Corporate Finance Questions and Answers Ch2

Chapter 02 1. The present value of $100 expected two years from today at a discount rate of 6 percent is D. $89.00. 2. Present value is defined as A. future cash flows discounted to the present by an appropriate discount rate. 3. If the annual interest rate is 12 percent, what is the two-year discount factor? A. 0.7972 4. If the present value of cash flow X is $240 and the present value of cash flow Y is $160, then the present value of the combined cash flows is D. $400. 5. The rate of return is also called the C. discount rate, hurdle rate, and opportunity cost of capital. 6. The present value of $121,000 expected one year from today at an interest rate (discount rate) of 10 percent per year is C. $110,000. 7. The one-year discount factor, at a discount rate of 25 percent per year, is C. 0.8. 8. The one-year discount factor, at an interest rate of 100 percent per year, is B. 0.50. 9. The present value of $100,000 expected at the end of one year, at a discount rate of 25 percent per year, is A. $80,000. 10. If the one-year discount factor is 0.8333, what is the discount rate (interest rate) per year? B. 20 percent 11. If the present value of $480 to be paid at the end of one year is $400, what is the one-year discount factor? A. 0.8333 12. If the present value of $250 expected one year from today is $200, what is the one-year discount rate? C. 25 percent 13. If the one-year discount factor is 0.90, what is the present value of $120 expected one year from today? C. $108 14. If the present value of $600, expected one year from today, is $400, what is the one-year discount rate? D. 50 percent 15. The present value formula for a cash flow expected one period from now is B. PV = C1/(1 + r). Chapter 02 16. The net present value formula for one period is A. NPV = C0 + [C1/(1 + r)]. 17. An initial investment of $400,000 is expected to produce an end-of-year cash flow of $480,000. What is the NPV of the project at a discount rate of 20 percent? C. $0 (zero) 18. If the present value of a cash flow generated by an initial investment of $200,000 is $250,000, what is the NPV of the project? B. $50,000 19. What is the present value of the following cash flows at a discount rate of 9 percent? A. $372,431.81 20. At an interest rate of 10 percent, which of the following sequences of cash flows should you prefer? A. Option A 21. What is the net present value of the following cash flow sequence at a discount rate of 11 percent? A. $69,108.03 22. What is the net present value of the following sequence of annual cash flows at a discount rate of 16 percent APR? A. $136,741.97 23. What is the net present value (NPV) of the following sequence of cash flows at a discount rate of 9 percent? A. $122,431.81 24. Which of the following statements regarding the NPV rule and the rate of return rule is false? C. Accept a project if its rate of return > 0. 25. An initial investment of $500 produces a cash flow of $550 one year from today. Calculate the rate of return on the project. A. 10 percent 26. According to the net present value rule, an investment in a project should be made if the C. net present value is positive. Chapter 02 27. Which of the following statements regarding the net present value rule and the rate of return rule is false? A. Accept a project if NPV > cost of investment. 28. The opportunity cost of capital for a risky project is C. the expected rate of return on a security of similar risk as the project. 29. A perpetuity is defined as a sequence of B. equal cash flows occurring at equal intervals of time forever. 30. Which of the following is generally considered an example of a perpetuity? C. Interest payments on a consol 31. You would like to have enough money saved after your retirement such that you and your heirs can receive $100,000 per year in perpetuity. How much would you need to have saved at the time of your retirement in order to achieve this goal? (Assume that the perpetuity payments start one year after the date of your retirement. The annual interest rate is 12.5 percent.) C. $800,000 32. What is the present value of $10,000 per year in perpetuity at an annual interest rate of 10 percent? Assume the perpetuity starts in one year. B. $100,000 33. You would like to have enough money saved to receive $80,000 per year in perpetuity after retirement for you and your heirs. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start one year from the date of your retirement. The annual interest rate is 8 percent.) C. $1,000,000 34. You would like to have enough money saved to receive a $50,000 per year perpetuity after retirement. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 8 percent.) B. $675,000 35. You would like to have enough money saved to receive an $80,000 per year perpetuity after retirement. How much would you need to have saved in your retirement fund to achieve this goal? (Assume that the perpetuity payments start on the day of your retirement. The annual interest rate is 10 percent.) B-$880,000 36. An annuity is defined as a set of A. equal cash flows occurring at equal intervals of time for a specified period. 