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Chapter 11

Capital Budgeting and Risk Analysis

True/False

1. In order to implement the certainty equivalent approach, we must know the financial manager’s preference for bearing risk.

Difficulty: Moderate

Keywords: certainty equivalent approach

2. The appropriate discount rate to use with the certainty equivalent approach is the marginal cost of capital.

Difficulty: Moderate

Keywords: certainty equivalent approach

3. The certainty equivalent approach compares the internal rate of return to the risk-free rate of interest of a risky project.

Difficulty: Moderate

Keywords: certainty equivalent approach

4. The use of risk-adjusted discount rates is based on the concept that investors require a higher rate of return for more risky projects.

Difficulty: Easy

Keywords: risk-adjusted discount rates

5. The risk-adjusted discount rate assumes that distant cash flows have the same risk as near cash flows.

Difficulty: Easy

Keywords: risk-adjusted discount rates

6. One benefit of simulation is that only a simple estimate of each variable included in the simulation is required rather than the probability distribution of each variable.

Difficulty: Moderate

Keywords: simulation

7. Sensitivity analysis is a benefit of simulation.

Difficulty: Moderate

Keywords: sensitivity analysis

8. Probability trees allow the financial manager to see possible future events, their probabilities, and their outcomes.

Difficulty: Easy

Keywords: probability trees

9. The lower the correlation coefficient between cash flows over time, the greater is the standard deviation of the probability distribution of the present value of the cash flows.

Difficulty: Moderate

Keywords: correlation coefficient

10. The cash flows of a project are based on possible outcomes and their assigned probabilities.

Difficulty: Easy

Keywords: cash flows, probability distributions

11. Correlation between the cash flows of two projects measures how closely the two cash flows move together.

Difficulty: Moderate

Keywords: correlation

12. A project’s contribution-to-firm risk includes the effects of diversification of the firm’s shareholders.

Difficulty: Moderate

Keywords: project’s contribution-to-firm risk

13. A project’s stand-alone risk can be diversified away within a firm.

Difficulty: Easy

Keywords: project stand-alone risk

14. If the cash flows of an accepted investment project are positively correlated with the average cash flow of the firm’s existing assets, then the company’s total exposure to risk can decrease.

Difficulty: Moderate

Keywords: cash flow, correlation

15. In spite of varying project risk, as long as proposed investment projects are evaluated at the average cost of capital, the maximization of shareholder wealth will be assured.

Difficulty: Moderate

Keywords: maximization of shareholders wealth

16. Research and development projects will have a higher risk-adjusted discount rate than that of replacement projects.

Difficulty: Easy

Keywords: risk-adjusted discount rate, type of project

17. A typical decision rule used in simulation is to accept the project if the probability of a net present value is sufficiently high.

Difficulty: Moderate

Keywords: simulation

18. The use of probability trees does not assume that the cash flow in one period is independent of the cash flows in the previous periods.

Difficulty: Moderate

Keywords: probability trees

19. AXZ Corporation’s sales are highly dependent upon the condition of the economy, while XYZ Corporation’s sales are relatively constant over time. If these two firms are combined, then the new firm would benefit from diversification.

Difficulty: Moderate

Keywords: diversification

20. Risk of a project is reflected by the variability of cash flows.

Difficulty: Easy

Keywords: project risk, variability of cash flows

21. The best measure of risk for undiversified shareholders is systematic risk.

Difficulty: Moderate

Keywords: undiversified shareholders

22. Bankruptcy costs violate the theory of using systematic risk as the measure of project risk.

Difficulty: Moderate

Keywords: bankruptcy cost, systematic risk

23. In reality, anticipated cash flows are only estimates and are thus uncertain.

Difficulty: Easy

Keywords: uncertainty of cash flows

24. Risk is defined as an absolute measure of the degree of variability of possible outcomes over time.

Difficulty: Moderate

Keywords: risk, variability

25. While the behavior of some individuals appears to indicate a risk-seeking attitude, when intangible rewards are considered, their behavior is congruent with that of typical risk-averse individuals.

Difficulty: Moderate

Keywords: risk-averse, risk-seeking

26. Financial theory assumes that individuals are risk-averse.

Difficulty: Easy

Keywords: risk-averse

27. Using simulation provides the financial manager with a probability distribution of an investment’s net present value or internal rate of return.

Difficulty: Moderate

Keywords: simulation

28. One drawback of simulation is that the resulting decisions are based solely on point estimates rather than on a range of possible outcomes.

Difficulty: Moderate

Keywords: simulation

29. A probability tree presents the decision maker with a schematic representation of the investment problem.

Difficulty: Easy

Keywords: probability tree

30. The greater the degree of correlation between cash flows over time, the smaller is the dispersion of the probability distribution.

Difficulty: Moderate

Keywords: correlation, cash flows

31. The certainty equivalent is calculated by dividing the risky cash flow by the certain cash flow.

Difficulty: Easy

Keywords: certainty equivalent approach

32. The risk-adjusted discount rate makes the implicit assumption that risk becomes greater over time.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

33. The risk-adjusted discount rate is used more than the certainty equivalent approach due to its ease of implementation.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

34. If the required rate of return is not adjusted to compensate for added risk, acceptance of marginal projects can lower the firm’s share price.

Difficulty: Moderate

Keywords: required rate of return

35. The time dependence of cash flows indicates that if the early cash flows are lower, they will increase their value over time.

Difficulty: Moderate

Keywords: time dependence of cash flows

36. The probability tree approach assumes that the cash flow in one period is independent of the cash flow in the previous period.

Difficulty: Moderate

Keywords: probability tree approach

37. The capital asset pricing model (CAPM) assumes that unsystematic risk is the appropriate measure of project risk.

Difficulty: Easy

Keywords: systematic risk, capital asset pricing model

38. The use of the risk-adjusted discount rate assumes that risk increases over time and that cash flows occurring further in the future should be more severely penalized.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

39. Decision making with probability trees means accepting any project with an internal rate of return greater than the firm’s required return.

