Chapter 05

Chapter 5 Introduction to Valuation: The Time Value of Money 1. If the rate at which you can invest is 0%, the value today of $1 to be received in the future is less than $1. Ans: False

Level: Basic

Subject: Opportunity Rates

Type: Concepts

2. The amount an investment is worth after one or more periods of time is the ___________. A) future value B) present value C) principal value D) compound interest rate E) simple interest rate Ans: A

Level: Basic

Subject: Future Value

Type: Definitions

3. The process of accumulating interest on an investment over time to earn more interest is called: A) Growth. B) Compounding. C) Aggregation. D) Accumulation. Ans: B

Level: Basic

Subject: Compounding

Type: Definitions

4. Interest earned on the reinvestment of previous interest payments is called _____________. A) free interest B) annual interest C) simple interest D) interest on interest E) compound interest Ans: D

Level: Basic

Subject: Interest On Interest

Type: Definitions

5. Interest earned on both the initial principal and the interest reinvested from prior periods is called ____________. A) free interest B) annual interest C) simple interest D) interest on interest E) compound interest Ans: E

Level: Basic

Subject: Compound Interest

Type: Definitions

6. Interest earned only on the original principal amount invested is called _______________. A) free interest B) annual interest C) simple interest D) interest on interest E) compound interest Ans: C

Level: Basic

Subject: Simple Interest

Type: Definitions

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 1

Chapter 5 Introduction to Valuation: The Time Value of Money

7. The future value interest factor is calculated as: A) (1 + r)t B) (1 + rt) C) (1 + r)(t) D) 1+r–t E) None of the above are correct Ans: A

Level: Basic

Subject: Future Value Interest Factor

Type: Definitions

8. The current value of future cash flows discounted at the appropriate discount rate is called the: A) Principal value. B) Future value. C) Present value. D) Simple interest rate. E) Compound interest rate. Ans: C

Level: Basic

Subject: Present Value

Type: Definitions

9. The process of finding the present value of some future amount is often called _____________. A) growth B) discounting C) accumulation D) compounding E) reduction Ans: B

Level: Basic

Subject: Discounting

Type: Definitions

10. The present value interest factor is calculated as: A) 1/(1 + r – t) B) 1/(1 + rt) C) 1/(1 + r)(t) D) 1/(1 + r)t E) 1+r+t Ans: D

Level: Basic

Subject: Present Value Interest Factor

Type: Definitions

11. The interest rate used to calculate the present value of future cash flows is called the ____________ rate. A) free interest B) annual interest C) compound interest D) simple interest E) discount Ans: E

Level: Basic

Subject: Discount Rate

Type: Definitions

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Page 2

Chapter 5 Introduction to Valuation: The Time Value of Money

12. The concept that a dollar received today is worth more than a dollar received tomorrow is referred to as the: A) Present value. B) Simple interest value. C) Compound value. D) Time value of money. E) Future value of money. Ans: D

Level: Basic

Subject: Time Value Of Money

Type: Definitions

13. The factor (1 + r)t is called the: A) Simple rate of interest. B) Current factor. C) Future value factor. D) Present value factor. E) Discount factor. Ans: C

Level: Basic

Subject: Future Value Factor

Type: Definitions

14. The value computed using the factor 1 / (1 + r)t is called the: A) Present value. B) Interest rate. C) Number of periods. D) Future value. E) Compound value. Ans: A

Level: Basic

Subject: Present Value

Type: Definitions

15. Compound interest means that you earn: A) Interest only on the initial amount invested. B) Interest on the initial principal only. C) Interest on both the principal and prior reinvested interest. D) A decreasing amount of interest each year. E) The same amount of interest each year. Ans: C

Level: Basic

Subject: Compound Interest

Type: Definitions

16. Calculating the present value of a future cash flow to determine its value today is called: A) Discounted cash flow valuation. B) The discount rate. C) Future value compounding. D) Present value compounding. E) Timing the cash flow. Ans: A

Level: Basic

Subject: Discounted Cash Flow

Type: Definitions

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Page 3

Chapter 5 Introduction to Valuation: The Time Value of Money

17. The rate used to find the present value of a future payment is called the: A) Simple rate. B) Discount rate. C) Compound rate. D) Future value rate. E) Loan rate. Ans: B

Level: Basic

Subject: Discount Rate

Type: Definitions

18. The discounted value of money is called the: A) Compound value. B) Simple value. C) Future value. D) Complex value. E) Present value. Ans: E

Level: Basic

Subject: Present Value

Type: Definitions

19. The rate of return used when computing a present value is referred to as the ______ rate while the rate used when computing a future value is referred to as the _____ rate. A) Compound; discount B) Compound; simple C) Compound; compound D) Discount; discount E) Discount; compound Ans: E

