earnings Quality and Nonrecurring Items1.Earnings qualitya.Stock optionsb.Revenue recognitionc.Assumptionsd.Reserves2.Nonrecurring itemsa.Extraordinary itemsb.Restructuring chargesc.Unusual itemsD.Analysis of Inventories1.Relationship between inventory and cost of goods solda.Stable pricesb.Rising prices2.Inventory methodsa.Specific identificationb.First-in, first-out (FIFO)c.Average costst-in, first-out (LIFO)e.Adjustment from LIFO to FIFO(1)Adjustment of inventory balances(2)Adjustment of cost of goods soldf.Adjustment of income to current cost incomeg.Effect of LIFO/FIFO choice on financial ratios (e.g., profitability, liquidity,activity, solvency)h.Analysis implications of changes to and from LIFOparison of companies using different inventory valuation methodsj.International comparisons of inventory accounting methodsE.Analysis of Long-Lived Assets1.Capitalization versus expensinga.Financial statement effects of capitalization (e.g., income variability, profitability,cash flow from operations, leverage ratios)b.Capitalization of interest costsc.Intangible assets (e.g., research and development, patents and copyrights,franchises and licenses, brands and trademarks, goodwill)d.Asset revaluatione.International differencesf.Adjustments for capitalization and expensingg.Need for analytic adjustments2.Depreciation methodsa.Alternatives (e.g., annuity or sinking fund depreciation, straight line depreciation,accelerated depreciation)b.Depletionc.Amortizationd.Depreciation method disclosurese.Impact of depreciation methods on financial statementsf.Accelerated depreciation and taxesg.Impact of inflation on depreciationh.Changes in depreciation method3.Analysis of fixed asset disclosures4.Impairment of long-lived assets5.Retirement of long-term assets6.Liabilities for closure and environmental costsF.Analysis of Income Taxes1.Issues in tax and financial reporting2.Deferred tax assets and liabilitiesa.Accounting for deferred taxesb.Analysis of deferred tax assetsc.Non-U.S. financial reporting (e.g., IASC standards)G.Analysis of Financing Liabilities1.Analysis of balance sheet debta.Analysis of current liabilitiesb.Analysis of long-term debtc.Analysis of debt with equity features (e.g., convertible bonds, warrants,commodity bonds, perpetual debt, preferred stock)d.Analysis of changes in interest rates (e.g., estimating the market value of a firm’sdebt)e.Retirement of debt prior to maturity2.Bond covenants3.International accounting and reporting practices for balance sheet debtH.Analysis of Leases1.Incentives for leasing2.Lease classification issues from lessee perspective (e.g., capital lease, operating lease)3.Financial reporting by lessees4.Financial reporting by lessors5.Financial reporting for sales with leasebacksI.Analysis of Off-Balance-Sheet Assets and Liabilities1.Disclosure of off-balance-sheet assets2.Disclosure of off-balance-sheet liabilities3.Take-or-pay and throughput arrangements4.Sale of receivables5.Finance subsidiaries6.Joint ventures and investment in affiliatesJ.Analysis of Pensions, Stock Compensation, and Other Employee Benefits1.Disclosuresponents of pension costb.Plan statusc.Reconciliationd.Assumptions used to calculate pension cost and obligations2.Analysis of pension costs and liabilitya.Importance of assumptions(1)Factors affecting benefit obligations (e.g., service cost, interest cost, actuarialgains and losses, prior service cost from plan amendments, benefits paid)(2)Factors affecting plan assets (e.g., employer contribution, return on assets,benefits paid)(3)Factors affecting pension expense (e.g., service cost and interest cost,expected return on assets, amortization of gains or losses, amortization ofprior service cost, amortization of transition asset or liability)b.Analysis of plan status, costs, and cash flowsc.Impact of pension reporting on corporate earnings3.Employee stock compensation plansa.Disclosuresb.Analysis of costs and liabilityK.Analysis of Inter-Corporate Investments1.Accounting for marketable securitiesa.Cost methodb.Market methodc.Lower of cost or market methodd.U.S. and international accounting requirements2.Analysis of marketable securitiesa.Separation of operating from investment resultsb.Effects of classification of marketable securitiesc.Analysis of investment performance3.Equity method of accountinga.Conditions for useb.Equity accounting and analysis4.Consolidations policy and proceduresparison of consolidation with the equity methodb.Analysis of minority interestc.Non-U.S. consolidation practicesd.Analysis of segment dataL.Analysis of Business Combinations1.Accounting for acquisitions2.Effects of accounting methods3.International differences in accounting for business combinations4.Analysis of goodwill5.Choosing the acquisition method6.Spin-offs and tracking stocksM.Analysis of Multinational Operations1.Effects of exchange rate changes on a firm’s actual and reported performancea.Flow effectb.Holding gain/loss effect2.Basic accounting issuesa.Choice of exchange rates (e.g., historical rate or current rate)b.Assets or liabilities to be adjusted for exchange rate changesc.Treatment of translation gains and losses3.Prescribed foreign currency translation4.Choice of the functional currency for a foreign subsidiaryparison of translation and remeasurementa.Income statement effectsb.Balance sheet effectsc.Impact on financial ratiosd.Impact on reported cash flows6.Analysis of foreign currency disclosuresa.Exchange rate changes: exposure and effectsN.Ratio and Financial Analysismon-size statements2.Activity analysis and turnover ratiosa.Short-term and long-term activity ratiosb.Turnover ratios (inventory, receivables, payables, working capital, fixed asset andtotal asset)3.Liquidity analysisa.Length of cash cycleb.Working capital ratios4.Long-term debt analysisa.Debt covenantsb.Debt ratiosc.Interest coverage ratios5.Profitability analysisa.Return on sales (gross margin, operating margin, pretax margin, profit margin)b.Return on investment (e.g., return on assets, return on total capital, return onequity)6.Operating and financial leverage7.Earnings per share (EPS)a.Basic EPSb.Diluted EPSc.Weighted-average number of common shares outstandingd.Convertible securitiese.Options and warrantsf.Contingent shares8.Other ratios and value metricsa.Earnings before interest, taxes, depreciation and amortization (EBITDA)b.Price-to-earnings (P/E)c.Price-to-book value (P/B)9.Integrated ratio analysis10.Valuation implications of financial statement analysisa.Inter-corporate investmentsb.Business combinationsc.Multinational operationsd.Ratio and financial analysisV.CORPORATE FINANCEA.Fundamental Issues1.Forms of business organizationa.Sole proprietorshipb.Partnershipc.Corporation2.Corporate governance issuesa.Agency relationships (i.e., stockholders, management, other stakeholders)b.Managerial incentives to act in stockholders’ interestsB.Capital Investment Decisions1.Investment decision criteria present value (NPV) approachb.Payback period rulec.Discounted payback ruled.Average accounting returne.Internal rate of return (IRR) approachf.Profitability index2.Cash flow projectionsa.Incrementalmon pitfalls (e.g., sunk costs, opportunity costs, side effects, net workingcapital, financing costs)c.Project cash flows and alternative definitions of operating cash flowses of discounted cash flow analysis3.Project analysis and evaluationa.Scenario analysisb.Sensitivity analysisc.Simulation analysis4.Capital rationingC.Business and Financial Risk1.Breakeven analysisa.Fixed versus variable costsb.Accounting break-even2.Operating leveragea.Implications (e.g., forecasting risk)b.Measurement (i.e., degree of operating leverage)3.Financial leveragea.Implications (e.g., forecasting risk)b.Measurement (e.g., degree of financial leverage)4.Total combined leverageD.Long Term Financial Policy1.Cost of capitala.Required return and cost of capitalb.Cost of equity (e.g., dividend growth model approach and security market lineapproach)c.Cost of debt and preferred stock。
罗斯《公司理财》第9版精要版英文原书课后部分章节答案