Difficulty: Moderate

Keywords: probability tree approach

40. In capital-budgeting decisions, simulation analysis gives a probability distribution only for cash flows.

Difficulty: Moderate

Keywords: simulation

41. Contribution-to-firm risk represents the amount of risk that a project contributes to the firm as a whole.

Difficulty: Easy

Keywords: contribution-to-firm risk

42. One advantage of simulation is that it can differentiate between unsystematic and systematic risk.

Difficulty: Moderate

Keywords: simulation

43. Sensitivity analysis shows how the distribution of possible net present values is affected by a change in one input variable.

Difficulty: Easy

Keywords: sensitivity analysis

44. Simulation provides a complete measure of risk assessment.

Difficulty: Moderate

Keywords: simulation, risk

45. Problems associated with accepting systematic risk as the only relevant project risk include the reality that not all of the firm’s shareholders are well diversified.

Difficulty: Moderate

Keywords: systematic risk, diversification

46. The certainty equivalent approach to incorporating risk in the capital-budgeting decision substitutes equivalent risk-free cash flows for the project’s expected cash flows, and then discounts these cash flows using a risk-adjusted discount rate.

Difficulty: Moderate

Keywords: certainty equivalent approach

47. In the certainty equivalent approach to capital budgeting, managers are indifferent between the risky outcome and the certain outcome.

Difficulty: Moderate

Keywords: certainty equivalent approach

48. When using the certainty equivalent approach to make capital-budgeting decisions, the project’s internal rate of return is compared to the required rate of return.

Difficulty: Moderate

Keywords: certainty equivalent approach

49. Certainty equivalent coefficients will be 1 when there is no uncertainty associated with a project’s cash flows.

Difficulty: Moderate

Keywords: certainty equivalent approach

50. The firm’s required rate of return is used as the discount rate in capital-budgeting decisions when the project has the same level of risk as a typical project for the firm.

Difficulty: Moderate

Keywords: firm’s required rate of return

51. If the risk associated with a project is greater than the risk involved in a typical project, then the discount rate is adjusted downward when using the risk-adjusted discount rate technique.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

52. If the firm does not adjust for the risk of higher-than-typical risk projects, then the marginal projects containing above-average risk could actually lower the firm’s value.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

53. If a firm does not account for the risk of potential projects, then it might accept projects that have negative net present value.

Difficulty: Moderate

Keywords: project risk

54. Regardless of whether the certainty equivalent approach or the risk-adjusted discount rate approach is used to account for riskier-than-normal projects, the project’s net present value will be less than if risk is not taken into consideration.

Difficulty: Moderate

Keywords: certainty equivalent approach

55. A joint probability involves the probability of two different independent outcomes occurring at the same time.

Difficulty: Easy

Keywords: joint probability

56. Sensitivity analysis is an important component of simulation.

Difficulty: Easy

Keywords: sensitivity analysis

57. Probability trees help financial managers determine whether enough of the distribution of a project’s possible outcomes is at a level that warrants acceptance of the project.

Difficulty: Moderate

Keywords: probability trees

58. Scenario analysis identifies the range of possible outcomes if a project is adopted under the worst, best, and most likely cases.

Difficulty: Moderate

Keywords: scenario analysis

59. The pure play method identifies privately traded firms in order to use their betas as a proxy for a given project.

Difficulty: Easy

Keywords: pure play method

60. The primary difference between the certainty equivalent approach and the risk-adjusted discount rate approach is that the certainty equivalent approach adjusts the cash flows upward.

Difficulty: Moderate

Keywords: certainty equivalent approach

Multiple Choice

61. Evaluating risky capital investments by meanswer of the risk-adjusted discount rate:

a. assumes that the risk of the project equals the average risk of the firm.

b. requires the certainty equivalent of the project to be determined.

c. assumes that the risk of the project increases through time.

d. results in a lower risk-adjusted net present value for projects with above-average risk than would be obtained by discounting cash flows at the marginal cost of capital.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

62. Projects of varying risk can be evaluated by:

a. identical certainty equivalents.

b. high-risk projects having high certainty equivalents.

c. comparable risk-adjusted net present values.

d. usage of cumulative probability beta analysis.

Difficulty: Moderate

Keywords: risk-adjusted net present values

63. The major difference between the risk-adjusted discount rate and the certainty equivalent method of evaluating capital investments is that:

a. the risk-adjusted discount rate adjusts the expected cash flows downward for risk.

b. the certainty equivalent method adjusts the discount rate down for more risky projects.

c. the certainty equivalent approach requires projects to be discounted at the marginal costs of capital.

d. the risk-adjusted discount rate is larger for projects of greater risk than for projects of lesser risk.

Difficulty: Moderate

Keywords: risk-adjusted discount rates

64. Outstanding Records is interested in signing up two new artists. Artist A recently became a popular mainstream singer with a strong following. Artist B has not previously recorded any music, but her work has a chance to be very successful because she is so unusual. Outstanding Records typically makes a forecast of the expected sales and profits from new releases of new artists in order to determine the contract price. How could Outstanding Records best consider the risk associated with offering contracts to these artists?

a. Apply a higher rate of return to Artist A’s expected sales and profits.

b. Give more weight to later years’ potential profits.

c. Apply a higher rate of return to Artist B’s expected sales and profits.

d. Ignore risk because the record business is a risky business to begin with.

Difficulty: Moderate

Keywords: risk-adjusted discount rates

65. Consolidated Industries has three major business lines: (1) manufacturing pharmaceutical drugs (high risk), (2) retailing consumer sundries and toiletries (low risk), and (3) retailing women’s clothing (medium risk). The average rate of return that Consolidated applies to investment projects is 11.5%. The firm adds 4% to the rate of return for high-risk projects and reduces the required rate of return by 2% for low-risk projects. What rate of return should Consolidated require for the pharmaceutical drugs business?

a. 11.5%

b. 13.5%

c. 15.5%

d. 9.5%

Difficulty: Moderate

Keywords: risk-adjusted discount rates

66. The risk-adjusted discount rate is preferred over the certainty equivalent approach because of:

a. ease of implementation.

b. the focus on cash flows.

c. greater certainty of cash flows.

d. both a and c.

Difficulty: Moderate

Keywords: risk-adjusted discount rates

67. The financial manager selecting one of two projects of differing risk should select the project with the:

a. largest risk-adjusted net present value.

b. least relative risk.

c. greatest return even if that project has greater risk.

d. least risk even though that project has less return.

Difficulty: Moderate

Keywords: risk-adjusted net present value

68. Accounting return data can be used to:

a. measure systematic risk.

b. calculate beta for publicly-traded firms.

c. explain a firm’s alpha.

d. both a and c.

e. all of the above.

Difficulty: Moderate

Keywords: accounting return data, systematic risk

69. An advantage of the simulation approach is that:

a. cash flows are adjusted for risk.

b. a range of possible outcomes is presented.

c. it measures single period investment returns.

d. the pure play beta is created.

Difficulty: Moderate

Keywords: simulation

70. Probability tree analysis:

a. illustrates the impact of diversification.

b. ignores the probability distribution of cash flows.

c. can only measure one outcome at a time.

d. graphically displays all possible outcomes of the investment.

Difficulty: Moderate

Keywords: probability tree analysis

71. Most individuals are:

a. risk-averse.

b. gamblers.

c. risk-neutral.

d. unfamiliar with risk.

Difficulty: Easy

Keywords: risk-averse

72. Two normal distributions are independent if their correlation coefficient is:

a. 0.

b. +1.

c. -.5.

d. +2.

Difficulty: Moderate

Keywords: correlation

73. Which of the following is not considered when using probability trees?

a. Risk-adjusted returns

b. Internal rates of return

c. Unsystematic risk

d. Both a and c

Difficulty: Easy

Keywords: probability tree, unsystematic risk

74. The certainty equivalent approach is characterized by:

a. risky expected cash flows being deflated to risk-free cash flows.

b. a risk-adjusted discount rate being estimated to calculate the present value of the risky cash flows.

c. utilizing a higher initial cash outlay than would be otherwise.

d. assuming that all cash flows are known with certainty and that they are risk-free.

Difficulty: Moderate

Keywords: certainty equivalent approach

75. Certainty equivalent coefficients are defined as:

a. risky cash flow_t/certain cash flow_t.

b. certain cash flow_t/risky cash flow_t.

c. certain cash flow_t/(1 + k).

d. risky cash flow_t/(1 + k).

Difficulty: Easy

Keywords: certainty equivalent approach

76. What method is used for calculation of the accounting beta?

a. Simulation

b. Regression analysis

c. Sensitivity analysis

d. Correlation trees

Difficulty: Moderate

Keywords: regression analysis

77. All of the following variables are used in the calculation of the certainty equivalent approach except:

a. number of possible outcomes.

b. project’s expected life.

c. risk-free interest rate.

d. initial cash outlay.

Difficulty: Moderate

Keywords: certainty equivalent approach

78. The certainty equivalent approach uses all the following steps EXCEPT:

a. alpha.

b. capital budgeting criterion.

c. adjusted discount rate.

d. the terminal cash flow.

Difficulty: Moderate

Keywords: certainty equivalent approach

79. An increase in the ____________ would increase the net present value of a project evaluated with the risk-adjusted discount rate method.

a. discount rate

b. future value of cash inflows

c. initial outlay

d. alpha

Difficulty: Moderate

Keywords: risk-adjusted discount rate

80. The simulation approach provides us with:

a. a single value for the risk-adjusted net present value.

b. an approximation of the systematic risk level.

c. a probability distribution of the project’s net present value or internal rate of return.

d. a graphic exposition of the year-by-year sequence of possible outcomes.

Difficulty: Moderate

Keywords: simulation approach

81. Different discounted cash flow evaluation methods may provide conflicting rankings of investment projects when the:

a. size of investment outlays differs.

b. projects have unequal lives.

c. timing of the cash flows differs.

d. all of the above.

Difficulty: Easy

Keywords: discounted cash flow evaluation, ranking conflicts

82. __________ is a method of quantifying uncertainty without having to estimate probabilities.

a. Standard deviation

b. Sensitivity analysis

c. Coefficient of variation

d. Decision tree analysis

Difficulty: Easy

Keywords: sensitivity analysis

83. __________ is a risk analysis technique in which the best- and worst-case net present values are compared with the project’s expected net present value.

a. Project standing alone risk

b. Decision tree analysis

c. Scenario analysis

d. Pure play method

Difficulty: Easy

Keywords: scenario analysis

84. Which of the following statements is inconsistent with the usage of systematic risk as the relevant measure of risk for capital budgeting purposes?

a. It ignores the fact that much of a project’s risk will be diversified away.

b. It assumes that the firm’s stock is but one of many stocks held by shareholders.

c. It is a project’s risk taking into account the fact that this project is only one of many of a firm’s projects.

d. It measures the risk of a project from the point of view of a well-diversified investor.

Difficulty: Moderate

Keywords: systematic risk

85. Project standing alone risk is not a relevant measure of risk for capital budgeting purposes because it ignores:

a. the effects of shareholder diversification.

b. the diversification from combining with other projects of a firm.

c. the variability of a project’s expected returns.

d. both a and b.

Difficulty: Moderate

Keywords: project stand-alone risk

86. Which risk is most relevant to undiversified shareholders?

a. Systematic risk

b. Contribution-to-firm risk

c. Project stand-alone risk

d. Certainty equivalent risk

Difficulty: Moderate

Keywords: contribution-to-firm risk

87. Which of the following is not an important consideration in measuring risk for a capital budgeting project for a well-diversified firm?

a. Systematic risk

b. Contribution-to-firm risk

c. Total project risk

d. Project stand alone risk

Difficulty: Moderate

Keywords: total project risk

88. According to the pure play method, a new project’s risk level can me measured using:

a. the beta of a company that solely engages in the same business as the new project.

b. the alpha of a company that solely engages in the same business as the new project.

c. the cash flow of a company that solely engages in the same business as the new project.

d. the unsystematic risk of a company that solely engages in the same business as the new project.