Level: Basic

Subject: Discount Rate Versus Compound Rate

Type: Definitions

20. On a financial calculator, the symbol "N" represents the: A) Current value. B) Time periods. C) Future value. D) Rate of simple interest. E) Rate of compound interest. Ans: B

Level: Basic

Subject: Number Of Periods

Type: Definitions

21. The present value equation is: A) PV = FVt + (1 + r)t. B) PV = FVt - (1 + r)t . C) PV = FVt / [1 / (1 + r)t]. D) PV = FVt / (1 + r)t . E) PV = FVt * (1 + r)t . Ans: D

Level: Basic

Subject: Present Value Equation

Type: Definitions

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Page 4

Chapter 5 Introduction to Valuation: The Time Value of Money

22. You are choosing between investments offered by two different banks. One promises a return of 10% for three years using simple interest while the other offers a return of 10% for three years using compound interest. You should: A) Choose the simple interest option because both have the same basic interest rate. B) Choose the compound interest option because it provides a higher return. C) Choose the compound interest option only if the compounding is for monthly periods. D) Choose the simple interest option only if compounding occurs more than once a year. E) Choose the compound interest option only if you are investing less than $5,000. Ans: B

Level: Basic

Subject: Simple vs. Compound Interest

Type: Concepts

23. Suppose you are trying to find the present value of two different cash flows using the same interest rate for each. One cash flow is $1,000 ten years from now, the other $800 seven years from now. Which of the following is true about the discount factors used in these valuations? A) The discount factor for the cash flow ten years away is always less than or equal to the discount factor for the cash flow that is received seven years from now. B) Both discount factors are greater than one. C) Regardless of the interest rate, the discount factors are such that the present value of the $1,000 will always be greater than the present value of the $800. D) Since the payments are different, no statement can be made regarding the discount factors. E) You should factor in the time differential and choose the payment that arrives the soonest. Ans: A

Level: Basic

Subject: Present Value Factors

Type: Concepts

24. Given r and t greater than zero: I. Present value interest factors are less than one. II. Future value interest factors are less than one. III. Present value interest factors are greater than future value interest factors. IV. Present value interest factors grow as t grows, provided r is held constant. A) I only B) I and III only C) I and IV only D) II and III only E) II and IV only Ans: A

Level: Basic

Subject: Time Value

Type: Concepts

25. Which of the following statements is/are accurate? All else the same, ______________. I. present values increase as the discount rate increases II. present values increase the further away in time the future value III. present values are always smaller than future values when both r and t are positive A) I only B) I and II only C) II only D) III only E) II and III only Ans: D

Level: Basic

Subject: Present Value

Type: Concepts

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Page 5

Chapter 5 Introduction to Valuation: The Time Value of Money

26. Fresh out of college, you are negotiating with your prospective new employer. They offer you a signing bonus of $2,000,000 today or a lump sum payment of $2,500,000 three years from now. If you can earn 7% on your invested funds, which of the following is true? A) Take the signing bonus because it has the lower present value. B) Take the signing bonus because it has the higher future value. C) Take the lump sum because it has the higher present value. D) Take the lump sum because it has the lower future value. E) Based on these numbers, you are indifferent between the two. Ans: C

Level: Basic

Subject: Present Value Lump Sum

Type: Concepts

27. Mary plans on saving $1,000 a year for ten years. She would like to know the value of these savings today. Mary should solve for the: A) Present value. B) Present value factor. C) Future value. D) Future value factor. E) Compounded value. Ans: A

Level: Basic

Subject: Present Value

Type: Concepts

28. As long as the interest rate is greater than zero, the present value of a single sum will always: A) Increase as the interest rate increases. B) Be less than the future value. C) Decrease as the period of time decreases. D) Equal the future value if the time period is one year. E) Increase as the number of periods increases. Ans: B

Level: Intermediate

Subject: Present Value

Type: Concepts

29. Which of the following statements is (are) true concerning the present value of a single sum? I. The higher the discount rate, the higher the present value. II. The longer the time period, the higher the present value. III. The larger the future value, the larger the present value. IV. The larger the present value factor, the larger the present value. A) IV only B) I and IV only C) III and IV only D) I, III, and IV only E) I, II, III, and IV Ans: C

Level: Intermediate

Subject: Present Value

Type: Concepts

30. The greater the number of years, the: A) Smaller the future value of a single sum. B) Larger the present value of a single sum. C) Larger the present value factor. D) Smaller the future value factor. E) Greater the compounding effect. Ans: E

Level: Intermediate

Subject: Number Of Periods

Type: Concepts

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Page 6

Chapter 5 Introduction to Valuation: The Time Value of Money

31. Monika has $6,000 in her investment account. She wants to withdraw her funds when her account reaches $10,000. A decrease in the rate of return she earns will: A) Increase the value of her account faster. B) Cause her to wait longer before withdrawing her money. C) Cause the present value of her account to decrease. D) Allow her to withdraw more money sooner. E) Cause the compounding effect to increase. Ans: B