CH5 11，13，18，19，2011.To find the PV of a lump sum, we use:PV = FV / (1 + r)tPV = $1,000,000 / (1.10)80 = $488.1913.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for r, we get:r = (FV / PV)1 / t– 1r = ($1,260,000 / $150)1/112– 1 = .0840 or 8.40%To find the FV of the first prize, we use:FV = PV(1 + r)tFV = $1,260,000(1.0840)33 = $18,056,409.9418.To find the FV of a lump sum, we use:FV = PV(1 + r)tFV = $4,000(1.11)45 = $438,120.97FV = $4,000(1.11)35 = $154,299.40Better start early!19. We need to find the FV of a lump sum. However, the money will only be invested for six years,so the number of periods is six.FV = PV(1 + r)tFV = $20,000(1.084)6 = $32,449.3320.To answer this question, we can use either the FV or the PV formula. Both will give the sameanswer since they are the inverse of each other. We will use the FV formula, that is:FV = PV(1 + r)tSolving for t, we get:t = ln(FV / PV) / ln(1 + r)t = ln($75,000 / $10,000) / ln(1.11) = 19.31So, the money must be invested for 19.31 years. However, you will not receive the money for another two years. Fro m now, you’ll wait:2 years + 19.31 years = 21.31 yearsCH6 16，24，27，42，5816.For this problem, we simply need to find the FV of a lump sum using the equation:FV = PV(1 + r)tIt is important to note that compounding occurs semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get:FV = $2,100[1 + (.084/2)]34 = $8,505.9324.This problem requires us to find the FVA. The equation to find the FVA is:FVA = C{[(1 + r)t– 1] / r}FVA = $300[{[1 + (.10/12) ]360 – 1} / (.10/12)] = $678,146.3827.The cash flows are annual and the compounding period is quarterly, so we need to calculate theEAR to make the interest rate comparable with the timing of the cash flows. Using the equation for the EAR, we get:EAR = [1 + (APR / m)]m– 1EAR = [1 + (.11/4)]4– 1 = .1146 or 11.46%And now we use the EAR to find the PV of each cash flow as a lump sum and add them together: PV = $725 / 1.1146 + $980 / 1.11462 + $1,360 / 1.11464 = $2,320.3642.The amount of principal paid on the loan is the PV of the monthly payments you make. So, thepresent value of the $1,150 monthly payments is:PVA = $1,150[(1 – {1 / [1 + (.0635/12)]}360) / (.0635/12)] = $184,817.42The monthly payments of $1,150 will amount to a principal payment of $184,817.42. The amount of principal you will still owe is:$240,000 – 184,817.42 = $55,182.58This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal will be:Balloon payment = $55,182.58[1 + (.0635/12)]360 = $368,936.5458.To answer this question, we should find the PV of both options, and compare them. Since we arepurchasing the car, the lowest PV is the best option. The PV of the leasing is simply the PV of the lease payments, plus the $99. The interest rate we would use for the leasing option is thesame as the interest rate of the loan. The PV of leasing is:PV = $99 + $450{1 – [1 / (1 + .07/12)12(3)]} / (.07/12) = $14,672.91The PV of purchasing the car is the current price of the car minus the PV of the resale price. The PV of the resale price is:PV = $23,000 / [1 + (.07/12)]12(3) = $18,654.82The PV of the decision to purchase is:$32,000 – 18,654.82 = $13,345.18In this case, it is cheaper to buy the car than leasing it since the PV of the purchase cash flows is lower. To find the breakeven resale price, we need to find the resale price that makes the PV of the two options the same. In other words, the PV of the decision to buy should be:$32,000 – PV of resale price = $14,672.91PV of resale price = $17,327.09The resale price that would make the PV of the lease versus buy decision is the FV of this value, so:Breakeven resale price = $17,327.09[1 + (.07/12)]12(3) = $21,363.01CH7 3，18，21，22，313.The price of any bond is the PV of the interest payment, plus the PV of the par value. Notice thisproblem assumes an annual coupon. The price of the bond will be:P = $75({1 – [1/(1 + .0875)]10 } / .0875) + $1,000[1 / (1 + .0875)10] = $918.89We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:PVIF R,t = 1 / (1 + r)twhich stands for Present Value Interest FactorPVIFA R,t= ({1 – [1/(1 + r)]t } / r )which stands for Present Value Interest Factor of an AnnuityThese abbreviations are short hand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in remainder of the solutions key.18.The bond price equation for this bond is:P0 = $1,068 = $46(PVIFA R%,18) + $1,000(PVIF R%,18)Using a spreadsheet, financial calculator, or trial and error we find:R = 4.06%This is the semiannual interest rate, so the YTM is:YTM = 2 4.06% = 8.12%The current yield is:Current yield = Annual coupon payment / Price = $92 / $1,068 = .0861 or 8.61%The effective annual yield is the same as the EAR, so using the EAR equation from the previous chapter:Effective annual yield = (1 + 0.0406)2– 1 = .0829 or 8.29%20. Accrued interest is the coupon payment for the period times the fraction of the period that haspassed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are four months until the next coupon payment, so two months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $74/2 × 2/6 = $12.33And we calculate the clean price as:Clean price = Dirty price – Accrued interest = $968 – 12.33 = $955.6721. Accrued interest is the coupon payment for the period times the fraction of the period that haspassed since the last coupon payment. Since we have a semiannual coupon bond, the coupon payment per six months is one-half of the annual coupon payment. There are two months until the next coupon payment, so four months have passed since the last coupon payment. The accrued interest for the bond is:Accrued interest = $68/2 × 4/6 = $22.67And we calculate the dirty price as:Dirty price = Clean price + Accrued interest = $1,073 + 22.67 = $1,095.6722.To find the number of years to maturity for the bond, we need to find the price of the bond. Sincewe already have the coupon rate, we can use the bond price equation, and solve for the number of years to maturity. We are given the current yield of the bond, so we can calculate the price as: Current yield = .0755 = $80/P0P0 = $80/.0755 = $1,059.60Now that we have the price of the bond, the bond price equation is:P = $1,059.60 = $80[(1 – (1/1.072)t ) / .072 ] + $1,000/1.072tWe can solve this equation for t as follows:$1,059.60(1.072)t = $1,111.11(1.072)t– 1,111.11 + 1,000111.11 = 51.51(1.072)t2.1570 = 1.072tt = log 2.1570 / log 1.072 = 11.06 11 yearsThe bond has 11 years to maturity.31.The price of any bond (or financial instrument) is the PV of the future cash flows. Even thoughBond M makes different coupons payments, to find the price of the bond, we just find the PV of the cash flows. The PV of the cash flows for Bond M is:P M= $1,100(PVIFA3.5%,16)(PVIF3.5%,12) + $1,400(PVIFA3.5%,12)(PVIF3.5%,28) + $20,000(PVIF3.5%,40)P M= $19,018.78Notice that for the coupon payments of $1,400, we found the PVA for the coupon payments, and then discounted the lump sum back to today.Bond N is a zero coupon bond with a $20,000 par value, therefore, the price of the bond is the PV of the par, or:P N= $20,000(PVIF3.5%,40) = $5,051.45CH8 4，18，20，22，24ing the constant growth model, we find the price of the stock today is:P0 = D1 / (R– g) = $3.04 / (.11 – .038) = $42.2218.The price of a share of preferred stock is the dividend payment divided by the required return.We know the dividend payment in Year 20, so we can find the price of the stock in Year 19, one year before the first dividend payment. Doing so, we get:P19 = $20.00 / .064P19 = $312.50The price of the stock today is the PV of the stock price in the future, so the price today will be: P0 = $312.50 / (1.064)19P0 = $96.1520.We can use the two-stage dividend growth model for this problem, which is:P0 = [D0(1 + g1)/(R –g1)]{1 – [(1 + g1)/(1 + R)]T}+ [(1 + g1)/(1 + R)]T[D0(1 + g2)/(R –g2)]P0= [$1.25(1.28)/(.13 – .28)][1 – (1.28/1.13)8] + [(1.28)/(1.13)]8[$1.25(1.06)/(.13 – .06)]P0= $69.5522.We are asked to find the dividend yield and capital gains yield for each of the stocks. All of thestocks have a 15 percent required return, which is the sum of the dividend yield and the capital gains yield. To find the components of the total return, we need to find the stock price for each stock. Using this stock price and the dividend, we can calculate the dividend yield. The capital gains yield for the stock will be the total return (required return) minus the dividend yield.W: P0 = D0(1 + g) / (R–g) = $4.50(1.10)/(.19 – .10) = $55.00Dividend yield = D1/P0 = $4.50(1.10)/$55.00 = .09 or 9%Capital gains yield = .19 – .09 = .10 or 10%X: P0 = D0(1 + g) / (R–g) = $4.50/(.19 – 0) = $23.68Dividend yield = D1/P0 = $4.50/$23.68 = .19 or 19%Capital gains yield = .19 – .19 = 0%Y: P0 = D0(1 + g) / (R–g) = $4.50(1 – .05)/(.19 + .05) = $17.81Dividend yield = D1/P0 = $4.50(0.95)/$17.81 = .24 or 24%Capital gains yield = .19 – .24 = –.05 or –5%Z: P2 = D2(1 + g) / (R–g) = D0(1 + g1)2(1 + g2)/(R–g2) = $4.50(1.20)2(1.12)/(.19 – .12) = $103.68P0 = $4.50 (1.20) / (1.19) + $4.50 (1.20)2/ (1.19)2 + $103.68 / (1.19)2 = $82.33Dividend yield = D1/P0 = $4.50(1.20)/$82.33 = .066 or 6.6%Capital gains yield = .19 – .066 = .124 or 12.4%In all cases, the required return is 19%, but the return is distributed differently between current income and capital gains. High growth stocks have an appreciable capital gains component but a relatively small current income yield; conversely, mature, negative-growth stocks provide a high current income but also price depreciation over time.24.Here we have a stock with supernormal growth, but the dividend growth changes every year forthe first four years. We can find the price of the stock in Year 3 since the dividend growth rate is constant after the third dividend. The price of the stock in Year 3 will be the dividend in Year 4, divided by the required return minus the constant dividend growth rate. So, the price in Year 3 will be:P3 = $2.45(1.20)(1.15)(1.10)(1.05) / (.11 – .05) = $65.08The price of the stock today will be the PV of the first three dividends, plus the PV of the stock price in Year 3, so:P0 = $2.45(1.20)/(1.11) + $2.45(1.20)(1.15)/1.112 + $2.45(1.20)(1.15)(1.10)/1.113 + $65.08/1.113 P0 = $55.70CH9 3，4，6，9，153.Project A has cash flows of $19,000 in Year 1, so the cash flows are short by $21,000 ofrecapturing the initial investment, so the payback for Project A is:Payback = 1 + ($21,000 / $25,000) = 1.84 yearsProject B has cash flows of:Cash flows = $14,000 + 17,000 + 24,000 = $55,000during this first three years. The cash flows are still short by $5,000 of recapturing the initial investment, so the payback for Project B is:B: Payback = 3 + ($5,000 / $270,000) = 3.019 yearsUsing the payback criterion and a cutoff of 3 years, accept project A and reject project B.4.When we use discounted payback, we need to find the value of all cash flows today. The valuetoday of the project cash flows for the first four years is:Value today of Year 1 cash flow = $4,200/1.14 = $3,684.21Value today of Year 2 cash flow = $5,300/1.142 = $4,078.18Value today of Year 3 cash flow = $6,100/1.143 = $4,117.33Value today of Year 4 cash flow = $7,400/1.144 = $4,381.39To find the discounted payback, we use these values to find the payback period. The discounted first year cash flow is $3,684.21, so the discounted payback for a $7,000 initial cost is:Discounted payback = 1 + ($7,000 – 3,684.21)/$4,078.18 = 1.81 yearsFor an initial cost of $10,000, the discounted payback is:Discounted payback = 2 + ($10,000 – 3,684.21 – 4,078.18)/$4,117.33 = 2.54 yearsNotice the calculation of discounted payback. We know the payback period is between two and three years, so we subtract the discounted values of the Year 1 and Year 2 cash flows from the initial cost. This is the numerator, which is the discounted amount we still need to make to recover our initial investment. We divide this amount by the discounted amount we will earn in Year 3 to get the fractional portion of the discounted payback.If the initial cost is $13,000, the discounted payback is:Discounted payback = 3 + ($13,000 – 3,684.21 – 4,078.18 – 4,117.33) / $4,381.39 = 3.26 years6.Our definition of AAR is the average net income divided by the average book value. The averagenet income for this project is:Average net income = ($1,938,200 + 2,201,600 + 1,876,000 + 1,329,500) / 4 = $1,836,325And the average book value is:Average book value = ($15,000,000 + 0) / 2 = $7,500,000So, the AAR for this project is:AAR = Average net income / Average book value = $1,836,325 / $7,500,000 = .2448 or 24.48%9.The NPV of a project is the PV of the outflows minus the PV of the inflows. Since the cashinflows are an annuity, the equation for the NPV of this project at an 8 percent required return is: NPV = –$138,000 + $28,500(PVIFA8%, 9) = $40,036.31At an 8 percent required return, the NPV is positive, so we would accept the project.The equation for the NPV of the project at a 20 percent required return is:NPV = –$138,000 + $28,500(PVIFA20%, 9) = –$23,117.45At a 20 percent required return, the NPV is negative, so we would reject the project.We would be indifferent to the project if the required return was equal to the IRR of the project, since at that required return the NPV is zero. The IRR of the project is:0 = –$138,000 + $28,500(PVIFA IRR, 9)IRR = 14.59%15.The profitability index is defined as the PV of the cash inflows divided by the PV of the cashoutflows. The equation for the profitability index at a required return of 10 percent is:PI = [$7,300/1.1 + $6,900/1.12 + $5,700/1.13] / $14,000 = 1.187The equation for the profitability index at a required return of 15 percent is:PI = [$7,300/1.15 + $6,900/1.152 + $5,700/1.153] / $14,000 = 1.094The equation for the profitability index at a required return of 22 percent is:PI = [$7,300/1.22 + $6,900/1.222 + $5,700/1.223] / $14,000 = 0.983We would accept the project if the required return were 10 percent or 15 percent since the PI is greater than one. We would reject the project if the required return were 22 percent since the PI is less than one.CH10 9，13，14，17，18ing the tax shield approach to calculating OCF (Remember the approach is irrelevant; the finalanswer will be the same no matter which of the four methods you use.), we get:OCF = (Sales – Costs)(1 – t C) + t C DepreciationOCF = ($2,650,000 – 840,000)(1 – 0.35) + 0.35($3,900,000/3)OCF = $1,631,50013.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation = $560,000/5Annual depreciation = $112,000Now, we calculate the aftertax salvage value. The aftertax salvage value is the market price minus (or plus) the taxes on the sale of the equipment, so:Aftertax salvage value = MV + (BV – MV)t cVery often the book value of the equipment is zero as it is in this case. If the book value is zero, the equation for the aftertax salvage value becomes:Aftertax salvage value = MV + (0 – MV)t cAftertax salvage value = MV(1 – t c)We will use this equation to find the aftertax salvage value since we know the book value is zero.So, the aftertax salvage value is:Aftertax salvage value = $85,000(1 – 0.34)Aftertax salvage value = $56,100Using the tax shield approach, we find the OCF for the project is:OCF = $165,000(1 – 0.34) + 0.34($112,000)OCF = $146,980Now we can find the project NPV. Notice we include the NWC in the initial cash outlay. The recovery of the NWC occurs in Year 5, along with the aftertax salvage value.NPV = –$560,000 – 29,000 + $146,980(PVIFA10%,5) + [($56,100 + 29,000) / 1.105]NPV = $21,010.2414.First we will calculate the annual depreciation of the new equipment. It will be:Annual depreciation charge = $720,000/5Annual depreciation charge = $144,000The aftertax salvage value of the equipment is:Aftertax salvage value = $75,000(1 – 0.35)Aftertax salvage value = $48,750Using the tax shield approach, the OCF is:OCF = $260,000(1 – 0.35) + 0.35($144,000)OCF = $219,400Now we can find the project IRR. There is an unusual feature that is a part of this project.Accepting this project means that we will reduce NWC. This reduction in NWC is a cash inflow at Year 0. This reduction in NWC implies that when the project ends, we will have to increase NWC. So, at the end of the project, we will have a cash outflow to restore the NWC to its level before the project. We also must include the aftertax salvage value at the end of the project. The IRR of the project is:NPV = 0 = –$720,000 + 110,000 + $219,400(PVIFA IRR%,5) + [($48,750 – 110,000) / (1+IRR)5]IRR = 21.65%17.We will need the aftertax salvage value of the equipment to compute the EAC. Even though theequipment for each product has a different initial cost, both have the same salvage value. The aftertax salvage value for both is:Both cases: aftertax salvage value = $40,000(1 – 0.35) = $26,000To calculate the EAC, we first need the OCF and NPV of each option. The OCF and NPV for Techron I is:OCF = –$67,000(1 – 0.35) + 