A book

Chapter 6 Discounted Cash Flow Valuation 1. You hold a winning ticket from your provincial lottery. It entitles the bearer to receive payments of $50,000 at the end of each of the next 20 years. Given what you know about the time value of money, you should be able to sell this ticket for no less than $1 million in the open market. Ans: False

Level: Basic

Subject: Present Values

Type: Concepts

2. You have just won a lottery prize. You can choose to receive $750,000 today or an annual payment of $50,000 at the end of each of the next 20 years. The interest rate that makes you indifferent between the two is 2.91%, and at higher rates you should take the lump sum. Ans: True

Level: Basic

Subject: Present Value & Interest Rates

Type: Concepts

3. An annuity stream of cash flow payments is: A) A set of level cash flows occurring each time period for a fixed length of time. B) A set of level cash flows occurring each time period forever. C) A set of increasing cash flows occurring each time period for a fixed length of time. D) A set of increasing cash flows occurring each time period forever. E) A set of arbitrary cash flows occurring each time period for no more than 10 years. Ans: A

Level: Basic

Subject: Annuity

Type: Definitions

4. The present value factor for annuities is calculated as: A) (1 + present value factor)/r B) (1 - present value factor)/r C) Present value factor + (1/r) D) (Present value factor/r) + (1/r) Ans: B

Level: Basic

Subject: Present Value Factor For Annuities

Type: Definitions

5. The future value factor for annuities is calculated as: A) Future value factor + r B) (1/r) + (future value factor/r) C) (1/r) + future value factor D) (Future value factor - 1)/r E) (Future value factor + 1)/r Ans: D

Level: Basic

Subject: Future Value Factor For Annuities

Type: Definitions

6. Annuities where the payments occur at the end of each time period are called ________, whereas _____________ refer to annuity streams with payments occurring at the beginning of each time period. A) ordinary annuities; early annuities B) late annuities; straight annuities C) straight annuities; late annuities D) annuities due; ordinary annuities E) ordinary annuities; annuities due Ans: E

Level: Basic

Subject: Annuities Due

Type: Definitions

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 1

Chapter 6 Discounted Cash Flow Valuation

7. An annuity stream where the payments occur forever is called a(n) ___________. A) annuity due B) indemnity C) perpetuity D) amortized cash flow stream E) amortization table Ans: C

Level: Basic

Subject: Perpetuity

Type: Definitions

8. The interest rate expressed in terms of the interest payment made each period is called the: A) Stated interest rate. B) Compound interest rate. C) Effective annual rate. D) Periodic interest rate. E) Daily interest rate. Ans: A

Level: Basic

Subject: Stated Interest Rates

Type: Definitions

9. The interest rate expressed as if it were compounded once per year is called the: A) Stated interest rate. B) Compound interest rate. C) Effective annual rate. D) Periodic interest rate. E) Daily interest rate. Ans: C

Level: Basic

Subject: Effective Annual Rate

Type: Definitions

10. The interest rate charged per period multiplied by the number of periods per year is called the: A) Effective annual rate (EAR). B) Annual percentage rate (APR). C) Periodic interest rate. D) Compound interest rate. E) Daily interest rate. Ans: B

Level: Basic

Subject: Annual Percentage Rate

Type: Definitions

11. A loan where the borrower receives money today and repays a single lump sum at some time in the future is called a(n) ___________ loan. A) amortized B) continuous C) balloon D) pure discount E) interest-only Ans: D

Level: Basic

Subject: Pure Discount Loan

Type: Definitions

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 2

Chapter 6 Discounted Cash Flow Valuation

12. A loan where the borrower pays interest each period and repays the entire principal of the loan at some point in the future is called a(n) ___________ loan. A) amortized B) continuous C) balloon D) pure discount E) interest-only Ans: E

Level: Basic

Subject: Interest-Only Loan

Type: Definitions

13. A loan where the borrower pays interest each period, and repays some or all of the principal of the loan over time is called a(n) __________ loan. A) amortized B) continuous C) balloon D) pure discount E) interest-only Ans: A

Level: Basic

Subject: Amortized Loan

Type: Definitions

14. A loan where the borrower pays interest each period, repays part of the principal of the loan over time, and repays the remainder of the principal at the end of the loan, is called a(n) _____________ loan. A) amortized B) continuous C) balloon D) pure discount E) interest-only Ans: C

Level: Basic

Subject: Balloon Loan

Type: Definitions

15. Which of the following fit the definition of an annuity? I. $100 a quarter for 10 years II. $200 a year forever III. $10 a week for 1,000 weeks IV $150 a month for 72 months A) I and IV only B) II only C) III and IV only D) I, III, and IV only E) I, II, III, and IV Ans: D

Level: Basic

Subject: Annuity

Type: Definitions

16. The formula {C}{[1 * (1 / (1 + r)t )]/ r} is the _______ formula. A) Future value B) Future value of an annuity C) Present value D) Present value of an annuity E) Perpetuity Ans: D

Level: Basic

Subject: Present Value Factor For An Annuity

Copyright © 2005 McGraw-Hill Ryerson Limited.

Type: Definitions

Page 3

Chapter 6 Discounted Cash Flow Valuation

17. An annuity due is a series of: A) Equal payments that occur at the beginning of each time period and continue forever. B) Unequal payments that occur at the beginning of each time period for a set period of time. C) Equal payments that occur at the beginning of each time period for a set period of time. D) Unequal payments that occur at the end of each time period for a set period of time. E) Equal payments that occur at the end of each time period and continue forever. Ans: C

Level: Basic

Subject: Annuity Due

Type: Definitions

18. A perpetuity is a series of payments that: A) Are equal in amount and occur over a set period of time. B) Vary in amount but occur forever. C) Vary in amount and occur over a set period of time. D) Are unequal in amount and occur over a set period of time. E) Are equal in amount and continue forever. Ans: E

Level: Basic

Subject: Perpetuity

Type: Definitions

19. The effective annual rate is equal to: A) [1 - Quoted rate / m]t / r. B) [1 - Quoted rate / m)]m - 1. C) [(1)*(APR)*(m)] m - 1. D) [1 + Quoted rate / m]m - 1. E) [1- Quoted rate / m]m [r]. Ans: D

Level: Basic

Subject: Effective Annual Rate

Type: Definitions

20. When interest is credited the instant it is earned it is referred to as: A) Simple interest. B) Annually compounded interest. C) Continuously compounded interest. D) Amortized daily interest. E) Annuitized interest. Ans: C

Level: Basic

Subject: Continuous Compounding

Type: Definitions

21. A pure discount loan is one where the borrower receives money today and repays the loan with: A) A single lump sum in the future. B) Equal monthly payments called annuity payments. C) Partial monthly payments followed by a balloon payment. D) Even monthly payments that fully amortize the principal balance. E) Monthly interest only payments followed by a balloon payment. Ans: A

Level: Basic

Subject: Pure Discount Loan

Type: Definitions

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 4

Chapter 6 Discounted Cash Flow Valuation

22. The process of making regular payments that reduce the principal loan balance is called: A) Annuitizing the loan. B) Amortizing the loan. C) Depleting the loan. D) Discounting the loan. E) Compounding the loan. Ans: B

Level: Basic

Subject: Amortized Loan

Type: Definitions

23. The effective annual rate with continuous compounding is expressed as EAR=: A) [(1) (APR) (m)] m - 1. B) [1 + (Quoted rate) / m]m - 1. C) [1- Quoted rate / m]m [r]. D) eq - 1. E) (e) (q) -1. Ans: D

Level: Basic

Subject: Continuous Compounding

Type: Definitions

24. Which of the following fit the definition of a perpetuity? I. Preferred stock dividend II. Common stock dividend III. Endowment fund providing equal annual payments from accrued earnings IV. Monthly payments equal to 100% of the income earned by a restaurant A) I only B) III and IV only C) I and III only D) I, II, and IV only E) I, III, and IV only Ans: C