Level: Intermediate

Subject: Interest Rate

Type: Concepts

32. Tom and Antonio both want to open savings accounts today. Tom wants to have $1,000 in his savings account six years from now. Antonio wants to have $1,000 in his savings account three years from now. Which of the following statements is(are) correct assuming that both Antonio and Tom earn the same rate of interest? I. Tom needs to deposit more money into his account today than does Antonio. II. Tom will need to deposit twice the amount of money today as Antonio. III. Antonio needs to deposit more money into his account today than does Tom. IV. Antonio needs to deposit twice the amount of money today as Tom. A) I only B) III only C) I and II only D) III and IV only Ans: B

Level: Intermediate

Subject: Compound Interest

Type: Concepts

33. Isabelle wants to invest $1,000. She wants to withdraw her money three years from now. Which bank should she use if she wishes to maximize her investment? A) Bank A, which offers a simple rate of 4%. B) Bank B, which offers a simple rate of 5%. C) Bank C, which offers a rate of 4% compounded annually. D) Bank D, which offers a rate of 5% compounded monthly. E) Bank E, which offers a rate of 5% compounded annually. Ans: D

Level: Basic

Subject: Interest Rate

Type: Concepts

34. Neal wants to borrow $2,500 and has received the following offers from his local banks. Which offer should Neal accept if he wants to repay the loan in one single payment two years from now? A) Bank A, which offers a simple rate of 4%. B) Bank B, which offers a simple rate of 5%. C) Bank C, which offers a rate of 4% compounded annually. D) Bank D, which offers a rate of 5% compounded annually. E) Bank E, which offers a rate of 5% compounded monthly. Ans: A

Level: Intermediate

Subject: Interest Rate

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 7

Chapter 5 Introduction to Valuation: The Time Value of Money

35. The future value will increase: I. The longer the period of time. II. The shorter the period of time. III. The higher the rate of interest. IV The lower the rate of interest. A) I and III only. B) I and IV only. C) II and III only. D) II and IV only. Ans: A

Level: Basic

Subject: Future Value

Type: Concepts

36. At a 6% rate of interest you will double your money in approximately ___ years. A) 3 B) 6 C) 12 D) 24 E) 48 Ans: C

Level: Basic

Subject: Rule Of 72

Type: Concepts

37. At a 3% rate of interest, you will quadruple your money in approximately ____ years. A) 3 B) 6 C) 12 D) 24 E) 48 Ans: E

Level: Intermediate

Subject: Rule Of 72

Type: Concepts

38. The present value factor will decrease: A) The longer the period of time. B) The higher the future value. C) The lower the interest rate. D) The higher the present value. E) The slower the rate of growth. Ans: A

Level: Intermediate

Subject: Present Value Factor

Type: Concepts

39. The future value factor will decrease: A) The longer the period of time. B) The lower the present value factor. C) The lower the interest rate. D) The higher the present value. E) The higher the future value. Ans: C

Level: Intermediate

Subject: Future Value Factor

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 8

Chapter 5 Introduction to Valuation: The Time Value of Money

40. The future value of a single sum will increase more rapidly when: I. The interest rate increases. II. The interest rate decreases. III. The frequency of compounding increases. IV. The frequency of compounding decreases. A) I only. B) III only. C) I and III only. D) II and III only. E) I and IV only. Ans: C

Level: Intermediate

Subject: Compound Growth

Type: Concepts

41. Kurt invests $1,000 at a 10% rate of return for twenty years. The return is based on simple interest that is paid at the end of each year. Which one of the following is correct? A) Kurt will receive more interest in year twenty than in year one. B) Kurt will receive the same amount of interest each year. C) Kurt will not receive any interest for the first year. D) Kurt will receive less interest in year twelve than in year eight. E) Kurt will receive interest on both the principal and year one's interest in year two. Ans: B

Level: Intermediate

Subject: Simple Interest

Type: Concepts

42. Many financial calculators require that: A) The interest rate be input as a decimal, such as .07. B) Interest be compounded on an annual basis. C) The present value be input as a negative number when solving for the interest rate. D) Interest be computed on a monthly basis. E) Either the present value or the future value be input as a negative number when solving for the number of periods. Ans: E

Level: Intermediate

Subject: Financial Calculator

Type: Concepts

43. When using a financial calculator, you should: I. Check the mode for beginning or ending. II. Clear the calculator before starting a problem. III. Use a sufficient number of decimal places. IV. Check the number of payments per year. A) Do II and III only. B) Do I, II, and III only. C) Do I and II only. D) Do II, III, and IV only. E) Do I, II, III, and IV. Ans: E

Level: Intermediate

Subject: Financial Calculator

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 9

Chapter 5 Introduction to Valuation: The Time Value of Money

44. The formula for a present value calculation using Excel is: A) PV (rate, nper, pmt, pv). B) PV (nper, pmt, fv). C) PV (rate, pmt, pv, fv). D) PV (rate, nper, pmt, fv). E) PV (rate, nper, pmt). Ans: D

Level: Intermediate

Subject: Spreadsheet

Type: Concepts

45. The future value of C invested at r percent for t periods is: A) FV = C / (1 + r)t. B) FV = (C)(1 + t)r . C) FV = (C)(1 + r)t . D) FV = [C][1 / (1 + r)t]. E) FV = (C)(1 + r)(t). Ans: C

Level: Basic

Subject: Future Value

Type: Concepts

46. You received a $1 savings account earning 5% on your 1st birthday. How much will you have in the account on your 40th birthday if you don't withdraw any money before then? A) $5.89 B) $6.34 C) $6.70 D) $7.00 E) $7.04 Ans: C

Level: Basic

Subject: Future Value Lump Sum

Type: Problems

47. What is the future value of $25,000 received today if it is invested at 6.5% compounded annually for six years? A) $17,133.35 B) $27,476.42 C) $36,478.56 D) $39,521.75 E) $41,374.89 Ans: C

Level: Basic

Subject: Future Value Lump Sum

Type: Problems

48. Your parents agree to pay half of the purchase price of a new car when you graduate from college. You will graduate and buy the car two years from now. You have $6,000 to invest today and can earn 10% on invested funds. If your parents match the amount of money you have in two years, what is the maximum you can spend on the new car? A) $7,260 B) $11,948 C) $12,000 D) $13,250 E) $14,520 Ans: E

Level: Basic

Subject: Future Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 10

Chapter 5 Introduction to Valuation: The Time Value of Money

49. Many economists view a 3% annual inflation rate as "acceptable". Assuming a 3% annual increase in the price of automobiles, how much will a new Suburban cost you five years from now, if today's price is $38,000? A) $32,779 B) $36,110 C) $40,575 D) $42,813 E) $44,052 Ans: E

Level: Basic

Subject: Compounding

Type: Problems

50. An account paying annual compound interest was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the same interest rate is offered on an account paying simple interest, how much income would be earned over the same time period? A) $86.20 B) $92.47 C) $413.80 D) $436.29 E) $500.00 Ans: C

Level: Basic

Subject: Simple Interest

Type: Problems

51. An account paying annual compound interest was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the same interest rate is offered on an account paying simple interest, how much income would be earned each year over the same time period? A) $36.97 B) $40.41 C) $40.75 D) $41.38 E) $50.00 Ans: D

Level: Basic

Subject: Simple Interest

Type: Problems

52. An account was opened with $1,000 three years ago. Today, the account balance is $1,157.63. If the account earns a fixed annual interest rate, how long will it take until the account has earned a total of $225 in simple interest? A) Less than one more year. B) Between one and two more years. C) Between two and three more years. D) Between three and four more years. E) Between four and five more years. Ans: B

Level: Intermediate

Subject: Simple Interest

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 11

Chapter 5 Introduction to Valuation: The Time Value of Money

53. You have $500 in an account which pays 5% compound interest. How much additional dollars of interest would you earn over four years if you moved the money to an account earning 6%? A) $21.89 B) $23.49 C) $24.93 D) $25.88 E) $29.94 Ans: B

Level: Intermediate

Subject: Annual Interest

Type: Problems

54. An account was opened with an investment of $1,000 ten years ago. The ending balance in the account is $1,500. If interest was compounded annually, what rate was earned on the account? A) 1.0% B) 2.2% C) 2.9% D) 3.8% E) 4.1% Ans: E

Level: Basic

Subject: Investment Returns

Type: Problems

55. An account was opened with $1,000 ten years ago. Today, the account balance is $1,500. If the account paid interest compounded annually, how much interest on interest was earned? A) $86.20 B) $93.10 C) $102.39 D) $130.28 E) $500.00 Ans: A

Level: Intermediate

Subject: Interest On Interest

Type: Problems

56. How much would you have to invest today at 8% compounded annually to have $25,000 available for the purchase of a car four years from now? A) $18,267.26 B) $18,375.75 C) $19,147.25 D) $21,370.10 E) $22,149.57 Ans: B

Level: Basic

Subject: Present Value Lump Sum

Type: Problems

57. You will receive a $100,000 inheritance in 20 years. You can invest that money today at 6% compounded annually. What is the present value of your inheritance? A) $27,491.53 B) $29,767.15 C) $31,180.47 D) $35,492.34 E) $100,000.00 Ans: C

Level: Basic

Subject: Present Value Lump Sum

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 12

Chapter 5 Introduction to Valuation: The Time Value of Money

58. You just won the lottery and want to put some money away for your child's college education. College will cost $65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest today? A) $9,828.18 B) $11,763.07 C) $13,690.82 D) $15,258.17 E) $16,266.19 Ans: E