0.35($290,000/3) = –9,716.67NPV = –$290,000 – $9,716.67(PVIFA10%,3) + ($26,000/1.103) = –$294,629.73EAC = –$294,629.73 / (PVIFA10%,3) = –$118,474.97And the OCF and NPV for Techron II is:OCF = –$35,000(1 – 0.35) + 0.35($510,000/5) = $12,950NPV = –$510,000 + $12,950(PVIFA10%,5) + ($26,000/1.105) = –$444,765.36EAC = –$444,765.36 / (PVIFA10%,5) = –$117,327.98The two milling machines have unequal lives, so they can only be compared by expressing both on an equivalent annual basis, which is what the EAC method does. Thus, you prefer the Techron II because it has the lower (less negative) annual cost.18.To find the bid price, we need to calculate all other cash flows for the project, and then solve forthe bid price. The aftertax salvage value of the equipment is:Aftertax salvage value = $70,000(1 – 0.35) = $45,500Now we can solve for the necessary OCF that will give the project a zero NPV. The equation for the NPV of the project is:NPV = 0 = –$940,000 – 75,000 + OCF(PVIFA12%,5) + [($75,000 + 45,500) / 1.125]Solving for the OCF, we find the OCF that makes the project NPV equal to zero is:OCF = $946,625.06 / PVIFA12%,5 = $262,603.01The easiest way to calculate the bid price is the tax shield approach, so:OCF = $262,603.01 = [(P – v)Q – FC ](1 – t c) + t c D$262,603.01 = [(P – $9.25)(185,000) – $305,000 ](1 – 0.35) + 0.35($940,000/5)P = $12.54CH14 6、9、20、23、246. The pretax cost of debt is the YTM of the company’s bonds, so:P0 = $1,070 = $35(PVIFA R%,30) + $1,000(PVIF R%,30)R = 3.137%YTM = 2 × 3.137% = 6.27%And the aftertax cost of debt is:R D = .0627(1 – .35) = .0408 or 4.08%9. ing the equation to calculate the WACC, we find:WACC = .60(.14) + .05(.06) + .35(.08)(1 – .35) = .1052 or 10.52%b.Since interest is tax deductible and dividends are not, we must look at the after-tax cost ofdebt, which is:.08(1 – .35) = .0520 or 5.20%Hence, on an after-tax basis, debt is cheaper than the preferred stock.ing the debt-equity ratio to calculate the WACC, we find:WACC = (.90/1.90)(.048) + (1/1.90)(.13) = .0912 or 9.12%Since the project is riskier than the company, we need to adjust the project discount rate for the additional risk. Using the subjective risk factor given, we find:Project discount rate = 9.12% + 2.00% = 11.12%We would accept the project if the NPV is positive. The NPV is the PV of the cash outflows plus the PV of the cash inflows. Since we have the costs, we just need to find the PV of inflows. The cash inflows are a growing perpetuity. If you remember, the equation for the PV of a growing perpetuity is the same as the dividend growth equation, so:PV of future CF = $2,700,000/(.1112 – .04) = $37,943,787The project should only be undertaken if its cost is less than $37,943,787 since costs less than this amount will result in a positive NPV.23. ing the dividend discount model, the cost of equity is:R E = [(0.80)(1.05)/$61] + .05R E = .0638 or 6.38%ing the CAPM, the cost of equity is:R E = .055 + 1.50(.1200 – .0550)R E = .1525 or 15.25%c.When using the dividend growth model or the CAPM, you must remember that both areestimates for the cost of equity. Additionally, and perhaps more importantly, each methodof estimating the cost of equity depends upon different assumptions.Challenge24.We can use the debt-equity ratio to calculate the weights of equity and debt. The debt of thecompany has a weight for long-term debt and a weight for accounts payable. We can use the weight given for accounts payable to calculate the weight of accounts payable and the weight of long-term debt. The weight of each will be:Accounts payable weight = .20/1.20 = .17Long-term debt weight = 1/1.20 = .83Since the accounts payable has the same cost as the overall WACC, we can write the equation for the WACC as:WACC = (1/1.7)(.14) + (0.7/1.7)[(.20/1.2)WACC + (1/1.2)(.08)(1 – .35)]Solving for WACC, we find:WACC = .0824 + .4118[(.20/1.2)WACC + .0433]WACC = .0824 + (.0686)WACC + .0178(.9314)WACC = .1002WACC = .1076 or 10.76%We will use basically the same equation to calculate the weighted average flotation cost, except we will use the flotation cost for each form of financing. Doing so, we get:Flotation costs = (1/1.7)(.08) + (0.7/1.7)[(.20/1.2)(0) + (1/1.2)(.04)] = .0608 or 6.08%The total amount we need to raise to fund the new equipment will be:Amount raised cost = $45,000,000/(1 – .0608)Amount raised = $47,912,317Since the cash flows go to perpetuity, we can calculate the present value using the equation for the PV of a perpetuity. The NPV is:NPV = –$47,912,317 + ($6,200,000/.1076)NPV = $9,719,777CH16 1，4，12，14，171. a. A table outlining the income statement for the three possible states of the economy isshown below. The EPS is the net income divided by the 5,000 shares outstanding. The lastrow shows the percentage change in EPS the company will experience in a recession or anexpansion economy.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 0 0 0NI $14,000 $28,000 $36,400EPS $ 2.80 $ 5.60 $ 7.28%∆EPS –50 –––+30b.If the company undergoes the proposed recapitalization, it will repurchase:Share price = Equity / Shares outstandingShare price = $250,000/5,000Share price = $50Shares repurchased = Debt issued / Share priceShares repurchased =$90,000/$50Shares repurchased = 1,800The interest payment each year under all three scenarios will be:Interest payment = $90,000(.07) = $6,300The last row shows the percentage change in EPS the company will experience in arecession or an expansion economy under the proposed recapitalization.Recession Normal ExpansionEBIT $14,000 $28,000 $36,400Interest 6,300 6,300 6,300NI $7,700 $21,700 $30,100EPS $2.41 $ 6.78 $9.41%∆EPS –64.52 –––+38.714. a.Under Plan I, the unlevered company, net income is the same as EBIT with no corporate tax.The EPS under this capitalization will be:EPS = $350,000/160,000 sharesEPS = $2.19Under Plan II, the levered company, EBIT will be reduced by the interest payment. The interest payment is the amount of debt times the interest rate, so:NI = $500,000 – .08($2,800,000)NI = $126,000And the EPS will be:EPS = $126,000/80,000 sharesEPS = $1.58Plan I has the higher EPS when EBIT is $350,000.b.Under Plan I, the net income is $500,000 and the EPS is:EPS = $500,000/160,000 sharesEPS = $3.13Under Plan II, the net income is:NI = $500,000 – .08($2,800,000)NI = $276,000And the EPS is:EPS = $276,000/80,000 sharesEPS = $3.45Plan II has the higher EPS when EBIT is $500,000.c.To find the breakeven EBIT for two different capital structures, we simply set the equationsfor EPS equal to each other and solve for EBIT. The breakeven EBIT is:EBIT/160,000 = [EBIT – .08($2,800,000)]/80,000EBIT = $448,00012. a.With the information provided, we can use the equation for calculating WACC to find thecost of equity. The equation for WACC is:WACC = (E/V)R E + (D/V)R D(1 – t C)The company has a debt-equity ratio of 1.5, which implies the weight of debt is 1.5/2.5, and the weight of equity is 1/2.5, soWACC = .10 = (1/2.5)R E + (1.5/2.5)(.07)(1 – .35)R E = .1818 or 18.18%b.To find the unlevered cost of equity we need to use M&M Proposition II with taxes, so:R E = R U + (R U– R D)(D/E)(1 – t C).1818 = R U + (R U– .07)(1.5)(1 – .35)R U = .1266 or 12.66%c.To find the cost of equity under different capital structures, we can again use M&MProposition II with taxes. With a debt-equity ratio of 2, the cost of equity is:R E = R U + (R U– R D)(D/E)(1 – t C)R E = .1266 + (.1266 – .07)(2)(1 – .35)R E = .2001 or 20.01%With a debt-equity ratio of 1.0, the cost of equity is:R E = .1266 + (.1266 – .07)(1)(1 – .35)R E = .1634 or 16.34%And with a debt-equity ratio of 0, the cost of equity is:R E = .1266 + (.1266 – .07)(0)(1 – .35)R E = R U = .1266 or 12.66%14. a.The value of the unlevered firm is:V U = EBIT(1 – t C)/R UV U = $92,000(1 – .35)/.15V U = $398,666.67b.The value of the levered firm is:V U = V U + t C DV U = $398,666.67 + .35($60,000)V U = $419,666.6717.With no debt, we are finding the value of an unlevered firm, so:V U = EBIT(1 – t C)/R UV U = $14,000(1 – .35)/.16V U = $56,875With debt, we simply need to use the equation for the value of a levered firm. With 50 percent debt, one-half of the firm value is debt, so the value of the levered firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(.50)($56,875)V L = $66,828.13And with 100 percent debt, the value of the firm