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1、Corporate Finance: The Core (Berk/DeMarzo)Chapter 4 - The Time Value of MoneyUse the table for the question(s) below.YearAB0-$150-$2251401752801253100-506) Draw a timeline detailing the cash flows from investment A. Answer: Diff: 1 Topic: 4.1 The Timeline Skill: Conceptual 7) Draw a timeline detaili
2、ng the cash flows from investment B. Answer: Diff: 1 Topic: 4.1 The Timeline Skill: Conceptual Use 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 childs college education
3、. 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
4、 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: $25,322.71$25,322.71(1.04)1$25,322.71(1.04)2$25,322.71(1.04)318192021Note that the tuition for the first year is ca
5、lculated as: $12,5000(1.04)18 = $25,322.71 Diff: 2 Topic: 4.1 The Timeline Skill: Conceptual 9) 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 childs college education. They decide to make deposits into an educat
6、ional savings account on each of their daughters birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The parents deposit $2000 on their daughters first birthday and plan to increase the size of their deposits by 5% each year. Draw a tim
7、eline that details the amount that would be available for the daughters college expenses on her 18th birthday. Answer: Diff: 2 Topic: 4.1 The Timeline Skill: Analytical 3) Which of the following statements is false? A) The process of moving a value or cash flow backward in time is known as discounti
8、ng. 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: B Explanation: A) B) FV = C(1 + r)n C) D) Diff: 1 Topic: 4.2 The Three Rules of Time Travel Skill: Concep
9、tual 5) Consider the following timeline:If the current market rate of interest is 10%, then the future value of this timeline is closest to: A) $666 B) $500 C) $605 D) $650 Answer: A Explanation: A) FV = PV(1 + r)n = 500(1.10)3 = 665.50 which is approximately $666 B) C) D) Diff: 1 Topic: 4.2 The Thr
10、ee Rules of Time Travel Skill: Analytical 7) 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) $1720 B) $1500 C) $1404 D) $1717 Answer: A Explanation: A) FV = PV(1 + r)nFV = 500(1.07)3 + 500(1.07)2 + 50
11、0(1.07)1 = $1719.97 or approximately $1720 B) C) D) Diff: 3 Topic: 4.2 The Three Rules of Time Travel Skill: Analytical 8) Consider the following timeline:If the current market rate of interest is 9%, then the present value of this timeline as of year 0 is closest to: A) $492 B) $637 C) $600 D) $400
12、 Answer: A Explanation: 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 $492 B) C) D) Diff: 3 Topic: 4.2 The Three Rules of Time Travel Skill: Analytical 9) Consider the following timeline:If the current market rate of interest i
13、s 8%, then the value as of year 1 is closest to: A) $0 B) $1003 C) $540 D) $77 Answer: D Explanation: A) B) C) 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 = $77 Diff: 2 Topic: 4.2 The Three Rules of Time Travel Skill:
14、Analytical 4.3 The Power of Compounding: An Application 2) It has long been told that the Dutch purchased Manhattan island in 1626 for the value of 60 guilders ($24). Assuming that the Dutch invested this money into an account earning 5%, approximately how much would their investment be worth 380 ye
15、ars later in 2006? A) $2.7 billion B) $3.1 billion C) $4.5 billion D) $1.9 trillion Answer: A Explanation: A) FV = 24(1.05)380 = 2,704,860,602 or 2.7 billion B) C) D) Diff: 1 Topic: 4.3 The Power of Compounding: An Application Skill: Analytical 2) Which of the following statements is false? A) FV =
16、B) PV = C) FV = Cn (1 + r)n D) Most investment opportunities have multiple cash flows that occur at different points in time. Answer: A Explanation: A) B) C) D) Diff: 1 Topic: 4.4 Valuing a Stream of Cash Flows Skill: Conceptual 4) Consider the following timeline detailing a stream of cash flows:If
17、the current market rate of interest is 10%, then the present value of this stream of cash flows is closest to: A) $674 B) $600 C) $460 D) $287 Answer: C Explanation: A) B) C) PV = 100 / (1.10)1 + 100 / (1.10)2 + 200 / (1.10)3 + 200 / (1.10)4 = $460 D) Diff: 2 Topic: 4.4 Valuing a Stream of Cash Flow
18、s Skill: Analytical Use 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 wil
19、l 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%. 6) 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
20、+ $75,000 / (1.06)3 = $254,641 Diff: 2 Topic: 4.4 Valuing a Stream of Cash Flows Skill: Analytical 4.5 The Net Present Value of a Stream of Cash Flows 1) 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 ye
21、ars. Assuming that you could otherwise earn 10% per year on your money, the NPV for this opportunity is closest to: A) $12 B) $18 C) -$13 D) $500 Answer: C Explanation: A) B) C) NPV = -2500 + 1000 / (1.10)1 + 1000 / (1.10)2 + 1000 / (1.10)3 = -13.15 which is approximately -$13 D) Diff: 2 Topic: 4.5
22、The Net Present Value of a Stream of Cash Flows Skill: Analytical Use 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 off
23、ered 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) Suppose a second entrepreneur approaches Joe and offers him $250,000 today for the business. Should Jo
24、e accept the new entrepreneurs offer or stick with the original offer of $100,000 and the series of payments over three years? Why? Answer: Joe should take the original offer of $100,000 + payments.PV of the original offer = $100,000 + $50,000 / (1.06)1 + $50,000 / (1.06)2 + $75,000 / (1.06)3 = $254
25、,641 So, the NPV of taking the second offer is $250,000 - $254,641 = -$4,641 Since the NPV is negative we would not take the second offer. Diff: 2 Topic: 4.5 The Net Present Value of a Stream of Cash Flows Skill: Analytical Use the table for the question(s) below.YearAB0-$150-$2251401752801253100-50
26、5) If the interest rate is 10%, then which investment(s), if any, would you take and why? Answer: NPVA = -150 + 40 / (1.10)1 + 80 / (1.10)2 + 100 / (1.10)3 = $27.61NPVB = -225 + 175 / (1.10)1 + 125 / (1.10)2 + -50 / (1.10)3 = -$0.17Therefore, you should take A since NPVA 0 and reject B since NPVB 0.