Level: Basic

Subject: Present Value Lump Sum

Type: Problems

59. You are supposed to receive $2,000 five years from now. At an interest rate of 6%, what is that $2,000 worth today? A) $1,491.97 B) $1,492.43 C) $1,494.52 D) $1,497.91 E) $1,499.01 Ans: C

Level: Basic

Subject: Present Value Lump Sum

Type: Problems

60. Andy promises Opie that he will give him $5,000 upon his graduation from college at Mayberry U. How much must Andy invest today to make good on his promise, if Opie is expected to graduate in 12 years and Andy can earn 5% on his money? A) $2,135.32 B) $2,784.19 C) $2,881.11 D) $3,012.88 E) $8,979.28 Ans: B

Level: Basic

Subject: Present Value Lump Sum

Type: Problems

61. Your grandfather placed $2,000 in a trust fund for you. In 10 years the fund will be worth $5,000. What is the rate of return on the trust fund? A) 5.98% B) 8.76% C) 9.60% D) 9.98% E) 10.14% Ans: C

Level: Basic

Subject: Interest Rate

Type: Problems

62. All County Insurance, Inc. promises to pay Ted $1 million on his 65th birthday in return for a one-time payment of $75,000 today. (Ted just turned 25. ) At what rate of interest would Ted be indifferent between accepting the company's offer and investing the premium on his own? A) 2.4% B) 5.5% C) 6.1% D) 6.7% E) 7.2% Ans: D

Level: Basic

Subject: Interest Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 13

Chapter 5 Introduction to Valuation: The Time Value of Money

63. In 1889, Vincent Van Gogh's painting, "Sunflowers", sold for $125. One hundred years later it sold for $36 million. Had the painting been purchased by your great-grandfather and passed on to you, what annual return on investment would your family have earned on the painting? A) 9.11% B) 10.09% C) 11.88% D) 11.99% E) 13.40% Ans: E

Level: Basic

Subject: Compounding

Type: Problems

64. You need $2,000 to buy a new stereo for your car. If you have $800 to invest at 5% compounded annually, how long will you have to wait to buy the stereo? A) 6.58 years B) 8.42 years C) 14.58 years D) 15.75 years E) 18.78 years Ans: E

Level: Basic

Subject: Number Of Periods

Type: Problems

65. Granny puts $35,000 into a bank account earning 4%. You can't withdraw the money until the balance has doubled. How long will you have to leave the money in the account? A) 16 years B) 17 years C) 18 years D) 19 years E) 20 years Ans: C

Level: Basic

Subject: Rule Of 72

Type: Problems

Use the following to answer questions 66-70: In a growing midwestern town, the number of eating establishments at the end of each of the last five years are as follows: Year 1 = 143; Year 2 = 149; Year 3 = 162; Year 4 = 171; Year 5 = 178 66. From the end of year 1 to the end of year 5, the number of eating establishments grew at a rate of ____________ compounded annually. A) 4.2% B) 4.7% C) 5.6% D) 8.7% E) 9.3% Ans: B

Level: Basic

Subject: Growth Rates

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

67. Between the end of year 2 and the end of year 3, the number of eating establishments grew at a rate of _________ compounded annually. A) 4.2% B) 4.7% C) 5.6% D) 8.7% E) 9.3% Ans: D

Level: Basic

Subject: Growth Rates

Type: Problems

68. If, over the next five years, eating establishments are expected to grow at the same rate as they did during year 5, forecast the number of eating establishments at the end of year 10. A) 217 B) 219 C) 221 D) 223 E) 225 Ans: A

Level: Basic

Subject: Future Value

Type: Problems

69. If the number of eating establishments are expected to grow in year 6 at the same rate as the percentage increase in year 5, how many new eating establishments will be added in year 6? A) 5 B) 6 C) 7 D) 8 E) 9 Ans: C

Level: Basic

Subject: Future Value

Type: Problems

70. If the town's population was 62,000 at the end of year 5, and the population grew at the same annual rate as the number of eating establishments between the end of year 1 and the end of year 5, what was the town's population at the end of year 1? A) 49,809 B) 51,435 C) 53,230 D) 54,330 E) 56,730 Ans: A

Level: Basic

Subject: Present Value

Type: Problems

Use the following to answer questions 71-77: A savings account, which started with a balance of $500, has the following end of year balances. No withdrawals were made over the life of the account, but there was one additional deposit of $50 made at the beginning of year 5. Year 1 = $550; Year 2 = $580; Year 3 = $660; Year 4 = $772; Year 5 = $950

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 15

Chapter 5 Introduction to Valuation: The Time Value of Money

71. If you leave the money in the account for another five years and the account earns 8% compounded annually, what will the balance in the account grow to? A) $1,341.05 B) $1,347.82 C) $1,395.86 D) $1,406.23 E) $1,491.15 Ans: C