Level: Basic

Subject: Perpetuity

Type: Definitions

25. You are going to invest $500 at the end of each year for 10 years. Given an interest rate, you can find the future value of this investment by: I. Adding the cash flows together and finding the future value of the sum using the appropriate future value factor. II. Applying the proper future value factor to each cash flow, then adding up these future values. III. Finding the present value of each cash flow, adding all of the present values together, then finding the future value at the end of year 10 of this lump sum. IV. Finding the present value of the entire payment stream. A) II only B) III only C) II and III only D) I, II, and IV only E) II, III, and IV only Ans: C

Level: Basic

Subject: Present Value Annuity

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 5

Chapter 6 Discounted Cash Flow Valuation

26. Suppose you are evaluating two annuities. They are identical in every way, except that one is an ordinary annuity and one is an annuity due. Assuming an interest rate of 10%, which of the following is true? A) The ordinary annuity must have a higher present value than the annuity due. B) The annuity due must have the same present value as the ordinary annuity. C) The regular annuity must have a lower future value than the annuity due. D) The two annuities will differ in present value by the amount of exactly one of the annuity payments. E) The annuity due will be larger than the regular annuity by an amount equal to the present value of the last annuity payment. Ans: C

Level: Basic

Subject: Annuities

Type: Concepts

27. Which of the following CANNOT be calculated? A) The present value of a perpetuity. B) The interest rate on a perpetuity given the present value and payment amount. C) The present value of an annuity due. D) The future value of an annuity due. E) The future value of a perpetuity. Ans: E

Level: Basic

Subject: Perpetuity

Type: Concepts

28. You are considering two perpetuities which are identical in every way, except that perpetuity A will begin making annual payments of $P to you two years from today while the first $P payment for perpetuity B will occur one year from today. It must be true that the present value of perpetuity: A) A is greater than that of B by $P. B) B is greater than that of A by $P. C) B is equal to that of perpetuity A. D) A exceeds that of B by the PV of $P for one year. E) B exceeds that of A by the PV of $P for one year. Ans: E

Level: Basic

Subject: Present Value Perpetuity

Type: Concepts

29. In order to compare different investment opportunities (each with the same risk) with interest rates reported in different manners you should: A) Convert each interest rate to an annual nominal rate. B) Convert each interest rate to a monthly nominal rate. C) Convert each interest rate to an effective annual rate. D) Compare them by using the published annual rates. E) Convert each interest rate to an APR. Ans: C

Level: Basic

Subject: Effective Annual Rate

Type: Concepts

30. Which of the following is a true statement? A) When comparing investments it is best not to rely solely on quoted rates. B) Compounding will typically not lead to differences between quoted and effective rates. C) The APR on a loan requiring monthly payments is the annual interest rate you actually pay. D) An APR is the interest rate per period divided by the number of periods per year. E) With monthly compounding, the APR will be larger than the effective annual rate. Ans: A

Level: Basic

Subject: Annual Percentage Rate

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 6

Chapter 6 Discounted Cash Flow Valuation

31. You have $500 that you would like to invest. You have two choices: Savings account A which earns 8% compounded annually, or savings account B which earns 7.75% compounded semiannually. Which would you choose and why? A) A because it has a higher effective annual rate. B) A because the future value in one year is lower. C) B because it has a higher effective annual rate. D) B because the future value in one year is lower. E) B because it has the higher quoted rate. Ans: A

Level: Intermediate

Subject: Comparing Savings Accounts

Type: Concepts

32. You have $500 that you would like to invest. You have two choices:Savings account A which earns 8% compounded annually, or savings account B which earns 7.75% compounded monthly. Which would you choose and why? A) A because it has a higher effective annual rate. B) A because the future value in one year is lower. C) B because it has a higher effective annual rate. D) B because the future value in one year is lower. E) A because it has the higher quoted rate. Ans: C

Level: Intermediate

Subject: Comparing Savings Accounts

Type: Concepts

33. You are planning to save your Christmas bonuses from work and are comparing savings accounts:Account A compounds semiannually while account B compounds monthly. If both accounts have the same effective annual rate of interest and you place only the bonuses in the account, you should choose ___________. A) account A because it has a higher APR B) account B because it has a higher APR C) account B because it is compounded more often D) account A because you will pay less in taxes E) either since you would be indifferent between the two Ans: E

Level: Intermediate

Subject: Comparing Savings Accounts

Type: Concepts

34. Which of the following is NOT a true statement? A) Present values and discount rates move in the opposite directions from one another. B) On monthly compounded loans, the EAR will exceed the APR. C) Compounding essentially means earning interest on interest. D) Future values increase with increases in interest rates. E) All else the same, the longer the term of a loan the lower will be the total interest you pay on it. Ans: E

Level: Basic

Subject: Various Statements

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 7

Chapter 6 Discounted Cash Flow Valuation

35. Your banker quotes you two different loan payments on a $12,000 car loan, one calling for 36 monthly payments and the other calling for 24 monthly payments. Both loans have the same APR and EAR. She then tells you that the shorter loan is a better deal because the total payments you would make over the life of the loan would be lower. What is she ignoring? A) The payment would be lower on the 24 month loan. B) The 24 month contract will actually cost you more in total payments, not less. C) The interest you could earn by saving the difference between the two loan payments. D) The fact that you must make 12 more payments on the longer term loan. E) The APR and EAR for the two loans are irrelevant. Ans: C

Level: Intermediate

Subject: Comparing Loans

Type: Concepts

36. To compare interest rates offered by various financial institutions, you should compare the: A) Quoted rates. B) Annual percentage rates. C) Stated annual rates. D) Nominal rates. E) Effective annual rates. Ans: E

Level: Basic

Subject: Effective Annual Rate

Type: Concepts

37. Which one of the following will increase the present value of an annuity? A) Lowering the discount rate B) Reducing the cash flow amount C) Decreasing the number of payments D) Reducing the future value of the cash flow E) Lowering the payment amount Ans: A

Level: Intermediate

Subject: Present Value Of An Annuity

Type: Concepts

38. Which one of the following would have the greatest present value? A) $1,000 today plus $100 a month for 2 years B) $1,000 today plus $200 a month for a year C) $1,000 today plus $400 a month for six months D) $2,200 today plus $200 a month for six months E) $2,200 today plus $100 a month for a year Ans: D

Level: Intermediate

Subject: Present Value Of Unequal Payments

Type: Concepts

39. Which one of the following will increase the future value of a stream of unequal payments for a ten year project? The rate of return is positive. A) Delaying some cash inflows from years 1 and 2 until year 9 B) Lowering the discount rate applicable to all ten years C) Increasing the initial cash outflow to start the project D) Moving more of the cash inflows to the earlier years of the project E) Lowering the effective annual rate applicable to the project Ans: D

Level: Intermediate

Subject: Future Value Of Unequal Payments

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 8

Type: Concepts

Chapter 6 Discounted Cash Flow Valuation

40. Which of the following comparison statements is (are) true? I. An annuity has equal payments, a perpetuity does not. II. Both an annuity and a perpetuity have equal payments. III. An annuity covers a longer period of time than a perpetuity. IV. An annuity has a constant rate of return, a perpetuity does not. A) I only B) II only C) I and III only D) II and IV only E) I and IV only Ans: B

Level: Intermediate

Subject: Annuity Versus Perpetuity

Type: Concepts

41. Given a fixed stream of monthly income the: A) Present value will increase as the time period increases. B) Future value will decrease as the time period increases. C) Present value will decrease as the annual percentage rate decreases. D) Future value will increase as the annual percentage rate decreases. E) Future value will increase if payments are made at the end of the period rather than the beginning. Ans: A

Level: Intermediate

Subject: Number Of Time Periods

Type: Concepts

42. Which of the following is (are) correct concerning perpetuities? I. Perpetuities consist of a stream of equal payments. II. Perpetuities have a life of between twenty and one hundred years. III. Perpetuities have a variable rate of return. IV. The present value perpetuity formula for a stream of annual payments is: A) I only B) I and IV only C) II and IV only D) I, II, and III only E) I, II, and IV only Ans: A

Level: Intermediate

Subject: Perpetuity

C / (1 + r/12)12.

Type: Concepts

43. Which of the following will increase the effective annual rate? I. Increasing the frequency of the compounding II. Decreasing the frequency of the compounding III. Increasing the stated rate IV. Decreasing the annual percentage rate A) I only B) II only C) I and III only D) I and IV only E) II and IV only Ans: C

Level: Intermediate

Subject: Effective Annual Rate

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 9

Chapter 6 Discounted Cash Flow Valuation

44. Which one of the following is correct concerning the annual percentage rate (APR)? A) The APR is greater than the effective annual rate. B) The APR formula for rate disclosure is [1 + (r / m)]m - 1. C) The APR is the rate which lenders are required to disclose. D) The APR is best used to compare offers from various lenders. E) The APR considers all the effects of compounding. Ans: C

Level: Intermediate

Subject: Annual Percentage Rate

Type: Concepts

45. Which one of the following is true concerning amortized loans? A) A loan where annual payments include the interest due plus some set amount of principal is an amortized loan. B) Amortized loans all have a balloon payment at the end of the loan term. C) Amortized loan payments consist of interest only. D) An amortized loan requires only one lump sum payment at the end of the loan term. E) An amortized loan is a type of a pure discount loan. Ans: A

Level: Intermediate

Subject: Amortized Loans

Type: Concepts

46. Which of the following is (are) correct concerning interest-only loans? I. Most corporate bonds are examples of interest-only loans. II. The amount of principal due at the end of the loan term is equal to the amount borrowed. III. Each payment amortizes a portion of the loan principal. IV. The amount borrowed is the present value of the amount due at maturity given a stated discount rate. A) I only B) II only C) I and II only D) I and III only E) II and IV only Ans: C

Level: Intermediate

Subject: Interest Only Loan

Type: Concepts

47. Tomas wants to save $1,200 a year in a manner that maximizes his savings. To do this, he should: A) Deposit $1,200 into his savings account on the last day of each year. B) Treat his $100 monthly savings deposits as an annuity due. C) Treat his $100 monthly savings deposits as an ordinary annuity. D) Deposit $300 into his account at the end of each quarter. E) Deposit $600 into his account at the end of every six month period. Ans: B

Level: Intermediate

Subject: Annuity Due

Type: Concepts

48. Beatrice has a credit card that applies interest every month to her account balance. In this case, Beatrice is paying an interest rate that: A) Equals the rate stated on her billing statement as the APR. B) Is equal to the APR compounded continuously. C) Is greater than the APR shown on her billing statement. D) Is equal to the annual percentage rate as required by the government. E) Will decline automatically as her account balance declines. Ans: C

Level: Intermediate

Subject: Effective Annual Rate

Type: Concepts

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 10

Chapter 6 Discounted Cash Flow Valuation

49. If you are borrowing money, which one of the following rates would you prefer? A) 9% paid annually B) 9% compounded semi-annually C) 9% compounded quarterly D) 9% compounded monthly E) 9% compounded continuously Ans: A

Level: Basic

Subject: Effective Annual Rate

Type: Concepts

50. The effective annual rate on your savings account assumes that: A) You withdraw the interest as soon as it is earned. B) All interest is withdrawn from the account at the end of each year. C) The annual percentage rate varies as the prime rate varies. D) All interest is compounded continuously and immediately added to the account balance. E) All interest payments are reinvested at the same rate as the original deposit into the account. Ans: E

Level: Intermediate

Subject: Effective Annual Rate

Type: Concepts

51. Which one of the following statements concerning an ordinary annuity is true? A) An ordinary annuity consists of equal payments that occur at the beginning of each period over a set period of time. B) If two annuities are equal in every way except that one is an ordinary annuity and one is an annuity due, then the ordinary annuity will have a larger future value than the annuity due. C) The future value of an ordinary annuity can be computed by dividing the future value of an annuity due by (1+r). D) If two annuities are equal in every way except that one is an ordinary annuity and one is an annuity due, then the ordinary annuity will have a larger present value than the annuity due. E) Most financial calculators can compute ordinary annuity problems but not annuity due problems. Ans: C

Level: Intermediate

Subject: Future Value Of An Ordinary Annuity

Type: Concepts

52. Which of the following statements is (are) true concerning a time line? I. A timeline is a visual drawing depicting cash flows. II. As you move leftward on a timeline, you move further into the future. III. Time 0 generally represents today. IV. A timeline with no future ending point is a perpetuity. A) I and II only B) I and III only C) II and IV only D) I, II, and III only E) I, III, and IV only Ans: E

Level: Intermediate

Subject: Time Line

Type: Concepts

53. In the annuity present value formula, the variable "r" must be expressed as a(n): A) Annual percentage rate. B) Effective annual rate. C) Stated annual rate. D) Stated rate per period of time t. E) Continuously compounded rate. Ans: D

Level: Intermediate

Subject: Annuity Present Value Formula

Copyright © 2005 McGraw-Hill Ryerson Limited.

Type: Concepts

Page 11

Chapter 6 Discounted Cash Flow Valuation

54. You are trying to use your financial calculator to solve a present value problem that has unequal cash flows. You input monies you receive as positive values. Which one of the following statements is true? A) Cash outflows should be input as positive values for each year in which they occur. B) Any cash flow occurring today should be input as a Year 1 cash flow. C) You have annual cash flows starting with Year 1 of $100, $0, $200, and $300. The $300 cash flow should be input as occurring in year 3. D) Because you are solving for the present value, any cash flow that occurs today can be ignored. E) A negative present value indicates that this series of cash flows causes you to lose money today given a certain discount rate. Ans: E Level: Intermediate Type: Concepts

Subject: Financial Calculator And Unequal Cash Flows

55. Which one of the following is correct concerning ordinary annuities and annuities due? A) An ordinary annuity will have a larger present value than an annuity due given that the annuities are otherwise identical. B) An annuity due will have a larger future value than an ordinary annuity given that the annuities are otherwise identical. C) An annuity due applies only to equal payments made in annual increments. D) The majority of annuities are annuities due. E) An ordinary annuity is one where the payment occurs at the beginning of the period. Ans: B

Level: Intermediate

Subject: Ordinary Annuity Versus Annuity Due

Type: Concepts

56. What is the total future value six years from now of $50 received in one year, $200 received in two years, and $800 received in six years if the discount rate is 8%? A) $1,050.00 B) $1,047.93 C) $1,145.56 D) $1,237.21 E) $1,269.15 Ans: C

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

57. What is the future value at the end of year 4 of the following set of cash flows? Assume an interest rate of 8%. Year 1 2 3 4 Cash $1000 -$1000 $1000 -$1000 Flow A) B) C) D) E)

$ 0.00 $ 127.38 $ 173.31 $ 379.41 $3,312.13

Ans: C

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

58. What is the future value of the following set of cash flows four years from now? Assume an interest rate of 5.5%. Year 0 1 2 3 4 Cash -$800 $100 $300 $500 $700 Flow

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 12

Chapter 6 Discounted Cash Flow Valuation

A) B) C) D) E)

$555.18 $585.72 $642.12 $687.77 $800.00

Ans: D

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

59. You deposit $1,000 in an account today. You will deposit $600 at the end of each month for the next 12 months and $800 each month for the following 12 months. How much interest will you have earned in two years if the account pays 5.5% compounded monthly? A) $795.42 B) $827.65 C) $849.42 D) $962.57 E) $979.00 Ans: D

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

60. When you were born, your dear old Aunt Minnie promised to deposit $1,000 into a savings account bearing a 5% compounded annual rate on each birthday, beginning with your first. You have just turned 22 and want the dough. However, it turns out that dear old (forgetful) Aunt Minnie made no deposits on your fifth and eleventh birthdays. How much is in the account right now? A) $31,976 B) $34,503 C) $43,888 D) $47,983 E) $51,889 Ans: B

Level: Intermediate

Subject: Future Value Of Uneven Cash Flows

Type: Problems

61. What is the total present value of $50 received in one year, $200 received in two years, and $800 received in six years if the discount rate is 8%? A) $482.72 B) $661.68 C) $697.25 D) $721.90 E) $852.83 Ans: D

Level: Intermediate

Subject: Present Value Uneven Cash Flows

Type: Problems

62. Given the following cash flows, what is the present value if the discount rate is 8%? Year 1 2 3 4 Cash $200 $350 $800 $1125 Flow

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 13

Chapter 6 Discounted Cash Flow Valuation

A) B) C) D) E)

$1,115.07 $1,947.23 $2,165.70 $2,358.96 $2,922.62

Ans: B

Level: Intermediate

Subject: Present Value Uneven Cash Flows

Type: Problems

63. What is the present value of the following set of cash flows at an 8% discount rate? Year 1 2 3 4 Cash $1000 -$1000 $1000 -$1000 Flow A) B) C) D) E)

$ 0.00 $ 127.39 $ 173.31 $ 379.41 $3,312.13

Ans: B

Level: Intermediate

Subject: Present Value Uneven Cash Flows

Type: Problems

64. Analysts expect Marble Comics to pay shareholders $1.00 per share annually for the next five years. After that, the dividend will be $1.50 annually forever. Given a discount rate of 10%, what is the value of the stock today? A) $ 6.55 B) $ 9.87 C) $12.37 D) $13.10 E) $21.88 Ans: D

Level: Intermediate

Subject: Present Value Of Uneven Cash Flows

Type: Problems

65. The monthly mortgage payment on your house is $586.84. It is a 30 year mortgage at a quoted rate of 7.8%. How much did you borrow? A) $75,000 B) $75,500 C) $80,000 D) $82,500 E) $85,000 Ans: D

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 14

Chapter 6 Discounted Cash Flow Valuation

66. You win the lottery and are given the option of receiving $250,000 now or an annuity of $25,000 at the end of each year for 30 years. Which of the following is correct? (Ignore taxes) A) You cannot choose between the two without first calculating future values. B) You will always choose the lump regardless of interest rates. C) You will choose the annuity payment if the interest rate is 7%. D) You will always choose the annuity. E) Comparing the future value of the two alternatives will lead to a different decision than you will reach from a comparison of the present values. Ans: C

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

67. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. How much must there be in the account today in order for the account to reduce to a balance of zero after the last withdrawal? A) $793.83 B) $2,577.10 C) $2,602.29 D) $2,713.75 E) $2,775.67 Ans: B

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

68. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much money will be in the account immediately after the second withdrawal is made? A) $925.93 B) $977.10 C) $982.29 D) $1,000.00 E) $2,000.00 Ans: A

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

69. At the end of each year for the next 10 years you will receive cash flows of $50. If the appropriate discount rate is 5.5%, how much would you pay for the annuity? A) $259.82 B) $299.02 C) $338.99 D) $376.88 E) $379.16 Ans: D

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 15

Chapter 6 Discounted Cash Flow Valuation

70. Your brother-in-law borrowed $2,000 from you four years ago and then disappeared. Yesterday he returned and expressed a desire to pay back the loan, including the interest accrued. Assuming that you had agreed to charge him 10%, and assuming that he wishes to make five equal annual payments beginning in one year, how much would your brother-in-law have to pay you annually in order to pay off the debt? (Assume that the loan continues to accrue interest at 10% per year.) A) $697.43 B) $738.63 C) $751.46 D) $772.45 E) $798.24 Ans: D

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

71. Mr. Dubofsky just won a "Name That Tune" contest with a grand prize of $250,000. However, the contest stipulates that the winner will receive $100,000 immediately, and $15,000 at the end of each of the next 10 years. Assuming that he can earn 5% on his money, how much has he actually won? A) $92,156.46 B) $98,225.11 C) $115,826.02 D) $215,826.02 E) $250,000.00 Ans: D

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

72. In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting next year, you plan to withdraw equal amounts from the account at the end of each of the next four years. What is the MOST you can withdraw annually? A) $6,125.43 B) $6,988.91 C) $7,133.84 D) $7,548.02 E) $8,154.71 Ans: D

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

73. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. How much do you need to charge for the bedroom set during the sale in order to earn your usual combined return on the sale and the financing? A) $2,500 B) $2,827 C) $3,349 D) $3,437 E) $3,784 Ans: C

Level: Intermediate

Subject: Present Value With Zero Interest...

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 16

Type: Problems

Chapter 6 Discounted Cash Flow Valuation

74. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. How much do you need to raise the price of the bedroom set during the sale in order to earn your usual combined return on the sale and the financing? A) $0 B) $849 C) $892 D) $937 E) $1,284 Ans: B

Level: Intermediate

Subject: Present Value With Zero Interest...

Type: Problems

75. Four years from now you will receive the first of seven annual $10,000 payments. The current interest rate is 6%, but by the beginning of year 4, the rate will rise to 8%. What is the present value of this cash flow stream? A) $41,827.25 B) $42,554.48 C) $43,713.69 D) $46,864.48 E) $55,692.25 Ans: C

Level: Intermediate

Subject: Present Value With Multiple Rates

Type: Problems

76. You need to borrow $18,000 to buy a truck. The current loan rate is 9.9% compounded monthly and you want to pay the loan off in equal monthly payments over five years. What is the size of your monthly payment? A) $363.39 B) $374.04 C) $381.56 D) $394.69 E) $455.66 Ans: C

Level: Basic

Subject: Annuity Payment

Type: Problems

77. You are considering investing $750 in a 10 year annuity. The rate of return you require is 6.5%. What annual cash flow from the annuity will provide the required return? A) $70.77 B) $102.96 C) $104.33 D) $114.31 E) $129.27 Ans: C

Level: Basic

Subject: Annuity Payment

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 17

Chapter 6 Discounted Cash Flow Valuation

78. Daryl wishes to save money to provide for his retirement. Beginning one month from now, he will begin depositing a fixed amount into a retirement savings account that will earn 12% compounded monthly. He will make 360 such deposits. Then, one year after making his final deposit, he will withdraw $100,000 annually for 25 years. The fund will continue to earn 12% compounded monthly. How much should the monthly deposits be for his retirement plan? A) $189.58 B) $199.58 C) $214.21 D) $234.89 E) $249.38 Ans: C

Level: Intermediate

Subject: Annuity Payment

Type: Problems

79. What would your payment be on a 10-year, $150,000 loan at 10% interest compounded semiannually assuming the payments are made annually? A) $19,716.67 B) $20,743.77 C) $24,411.81 D) $24,674.60 E) $25,366.63 Ans: D Level: Challenge Type: Problems

Subject: Annuity Payment With Mismatched Compound

80. You work for a furniture store. You normally sell a living room set for $2,500 and finance the full purchase price for 30 monthly payments at 24% APR. You are planning to run a zero-interest financing sale during which you will finance the set over 30 months at 0% interest. What is the monthly payment on a zerointerest loan that you must charge during the sale in order to earn your usual combined return on the sale and the financing? A) $ 83.33 B) $ 89.72 C) $ 95.24 D) $111.62 E) $128.43 Ans: D

Level: Challenge

Subject: Annuity Payments With Zero Interest...

Type: Problems

81. The company you work for will deposit $600 at the end of each month into your retirement fund. Interest is compounded monthly. You plan to retire 15 years from now and estimate that you will need $2,000 per month out of the account for the next 20 years. If the account pays 8% compounded monthly, how much do you need to put into the account in addition to your company deposit in order to meet your objective? A) $0.00 B) $57.59 C) $90.99 D) $95.88 E) $104.49 Ans: C

Level: Challenge

Subject: Annuities

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 18

Chapter 6 Discounted Cash Flow Valuation

82. You borrowed $1,500 at 6% compounded annually. Your payments are $90 at the end of each year. How many years will you make payments on the loan? A) 9 years B) 10 years C) 11 years D) 12 years E) forever Ans: E

Level: Basic

Subject: Number Of Periods

Type: Problems

83. You are going to withdraw $1,000 at the end of each year for the next three years from an account that pays interest at a rate of 8% compounded annually. The account balance will reduce to zero when the last withdrawal is made. How much interest will you earn on the account over the three year life? A) $0.00 B) $240.00 C) $422.90 D) $576.24 E) $3,000.00 Ans: C

Level: Intermediate

Subject: Annuity Interest

Type: Problems

84. At the end of each year for the next 10 years you will receive cash flows of $50. The initial investment is $320. What rate of return are you expecting from this investment? A) 9.06% B) 10.27% C) 12.01% D) 12.28% E) 13.21% Ans: A

Level: Intermediate

Subject: Return On Annuity

Type: Problems

85. You are planning to borrow $2,500. You can repay the loan in 40 monthly payments of $79.06 each or 36 monthly payments of $85.93 each. You decide to take the 40 month loan. During each of the first 36 months you make the loan payment and place the difference between the two payments ($6.87) into a savings account earning 14.4% APR. Beginning with the 37th payment you will withdraw money from the savings account to make your payments. How much money will remain in the savings account after your loan is repaid? A) -$5.00 B) $0.00 C) $5.25 D) $19.78 E) $495.50 Ans: B

Level: Challenge

Subject: Comparing Loans

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 19

Chapter 6 Discounted Cash Flow Valuation

86. If you deposit $2,500 at the end of each six months into an account which earns 5.5% interest compounded quarterly, how much will be in the account in five years? A) $13,953 B) $16,931 C) $26,605 D) $28,357 E) $32,188 Ans: D Level: Intermediate Type: Problems

Subject: Future Value With Mismatched Compounding

87. What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%. A) $12,259.63 B) $12,949.23 C) $13,679.45 D) $14,495.48 E) $14,782.15 Ans: C

Level: Intermediate

Subject: Future Value Annuity Due

Type: Problems

88. What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%. A) $7,069.13 B) $7,093.62 C) $7,492.64 D) $7,914.10 E) $8,165.12 Ans: D

Level: Basic

Subject: Present Value Annuity Due

Type: Problems

89. In order to help you through college, your parents just deposited $25,000 into a bank account paying 8% interest. Starting tomorrow, you plan to withdraw equal amounts from the account at the beginning of each of the next four years. What is the MOST you can withdraw annually? A) $6,125.43 B) $6,988.91 C) $7,133.84 D) $7,548.02 E) $8,154.71 Ans: B

Level: Challenge

Subject: Present Value Annuity Due

Type: Problems

90. What is the present value of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.49% compounded monthly. A) $7,069.13 B) $7,093.62 C) $7,492.64 D) $7,912.50 E) $7,955.26 Ans: D

Level: Basic

Subject: Present Value Annuity Due With. . .

Copyright © 2005 McGraw-Hill Ryerson Limited.

Type: Problems

Page 20

Chapter 6 Discounted Cash Flow Valuation

91. You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. What is the present value of your winnings at an 8% discount rate? A) $182,500 B) $200,000 C) $287,500 D) $312,500 E) $337,500 Ans: D

Level: Basic

Subject: Present Value Perpetuity

Type: Problems

92. You own a bond issued by the Canadian Pacific railroad that promises to pay the holder $100 annually forever. You plan to sell the bond five years from now. If similar investments yield 8% at that time, how much will the bond be worth? A) $918.79 B) $1,014.28 C) $1,250.00 D) $1,489.42 E) $1,958.20 Ans: C

Level: Basic

Subject: Present Value Perpetuity

Type: Problems

93. Five years from now you will begin to receive cash flows of $75 per year. These cash flows will continue forever. If the discount rate is 6%, what is the present value of these cash flows? A) $799.68 B) $894.22 C) $934.07 D) $990.12 E) $1,104.67 Ans: D

Level: Basic

Subject: Present Value Perpetuity

Type: Problems

94. Moe purchases a $100, 30-year annuity. Larry purchases a $100 perpetuity. In both cases, payments begin in one year, and the appropriate interest rate is 10%. What is the present value of Larry's payments that will occur from year 31 onwards? A) $57.31 B) $58.11 C) $81.21 D) More than $100 Ans: A

Level: Challenge

Subject: Comparing Present Values

Type: Problems

95. You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. If the present value of the lottery is $416,667, what is the discount rate used to value this perpetuity? A) 4.0% B) 5.0% C) 6.0% D) 7.0% E) 8.0% Ans: C

Level: Intermediate

Subject: Perpetuity Interest Rate

Copyright © 2005 McGraw-Hill Ryerson Limited.

Type: Problems

Page 21

Chapter 6 Discounted Cash Flow Valuation

96. The preferred stock of Marble Comics currently sells for $31.25 per share. The annual dividend of $2.50 is fixed. Assuming a constant dividend forever, what is the rate of return on this stock? A) 4.5% B) 6.0% C) 8.0% D) 9.5% E) 12.5% Ans: C

Level: Intermediate

Subject: Perpetuity Return

Type: Problems

97. You just won the lottery. You and your heirs will receive $25,000 per year forever, with the first payment received immediately. What is the present value at an 8% discount rate? A) $182,500 B) $200,000 C) $287,500 D) $312,500 E) $337,500 Ans: E

Level: Basic

Subject: Present Value Perpetuity Due

Type: Problems

98. Moe purchases a $100 annual perpetuity for which payments begin in one year. Larry purchases a $100 annual perpetuity for which payments begin immediately. If a 10% interest rate is appropriate for both cash flow streams, which of the following statements is true? A) Moe's perpetuity is worth $100 more than Larry's. B) Larry's perpetuity is worth $100 more than Moe's. C) The perpetuities are of equal value today. D) Larry's perpetuity is worth $90.91 more than Moe's. E) Moe's perpetuity is worth $90.91 more than Larry's. Ans: B

Level: Intermediate

Subject: Comparing Present Values

Type: Problems

99. Your recently departed rich, eccentric uncle has left for you in his will a large sum of money. Unfortunately, rather than give you this sum of money immediately, he has instructed the executor of the will to pay you $10,000 in one year. This payment is to grow by 9% each year and to be made each year forever. If the appropriate discount rate is 10%, how much have you actually inherited? A) $100,000 B) $1,000,000 C) $11,111.11 D) $9,090.90 E) $10,000,000 Ans: B

Level: Challenge

Subject: Growing Perpetuities

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 22

Chapter 6 Discounted Cash Flow Valuation

100. Strapped for cash, your neighbour makes you the following offer. He will pay you back the money he borrows today over the next 10 years. He will make yearly payments with the first payment being for $1,000 at the end of this year. The payments will grow by 10% every year thereafter. If the appropriate discount rate is 12%, how much would you be willing to lend your neighbour today? A) $5,650.22 B) $6,144.57 C) $8,244.22 D) $10,000.00 E) $50,000.00 Ans: C

Level: Challenge

Subject: Present Value Growing Annuity

Type: Problems

101. Strapped for cash, your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making yearly payments with the first payment being for $1,000 at the end of this year. The payments will grow by 10% every year thereafter. If the appropriate discount rate is 12%, how long will it take for your neighbour to repay the loan? A) 12.38 years B) 10 years C) 13.28 years D) 18.32 years E) 21.38 years Ans: A

Level: Challenge

Subject: Number of Periods Growing Annuity

Type: Problems

102. Strapped for cash, your neighbour makes you the following offer. He would like to borrow $10,000 today. He will repay the $10,000 by making 10 yearly payments with the first payment being made at the end of this year. If the payments are to grow by 10% each year and the appropriate discount rate is 12%, how much will your neighbour have to pay at the end of the first year? A) $108.98 B) $1,212.97 C) $1,627.45 D) $1,769.84 E) $1,867,94 Ans: A

Level: Challenge

Subject: Growing Annuity Payment

Type: Problems

103. What is the effective annual rate of 8% compounded quarterly? A) 8.00% B) 8.16% C) 8.24% D) 8.53% E) 16.64% Ans: C

Level: Basic

Subject: Effective Annual Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 23

Chapter 6 Discounted Cash Flow Valuation

104. What is the effective annual rate of 12% compounded semiannually? A) 11.24% B) 12.00% C) 12.36% D) 12.54% E) 12.96% Ans: C

Level: Basic

Subject: Effective Annual Rate

Type: Problems

105. What is the effective annual rate of 12% compounded monthly? A) 11.27% B) 12.00% C) 12.36% D) 12.54% E) 12.68% Ans: E

Level: Basic

Subject: Effective Annual Rate

Type: Problems

106. You are considering an investment with a quoted return of 10% per year. If interest is compounded daily, what is the effective return on this investment? A) 1.11% B) 10.00% C) 10.25% D) 10.47% E) 10.52% Ans: E

Level: Basic

Subject: Effective Annual Rate

Type: Problems

107. What is the effective annual rate of 12% compounded continuously? A) 11.27% B) 12.00% C) 12.68% D) 12.75% E) 12.89% Ans: D

Level: Basic

Subject: Effective Annual Rate

Type: Problems

108. Vito Corleone will loan you money on a "five-for-six" arrangement; i.e., for every $5 he gives you today, you give him $6 one week from now. What is the EAR of this loan? A) 410% B) 540% C) 860% D) 1,040% E) 13,104% Ans: E

Level: Basic

Subject: Effective Annual Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 24

Chapter 6 Discounted Cash Flow Valuation

109. Fast Eddie's Used Cars will sell you a 1996 Ford Escort for $3,000 with no money down. You agree to make weekly payments of $40 for two years, beginning one week after you buy the car. What is the EAR of this loan? A) 34.43% B) 36.55% C) 40.94% D) 42.34% E) 53.01% Ans: C

Level: Basic

Subject: EAR Loan Rate

Type: Problems

110. You have $10,000 to invest. The First National Bank offers one-year certificates of deposit with a stated rate of 5.50% compounded quarterly. What rate compounded semiannually would provide you with the same amount of money at the end of one year? A) 5.487% B) 5.500% C) 5.507% D) 5.512% E) 5.538% Ans: E

Level: Intermediate

Subject: Comparing Rates

Type: Problems

111. You agree to loan your parents $22,000 to buy a new van. They agree to pay you $450 a month for five years. The ______________________. A) interest rate on the loan is 0.75% per month B) APR on the loan is 8.17% C) EAR on the loan is 8.37% D) APR on the loan is 8.68% E) EAR on the loan is 8.70% Ans: E

Level: Basic

Subject: APR/EAR

Type: Problems

112. Fast Eddie's Used Cars will sell you a 1996 Ford Escort for $3,000 with no money down. You agree to make weekly payments for two years, beginning one week after you buy the car. The stated rate on the loan is 26%. How much is each payment? A) $32.96 B) $37.06 C) $38.19 D) $45.90 E) $69.65 Ans: B

Level: Intermediate

Subject: Loan Payments

Type: Problems

113. Vito Corleone will loan you money on a "five-for-six" arrangement; i.e., for every $5 he gives you today, you give him $6 one week from now. What is the APR of this loan? A) 410% B) 540% C) 860% D) 1,040% E) 1,310% Ans: D

Level: Basic

Subject: Annual Percentage Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 25

Chapter 6 Discounted Cash Flow Valuation

114. You notice a local consumer finance company is offering 20% APR loans, but compounds interest continuously. What is the EAR? A) 12.21% B) 22.14% C) 23.61% D) 24.97% E) 25.83% Ans: B

Level: Basic

Subject: Continuous Compounding

Type: Problems

115. A given rate is quoted as 12% APR, but has an EAR of 12.55%. What is the rate of compounding during the year? A) Annually B) Semiannually C) Quarterly D) Monthly E) Continuously Ans: C

Level: Intermediate

Subject: Effective Annual Rate Compounding

Type: Problems

116. A given rate is quoted as 8% APR, but has an EAR of 8.33%. What is the rate of compounding during the year? A) Annually B) Semiannually C) Quarterly D) Monthly E) Continuously Ans: E

Level: Intermediate

Subject: Effective Annual Rate Compounding

Type: Problems

117. What continuously compounded rate of return allows you to triple your money in 20 years? A) 5.49% B) 5.98% C) 6.86% D) 6.92% E) 8.99% Ans: A

Level: Intermediate

Subject: Continuous Compounding

Type: Problems

118. Your local bank just loaned you $1,500. This amount is net of a 10% discount on the loan proceeds, which serves as interest on the loan. You are to repay the loan in one year. What is the effective rate at which you borrowed? A) 11.00% B) 11.11% C) 11.97% D) 12.58% E) 12.64% Ans: B

Level: Intermediate

Subject: Discount Loans

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 26

Chapter 6 Discounted Cash Flow Valuation Use the following to answer questions 119-122: You and your spouse have found your dream home in Moose Jaw, Saskatchewan. The selling price is $120,000; you will put $20,000 down and obtain a 25-year fixed-rate mortgage at 8.25% for the rest. 119. Assume that monthly payments begin in one month. What will each payment be? A) $725.01 B) $751.27 C) $779.23 D) $825.45 E) $901.52 Ans: C

Level: Basic

Subject: Calculating Payments

Type: Problems

120. How much interest will you pay (in dollars) over the life of the loan? (Assume you make each of the required 300 payments on time.) A) $133,769 B) $145,583 C) $170,457 D) $190,457 E) $270,457 Ans: A

Level: Basic

Subject: Calculating Interest Costs

Type: Problems

121. Although you will get a 25-year mortgage, you plan to prepay the loan by making an additional payment each month along with your regular payment. How much extra must you pay each month if you wish to pay off the loan in 20 years? A) $24.56 B) $54.88 C) $64.17 D) $93.28 E) $106.86 Ans: C

Level: Challenge

Subject: Calculating Payments

Type: Problems

122. Your banker suggests that, rather than obtaining a 25-year mortgage and paying it off early, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 7.75%. By how much will your monthly payment be (higher/lower) for the 15-year loan than the regular payment on the 25-year loan? A) lower; $111.57 B) lower; $54.72 C) higher; $9.26 D) higher; $155.06 E) higher; $194.59 Ans: D

Level: Challenge

Subject: Loan Prepayment

Type: Problems

Use the following to answer questions 123-126: Rob and Laura wish to buy a new home. The price is $187,500 and they plan to put 20% down. New Rochelle Savings and Loan will lend them the remainder at a 10% fixed rate for 25 years, with monthly payments to begin in one month.

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 27

Chapter 6 Discounted Cash Flow Valuation

123. How much will their monthly payments be? A) $1,316.36 B) $1,341.73 C) $1,512.56 D) $1,645.45 E) $1,760.45 Ans: B

Level: Basic

Subject: Calculating Payments

Type: Problems

124. Assuming they pay off the loan over the 25 year period as planned, what will the total cost (principal + interest + down payment) of the house be? A) $187,500 B) $271,996 C) $354,234 D) $440,019 E) $511,390 Ans: D

Level: Basic

Subject: Total Loan Cost

Type: Problems

125. What will the outstanding balance of the loan be after 10 years assuming you make the first 120 payments right on time? A) $99,610 B) $126,308 C) $136,407 D) $139,144 E) $170,509 Ans: B

Level: Intermediate

Subject: Present Value Annuity

Type: Problems

126. Suppose Rob wants to pay off the loan in 15 years. How much extra must he pay each month to do so? A) $11.25 B) $201.99 C) $251.67 D) $311.95 E) $314.47 Ans: C

Level: Challenge

Subject: Calculating Payments

Type: Problems

Use the following to answer questions 127-132: With auto loans extending five, six, seven or more years these days, it is common for buyers who wish to trade in their cars after a few years to find themselves to be "upside down" on the loan. In other words, the outstanding principal on the car loan exceeds the value of the car being traded. Suppose you buy a new Toyota for $20,000, paying nothing down. You agree to a repayment schedule of six equal annual payments beginning one year from today. The banker's required return is 9%, compounded annually. Assume the car will lose 20% of its value the first year and further lose $2,000 each year thereafter.

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 28

Chapter 6 Discounted Cash Flow Valuation

127. How much will your annual payments be? A) $3,729.03 B) $4,458.40 C) $5,121.24 D) $6,664.91 E) $7,563.01 Ans: B

Level: Challenge

Subject: Loan Payment

Type: Problems

128. Given the depreciation schedule above, how much will the car be worth after three years? A) $10,000 B) $12,000 C) $14,000 D) $16,000 E) $20,000 Ans: B

Level: Challenge

Subject: Depreciation

Type: Problems

129. Given the depreciation schedule above, how much will the car be worth after you have made your final payment? A) $4,000 B) $6,000 C) $8,000 D) $10,000 E) $12,000 Ans: B

Level: Challenge

Subject: Depreciation

Type: Problems

130. Including principal and interest, what is your total cost for this car? (Assume you make all of your payments on time. ) A) $20,000 B) $24,999 C) $26,750 D) $27,899 E) $31,872 Ans: C

Level: Challenge

Subject: Loan Cost

Type: Problems

131. After which loan payment will you be "right-side up" for the first time? In other words, when does the market value of the car exceed the outstanding balance of the loan for the first time? A) After payment number 1 B) After payment number 2 C) After payment number 3 D) After payment number 4 E) After payment number 5 Ans: C

Level: Challenge

Subject: Market Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 29

Chapter 6 Discounted Cash Flow Valuation

132. Assume the information as given above, except that you put $2,000 down on the car, so that you only had to borrow $18,000. Now, after which loan payment will you be "right-side up" for the first time? A) After payment number 1 B) After payment number 2 C) After payment number 3 D) After payment number 4 E) After payment number 5 Ans: A

Level: Challenge

Subject: Market Value

Type: Problems

133. What is the present value of the following set of cash flows if the discount rate is 5.25%? Year 0 1 Cash Flow -$1,200 $300 A) B) C) D) E)

3 $600

$196.87 $205.22 $206.90 $213.64 $223.73

Ans: B

Level: Basic

Subject: Present Value Uneven Cash Flows

Type: Problems

134. What is the present value of the following set of cash flows if the discount rate is 11.5%? Year 0 1 Cash Flow -$5,000 $900 A) B) C) D) E)

2 $400

2 $0

3 $3,500

-$50.44 -$16.98 $16.81 $268.37 $425.93

Ans: A

Level: Basic

Subject: Present Value Uneven Cash Flows

Type: Problems

135. Sue just signed a contract wherein she will receive the following payments. What is the contract worth to her today if she can earn 7% on her investments? Year 0 1 2 Cash Flow $1,200 $3,500 $2,500 A) B) C) D) E)

$6,168.67 $6,282.53 $6,295.37 $7,139.87 $8,695.37

Ans: E

Level: Intermediate

Subject: Present Value Uneven Cash Flows

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 30

Type: Problems

Chapter 6 Discounted Cash Flow Valuation

136. Jamie is a self-employed consultant. A prospective client has offered her three payment options. Jamie is currently earning 8.5% on her funds. Which one of the following statements is correct concerning Jamie's payment options? Option 1: $10,000 today plus $25,000 at the end of year 2 Option 2: $5,000 today plus $9,000 at the end of year 1 and $22,000 at the end of year 2 Option 3: $36,000 at the end of year 2 A) At a 2% rate of return Option 3 is the best choice. B) At a 6% rate of return Option 1 is the worst choice. C) At an 8.5% rate of return Option 2 is the best choice. D) At a 0% rate of return all options are equivalent. E) At a 6% rate of return, Option 1 is the best choice. Ans: C

Level: Challenge

Subject: Present Value Uneven Cash Flows

Type: Problems

137. What is the future value at the end of year 3 of the following set of cash flows if the interest rate is 8%? Year 0 1 Cash Flow -$1,500 $100 A) B) C) D) E)

2 $100

-$64.93 $366.89 $1,824.64 $2,698.13 $3,714.21

Ans: A

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

138. What is the future value at the end of year 3 of the following set of cash flows if the interest rate is 14%? Year 0 1 2 Cash Flow $900 $400 -$600 A) B) C) D) E)

-$649.32 -$268.88 $0 $316.72 $469.23

Ans: E

Level: Intermediate

Subject: Future Value Uneven Cash Flows

Type: Problems

139. Poor Dog, Inc. borrowed $135,000 from the bank today. They must repay this money over the next six years by making monthly payments of $2,215.10. What is the interest rate on the loan? A) 4.71% B) 5.65% C) 6.13% D) 6.38% E) 9.63% Ans: B

Level: Intermediate

Subject: Interest Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 31

3 $

Chapter 6 Discounted Cash Flow Valuation

140. A credit card company charges you an interest rate of 1.25% monthly. The annual percentage rate is ____ and the effective annual rate is _______ A) 15.00%; 15.00% B) 15.00%; 14.55% C) 14.55%; 15.00% D) 15.00%; 16.08% E) 16.08%; 15.00% Ans: D

Level: Intermediate

Subject: Effective Interest Rate

Type: Problems

141. A so-called friend has offered to loan you $1,000 for one year. At the end of the year you must pay your friend $2,000. What is the APR on this loan if interest is compounded daily? A) 50.00% B) 69.38% C) 81.33% D) 96.30% E) 100.00% Ans: B

Level: Intermediate

Subject: Annual Percentage Rate

Type: Problems

142. Freeda Mai has a $65,000 insurance annuity. The company has offered monthly payments for twenty years as a payout option for this annuity. The insurance company will use a 3% rate of return. How much more per month would Freda Mai receive if the insurance company would pay her a 5% rate of return on her annuity? A) $13.13 B) $29.37 C) $68.48 D) $71.18 E) $73.01 Ans: C

Level: Intermediate

Subject: Annuity Payment

Type: Problems

143. Sun Woo wants to purchase an annuity that will pay him $1,000 a month for fifteen years. If he can negotiate a 4.5% rate of return, how much will he have to pay today in order to purchase this annuity? A) $96,489 B) $123,185 C) $130,720 D) $154,327 E) $185,171 Ans: C

Level: Intermediate

Subject: Annuity Present Value

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 32

Chapter 6 Discounted Cash Flow Valuation

144. Douglass Inc. wants to establish an employee reward program whereby they can pay five employees $1,000 a year each for twenty years. The first payment is to begin one year from today. The company expects to earn 3.25% on the funds in this program. How much does the company have to deposit today to totally fund this reward program? A) $14,539 B) $31,333 C) $42,684 D) $56,667 E) $72,697 Ans: E

Level: Intermediate

Subject: Annuity Present Value

Type: Problems

145. The Frank Trust would like to gift some money to their local university so that the money gifted will provide $100,000 to the university each year from now on. The funds are expected to earn an 8% rate of return. How much money does the Frank Trust have to gift to the university today? A) $1,000,000 B) $1,250,000 C) $1,500,000 D) $2,000,000 E) $2,500,000 Ans: B

Level: Basic

Subject: Present Value Perpetuity

Type: Problems

146. ABC preferred stock pays a $3 annual dividend. The current market rate of return is 8% for this type of investment. What is one share of ABC preferred stock worth? A) $24.00 B) $30.00 C) $32.50 D) $37.50 E) $38.50 Ans: D

Level: Intermediate

Subject: Present Value Perpetuity

Type: Problems

147. An insurance company is offering monthly payments of $250 for the next twenty years in exchange for a one-time payment of $40,000 today. What is the rate of return on this offer? A) 3.63% B) 4.36% C) 5.21% D) 6.39% E) 7.50% Ans: B

Level: Intermediate

Subject: Annuity Interest Rate

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 33

Chapter 6 Discounted Cash Flow Valuation

148. Master Meter is planning on constructing a new $20 million facility. The company plans to pay 20% of the cost in cash and finance the balance. How much will each monthly loan payment be if they can borrow the necessary funds for 30 years at 9% compounded monthly? A) $128,740 B) $133,667 C) $141,982 D) $148,016 E) $160,925 Ans: A

Level: Intermediate

Subject: Loan Payments

Type: Problems

149. Jamie owes $21,750 at a 5% rate of interest. The minimum amount that she must pay monthly is $230.69. How much faster can she pay off this loan if she makes monthly payments of $300.00? A) 1.68 years sooner B) 2.54 years sooner C) 2.79 years sooner D) 2.93 years sooner E) 3.01 years sooner Ans: D

Level: Challenge

Subject: Loan Payments

Type: Problems

150. The Friendly Bank wants to earn an effective rate of 9% on its auto loans. If interest is compounded monthly, what APR must they charge? A) 8.44% B) 8.58% C) 8.65% D) 9.17% E) 9.38% Ans: C

Level: Intermediate

Subject: Annual Percentage Rate

Type: Problems

151. A 13% APR compounded continuously is equal to an effective rate of: A) 13.78% B) 13.80% C) 13.83% D) 13.88% E) 13.92% Ans: D

Level: Intermediate

Subject: Continuous Compounding

Type: Problems

152. Jessica will be receiving $3,600 five years from now. Her desire is to get a loan today and then repay it in one lump sum when she receives her funds. What is the maximum loan Jessica can get today if the bank changes 8.5% interest? A) $2,357.10 B) $2,394.16 C) $2,416.36 D) $2,433.86 E) $2,501.08 Ans: B

Level: Intermediate

Subject: Discount Loan

Type: Problems

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 34

Chapter 6 Discounted Cash Flow Valuation

153. There are three factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity. Ans: The factors are the interest rate, payment amount, and number of payments. An increase in the payment and number of payments will increase the present value, while an increase in the interest rate will decrease the present value. Level: Basic

Subject: Present Value Of An Annuity

Type: Essays

154. There are three factors that affect the future value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity. Ans: The factors are the interest rate, payment amount, and number of payments. An increase in any of these three will increase the future value of the annuity. Level: Basic

Subject: Future Value Of An Annuity

Type: Essays

155. A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000. At an interest rate of 10%, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments? Ans: The present value of the perpetuity is $10,000, and the present value of the first 25 payments is $9,077. 04, thus you should be willing to pay only $922. 96 for payments 26 and onwards. This suggests that the value of a perpetuity is derived primarily from the payments received early in its life, and the payments to be received later have little worth today. Level: Intermediate

Subject: Perpetuity Payments

Type: Essays

156. You are considering two annuities, both of which make total annuity payments of $10,000 over their life. Which would be worth more today: annuity A, which pays $1,000 at the end of each year for the next 10 years, or annuity B, which pays $775 at the end of the first year, but the annuity payment grows by $50 each year, reaching $1,225 at the end of year 10? Are there any circumstances in which the two would be equal? Explain. Ans: The second annuity weights its payments more toward the back of the period, rather than the front, making it less valuable unless the discount rate is zero. Some students may get tripped up by the fact that the two annuities have the same total payments. This would clearly demonstrate a lack of understanding of the time value of money. Level: Challenge

Subject: Comparing Annuities

Type: Essays

157. Annuity A makes annual payments of $813.73 for each of the next 10 years, while annuity B makes annual payments of $500 per year forever. At what interest rate would you be indifferent between the two? At interest rates above/below this break-even rate, which annuity would you choose? Ans: This requires the students to actually use the present value formulas, setting the present value annuity equal to the present value of a perpetuity and solving for the interest rate that makes the two equivalent. The first step is recognizing that the indifference point occurs when the two present values are equal. The break-even rate is 10%:below that rate, the perpetuity is better, while above that rate, the 10-year annuity is preferred. Level: Challenge

Subject: Comparing Annuities & Perpetuities

Copyright © 2005 McGraw-Hill Ryerson Limited.

Type: Essays

Page 35

Chapter 6 Discounted Cash Flow Valuation

158. Using the example of a savings account, explain the difference between the EAR and the APR. Ans: The EAR is what you actually earn, the APR is a quoted rate. If interest is compounded during the year, the ending balance of a savings account cannot be calculated directly using the APR. Also, in the case of the savings account, the EAR will always be higher than the APR as long as the account is compounded more than once a year and the interest rate is greater than zero. Level: Basic

Subject: EAR versus APR

Type: Essays

159. If you ran a bank, which rate would you rather advertise on monthly-compounded loans, the EAR or the APR? Which rate would you rather advertise on quarterly-compounded savings accounts, the EAR or the APR? Explain. As a consumer, which would you prefer to see and why? Ans: A bank would rather advertise the APR on loans since this rate appears to be lower and the EAR on savings accounts since this appears to be higher. As a consumer, the EAR is the more important rate since it represents the rate actually paid or earned. Level: Basic

Subject: EAR versus APR

Type: Essays

160. Should lending laws be changed to require lenders to report the EAR rather than the APR? Explain. Ans: It would be more meaningful for consumers to know the EAR rather than the APR. The EAR is slightly more difficult to calculate and also more difficult to explain, and may add confusion to the loan process. However, regardless of the costs, it would appear that consumers would benefit from learning what the EAR is as opposed to the APR. Level: Basic

Subject: EAR versus APR

Type: Essays

161. Explain both the mathematical difference between APR and EAR for a monthly stream of cash flows and also how time affects this difference. Ans: The annual percentage rate is equal to the monthly rate multiplied by 12. The effective annual rate is a compounding of the monthly rate to the 12th power. The difference between a straight multiplication and the compounding effects of raising a number to a power magnifies as time increases. Level: Intermediate

Subject: APR Versus EAR

Type: Essays

162. Explain how increasing the amount of each monthly payment affects an amortized loan. Ans: An amortized loan is a loan where the monthly payment includes both interest and principal. The interest is calculated based on the remaining principal balance. When the monthly loan payment is increased, the additional amount reduces the principal balance. This in turn reduces the amount of interest due for each remaining payment over the life of the loan. Thus, the extra principal payment saves future interest expenditures. Level: Intermediate

Subject: Amortized Loans

Type: Essays

Copyright © 2005 McGraw-Hill Ryerson Limited.

Page 36