Difficulty: Moderate

Keywords: pure play method, beta

89. Which of the following is not an acceptable method of accounting for risk in capital budgeting?

a. Certainty equivalent approach

b. Beta distribution analysis

c. Probability trees

d. Scenario analysis

Difficulty: Moderate

Keywords: beta distribution analysis

90. Which of the following methods for incorporating risk into capital budgeting considers the decision maker’s utility function?

a. Simulation

b. Risk-adjusted discount rate

c. Certainty equivalent method

d. Probability trees

Difficulty: Moderate

Keywords: certainty equivalent approach

91. Which of the following statements is false?

a. The certainty equivalent method results in a lower net present value for a risky project.

b. The risk-adjusted discount rate leaves cash flows at their expected value and adjusts the discount rate downward to compensate for additional risk.

c. The certainty equivalent penalizes or adjusts downward the value of the expected annual free cash flows of a project.

d. The risk-adjusted discount rate leaves cash flows at their expected value and adjusts the discount rate upward to compensate for additional risk.

Difficulty: Moderate

Keywords: risk-adjusted discount rate

92. Which of the following statements is false?

a. Ignoring risk in capital budgeting can lead to loss of firm value.

b. Risk occurs in capital budgeting when there is some question as to the certainty of future cash flows.

c. Several methods of accounting for risk in capital budgeting assume that although future cash flows of a project are not known with certainty, the probability distribution from which they come can be estimated.

d. Project standing alone risk is the relevant measure of risk for capital budgeting purposes.

Difficulty: Moderate

Keywords: project stand-alone risk

93. The Acu Punct Corporation is considering the purchase of a new machine with an initial outlay of $4,500 and expected cash flows in Years 1 through 4 of $2,200. The certainty equivalent coefficient for each period is 0.87. The appropriate discount rate for the firm is 12%, and the risk-free rate is 5%. Compute the net present value of this project using the certainty equivalent approach.

a. $2,114

b. $2,287

c. $2,399

d. $2,463

Difficulty: Moderate

Keywords: certainty equivalent approach

94. Humungous Corporation is a multidivisional conglomerate. The Food Division is undergoing a capital budgeting analysis and must estimate the division’s beta. This division has a different level of systematic risk than is typical for Humungous Corporation as a whole. The most appropriate method for estimating this beta is:

a. the regression coefficient from a time series regression of Humungous Corporation stock returns on a market index.

b. to multiply the company’s beta by the ratio of the Food Division’s total assets/Humungous Corporation total assets.

c. the regression coefficient from a time series regression of Food Division’s net income on the Humungous Corporation return on assets.

d. the regression coefficient from a time series regression of Food Division’s return on assets on a market index.

Difficulty: Moderate

Keywords: regression analysis

95. One method of accounting for systematic risk for a project involves identifying a publicly traded firm that is engaged in the same business as that project and using its required rate of return to evaluate the project. This method is referred to as:

a. the accounting beta method.

b. the certainty equivalent approach.

c. the pure play method.

d. sensitivity analysis.

Difficulty: Moderate

Keywords: pure play method

96. Mr. Kirk is considering the purchase of a new enterprise with the same risk as his firm’s current operations. There is a 10% chance it would be a flop after Year 1, at which time the project will be scrapped for a cash flow of $15,000 at the end of Year 1. There is a 90% chance of success in Year 1, in which case no cash flows will be received in Year 1, but there will be a 60% chance of receiving Year 2 cash flow of $39,063 and a 40% chance of receiving Year 2 cash flow of $34,810. Compute the expected internal rate of return on the investment if the initial outlay is $25,000.

a. 15.98%

b. 16.26%

c. 17.44%

d. 18.53%

Difficulty: Moderate

Keywords: internal rate of return

97. Which of the following methods for incorporating risk in capital budgeting does not assume that the cash flow in one period is independent of the cash flow in the previous period?

a. Certainty equivalent method

b. Scenario analysis

c. Probability tree analysis

d. Pure play method

Difficulty: Moderate

Keywords: probability tree analysis

98. Which of the following statements is true?

a. A probability tree is a graphic exposition of the sequence of possible outcomes.

b. Project standing alone risk is the relevant measure of risk for capital budgeting purposes.

c. The risk-adjusted discount rate leaves cash flows at their expected value and adjusts the discount rate downward to compensate for additional risk.

d. The pure play method is a highly useful method of accounting for risk in capital budgeting because once proxy firms are identified, they are useful for comparison purposes regardless of their capital structures.

Difficulty: Moderate

Keywords: probability tree analysis

99. If bankruptcy costs and/or shareholder underdiversification are an issue, what measure of risk is relevant when evaluating project risk in capital budgeting?

a. Total project risk

b. Contribution-to-firm risk

c. Systematic risk

d. Capital rationing risk

Difficulty: Moderate

Keywords: contribution-to-firm risk

100. Ghosthustlers, Inc. is considering an investment in a new ghost trapping machine. This project has the same level of risk as other projects the firm typically undertakes and would require an initial outlay of $7,500. There is a 5% probability that the ghost zopper will backfire the first year it is in use, in which case it will be sold for scrap metal generating a cash flow of $500 at the end of Year 1. There is a 95% chance the machine will work, in which case a Year 1 cash flow of $5,000 would be generated. If the machine worked in Year 1, there would be a 70% chance of a cash flow of $7,000 at the end of Year 2 and a 30% chance of a cash flow of $2,500 at the end of Year 2. If the required rate of return for the firm is 12%, what is the expected net present value of the project?

a. $796

b. $808

c. $955

d. $1,042

Difficulty: Moderate

Keywords: expected net present value

101. __________ is a capital budgeting procedure which involves changing one or more of the basic assumptions about cash flow variables and recomputing net present value and internal rate of return to determine how sensitive these criteria are to changes in the input factors.

a. Pure play method

b. Sensitivity analysis

c. Skewness estimation

d. Scenario analysis

Difficulty: Easy

Keywords: sensitivity analysis

102. In capital budgeting, a project’s risk can be viewed as:

a. project standing alone risk, which reflects the amount of risk the project contributes to the firm as a whole.

b. contribution-to-firm risk which considers the fact that some of the project’s risk will be diversified away and, therefore, reflects effects of diversification of the firm’s shareholders.

c. systematic risk, which is the risk of the project from the view of a well-diversified shareholder.

d. all of the above.

Difficulty: Moderate

Keywords: systematic risk

103. Problems associated with accepting systematic risk as the only relevant project risk include:

a. undiversified shareholders.

b. bankruptcy costs.

c. difficulty in measuring unsystematic risk.

d. both a and b.

e. all of the above.