Level: Basic

Subject: Future Values

Type: Problems

72. During year 2, the account earned ________. A) 1.3% B) 2.8% C) 4.6% D) 5.5% E) 7.5% Ans: D

Level: Basic

Subject: Interest Rate

Type: Problems

73. During year 5, the account earned ________ compounded annually. A) 11.6% B) 12.8% C) 14.6% D) 15.6% E) 23.1% Ans: D

Level: Intermediate

Subject: Interest Rate

Type: Problems

74. Over the first four years, the account earned ________ compounded annually. A) 11.5% B) 12.8% C) 14.6% D) 15.6% E) 23.1% Ans: A

Level: Basic

Subject: Interest Rate

Type: Problems

75. In which year did the account earn its highest annually compounded return? A) Year 1 at 10% B) Year 2 at 5.45% C) Year 3 at 13.8% D) Year 4 at 17.0% E) Year 5 at 15.6% Ans: D

Level: Intermediate

Subject: Interest Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 16

Chapter 5 Introduction to Valuation: The Time Value of Money

76. If the account earned a total of $300 in simple interest over its life, how much was earned in compound interest? A) $25 B) $50 C) $75 D) $100 E) $125 Ans: D

Level: Basic

Subject: Simple Interest

Type: Problems

77. During years 2 and 3 combined, the account earned $10 compound interest. How much was in simple interest? A) $30 B) $80 C) $105 D) $110 E) $120 Ans: C

Level: Intermediate

Subject: Compound Interest

Type: Problems

78. Tishie invests $3,000 today at a 9% rate of return. She wants to have $24,000 to give to her granddaughter Kathy for college 16 years from now. Which one of the following statements is correct concerning Tishie's situation? A) Tishie will have the $24,000 when she wants it. B) Tishie would have to wait an additional ten years to have $24,000. C) Tishie would have to earn a 10% rate of return to have $24,000 in 16 years. D) Tishie will only have approximately $12,000 sixteen years from now. E) Tishie should plan on only giving Kathy $10,000 in sixteen years. Ans: D

Level: Intermediate

Subject: Rule Of 72

Type: Problems

79. What is the present value of $2,800 to be received three years from now if the discount rate is 9.5%? A) $2,114.48 B) $2,132.63 C) $2,361.48 D) $2,734.54 E) $3,676.21 Ans: B

Level: Basic

Subject: Present Value

Type: Problems

80. The Blackwell Co. expects to receive $135,000 from an insurance settlement four years from now. If the company can earn 11% on its investments, what is the value of the insurance settlement worth today? A) $85,368.94 B) $87,693.43 C) $88,928.68 D) $130,161.39 E) $140,018.48 Ans: C

Level: Basic

Subject: Present Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

81. Isaac and Faith both want to have $5,000 in three years. Isaac expects to earn 8% on his investments and Faith expects a 7% rate of return. Which one of the following statements is correct concerning the amount of money they each need to invest today? A) Faith needs to deposit $112.33 more than Isaac today. B) Faith needs to deposit $173.33 more than Isaac today. C) Isaac needs to deposit $3,699.16 today. D) Faith needs to deposit $3,081.49 today. E) Both Faith and Isaac should deposit $3,969.16 today. Ans: A

Level: Intermediate

Subject: Present Value

Type: Problems

82. Courtney invests $1,200 today. If she can earn a 13.25% rate of return for the next two years, how much money will she have at the end of the two years? A) $1,203.18 B) $1,232.01 C) $1,359.00 D) $1,539.07 E) $1,742.99 Ans: D

Level: Basic

Subject: Future Value

Type: Problems

83. A customer makes two offers to settle a disputed account. He will either pay you $500 today or pay you $650 in three years. Which one of the following is correct if your company earns 10.5% on its surplus funds? A) The company should accept the $650 offer as it pays $150 more. B) The company should accept the $650 offer as it is worth more today. C) The company should accept the $650 offer as it is worth $12.42 more today. D) The company should accept the $500 offer as it is worth $18.24 more today. E) The company should accept the $500 offer as it is worth $512.42 today. Ans: D

Level: Intermediate

Subject: Present Value

Type: Problems

84. What is the future value of $7,540 invested at 6.5% interest for seven years? A) $10,330.45 B) $11,001.93 C) $11,041.26 D) $11,717.06 E) $11,337.37 Ans: D

Level: Basic

Subject: Future Value

Type: Problems

85. The James Co. plans on saving money to buy some new equipment. The company is opening an account today with a deposit of $15,000 and expects to earn 4% interest. After 3 years, the firm wants to add an additional $50,000 to the account. If the account continues to earn 4%, how much money will the James Co. have in their account five years from now? A) $66,872.96 B) $68,249.79 C) $70,952.96 D) $72,329.79 E) $81,361.18 Ans: D