27、 Diff: 3 Topic: 4.5 The Net Present Value of a Stream of Cash Flows Skill: Analytical 4.6 Perpetuities, Annuities, and Other Special Cases 1) 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 perpe
28、tuity 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: C Explanation: A) B) C) PV of a perpetuity = D) Diff: 1 Topic: 4.6 Perpetuities, Annuities, and Oth
29、er Special Cases Skill: Conceptual 3) 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 perpe
30、tuity is a cash flow stream that occurs at regular intervals and grows at a constant rate forever. Answer: A Explanation: A) B) C) D) Diff: 1 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical Use the information for the question(s) below.Suppose that a young couple has ju
31、st had their first baby and they wish to ensure that enough money will be available to pay for their childs 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.
32、 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) $12,500 B) $21,500 C) $320,568 D) $25,323 Answer: D Explanation: A) B) C) D) FV = PV(1 + i)N = $12,500(1.04)18 = $2
33、5,322.71 Diff: 2 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical 8) 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
34、available at age 18 to pay for all four years of her undergraduate education is closest to: A) $97,110 B) $107,532 C) $101,291 D) $50,000 Answer: A Explanation: 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
35、 figure out the value for four years of college.PV of a growing annuity due = C x (1 + r) = $25,322.71 (1 + .07) = $97,110.01 B) C) D) Diff: 3 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical 13) Suppose that a young couple has just had their first baby and they wish to
36、insure that enough money will be available to pay for their childs college education. They decide to make deposits into an educational savings account on each of their daughters birthdays, starting with her first birthday. Assume that the educational savings account will return a constant 7%. The pa
37、rents deposit $2000 on their daughters 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 daughters 18th birthday, then the amount available for the daughters college expenses on her 18th birthday is close
38、st to: A) $42,825 B) $97,331 C) $67,998 D) $103,063 Answer: B Explanation: A) B) FV of a growing annuity$2,000 (1.07)18= $97,331 C) D) Diff: 2 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical Use the information for the question(s) below.Assume that you are 30 years old
39、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
40、made on your 31st birthday and will be 8% of this years 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) $87,000 B) $108,000 C) $46,600 D)
41、 $75,230 Answer: A Explanation: A) First deposit = .08 $45,000 = $3,600$3,600 = $87,003 B) C) D) Diff: 2 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical 18) The future value at retirement (age 65) of your savings is closest to: A) $497,530 B) $928,895 C) $1,263,236 D) $
42、108,000 Answer: B Explanation: A) B) First deposit = .08 x $45,000 = $3,600$3,600 (1.07)35= $928,895 orPVA (growing) = $3,600 = $87,003FV = PV(1 + i)N = $87,003(1.07)35 = $928,895 C) D) Diff: 2 Topic: 4.6 Perpetuities, Annuities, and Other Special Cases Skill: Analytical 26) Assume that you are 30 y
43、ears old today, and that you are planning on retiring 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 w
44、ill be made on your 31st birthday and will be 8% of this years salary. Likewise, you expect to deposit 8% of your salary each year until you reach age 65. At retirement (age 65) you will begin withdrawing equal annual payments to pay for your living expenses during retirement (on your 65th birthday). If you expect to die one day before your 101st birthday (Your last withdraw will be on your 100th birthday) and if the annual rate of return is 7%, then how much money will you have to spend in each of your golden years of retirement? Answer:
