Chapter 5 for financial economics for Cairo university PDF

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Principles of Managerial Finance, 14e, Global Edition (Gitman/Zutter) Chapter 5 Time Value of Money 5.1 Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. 1) Since individuals are always confronted with opportunities to earn positive rates of return on their funds, the timing of cash flows does not have any significant economic consequences. Answer: FALSE Diff: 1 Topic: Role of Time Value in Finance Learning Obj.: LG 1 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 2) Time value of money is based on the belief that a dollar that will be received at some future date is worth more than a dollar today. Answer: FALSE Diff: 1 Topic: Role of Time Value in Finance Learning Obj.: LG 1 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 5.2 Understand the concepts of future value and present value, their calculation for single amounts, and the relationship between them. 1) For a given positive interest rate, the future value of $100 increases with the passage of time. Thus, the longer the period of time, the greater the future value. Answer: TRUE Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills

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2) Future value is the value of a future amount at the present time, found by applying compound interest over a specified period of time. Answer: FALSE Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 3) The greater the interest rate and the longer the period of time, the higher the present value. Answer: FALSE Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 4) Everything else being equal, the higher the interest rate, the higher the future value. Answer: TRUE Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 5) Future value increases with increases in the interest rate or the period of time funds are left on deposit. Answer: TRUE Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 6) Everything else being equal, the higher the discount rate, the higher the present value. Answer: FALSE Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 2 © Pearson Education Limited, 2015.

7) Everything else being equal, the longer the period of time, the lower the present value. Answer: TRUE Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 8) ________ is the amount earned on a deposit that has become the part of the principal at the end of a specified time period. A) Discount interest B) Compound interest C) Primary interest D) Future value Answer: B Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 9) The future value of $100 received today and deposited at 6 percent for four years is ________. A) $126 B) $ 79 C) $124 D) $116 Answer: A Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills

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10) The future value of $200 received today and deposited at 8 percent for three years is ________. A) $248 B) $252 C) $158 D) $200 Answer: B Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 11) The present value of $100 to be received 10 years from today, assuming an opportunity cost of 9 percent, is ________. A) $236 B) $699 C) $ 42 D) $ 75 Answer: C Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 12) The amount of money that would have to be invested today at a given interest rate over a specified period in order to equal a future amount is called ________. A) future value B) present value C) future value of an annuity D) compounded value Answer: B Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills

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13) The present value of $200 to be received 10 years from today, assuming an opportunity cost of 10 percent, is ________. A) $ 50 B) $200 C) $518 D) $ 77 Answer: D Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 14) The future value of a dollar ________ as the interest rate increases and ________ the further in the future an initial deposit is to be received. A) decreases; decreases B) decreases; increases C) increases; increases D) increases; decreases Answer: C Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 15) The annual rate of return is referred to as the ________. A) discount rate B) marginal rate C) risk-free rate D) marginal cost Answer: A Diff: 1 Topic: Basic Time Value Concepts Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills

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16) If you expect to retire in 30 years, live on $50,000 per year and expect the inflation to average 3% over the next 30 years, what amount of annual income will you need to live at the same comfort level in 30 years? A) $121,363 B) $$95,000 C) $20,599 D) $51,500 Answer: A Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 17) Calculate the future value of $4,600 received today if it is deposited at 9 percent for three years. Answer: FV = PV (1+ r)n = $4,600(1.09)3 = $5,957 Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 18) Calculate the present value of $89,000 to be received in 15 years, assuming an opportunity cost of 14 percent. Answer: PV = 89,000(1.14)-15 = $12,469 Diff: 1 Topic: Present Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills

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19) Aunt Tillie has deposited $33,000 today in an account which will earn 10 percent annually. She plans to leave the funds in this account for seven years earning interest. If the goal of this deposit is to cover a future obligation of $65,000, what recommendation would you make to Aunt Tillie? Answer: FV = 33,000(1.1)7 = $64,308 Aunt Tillie will only have $64,308 at the end of seven years under the stated arrangement. She must find an account with a higher interest rate or deposit a larger sum today. The amount Aunt Tillie should invest today to receive $65,000 after 7 years, PV = 65,000 / (1.1)7 = $33,355.28 Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 20) China Manufacturing Agents, Inc. is preparing a five-year plan. Today, sales are $1,000,000. If the growth rate in sales is projected to be 10 percent over the next five years, what will the dollar amount of sales be in year five? Answer: FV = 1,000,000(1.1)5 = $1,610,510 Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 21) Colin has inherited $6,000 from the death of Grandma Anna. He would like to use this money to buy his mom Hayley a new scooter costing $7,000, two years from now. Will Colin have enough money to buy the gift if he deposits his money in an account paying 8 percent compounded semiannually? Answer: n = 2, m = 2, r = 8% FV = 6,000(1+.08/2)2 × 2 = 6000(1.04)4 = $7,019 Yes, Colin will have enough money to buy the scooter. Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills

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22) Dan and Jia are newlyweds and have just purchased a condominium for $70,000. Since the condo is very small, they hope to move into a single-family house in 5 years. How much will their condo worth in 5 years if inflation is expected to be 8 percent? Answer: PV = $70,000, r = 8%, n = 5 FV = 70,000(1.08)5 = $102,853. Diff: 1 Topic: Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 23) Congratulations! You have just won the lottery! However, the lottery bureau has just informed you that you can take your winnings in one of two ways. Choice X pays $1,000,000. Choice Y pays $1,750,000 at the end of five years from now. Using a discount rate of 5 percent, based on present values, which would you choose? Using the same discount rate of 5 percent, based on future values, which would you choose? What do your results suggest as a general rule for approaching such problems? (Make your choices based purely on the time value of money.) Answer: The PV of X = $1,000,000; The PV of Y = $1,371,000; The FV of X = $1,276,000; The FV of Y = $1,500,000. Based on both present values and future values, B is the better choice. Finding present values and future values are simply reverse processes of one another, and that choosing between two lump sums based on PV will always give the same result as choosing between the same two lump sums based on FV. Diff: 1 Topic: Present Value and Future Value Learning Obj.: LG 2 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 5.3 Find the future value and the present value of both an ordinary annuity and an annuity due, and find the present value of a perpetuity. 1) An annuity due is an amount that occur at the beginning of each period. Answer: TRUE Diff: 1 Topic: Annuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills

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2) An ordinary annuity is an annuity in which cash flows occur at the beginning of each period. Answer: FALSE Diff: 1 Topic: Annuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 3) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity for interest rates greater than zero. Answer: TRUE Diff: 2 Topic: Annuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Dynamics of the Global Economy 4) Which of the following is true of annuities? A) An ordinary annuity is an equal payment paid or received at the beginning of each period. B) An annuity due is a payment paid or received at the beginning of each period that increases by an equal amount each period. C) An annuity due is an equal stream of cash flows is paid or received at the beginning of each period. D) An ordinary annuity is an equal payment paid or received at the end of each period that increases by an equal amount each period. Answer: C Diff: 1 Topic: Annuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 5) The present value of a $25,000 perpetuity at a 14 percent discount rate is ________. A) $178,571 B) $285,000 C) $350,000 D) $219,298 Answer: A Diff: 1 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 9 © Pearson Education Limited, 2015.

6) An annuity with an infinite life is called a(n) ________. A) perpetuity B) primia C) option D) deep discount Answer: A Diff: 1 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 7) The present value of a $20,000 perpetuity at a 7 percent discount rate is ________. A) $186,915 B) $285,714 C) $140,000 D) $325,000 Answer: B Diff: 1 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 8) A(n) ________ is an annuity with an infinite life making continual annual payments. A) amortized loan B) principal C) perpetuity D) APR Answer: C Diff: 1 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills

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9) Bill plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 20 years. If Bill can earn 12 percent on his contributions, how much will he have at the end of the twentieth year? A) $19,292 B) $14,938 C) $40,000 D) $144,104 Answer: D Diff: 1 Topic: Future Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 10) Dan plans to fund his individual retirement account (IRA) with the maximum contribution of $2,000 at the end of each year for the next 10 years. If Dan can earn 10 percent on his contributions, how much will he have at the end of the tenth year? A) $12,290 B) $20,000 C) $31,874 D) $51,880 Answer: C Diff: 1 Topic: Future Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 11) In comparing an ordinary annuity and an annuity due, which of the following is true? A) The future value of an annuity due is always greater than the future value of an otherwise identical ordinary annuity. B) The future value of an ordinary annuity is always greater than the future value of an otherwise identical annuity due. C) The future value of an annuity due is always less than the future value of an otherwise identical ordinary annuity, since one less payment is received with an annuity due. D) All things being equal, one would prefer to receive an ordinary annuity compared to an annuity due. Answer: A Diff: 1 Topic: Future Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 11 © Pearson Education Limited, 2015.