Level: Challenge

Subject: Future Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

86. Five friends all open investment accounts today. Which one will withdraw the largest amount of money from their account assuming that they each withdraw their funds at the end of their initial investment period? A) John, who invests $1,000 for eight years at 6% simple interest. B) Terry, who invests $1,000 for four years at 9% with interest compounded annually. C) Alicia, who invests $800 for ten years at 11% with interest compounded annually. D) Kristi, who invests $1,200 for six years at 8% simple interest. E) Roger, who invests $900 for nine years at 9% with interest compounded annually. Ans: C

Level: Challenge

Subject: Future Value

Type: Problems

87. Alexander Industries just had a very profitable year. The owner has decided to invest $225,000 of the profits in a venture that pays an 8% rate of return for fifteen years. How much more would the investment have been worth if the owner could have made 9% on this investment? A) $52,910.25 B) $105,820.50 C) $211,641.00 D) $713,738.05 E) $819,558.55 Ans: B

Level: Intermediate

Subject: Future Value

Type: Problems

88. Gretchen Enterprises borrowed $149,500 for two years from the bank. At the end of the two years, they repaid the loan with one payment of $176,590. What was the interest rate on the loan? A) 8.68% B) 9.06% C) 10.00% D) 10.42% E) 18.12% Ans: A

Level: Intermediate

Subject: Interest Rate

Type: Problems

89. Six years ago, Marti invested $3,500 in an account. No other investments or withdrawals have been made. Today the account is worth $7,403.16. What rate of return has Marti earned thus far? A) 12.86% B) 13.30% C) 15.96% D) 18.58% E) 19.20% Ans: B

Level: Intermediate

Subject: Interest Rate

Type: Problems

90. Ito invested $4,350. After seven years he had an account value of $6,980.58. Maria invested $5,920. After six years she had an account value of $8,834.62. Which one of the following statements is correct? A) Maria earned a rate of interest that was 0.9% higher than Ito's rate. B) Maria earned a rate of interest of 5.89%. C) Ito earned a rate of interest that was 0.09% higher than Maria's rate. D) Ito earned a rate of interest of 6.90%. E) Both Ito and Maria earned the same rate of interest. Ans: C

Level: Intermediate

Subject: Interest Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

91. Koji invested $3,300 at 7.75% interest. After a period of time he withdrew $9,383.31. How long did Koji have his money invested? A) 13 years B) 14 years C) 15 years D) 16 years E) 17 years Ans: B

Level: Basic

Subject: Number Of Periods

Type: Problems

92. Sampson, Inc. invested $1.325 million in a project that earned an 8.25% rate of return. Sampson sold their investment for $3,713,459. How much sooner could Sampson have sold the company if they only wanted $3 million from the project? A) 2.69 years B) 3.33 years C) 5.17 years D) 6.67 years E) 10.31 years Ans: A

Level: Challenge

Subject: Number Of Periods

Type: Problems

93. Lakeside Inc. invested $735,000 at an 11.25% rate of return. The company sold their investment for $1,067,425. How much longer would Lakeside have had to wait if they had wanted to sell their investment for $1.25 million? A) .98 year B) 1.48 years C) 1.98 years D) 2.31 years E) 3.50 years Ans: B

Level: Intermediate

Subject: Number Of Periods

Type: Problems

94. Martha is going to receive $6,000 in two years from Tom. She will receive an additional $4,000 in three years from Tom. She earns 7.15% on her investments. How much is this money from Tom worth to Martha today? A) $7,893.46 B) $8,477.47 C) $8,891.74 D) $9,225.97 E) $9,251.50 Ans: B

Level: Intermediate

Subject: Present Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

95. The I.C. James Co. invested $10,000 six years ago at 5% simple interest. The I.M. Smart Co. invested $10,000 six years ago at 5% interest which is compounded annually. Which one of the following statements is true concerning these two investments? I. The I.C. James Co. has an account value of $13,400.96 today. II. The I.C. James Co. will have an account value of $13,400.96 six years from now. III. The I.M Smart Co. will earn $525 interest in the second year. IV Both the I.C. James Co. and the I.M. Smart Co. will earn $500 interest in the first year. A) I and III only B) I, III and IV only C) II and IV only D) II, III and IV only E) III and IV only Ans: E

Level: Challenge

Subject: Interest Rate

Type: Problems

96. The Smith Co. has $450,000 to invest at 5.5% interest. How much more money will they have if they invest these funds for eight years instead of five years? A) $62,948.21 B) $68,851.36 C) $74,250.00 D) $78,408.62 E) $102,476.93 Ans: E

Level: Intermediate

Subject: Future Value

Type: Problems

97. Today Richard is investing $1,000 at 5% interest for five years. One year ago, Richard invested $1,000 at 6.25% for six years. How much money will Richard have saved in total five years from now if both investments compound interest annually? A) $2,543.77 B) $2,641.98 C) $2,678.81 D) $2,630.36 E) $2,714.99 Ans: E

Level: Intermediate

Subject: Future Value

Type: Problems

98. Draw a picture illustrating the future value of $1, using five different interest rates (including 0%) and maturities ranging from today to 10 years from now. Plot time to maturity on the horizontal axis and dollars on the vertical axis. (Note: you need not make any calculations, draw the figure using your intuition.) Ans: The student should basically replicate Figure 5.2. Level: Basic

Subject: Future Values

Type: Essays

99. Explain what compounding is and the relationship between compound interest earned and the number of years over which an investment is compounded. Ans: Compounding is earning interest on interest. Compounding is not significant over short time periods, but increases in importance the longer the time period considered. Level: Basic

Subject: Compounding

Type: Essays

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

100. Explain intuitively why it is that present values decrease as the discount rate increases. Ans: Intuitively, a dollar today is worth more than a dollar tomorrow. As a practical matter, the discount rate is an opportunity cost, and the higher the rate, the higher the cost. Level: Basic

Subject: Present Value & Discounting

Type: Essays

101. You are considering two lottery payment streams, choice A pays $1,000 today and choice B pays $1,750 at the end of five years from now. Using a discount rate of 5%, based on present values, which would you choose? Using the same discount rate of 5%, 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.) Ans: PV of A = $1,000; PV of B = $1,371; FV of A = $1,276; FV of B = $1,500. Based on both present values and future values, B is the better choice. The student should recognize that finding present values and finding 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. Level: Intermediate

Subject: Comparing Lump Sums

Type: Essays

102. At an interest rate of 10% and using the Rule of 72, how long will it take to double the value of a lump sum invested today? How long will it take after that until the account grows to four times the initial investment? Given the power of compounding, shouldn't it take less time for the money to double the second time? Ans: It will take 7.2 years to double the initial investment, then another 7.2 years to double it again. That is, it takes 14.4 years for the value to reach four times the initial investment. Compounding doesn't affect the amount of time it takes for an investment to double the second time, but note that during the first 7.2 years, the interest earned is equal to 100% of the initial investment. During the second 7.2 years, the interest earned is equal to 200% of the initial investment. That is the power of compounding. Level: Intermediate

Subject: The Rule of 72

Type: Essays

103. Some financial advisors recommend you increase the amount of federal income taxes withheld from your paycheque each month so that you will get a larger refund come April 15. That is, you take home less today but get a bigger lump sum when you get your refund. Based on your knowledge of the time value of money, what do you think of this idea? Explain. Ans: Some students may slip in a discussion about the benefits of forced savings, etc., but these issues are based on preferences, not the time value of money. Based on the time value of money, the students should recommend the opposite tack, that is, withhold as little as possible and pay the tax bill when it comes the following year. This is the usual dollar today versus a dollar tomorrow argument. Of course, the astute student will note the potential tax complications of this strategy, namely the CCRA penalty for insufficient withholding, but the basic argument still applies. Level: Intermediate

Subject: The Time Value Of Money

Type: Essays

Copyright © 2005 McGraw-Hill Ryerson Limited.

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Chapter 5 Introduction to Valuation: The Time Value of Money

104. The notion that money has "time-value" is based on the existence of a nonzero "opportunity rate", i.e., a rate of return at which it is possible to invest. Why is the opportunity rate so important? Ans: We have found that, while they are able to perform compounding and discounting computations successfully, some students never really grasp the "why" of the computation. This question is designed to probe the issue of "why time value procedures work" more deeply. An adequate answer will indicate that the opportunity rate is the rate of return that equates two different dollar values at two different points in time. That is, a rational investor will be indifferent to $.9091 today and $1.00 in one year. Level: Intermediate

Subject: Opportunity Rates

Type: Essays

105. Susie and Tim are twins. Susie invests $5,000 at age 20 and earns 5% compound interest. Tim invests $10,000 at age 40 and earns 5% compound interest. No matter how long they live, Tim will never have as much money as Susie. Explain why. Ans: By age 40, Susie's funds had grown to $13,266.49, which is more than the amount of money Tim is investing at that point in time. The key here is time. Time is the exponential function and therefore has a tremendous impact on the value of money. Even though Tim invests twice as much money, he will always have less than Susie. Level: Intermediate

Subject: Future Value

Type: Essays

106. Present value is used extensively by managers who are reviewing proposed projects. Why is this so and how does the present value of a cash flow assist management in making these business decisions? Ans: By converting cash flows into present values, management can compare and contrast various alternative opportunities and determine which course of action is best for the firm. The present value allows management to view projects on an equivalent basis. Also, by knowing the present value of the future cash flows of a project, management can determine if those cash inflows are sufficient to offset the required investment in the project. While students may have various answers, this question starts them thinking about financial decision-making, which is covered later in the text. Level: Intermediate

Subject: Present Value

Type: Essays

Copyright © 2005 McGraw-Hill Ryerson Limited.

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