37. If you are paid $1,000 at the end of each year for the next five years, what type of cash flow did you receive? B. An annuity 38. If the three-year present value annuity factor is 2.673 and the two-year present value annuity factor is 1.833, what is the present value of $1 received at the end of the three years? B. $0.84 39. If the five-year present value annuity factor is 3.60478 and the four-year present value annuity factor is 3.03735, what is the present value of the $1 received at the end of five years? C. $0.56743 40. What is the eight-year present value annuity factor at a discount rate of 11 percent? C. 5.1461 Chapter 02 41. What is the six-year present value annuity factor at an interest rate of 9 percent? B. 4.4859 42. What is the present value of a $1,000 per year annuity for five years at an interest rate of 12 percent? B. $3,604.78 43. What is the present value of a six-year $5,000 per year annuity at a discount rate of 10 percent? A. $21,776.30 44. After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income, if the annual interest rate is 9 percent per year? (Assume that the payments start on the day of your retirement.) B. $802,995.88 45. After retirement, you expect to live for 25 years. You would like to have $75,000 income each year. How much should you have saved in your retirement account to receive this income if the annual interest rate is 9 percent per year? (Assume that the payments start one year after your retirement.) A. $736,693.47 46. For $10,000, you can purchase a five-year annuity that will pay $2,504.57 per year for five years. The payments occur at the end of each year. Calculate the effective annual interest rate implied by this arrangement. A. 8 percent 47. If the present value annuity factor for 10 years at 10 percent interest rate is 6.1446, what is the present value annuity factor for an equivalent annuity due? C. 6.7590 48. If the present value annuity factor is 3.8896, what is the present value annuity factor for an equivalent annuity due if the interest rate is 9 percent? B. 4.2397 49. For $10,000, you can purchase a five-year annuity that will pay $2,358.65 per year for five years. The payments occur at the beginning of each year. Calculate the effective annual interest rate implied by this arrangement. B. 9 percent 50. John House has taken a $250,000 mortgage on his house at an interest rate of 6 percent per year. If the mortgage calls for 20 equal annual payments, what is the amount of each payment? A. $21,796.14 51. John House has taken a 20-year $250,000 mortgage on his house at an interest rate of 6 percent per year. What is the remaining balance (or value) of the mortgage after the payment of the fifth annual installment? B. $211,689.53 52. If the present value of $1 received n years from today at an interest rate of r is 0.3855, then what is the future value of $1 invested today at an interest rate of r percent for n years? B. $2.594 53. If the present value of $1 received n years from today at an interest rate of r is 0.621, then what is the future value of $1 invested today at an interest rate of r% for n years? B. $1.610 Chapter 02 54. If the future value of $1 invested today at an interest rate of r percent for n years is 9.6463, what is the present value of $1 to be received in n years at r percent interest rate? C. $0.1037 55. If the future value annuity factor at 10 percent and five years is 6.1051, calculate the equivalent present value annuity factor. B. 3.7908 56. If the present value annuity factor at 10 percent for 10 years is 6.1446, what is the equivalent future value annuity factor? B. 15.9375 57. If the present value annuity factor at 12 percent for five years is 3.6048, what is the equivalent future value annuity factor? B. 6.3529 58. If the present value annuity factor at 8 percent for 10 years is 6.71, what is the equivalent future value annuity factor? B. 14.486 59. You are considering investing in a retirement fund that requires you to deposit $5,000 per year, and you want to know how much the fund will be worth when you retire. What financial technique should you use to calculate this value? B. Future value of an annuity 60. Mr. Hopper expects to retire in 25 years, and he wishes to accumulate $750,000 in his retirement fund by that time. If the interest rate is 10 percent per year, how much should Mr. Hopper put into his retirement fund each year in order to achieve this goal? (Assume that he makes payments at the end of each year.) C. $7,626.05 61. Mr. Hopper expects to retire in 30 years, and he wishes to accumulate $1,000,000 in his retirement fund by that time. If the interest rate is 12 percent per year, how much should Mr. Hopper put into his retirement fund at the end of each year in order to achieve this goal? A. $4,143.66 62. You would like to have enough money saved to receive a growing annuity for 20 years, growing at a rate of 5 percent per year, with the first payment of $50,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 10 percent. C. $605,604.20 63. You would like to have enough money saved to receive a growing annuity for 25 years, growing at a rate of 4 percent per year, with the first payment of $60,000 occurring exactly one year after retirement. How much would you need to save in your retirement fund to achieve this goal? The interest rate is 12 percent. B. $632,390 64. The managers of a firm can maximize stockholder wealth by A. taking all projects with positive NPVs. 65. If you invest $100 at 12 percent for three years, how much would you have at the end of three years using compound interest? B. $140.49 66. Which of the following statements is true? A. The process of discounting is the inverse of the process of compounding. Chapter 02 67. The concept of compound interest is best described as C. interest earned on interest. 68. Ms. Colonial has just taken out a $150,000 mortgage at an interest rate of 6 percent per year. If the mortgage calls for equal monthly payments for 20 years, what is the amount of each payment? (Assume monthly compounding or discounting.) D. $1,074.65 69. An investment having a 10.47 percent effective annual rate (EAR) has what APR? (Assume monthly compounding.) C. 10.00 percent 70. An investment at 12 percent APR compounded monthly is equal to an effective annual rate of A. 12.68 percent. 71. Mr. Williams expects to retire in 30 years and would like to accumulate $1 million in his pension fund. If the annual interest rate is 12 percent, how much should Mr. Williams put into his pension fund each month in order to achieve his goal? (Assume that Mr. Williams will deposit the same amount each month into his pension fund, using monthly compounding.) A. $286.13 72. An investment at 10 percent compounded continuously has an equivalent annual rate of B. 10.517 percent. 73. The present value of a $100 per year perpetuity at 10 percent per year interest rate is $1,000. What would be the present value of this perpetuity if the payments were compounded continuously? B. $1,049.21 74. You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming an 8 percent annual interest rate, what is the value of this trust? B. $992,290 75. You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly four more years. Assuming a 10 percent annual interest rate, what is the value of this trust? B. $751,315 76. You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming an 8 percent annual interest rate, what is the value of this trust? B. $918,787 77. You just inherited a trust that will pay you $100,000 per year in perpetuity. However, the first payment will not occur for exactly five more years. Assuming a 10 percent annual interest rate, what is the value of this trust? B. $683,013 Chapter 02 78. The rate of return, discount rate, hurdle rate, and opportunity cost of capital all have the same meaning. TRUE Difficulty: Intermediate 79. A dollar today is worth more than a dollar tomorrow if the interest rate is positive. TRUE 80. One can find the present value of a future cash flow by dividing it by an appropriate discount factor. FALSE Difficulty: Intermediate 81. One can find a project's net present value by subtracting the present value of its required investment from the present value of its future cash flows. TRUE Difficulty: Intermediate Chapter 02 82. The opportunity cost of capital is higher for safe investments than for risky ones. FALSE Difficulty: Intermediate 83. A safe dollar is always worth less than a risky dollar because the rate of return on a safe investment is generally low and the rate of return on a risky investment is generally high. FALSE Difficulty: Challenge 84. "Accept investments that have positive net present values" is called the net present value rule. TRUE Difficulty: Intermediate 85. Generally, one should accept investments that offer rates of return in excess of their opportunity costs of capital. TRUE Difficulty: Intermediate 86. The rate of return on any perpetuity is equal to its cash flow multiplied by its price. FALSE Difficulty: Intermediate 87. An annuity is an asset that pays a fixed amount each period for a specified number of periods. TRUE 88. The value of a five-year annuity is equal to the sum of two perpetuities. One makes its first payment in year 1, and the other makes its first payment in year 6. FALSE Difficulty: Challenge 89. An equal-payment home mortgage is an example of an annuity. TRUE Difficulty: Intermediate 90. In the amortization of a mortgage loan with equal payments, the fraction of each payment devoted to interest steadily increases over time and the fraction devoted to reducing the loan balance decreases steadily. Chapter 02 FALSE Difficulty: Challenge 91. The present value of a growing perpetuity, with cash flow given by [C1/(r - g)], where r>g. C1 occurring one year from now, is TRUE Difficulty: Challenge 92. Briefly explain the term discount rate. The discount rate is the rate of return used for discounting future cash flows to obtain present values. The discount rate can be obtained by looking at the rate of return on an equivalent-risk investment opportunity in the financial market. Difficulty: Challenge 93. Intuitively explain the concept of present value. If you have $100 today, you can invest it and start earning interest on it. On the other hand, if you have to make a payment of $100 one year from today, you do not need to invest $100 today, but a lesser amount. The lesser amount invested today plus the interest earned on it should add up to $100. The present value of $100 one year from today at an interest rate of 10 percent is $90.91. [PV = 100/1.1 = 90.91.] Difficulty: Challenge 94. State the net present value rule. Invest in projects with positive net present values. Net present value is the difference between the present value of future cash flows from the project and the present value of the initial investment. Difficulty: Intermediate 95. Briefly explain the concept of risk. If the future cash flows from an investment are not certain, then we call such an investment risky. That means there is an uncertainty about the future cash flows or future cash flows could be different from expected cash flows. The degree of uncertainty varies from investment to investment. Uncertain cash flows are discounted using a higher discount rate than certain cash flows. This is only one method of dealing with risk. There are many ways to consider risk while making financial decisions. Difficulty: Challenge 96. State the rate of return rule. Invest as long as the rate of return on the investment exceeds the rate of return on equivalent-risk investments in the financial market. Difficulty: Intermediate 97. Define the term perpetuity. Chapter 02 A perpetuity is defined as a sequence of equal cash flows occurring each period forever. Difficulty: Intermediate 98. Describe how you would go about finding the present value of any annuity given the formula for the present value of a perpetuity. The present value of any annuity can be thought of as the difference between two perpetuities: one payment starting in year 1 (immediate) and one starting in year (n + 1) (delayed). By calculating the difference between the present values of these two perpetuities Today, we can find the present value of an annuity. Difficulty: Intermediate 99. What is the difference between simple interest and compound interest? When money is invested at compound interest, each interest payment is reinvested to earn more interest in subsequent periods. In the simple interest case, the interest is paid only on the initial investment. Difficulty: Intermediate 100. Briefly explain continuous compounding. As the frequency of compounding increases, the effective rate on an investment also increases. In the case of continuous compounding, the compounding frequency goes to infinity. In this case, the nature of the function also changes. The effective interest rate is given by (er - 1), where the value of e = 2.718, where e is the base for natural logarithms. Difficulty: Challenge