12) The future value of a $2,000 annuity due deposited at 8 percent compounded annually for each of the next 10 years is ________. A) $28,974 B) $31,291 C) $14,494 D) $13,420 Answer: B Diff: 2 Topic: Future Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 13) The future value of a $10,000 annuity due deposited at 12 percent compounded annually for each of the next 5 years is ________. A) $36,050 B) $63,530 C) $40,376 D) $71,152 Answer: D Diff: 2 Topic: Future Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 14) The future value of an ordinary annuity of $1,000 each year for 10 years, deposited at 3 percent, is ________. A) $11,808. B) $11,464. C) $ 8,530. D) $10,000. Answer: B Diff: 2 Topic: Future Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills

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15) The future value of an ordinary annuity of $2,000 each year for 10 years, deposited at 12 percent, is ________. A) $35,098 B) $20,000 C) $39,310 D) $11,300 Answer: A Diff: 2 Topic: Future Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 16) A college received a contribution to its endowment fund of $2 million. It can never touch the principal, but can use the earnings. At an assumed interest rate of 9.5 percent, how much can the college earn to help its operations each year? A) $95,000 B) $19,000 C) $190,000 D) $18,000 Answer: C Diff: 2 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Analytic Skills 17) If the present value of a perpetual income stream is increasing, the discount rate must be ________. A) increasing B) decreasing C) changing unpredictably D) increasing proportionally Answer: B Diff: 1 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills

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18) The present value of an ordinary annuity of $350 each year for five years, assuming an opportunity cost of 4 percent, is ________. A) $288 B) $1,896 C) $1,750 D) $1,558 Answer: D Diff: 1 Topic: Present Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 19) The present value of an ordinary annuity of $2,350 each year for eight years, assuming an opportunity cost of 11 percent, is ________. A) $ 1,020 B) $27,869 C) $18,800 D) $12,093 Answer: D Diff: 2 Topic: Present Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Analytic Skills 20) A generous benefactor to a local ballet plans to make a one-time endowment that would provide the ballet with $150,000 per year into perpetuity. The rate of interest is expected to be 5 percent for all future time periods. How large must the endowment be? A) $ 300,000 B) $3,000,000 C) $ 750,000 D) $1,428,571 Answer: B Diff: 2 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills

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21) A generous philanthropist plans to make a one-time endowment to a renowned heart research center which would provide the facility with $250,000 per year into perpetuity. The rate of interest is expected to be 8 percent for all future time periods. How large must the endowment be? A) $2,314,814 B) $2,000,000 C) $3,125,000 D) $3,000,000 Answer: C Diff: 3 Topic: Perpetuities Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 22) Mary will receive $12,000 per year for the next 10 years as royalty for her work on a finance book. What is the present value of her royalty income if the opportunity cost is 12 percent? A) $120,000 B) $ 67,800 C) $ 38,640 D) $ 72,560 Answer: B Diff: 2 Topic: Present Value of an Annuity Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 23) To pay for her college education, Gina is saving $2,000 at the beginning of each year for the next eight years in a bank account paying 12 percent interest. How much will Gina have in that account at the end of 8th year? A) $16,000 B) $17,920 C) $24,600 D) $27,552 Answer: D Diff: 2 Topic: Future Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills

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24) James plans to fund his individual retirement account, beginning today, with 20 annual deposits of $2,000, which he will continue for the next 20 years. If he can earn an annual compound rate of 8 percent on his deposits, the amount in the account upon retirement will be ________. A) $19,636 B) $91,524 C) $98,846 D) $21,207 Answer: C Diff: 2 Topic: Future Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Previous Edition AACSB Tag: Reflective Thinking Skills 25) You have been offered a project paying $300 at the beginning of each year for the next 20 years. What is the maximum amount of money you would invest in this project if you expect 9 percent rate of return to your investment? A) $ 2,738 B) $ 2,985 C) $15,347 D) $ 6,000 Answer: B Diff: 2 Topic: Present Value of an Annuity Due Learning Obj.: LG 3 Learning Outcome: F-03 Question Status: Revised AACSB Tag: Reflective Thinking Skills 26) Calculate the present value of a $10,000 perpetuity at a 6 percent discount rate. Answer: PV = 10,000/0.06 = $166,667 Diff: 1 Topic: Perp...