is:V L = V U + t C(D/V)V UV L = $56,875 + .35(1.0)($56,875)V L = $76,781.25c.The net cash flows is the present value of the average daily collections times the daily interest rate, minus the transaction cost per day, so:Net cash flow per day = $1,276,275(.0002) – $0.50(385)Net cash flow per day = $62.76The net cash flow per check is the net cash flow per day divided by the number of checksreceived per day, or:Net cash flow per check = $62.76/385Net cash flow per check = $0.16Alternatively, we could find the net cash flow per check as the number of days the system reduces collection time times the average check amount times the daily interest rate, minusthe transaction cost per check. Doing so, we confirm our previous answer as:Net cash flow per check = 3($1,105)(.0002) – $0.50Net cash flow per check = $0.16 per checkThis makes the total costs:Total costs = $18,900,000 + 56,320,000 = $75,220,000The flotation costs as a percentage of the amount raised is the total cost divided by the amount raised, so:Flotation cost percentage = $75,220,000/$180,780,000 = .4161 or 41.61%8.The number of rights needed per new share is:Number of rights needed = 120,000 old shares/25,000 new shares = 4.8 rights per new share.Using P RO as the rights-on price, and P S as the subscription price, we can express the price per share of the stock ex-rights as:P X = [NP RO + P S]/(N + 1)a.P X = [4.8($94) + $94]/(4.80 + 1) = $94.00; No change.b. P X = [4.8($94) + $90]/(4.80 + 1) = $93.31; Price drops by $0.69 per share.。
遇到并解决问题从中获得收获的英语作文
遇到并解决问题从中获得收获的英语作文全文共3篇示例，供读者参考篇1Conquering the Coding Conundrum: A Journey of Perseverance and GrowthAs students, we often find ourselves faced with challenges that test our resilience and determination. One such obstacle recently crossed my path, leaving me feeling overwhelmed and uncertain. However, through unwavering perseverance and a willingness to learn, I not only overcame this hurdle but also gained invaluable lessons that will undoubtedly shape my future endeavors.The ordeal began innocuously enough, with a programming assignment that seemed straightforward at first glance. Our task was to develop a simple web application using a language and framework we had recently covered in class. Confident in my abilities, I eagerly set out to tackle the project, eager to showcase my newfound coding skills.Little did I know, the universe had other plans.As I delved deeper into the assignment, I encountered a series of perplexing errors that seemed to defy logic. No matter how meticulously I reviewed my code or consulted online resources, the issues persisted, leaving me increasingly frustrated and discouraged. Each attempt to rectify the problem only led to a labyrinth of new errors, compounding the complexity of the situation.Doubt began to creep in, whispering insidious thoughts that perhaps I was not cut out for this field after all. The temptation to abandon the project and seek an easier path grew stronger with each passing day. Yet, deep within me, a resilient voice refused to be silenced, urging me to persevere and confront this challenge head-on.It was during this nadir of self-doubt that I sought guidance from my professors and peers. Their unwavering support and insightful suggestions proved invaluable, reigniting my determination and providing a fresh perspective on the problem at hand. Collaborating with others, I learned the value of teamwork and the power of collective knowledge.Armed with newfound inspiration, I dove back into the code, meticulously dissecting each line and scrutinizing every variable. Late nights became the norm, as I tirelessly troubleshot andexplored alternative solutions. Gradually, the fog began to lift, and the once-impenetrable errors revealed their underlying causes.With each breakthrough, my confidence soared, and the once-daunting task transformed into an exhilarating adventure. I realized that the true value of this experience extended far beyond the confines of the assignment itself. It was a crucible forging the essential qualities of a successful programmer: resilience, problem-solving skills, and an unyielding thirst for knowledge.Finally, after countless hours of perseverance and dedication, the elusive solution emerged, and my web application sprang to life. The euphoric sense of accomplishment that washed over me in that moment was indescribable, a testament to the power of perseverance and the rewards that await those who refuse to surrender.Reflecting on this journey, I am filled with gratitude for the lessons it has imparted. Firstly, I learned the importance of embracing challenges as opportunities for growth rather than insurmountable obstacles. Each setback provided a chance to hone my problem-solving abilities and expand my knowledge,ultimately making me a more well-rounded and capable individual.Secondly, I recognized the invaluable role of collaboration and seeking guidance when faced with daunting tasks. By reaching out to my professors and peers, I gained not only technical insights but also a deeper appreciation for the power of collective wisdom. In a rapidly evolving field like computer science, the ability to learn from others and contribute to a shared knowledge base is an indispensable skill.Furthermore, this experience instilled in me a profound sense of resilience and grit. The journey was arduous, fraught with frustrations and moments of self-doubt. Yet, by persevering through these challenges, I developed a tenacity that will serve me well in future endeavors, both academic and professional.Perhaps most importantly, I discovered a renewed passion for my chosen field. The exhilaration of overcoming this obstacle reignited my love for programming and solidified my commitment to pursuing a career in this dynamic andever-evolving industry. The satisfaction of creating something tangible from mere lines of code is a feeling that cannot be replicated, and it is a driving force that will propel me forward on this path.As I embark on the next chapter of my academic journey, I carry with me the invaluable lessons gleaned from this experience. The coding conundrum, once a daunting obstacle, has transformed into a testament to my growth and a reminder of the boundless potential that lies within each of us when we embrace challenges with unwavering determination and a thirst for knowledge.To my fellow students, I implore you to embrace the trials that inevitably arise, for they are not roadblocks but rather opportunities for personal and professional growth. Embrace the challenges, seek guidance when needed, and never surrender in the face of adversity. For it is in these moments of perseverance that we truly discover the depths of our resilience and the boundless potential that lies within us all.篇2Facing Challenges Head-On: How Resolving a Difficult Issue Unlocked Personal GrowthAs students, we often find ourselves navigating through a labyrinth of academic and personal challenges. These obstacles can seem daunting, even insurmountable at times, but it is in our ability to confront and resolve them that we truly unlock ourpotential for growth and self-discovery. I recently found myself grappling with a particularly complex issue that not only tested my resolve but also revealed the transformative power of perseverance and resilience.The Problem at HandIt all began with a group project in my advanced literature class. We were tasked with analyzing a renowned literary work and presenting our findings to the class. As the team leader, I took it upon myself to ensure that everyone's contributions were equally valued and that we maintained a harmonious dynamic throughout the process. However, as we delved deeper into the analysis, conflicting interpretations and differing perspectives soon emerged, threatening to derail our progress.Tensions mounted as each member passionately defended their stance, and I found myself caught in the crossfire, struggling to reconcile the divergent viewpoints. Theonce-cohesive group began to fracture, and the prospect of completing the project seemed increasingly distant. It was at this juncture that I realized the gravity of the situation and the urgent need to take action.Embracing Conflict ResolutionDetermined to find a resolution, I took a step back and reflected on the root causes of the conflict. It became evident that our differing backgrounds, experiences, and analytical lenses were fueling the divergence in our interpretations. Rather than viewing this as an obstacle, I recognized it as an opportunity to broaden our collective understanding and enrich our analysis.I scheduled a meeting with the group, during which I encouraged open and respectful dialogue. We agreed to actively listen to one another's perspectives, suspend judgments, and seek common ground. It was a challenging process, but as we engaged in thoughtful discussions and embraced the diversity of our viewpoints, a remarkable transformation occurred.Through this exercise in conflict resolution, we not only gained a deeper appreciation for the complexity of literary analysis but also developed invaluable interpersonal skills. We learned to navigate difficult conversations, compromise when necessary, and ultimately arrive at a synthesis that encompassed the most compelling elements of our individual interpretations.The culmination of our efforts was a nuanced and multifaceted analysis that truly did justice to the literary work we had studied. Our presentation captivated the audience, and thepositive feedback from our professor affirmed the value of our collaborative efforts.Lessons Learned and Personal GrowthReflecting on this experience, I can't help but marvel at the profound lessons I learned and the personal growth I underwent. Firstly, I recognized the importance of effective communication and active listening. By creating a safe and inclusive environment for open dialogue, we were able to navigate our differences and find common ground.Secondly, I gained a deeper appreciation for the richness of diverse perspectives. Rather than viewing differing viewpoints as obstacles, I learned to embrace them as opportunities for intellectual growth and personal development. This experience has undoubtedly equipped me with the skills to navigate future conflicts more effectively, both in academic and professional settings.Moreover, I developed a heightened sense of resilience and perseverance. Overcoming the initial challenges we faced instilled in me a belief in my ability to confront and overcome obstacles, no matter how daunting they may seem. This newfound confidence has empowered me to approach futurechallenges with a positive mindset and a determination to succeed.Perhaps most importantly, this experience fostered a deeper sense of empathy and understanding within our group. By actively listening to one another's perspectives and acknowledging the validity of our diverse experiences, we cultivated an environment of mutual respect and trust. This bond extended beyond the confines of the project, strengthening our interpersonal connections and laying the foundation for future collaborations.In retrospect, what initially seemed like a daunting obstacle transformed into a profound learning experience that transcended the boundaries of academia. The skills and insights I gained through this process have become invaluable tools in my personal and professional development, equipping me with the resilience, empathy, and problem-solving abilities that will undoubtedly serve me well in the years to come.As I reflect on this journey, I can't help but feel a sense of gratitude for the challenges I faced and the growth they facilitated. It is through these transformative experiences that we truly discover our inner strength, cultivate empathy, and unlock our full potential as individuals and collaborators.To my fellow students, I encourage you to embrace the challenges that come your way, for it is in conquering these obstacles that we truly learn, grow, and evolve. The path may be arduous, but the rewards of personal growth and self-discovery make it a journey well worth undertaking.篇3Here's an essay written from a student's perspective about encountering and overcoming a problem, and the lessons learned from the experience. The essay is approximately 2,000 words long and written in English.Title: Conquering the Coding Conundrum: A Journey of Perseverance and GrowthAs a computer science student, I've always been fascinated by the intricate world of programming. The idea of transforming abstract concepts into functional code that could solvereal-world problems ignited a fire within me. However, little did I know that my passion would soon be put to the ultimate test, revealing the true depths of my resilience and determination.It all started during my second year at university when I enrolled in an advanced programming course. The class was notorious for its challenging assignments and rigorousassessments, but I was undeterred. I had always excelled in my previous coding classes, and I was confident that this course would be no different.The first few weeks went smoothly, and I breezed through the introductory material. However, as we delved deeper into the curriculum, the complexity of the assignments escalated rapidly. It was during one particularly grueling project that I encountered my first major roadblock.The task was to develop a sophisticated algorithm capable of solving a complex optimization problem. At first, I approached the challenge with my usual fervor, meticulously analyzing the requirements and breaking down the problem into smaller, manageable components. However, as I began coding, I hit a brick wall.No matter how hard I tried, my code stubbornly refused to function as intended. I spent countless hours scouring online forums, consulting reference materials, and seeking guidance from teaching assistants, but the solution eluded me. Frustration mounted, and self-doubt began to creep in, threatening to extinguish the flame of my passion.It was during one of those late-night coding sessions, fueled by desperation and an ever-dwindling supply of caffeine, that Ihad a profound realization. I had been so focused on finding the perfect solution that I had lost sight of the bigger picture – the learning process itself.With a renewed sense of purpose, I stepped back andre-evaluated my approach. Instead of fixating on the end result, I began to appreciate the journey, embracing each setback as an opportunity for growth. I dissected my code line by line, scrutinizing every aspect, and seeking to understand the root。
石油经济学PetEconCh3
1.1. Sooner or Later?
It is generally accepted, that £1 [or $1] received today is preferable to £1 [or $1] received tomorrow or at some time in the future. The converse is that £1 paid out later is preferable to £1 paid sooner. One could conceive of a situation in which income received after an event, such as a robbery, would be preferable, but under most circumstances, early receipt carries logical benefits as follows:(a) Investment opportunity:- Funds invested wisely will grow in value over time. Therefore, the sooner one receives the money, the sooner it may be invested and the sooner it may start to grow. (b) Purchasing power:- Price inflation over time normally causes prices to rise and the purchasing power of the currency to diminish. Therefore, money spent sooner can buy more goods and services. Note that price increases are normal, but not inevitable. During periods of significant economic depression or unusual circumstances, such as the impact of an oil price collapse on oil producing economies in the Middle East, inflation can be negative, with falling prices. (c) Risk:- Over time, the world becomes less certain. Markets may change and commitments may be broken or forgotten. The further into the future one considers, the greater the opportunity for something to change or to fail. (d) Security, flexibility, opportunity:- personal circumstances and requirements vary. Early access to funds reduces risk of problems associated with cash shortage, including bankruptcy. It also means that funds are more likely to be available for that “once in a lifetime” opportunity.
《金融学基础》Module 3-Part I时间价值与NPV规则
School of Management and Economics
Calculation with Excel Functions
15
Finance
School of Management and Economics
The 5-Year Fixed Depository Account
Why is the amount accumulated in the 5-year fixed account more than that in the 1-year account with automatic rollover at the end of the fifth year?
Basic Concepts
– Present value (PV) – Future value (FV) – Simple interest: the interest on the original principal – Compound interest: the interest on the interest – Future value factor
2 1 (1 7%) 1.97
10
2 1 (1 1ool of Management and Economics
The Proof of 7-10 Rule
19
Finance
School of Management and Economics
FV $1 (1 0.06 / 12)12 1.06168
General formula
APR EFF APR, m 1 1 m
22
m
Finance
德州仪器金融计算器BAIIPlus教程
1.Calculate the total present value of each of the cash flows, starting from period 1 (leaveout the initial outlay). Use the calculator's NPV function just like we did in Example 3, above. Use the reinvestment rate as your discount rate to find the present value.2.Calculate the future value as of the end of the project life of the present value from step1. The interest rate that you will use to find the future value is the reinvestment rate.3.Finally, find the discount rate that equates the initial cost of the investment with thefuture value of the cash flows. This discount rate is the MIRR, and it can be interpreted as the compound average annual rate of return that you will earn on an investment if you reinvest the cash flows at the reinvestment rate.Suppose that you were offered the investment in Example 3 at a cost of $800. What is the MIRR if the reinvestment rate is 10% per year?Let's go through our algorithm step-by-step:So, we have determined that our project is acceptable at a cost of $800. It has a positive NPV, the IRR is greater than our 12% required return, and the MIRR is also greater than our 12% required return.。
近年来出现大学生就业难的现象英语作文
近年来出现大学生就业难的现象英语作文 $$The Challenges of University Graduates in the Job Market in Recent Years$$In recent years, the employment landscape foruniversity graduates has undergone significant changes, giving rise to a notable trend of increasing difficulty in finding suitable jobs. This phenomenon is not confined to a particular region or industry but rather spans a global scale, affecting millions of young individuals who have invested years of hard work and dedication in pursuing higher education.The first factor contributing to this trend is the rapid expansion of higher education systems worldwide. With the increasing availability of university education, more students are able to access and complete tertiary-level qualifications. This, in turn, has led to a surge in the number of graduates entering the job market each year. The supply of graduates has thus outpaced the demand forskilled workers in many sectors, resulting in intense competition for limited job opportunities.Moreover, the rapid pace of technological advancement and industrial transformation has also played a significant role in shaping the employment landscape. Many traditional industries are being disrupted by automation and digitization, leading to a decline in job opportunities in these sectors. At the same time, emerging industries suchas technology, healthcare, and renewable energy arecreating new job roles that require a different set ofskills and qualifications. This mismatch between the skills of graduates and the demands of the job market adds to the challenges faced by university students in finding employment.Furthermore, the global economic landscape has alsobeen volatile in recent years, with recessions, trade wars, and other economic uncertainties affecting job growth and stability. Such economic conditions can lead to a reduction in hiring or even layoffs, further compounding the employment challenges for graduates.To address these challenges, universities and governments need to collaborate and take proactive measures. Universities should align their curriculum with thechanging needs of the job market, emphasizing skills such as critical thinking, problem-solving, and adaptability. They should also provide career guidance and internship opportunities to help students gain practical experience and build their professional networks.Governments can play a role by investing in job creation and supporting industries that have high growth potential. They can also implement policies that encourage employers to hire graduates, such as tax incentives or subsidies. Additionally, promoting a culture of continuous learning and skill upgrading within society can help graduates adapt to the changing job market and enhance their employability.Individual graduates also need to take responsibility for their career development. They should actively seek opportunities to develop their skills and knowledge, such as through part-time jobs, volunteer work, or professional development courses. Building a strong resume and network of contacts can also increase their chances of finding suitable employment.In conclusion, the employment challenges faced by university graduates in recent years are multifaceted and require a collaborative effort from universities, governments, and individuals to address. By aligning education with job market demands, promoting economic growth, and encouraging continuous learning and skill upgrading, we can create a more conducive environment for graduates to find fulfilling and rewarding employment opportunities.。
指数的e的英文单词
指数的e的英文单词In the grand ballroom of the universe, a number stood alone, a solitary figure in an infinite sea of digits. It was 'e', the enigmatic exponent, the life of the logarithmic party. It wasn't just any number; it was the number that every math enthusiast would whisper in awe, the one that graced the pages of calculus textbooks and the dreams of mathematicians.'e' didn't just show up at the party; it was the life of the party. It danced with the natural logarithms, twirled with the exponential functions, and waltzed with the power series. It was the constant companion of growth and decay, the silent hero in compound interest equations, and the unsung star in the world of continuous compounding.But 'e' wasn't just a number to be revered; it was also the comedian of the mathematical realm. It had a sense of humor, a way of making light of the most complex situations. When asked about its value, 'e' would chuckle and say, "Approximately 2.71828, but who's counting?" It would then proceed to crack a joke about how it's the only number that can make pi feel inadequate.'e' was also a mentor, guiding the young and the curious through the labyrinth of mathematical concepts. It would often be found explaining the beauty of its own properties, like how it's its own derivative and integral, with a twinklein its eye.And when the night grew late, and the other numbers began to yawn and fade away, 'e' would still be there, the eternal constant, the unchanging variable in a world of change. It was the number that never slept, the constant reminder that in the vast expanse of the universe, some things remain constant, some values never decay.So, the next time you're solving for 'x' or integrating a function, remember 'e', the number that's always ready to lend a hand, crack a joke, and make the complex world of mathematics just a little bit more enjoyable.。
《金融理论与公司政策(第四版)》课后答案
= .18 d2 = .18 – ( .0961) (.6538) = –.02 Substituting these values into the Black-Scholes Formula, C = 44.375N(.18) – 45e N(–.02)
–.03
Using the Table of Normal Areas, we can determine N(.18) and N(–.02). Substituting these values into the formula yields C = 44.375(.5714) – 45(.9704)(.4920) = 25.3559 – 21.4847 = $3.87 5. Compare the payoffs at maturity of two portfolios. The first is a European put option with exercise price X1, and the second is a European put option written on the same stock, with the same time to maturity, but with exercise price X2 < X1. The payoffs are given in Table S7.1. Because portfolio A has a value either greater than or equal to the value of portfolio B in every possible state of nature, the put with a higher exercise price is more valuable. P(S, T, X1) > P(S, T, X2) Table S7.1 Portfolio a) P(S, T, X1) b) P(S, T, X2) Comparative Value of A and B S < X2 X1 – S X2 – S VA > VB if X2 < X1. X1 ≤ S 0 0 VA = VB
药学专业对未来的自己写一封信作文
药学专业对未来的自己写一封信作文英文回答：Dear Future Me,。
I hope this letter finds you well. As I sit here contemplating the future, I can't help but think about the journey we have taken in the field of pharmacy. It has been a long and challenging road, but one that I am grateful for.Looking back, I remember the excitement I felt when I first started studying pharmacy. The endless hours spent in the library, pouring over textbooks and lecture notes, seemed daunting at times. However, it was during those moments of struggle that I learned the most. I learned the importance of perseverance and dedication in achieving our goals.Throughout our pharmacy education, we were exposed to a wide range of subjects, from pharmaceutical chemistry topharmacotherapy. Each subject presented its own challenges, but also its own rewards. I remember the satisfaction of solving complex drug interactions and the thrill of compounding personalized medications for patients. These experiences solidified my passion for pharmacy and reaffirmed my decision to pursue this career.In addition to the academic aspect, our pharmacy education also provided valuable opportunities for personal growth. Through internships and clinical rotations, we had the chance to interact with patients and healthcare professionals. These experiences taught us the importance of effective communication and empathy in providingpatient-centered care. I will never forget the gratitude expressed by a patient whose pain was alleviated by a medication we recommended, or the joy of witnessing a patient's recovery after a successful treatment plan.As we look towards the future, I am excited about the potential opportunities that lie ahead. The field of pharmacy is constantly evolving, with new advancements in drug therapies and technology. I am eager to embrace thesechanges and continue to expand our knowledge and skills. Whether it be in a community pharmacy, a hospital setting, or even in research and academia, I am confident that our pharmacy education has equipped us with the necessary tools to succeed.中文回答：亲爱的未来的我，。
指南中提出数的分解和组成
指南中提出数的分解和组成英文回答：Decomposition and composition of numbers are fundamental concepts in mathematics. Decomposition refers to breaking down a number into its smaller parts or components, while composition involves combining smaller parts to form a larger number.Let's start with decomposition. When we decompose a number, we are essentially breaking it down into its individual digits or place values. For example, let's take the number 456. We can decompose it as follows:4 hundreds +5 tens +6 ones.In this case, we have broken down the number 456 into its hundreds, tens, and ones place values. This process helps us understand the value and position of each digit within a number.Composition, on the other hand, involves combining smaller parts to form a larger number. For instance, let's take the digits 2, 3, and 7. We can compose them to form the number 237. In this case, we have combined the individual digits to create a new number.Decomposition and composition are closely related and are used in various mathematical operations. For example, when we add or subtract numbers, we decompose them to perform the operation on each place value and then compose the results to obtain the final answer. Similarly, when we multiply or divide numbers, we decompose them into their prime factors or divisors and then compose the factors or divisors to find the product or quotient.Understanding decomposition and composition is essential for developing strong number sense and problem-solving skills in mathematics. It allows us to manipulate numbers more efficiently and make sense of complex mathematical concepts.中文回答：数的分解和组成是数学中的基本概念。
英文财务管理
Future Value of $100 = FV
FV $100 (1 r)t
5- 9
Solving for FV:
After 1 year:
FV1 = PV ( 1 + i ) = $100 (1.10) = $110.00
After 2 years: FV2 = PV ( 1 + i )2 = $100 (1.10)2 =$121.00
....
5- 26
Perpetuities & Annuities
Perpetuity（永续年金） A stream of level cash payments that never ends.
Annuity（年金） Equally spaced level stream of cash flows for a limited period of time.
Simple Interest - Interest earned only on the original investment.(单利)
5- 4
Future Values
Example - Simple Interest
Interest earned at a rate of 6% for five years on a principal balance of $100.
MMccGGrraaww Hilll//IIrrwwinin
Copyright ©C2o0p0y9ribgyhtT©he2M00c9GbraywT-hHeiMll CcGomrapwa-nHieisl,l ICnocm. Apallnriiegsh, tIsncr.esAerllvreidghts reserved
Analyzing Annuity Cash Flows
What is the difference between an ordinary annuity and an annuity due?
Ordinary Annuity
0
i%
1
2
3
PMT
PMT
2
PMT
3
Annuity Due
0
i%
1
PMT
PMT
PMT
In financial calculators, we need to tell the calculator that the payments occur at the beginning of each period. We do this by putting the calculator in BEGIN mode (represented by BGN)
0
1 100
2 100
3 100
90.91 82.64 75.13 = 248.68
Solving for PV: 3-year ordinary annuity of $100 at 10%
• $100 payments still occur at the end of each period, but now there is no FV.
PMT / I
= 2,000 / .10 = $20,000
Classifications of interest rates
• Nominal rate (iNOM) – also called the quoted or stated rate. An annual rate that ignores compounding effects.
Y085Lecture 4
4-15
Excel Spreadsheet Functions
• Excel TVM functions: = FV(rate,nper,pmt,pv) = PV(rate,nper,pmt,fv) = RATE(nper,pmt,pv,fv) = NPER(rate,pmt,pv,fv)
• Use the formula icon (ƒx) when you can’t remember the exact formula
4-5
Time Line of Cash Flows
•Tick marks at ends of periods • Time 0 is today; • Time 1 is the end of Period 1
0
1
2
3
r%
CF0
CF1
CF2
பைடு நூலகம்
CF3
+CF = Cash INFLOW -CF = Cash OUTFLOW PMT = Constant CF
– Formulas – A financial calculator （not required） – A spreadsheet
Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of McGraw-Hill Education.
• Future Value (FV)
– The amount an investment is worth after one or more periods.
solving for the number of compounding period, n
Example 9.2 B Calculating and Interpreting a Noninteger n
Rounded to the nearest month, how long will it take a city’s population to grow from 75,000 to 100,000 if the annual growth rate is 2%?
A financial contract guaranteed the payment of $4000 plus interest at a fixed rate of 9.6% compounded quarterly 2 years after the contract’s date of issue. Sometime before the maturity date, the original owner sold the contract for $4327.70. The sale price represented the fair market value given the market rate of 8.5% compounded semiannually for similar maturities. How long before the maturity date did the sale take place?
16
Solution: Suppose P=$1, S=$2 A, j=6% compounded annually 1 +/PV 0 PMT 6 1/Y 2 FV 6 P/Y 1 ENTER 1/Y i=6% CPT n CPT 11.896
11.896 n 11.896 years=11 years and 10.75 months. An investment earning 6% compounded annually will double in 11 years and 11 months (rounded to the nearest month).
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Example 9.2 B Calculating and Interpreting a Noninteger n
Rounded to the nearest month, how long will it take a city’s population to from 75,000 to 100,000 if the annual growth rate is 2%?
nln 1 (i)ln sln p
n
ln s ln p ln(1i)
ln
s p
ln1i
(9-2)
4
Financial Calculator Method:
Setting 1
P
0 iS
+/- PMT 1/Y FV CPT
PV
n
results
Setting 2
P
0 j S P/y
+/- PMT 1/Y FV m CPT
PV
ENTER n
results
5
Noninteger value for n
Sometimes an investment or a loan has a term that isn’t an integer number of compounding periods. In such cases, n is a noninteger. It includes the decimal fraction for the last partial compounding period. But the procedures are the same as for integer values of n. The algebraic method and financial calculator method work with both integer and noninteger values for n.
A stripped bond residue having a $10,000 face value was purchased for $3142.31. At this price, the bond residue provided the investor with a return of 7.938% compounded semiannually until its maturity. How long before the maturity date was the bond purchased? Assume that each half year is exactly 182 days long.
7
Solution:
p=75,000 s=100,000
j=i=2%
nln sln pl1 n0 0ln 0 70 5 0 1.5 0 42 07
ln 1i()
ln 12 (%)
75000 0
2 100000 CPT
+/- PV PMT 1/Y FV
n
14.527
2
CPT
P/Y
1 ENTER 1/Y
A financial contract guaranteed the payment of $4000 plus interest at a fixed rate of 9.6% compounded quarterly 2 years after the contract’s date of issue. Sometime before the maturity date, the original owner sold the contract for $4327.70. The sale price represented the fair market value given the market rate of 8.5% compounded semiannually for similar maturities. How long before the maturity date did the sale take place?
j=8.5% m=2 i=j/m=4.25% p=$4327.70 s=$4835.70
4327.70 +/PV
4.25 1/Y CPT
n
2.6666
Term of discount =2.6666*6months
=16 months
8.5 CPT
P/Y
2 ENTER 1/Y
n 2.6666
13
Example 9.2
Term=2 years j=9.6% m=4 i=j/m=2.4% n=2*4=8 p=$4000
4000
0 2.4 8 CPT
+/- PV PMT 1/Y n
FV
4835.70
9.6 CPT
P/Y
4 ENTER 1/Y FV 4835.7
12
Step 2: determine how long it was before the maturity date that $4327.70 was the present value of the maturity value.
n 14.527
0.527*12=6.32 months
8
Rounded to the nearest month, it will take 14 years and 6 months for the city’s population to reach 100,000.
9
Example 9.2 E
10
Solution:
0 $4000
$4327.70
9.6% compounded
quarterly
2 year Maturity value
8.5% compounded semiannually
11
Step 1: calculate the maturity value of $4000 when the contract maturity
Chapter 9 Compound Interest: Further Topics and Applications
9.2 solving for the number of compounding period, n
1
Algebraic method:
sp(1i)n
(1 i)n s p