Difficulty: Moderate

Keywords: systematic risk

Use the following information to answer questions 104-105. Following are a project’s risky cash flows and certain cash flows. The project’s initial cash outlay is $240,000 and is known with certainty. The firm’s required rate of return is 10%, and the risk-free rate is 6%.

Year Risky cash flow Certain cash flow

1 $ 20,000 $ 19,000

2 40,000 36,000

3 80,000 68,000

4 160,000 120,000

5 160,000 104,000

104. When using the certainty equivalent approach to make capital budgeting decisions:

a. certainty coefficients are less than 1.

b. cash flows are discounted at the required rate of return.

c. projects with net present values greater than zero should be accepted.

d. both a and c.

e. all of the above.

Difficulty: Moderate

Keywords: certainty equivalent approach

105. This project’s certainty equivalent coefficient in Year 5 is:

a. 0.45.

b. 0.55.

c. 0.65.

d. 0.75.

Difficulty: Moderate

Keywords: certainty equivalent coefficients

Use the following information to answer questions 106-107. Following are a project’s risky cash flows and certainty equivalent coefficients. The project’s initial cash outlay is $110,000 and is known with certainty. The firm’s required rate of return is 10%, and the risk-free rate is 6%.

Year Risky cash flow Certainty equivalent coefficients

1 $10,000 0.95

2 20,000 0.90

3 40,000 0.85

4 90,000 0.75

5 90,000 0.65

106. This project’s risk-adjusted net present value is (round to the nearest whole dollar):

a. $21,448.

b. $33,671.

c. $40,710.

d. $67,366.

Difficulty: Moderate

Keywords: certainty equivalent approach, net present value

107. This project’s certainty equivalent cash flow in Year 3 is:

a. $21,000.

b. $28,500.

c. $34,000.

d. $40,000.

Difficulty: Easy

Keywords: certainty equivalent approach

Use the following information to answer questions 108-109. Epsilon, Inc. is considering a project with an initial cash outflow of $125,000 that is expected to generate after-tax cash flows of $60,000 annually for the next five years. The normal required rate of return for the firm is 10%; however, the minimally acceptable rate of return on riskier projects is 15%.

108. This project’s risk-adjusted net present value is (round to the nearest whole dollar):

a. $53,027.

b. $60,710.

c. $76,129.

d. $89,360.

Difficulty: Moderate

Keywords: risk-adjusted net present value

109. Which of the following statements is true?

a. Epsilon will use 10% as the discount rate for analyzing this project.

b. Epsilon will use 10% as the discount rate for analyzing this project only if it is less risky than the firm’s typical endeavor.

c. Epsilon will use 15% as the discount rate for analyzing this project only if it is riskier than the firm’s typical endeavor.

d. Epsilon will be unable to analyze this project unless it knows the risk-free interest rate.

Difficulty: Moderate

Keywords: risk-adjusted rates of return

110. Williamson Manufacturing, Inc. is considering a project that has an initial outlay of $200,000 and that is expected to generate after-tax cash flows of $80,000 annually for the next four years. Using a risk-adjusted interest rate, the net present value of the project is $28,398. What risk-adjusted interest rate was used in the analysis?

a. 12%

b. 13%

c. 14%

d. 15%

Difficulty: Hard

Keywords: risk-adjusted rates of return

111. When a firm wants to use the CAPM to determine the appropriate risk/return tradeoffs for a particular project, the firm:

a. can use accounting data to directly estimate a project or division’s beta.

b. can identify a pure play firm and use its systematic risk as a proxy for the project’s or division’s level of systematic risk without regard for the pure play firm’s capital structure.

c. can determine a project’s CAPM through sensitivity analysis.

d. can identify a pure play firm and use its certainty equivalent to estimate the beta of a project.

Difficulty: Moderate

Keywords: pure play approach, certainty equivalent approach

Use the following information to answer questions 112-116. Assume that a project has an initial cash outlay of $100,000. The firm’s financial managers believe that there is a 50% chance that the project will return $60,000 in Year 1. If the project returns $60,000 in Year 1, then there is a 20% chance the project will return $30,000 in Year 2 and an 80% chance that it will return $60,000 in Year 2. In addition, the financial managers believe that there is a 50% chance that the project will return $80,000 in Year 1. If the project returns $80,000 in Year 1, then there is a 20% chance the project will return $60,000 in Year 2 and an 80% chance that it will return $80,000 in Year 2.

112. If the project returns $80,000 in Year 1 and $60,000 in Year 2, then the project’s internal rate of return will be:

a. 27.18%.

b. 31.98%.

c. 34.07%.

d. 42.55%.

Difficulty: Moderate

Keywords: internal rate of return

113. If the project returns $60,000 in Year 1 and $30,000 in Year 2, then the project’s internal rate of return will be:

a. -21.32%.

b. -15.97%.

c. -11.07%.

d. -9.61%.

e. -7.55%.

Difficulty: Moderate

Keywords: internal rate of return

114. The probability of the project returning $60,000 in Year 1 and $60,000 in Year 2 is:

a. 10%.

b. 70%.

c. 40%.

d. 80%.

Difficulty: Moderate

Keywords: probability of cash flows

115. The probability of the project returning $80,000 in Year 1 and $60,000 in Year 2 is:

a. 10%.

b. 70%.

c. 40%.

d. 80%.

Difficulty: Moderate

Keywords: probability of cash flows

116. The project’s expected internal rate of return is:

a. 23.89%.

b. 22.38%.

c. 19.67%.

d. 18.45%.

Difficulty: Hard

Keywords: expected internal rate of return

117. Which of the following is an acceptable method for analyzing risk in capital budgeting?

a. Sensitivity analysis

b. Simulation

c. Risk-adjusted discount rates

d. Certainty equivalent approach

e. All of the above

Difficulty: Easy

Keywords: methods to analyze risk

118. A firm is considering the purchase of an asset whose risk is greater than the current risk of the firm, based on any method for assessing risk. In evaluating this asset, the decision maker should increase the _______ to reflect greater risk.

a. internal rate of return

b. net present value

c. required rate of return

d. beta

Difficulty: Easy

Keywords: risk-adjusted discount rates

119. Which of the following is considered the major risk when analyzing projects in a multinational environment?

a. Currency fluctuations

b. Inflation

c. Political risk

d. Lack of available betas

Difficulty: Moderate

Keywords: multinational firms, capital budgeting

120. A company estimates that an average-risk project has a required rate of return (RRR) of 10%, a below-average risk project has a RRR of 8%, and an above-average risk project has a RRR of 12%. Which of the following independent projects should the company accept?

a. Project A has average risk and an internal rate of return of 9%.

b. Project B has below-average risk and an internal rate of return of 8.5%.

c. Project C has above-average risk and an internal rate of return of 11%.

d. The company should accept both Project A and Project B.

Difficulty: Moderate

Keywords: risk-adjusted discount rates

121. If a company uses the same discount rate for evaluating all projects, regardless of their risk, the firm might:

a. accept high-risk projects that have only average returns.

b. reject low-risk projects that have high returns.

c. not accept any projects.

d. generate rates of return that are too high.

Difficulty: Moderate

Keywords: projects and discount rates

122. If a typical U.S. company uses the same discount rate to evaluate all projects, the firm will most likely become:

a. riskier over time, and its value will decline.

b. riskier over time, and its value will rise.

c. less risky over time, and its value will rise.

d. less risky over time, and its value will decline.

Difficulty: Moderate

Keywords: projects and discount rates

123. Pay More Drug’s average required rate of return is 10%. Its pharmaceutical division is riskier than average, its cosmetics division has average risk, and its institutional foods division has below-average risk. Pay More adjusts for both divisional and project risk by adding or subtracting two percentage points. Thus, the maximum adjustment is four percentage points. What is the risk-adjusted required rate of return for an average-risk project in the pharmaceutical division?

a. 6%

b. 8%

c. 10%

d. 12%

e. 14%

Difficulty: Easy

Keywords: risk-adjusted required rate of return

124. Vaughn’s Super Duper Market’s average required rate of return is 14%. Its pharmaceutical division is riskier than average, its cosmetics division has average risk, and its institutional foods division has below-average risk. Vaughn’s adjusts for both divisional and project risk by adding or subtracting two percentage points. Thus, the maximum adjustment is four percentage points. What is the risk-adjusted required rate of return for an average-risk project in the institutional foods division?

a. 16%

b. 8%

c. 10%

d. 12%

e. 14%

Difficulty: Easy

Keywords: risk-adjusted required rate of return

125. Shop Smart Mart’s average required rate of return is 12%. Its pharmaceutical division is riskier than average, its cosmetics division has average risk, and its institutional foods division has below-average risk. Shop Smart adjusts for both divisional and project risk by adding or subtracting two percentage points. Thus, the maximum adjustment is four percentage points. What is the risk-adjusted required rate of return for an average-risk project in the cosmetics division?

a. 6%

b. 8%

c. 10%

d. 12%

e. 14%

Difficulty: Easy

Keywords: risk-adjusted required rate of return

126. A company estimates that an average-risk project has a WACC of 12%, a below-average risk project has a WACC of 10%, and an above-average risk project has a WACC of 14%. Which of the following independent projects should the company accept?

a. Project X has average risk and an internal rate of return of 11%.

b. Project Y has below-average risk and an internal rate of return of 9%.

c. Project Z has above-average risk and an internal rate of return of 15%.

d. All of the projects above should be accepted.

Difficulty: Moderate

Keywords: risk and project selection

127. Which of the following types of risk is relevant for capital budgeting purposes?

a. Project standing alone risk

b. Total project risk

c. Systematic risk

d. Both b and c

Difficulty: Moderate

Keywords: systematic risk

128. A company estimates that an average-risk project has a Required Rate of Return (RRR) of 9%, a below-average risk project has an RRR of 7%, and an above-average risk project has an RRR of 11%. Which of the following independent projects should the company accept?

a. Project Alpha has average risk and an internal rate of return of 9.5%.

b. Project Beta has below-average risk and an internal rate of return of 6.5%.

c. Project Gamma has above-average risk and an internal rate of return of 10%.

d. All of the projects above should be accepted.

Difficulty: Moderate

Keywords: risk and project selection

129. Which of the following methods of accounting for risk in capital budgeting substitutes a set of risk-free cash flows for the original risky cash flows?

a. Probability trees

b. Risk-adjusted rate of return

c. Scenario analysis

d. Certainty equivalent approach

Difficulty: Easy

Keywords: certainty equivalent approach

130. Which of the following methods of accounting for risk in capital budgeting involves determining how the distribution of possible returns for a given project is affected by a change in one particular input variable?

a. Simulation

b. Sensitivity analysis

c. “What if” analysis

d. Both b and c

Difficulty: Moderate

Keywords: sensitivity analysis

131. Which of the following methods of accounting for risk in capital budgeting attempts to identify publicly traded firms that are engaged solely in the same business as the project under analysis?

a. Sensitivity analysis

b. Simulation

c. Pure play method

d. Risk-adjusted rate of return approach

Difficulty: Moderate

Keywords: pure play method

Short Answer

132. Discuss the different types of project risk. Which type(s) of risk is(are) relevant, and why?

Difficulty: Moderate

Keywords: project risk

133. Discuss the importance of sensitivity analysis and how it relates to simulation.

Difficulty: Moderate

Keywords: sensitivity analysis, simulation

134. Knoko Systems is considering a capital budgeting project with a life of five years that requires an outlay of $90,000. It has free cash flows each period as shown in the following distribution:

P(FLF) FLF

0.10 $ 0

0.20 12,500

0.40 37,500

0.20 43,750

0.10 50,000

a. Assuming a risk-adjusted required rate of return of 0.20 is appropriate for projects of this level of risk, calculate the risk-adjusted net present value of the project.

b. Should the project be accepted?

a. X = (0)(0.10) + ($12,500)(0.20) + ($37,500)(0.40 +

($43,750)(0.20) + ($50,000)(0.10)

= 0 + $2,500 + $15,000 + $8,750 + $5,000 = $31,250

NPV = $31,250(2.991) - $90,000

NPV = $3,469

b. Accept: net present value is positive.

Difficulty: Moderate

Keywords: risk-adjusted required rate of return

135. The Merril Company is considering two mutually exclusive projects, each requiring an outlay of $40,000. The two projects, A and B, both have an expected life of 10 years. The probability distributions for the free cash flows are as follows:

Cash flows for Years 1-10

Project A Project B

P(FCF) FCF P(FCF) FCF

0.20 $ 7,000 0.25 $ 8,500

0.60 9,000 0.50 10,500

0.20 11,000 0.25 12,500

Management has decided that the project with the greater relative risk should have a required rate of return of 18%, while the less risky project’s required rate of return should be 16%.

a. Which project should be accepted?

b. What other factor(s) should be considered?

a. XA = ($7,000)(0.20) + ($9,000)(0.60) + ($11,000)(0.20)

XA = $9,000.00

σ2A = ($7,000 - $9,000)2(0.20) + ($9,000 - $9,000)2 +

($11,000 - $9,000)2(0.20)

? σ2A = $1,600,000

? σA = $1,265

CVA = $1,265/$9,000 = 0.140

XB = ($8,500)(0.25) + (10,500)(0.50) + ($12,500)(0.25) =

$10,500

σ2B = ($8,500 - $10,500)2(0.25) + ($10,500 - $10,500)2(0.50) + ($12,500 - $10,500)2(0.25)

? σ2B = $2,000,000

? σB = $1,414

? CVB = $1,414/$10,500 = 0.135

Discount A at 18% discount B at 16%

NPVA = $9,000(4.494) - $40,000

NPVA = $40,446 - $40,000 = $446

NPVB = $10,500(4.833) - $40,000

NPVB = $50,746 - $40,000 = $10,746

*Accept Project B; it has a higher risk-adjusted net present value.

b. Correlation with existing cash flows.

Difficulty: Hard

Keywords: risk and project selection

136. Armstrong Company has under consideration two mutually exclusive investment projects with the expected free cash flows shown below:

Year Project A Project B

0 $ -20,000 $ -22,500

1 6,000 10,000

2 6,000 12,000

3 6,000 12,000

4 6,000 12,000

5 6,000 12,000

The following schedule of certainty equivalent coefficients for the net free cash flows each year reflects the company’s aversion to risk:

Year Project A Project B

0 1.00 1.00

1 0.90 0.70

2 0.90 0.50

3 0.90 0.50

4 0.80 0.50

5 0.80 0.40

If the risk-free rate is 6%, which project should be selected?

Project A

Year FCF αt FCF times αt

0 -$20,000 1.00 -$20,000

1 6,000 0.90 5,400

2 6,000 0.90 5,400

3 6,000 0.90 5,400

4 6,000 0.80 4,800

5 6,000 0.80 4,800

NPVA = $5,400(2.673) + $4,800(1.833)(0.840) - $20,000

NPVA = $1,825

Project B

Year FCF αt FCF times αt

0 -$22,500 1.00 -$22,500

1 10,000 0.70 7,000

2 12,000 0.50 6,000

3 12,000 0.50 6,000

4 12,000 0.50 6,000

5 12,000 0.40 4,800

NPVB = $7,000(0.943) + $6,000(2.673)(0.943) + $4,800(0.747) - $22,500

NPVB = $2,821

Select Project B

Difficulty: Hard

Keywords: risk and project selection

137. Huang Imports is considering a new order processor. The cost outlay for the machine is $8,400, and due to rapidly advancing technology in their field, it is expected to be obsolete in two years. The free cash flow distributions are shown below.

Possible outcomes in Year 1

P(FCF1) FCF1

0.4 $4,800

0.5 6,000

0.1 7,200

Possible outcomes in Year 2

FCF1 = $4,800 FCF1 = $6,000 FCF1 = $7,200

P(FCF2) FCF2 P(FCF2) FCF2 P(FCF2) ACF2

0.2 $2,400 0.1 $3,600 0.2 $2,400

0.6 4,800 0.7 6,000 0.4 8,400

0.2 7,200 0.2 7,200 0.4 9,600

a. Construct a probability tree showing all of the possible outcomes.

b. Calculate the joint probability of each possible sequence of

events.

c. Calculate the expected internal rate of return for the project.

d. What is the range of internal rate of return?

a. and b

c. TE(IRR) = 21.6611

d. T - 10.82 to 58.03

Difficulty: Moderate

Keywords: probability tree approach

138. The F. Morgan Company must decide whether to accept Project X. The free cash flows for Project X are given below.

Cash Flows Years 1-2

Probability Outcome

.30 $ 20,000

.40 70,000

.30 100,000

Cash Flows Years 3-5

Probability Outcome

.20 $55,000

.60 70,000

.20 95,000

The certainty equivalent coefficient for each year is given below.

Certainty Equivalent

Year Coefficient

0 1.00

1 .90

2 .80

3 .60

4 .50

5 .40

The cost of the project is $200,000 and the risk-free rate of interest is 8%. Should the F. Morgan Company make this investment?

Expected free cash flows Years 1-2 = (.30)($20,000) + (.40)($70,000)

+ (.30)($100,000) = $64,000

Expected free cash flows Years 3-5 = (.20)($55,000) + (.60)($70,000)

+ (.20)($95,000) = $72,000

NPV = -$200,000 + (.90)($64,000) PVIF[8%, 1 yr.] +

(.80)($64,000) PVIF[8%, 2 yr.] + (.60)($72,000) PVIF[8%,

3 yr.] + (.50)($72,000) PVIF[8%, 4 yr.] + (.40)($72,000)

PVIF[8%, 5 yr.]

= -$200,000 + ($57,600)(.926) + ($51,200)(.857) +

($43,200)(.794) + ($36,000)(.735) + ($28,800)(.681) =

-$200,000 + $53,337.60 + $43,878.40 + $34,300.80 +

$26,460 + $19,612.80 = -$22,410.40

Difficulty: Moderate

Keywords: certainty equivalent approach

139. Maurice Toy Company is considering the production of a new game. The initial investment required to purchase the necessary equipment is $75,000. If the game is a success, the first year’s sales will be $300,000, and the company will continue production for another year. The probability that the product will be successful is .60. If the product is a failure, the first year’s sales will be $100,000, and the company will discontinue production. The equipment will be sold for $60,000 at that time. If the product is successful, the probability that sales will be $500,000 in the second year is .30, while the probability that sales will be $300,000 in the second year is .70. The equipment can be sold at the end of the second year for $10,000. Fixed costs associated with producing the game are $70,000 per year; variable costs are 40% of sales. The corporate income tax rate is 46%. The company uses straight-line depreciation and will depreciate the equipment over two years to an anticipated $10,000 salvage value.

a. Determine the joint probability of each possible sequence of events taking place.

b. What is the expected internal rate of return?

c. What is the range of possible internal rates of return for this project.

After-tax cash flow in Year 1 if sales are equal to $100,000:

[$100,000 - $70,000 - (.40)($100,000)][1 - .46] + .46[$32,500] + $60,000 - (.46)[$60,000 - ($75,000 - $32,500)] = $61,500

After-tax cash flow in Year 1 if sales are equal to $300,000:

[$300,000 - $70,000 - (.40)($300,000)][1 - .46] + .46[$32,500] = $74,350

After-tax cash flow in Year 2 if sales are equal to $300,000:

[$300,000 - $70,000 - (.40)($300,000)][1 - .46] + .46[$32,500] + $10,000 = $84,350

After-tax cash flow in Year 2 if sales are equal to $500,000:

[$500,000 - $70,000 - (.40)($500,000)][1 - .46] + .46[$32,500] + $10,000 = $149,150

b. E(IRR) = 38.6118

c. -18.00% to 99.04%

Difficulty: Moderate

Keywords: probability tree approach

140. The Slumber Corp. is considering two mutually exclusive mattress assemblers. Both require an initial outlay of $75,000 and will operate for five years. The probability distributions associated with each assembler for Years 1 through 5 are given below:

Free Cash Flow Years 1-5

Assembler A Assembler B

Probability Cash Flow Probability Cash Flow

.20 $30,000 .20 $18,000

.60 45,000 .60 54,000

.20 60,000 .20 90,000

Since Assembler B is the riskier of the two, management has decided to apply a required rate of return of 18% to its evaluation but only a 12% required rate of return to Assembler A.

a. Determine the expected value of each assembler’s cash flows.

b. Determine each assembler’s risk-adjusted net present value.

a.

XA = 0.20($30,000) + 0.60($45,000) + 0.20($60,000)

= $45,000

XB = 0.20($18,000) + 0.60($54,000) + 0.20($90,000)

= $54,000

b.

NPVA = $45,000(3.605) - $75,000 = $87,225

NPVB = $54,000(3.127) - $75,000 = $93,858

Difficulty: Moderate

Keywords: probability tree approach

141. Metro Communication Co. is considering two mutually exclusive projects. The expected values for each project’s cash flows are given below.

Year Project A Project B

0 $-600,000 $-600,000

1 200,000 400,000

2 400,000 400,000

3 400,000 400,000

4 600,000 600,000

5 600,000 800,000

Metro’s management has decided to evaluate these projects using the certainty equivalent method. The certainty equivalent coefficients for each project’s cash flows are given below.

Year Project A Project B

0 1.00 1.00

1 .95 .90

2 .90 .80

3 .85 .70

4 .80 .60

5 .75 .50

Given that this company’s normal required rate of return is 15% and the after-tax risk-free rate is 8%, which project should be selected?

NPV_A $813,760

NPVB 766,920

Difficulty: Hard

Keywords: certainty equivalent approach

142. Dave Company, Inc. is considering purchasing a new grinding machine with a useful life of five years. The initial outlay for the machine is $165,000. The expected cash inflows and certainty equivalents are as follows:

After-Tax

Given that the firm has a 10% required rate of return and the risk-free rate is 5%, what is the net present value?

Equivalent

Risk-free PVIF Present

Year Cashflow @ 5% Value

1 $14,250 .952 $13,566.00

2 31,500 .907 28,570.50

3 56,000 .864 48,384.00

4 63,000 .823 51,849.00

5 45,500 .784 35,672.00

Present value of cash flows $178,041.50

Initial outlay 165,000.00

Net present value $ 13,041.50

Difficulty: Moderate

Keywords: certainty equivalent approach

143. Referring to Dave Co. in the prior problem, what will the net present value be if the firm decides instead of the certainty equivalent method to use the risk-adjusted discount rate method of evaluating projects? Dave Co. feels the risk premium for the project is 3%.

Equivalent

Risk-free PVIF Present

Year Cash flow @ 5% Value

1 $15,000 .885 $13,275.00

2 35,000 .783 27,405.00

3 70,000 .693 48,510.00

4 90,000 .613 55,170.00

5 70,500 .543 38,281.50

Present value of cash flows $182,641.50

Initial outlay 165,000.00

Net present value $ 17,641.50

Difficulty: Hard

Keywords: certainty equivalent approach

144. April’s Stationary and Gift Store is considering two different lines of housewares. The probability distributions of free cash flows in each year associated with the two projects are:

Project A Project B

Probability Outcome Probability Outcome

.25 $ 4,000 .25 $ 3,000

.50 $ 8,000 .50 $ 6,000

.25 $12,000 .25 $ 9,000

Both projects will require an initial outlay of $13,000 and will have an estimated life of six years. Project A is considered a riskier investment and will have to have an adjusted required rate of return of 15%, while Project B’s required rate of return is 12%.

a. Determine the expected value of each project.

b. Determine each project’s risk-adjusted net present value.

Project A Project B

a. $ 8,000 $ 6,000

b. $17,275.86 $11,668.44

Difficulty: Moderate

Keywords: risk-adjusted rate of return

145. Akin, Gumble Co. is considering a new project that their research division has proposed and have decided to use the certainty equivalent approach to evaluate it. The expected free cash flows and the estimated certainty equivalent coefficients associated with this project are as follows:

Estimated Certainty

Year Expected Free Equivalent

Cash Flows Coefficients

0 -$95,000 1.00

1 $18,000 .95

2 $28,000 .90

3 $38,000 .85

4 $28,000 .80

5 $18,000 .75

Assuming a risk-free rate of 7%, calculate the net present value.

1 $15,981

2 22,010

3 26,366

4 17,089

5 9,625

$91,071

NPV = ($3,929)

Difficulty: Moderate

Keywords: certainty equivalent approach