1. Chapter 13 Risk Analysis and Project Evaluation

2. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-2 Slide Contents Principles Applied In This Chapter Learning Objectives 1.The Importance of Risk Analysis 2.Tools for Analyzing the Risk of Project Cash Flows 3.Break-Even Analysis 4.Real Options in Capital Budgeting Key Terms

3. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-3 Learning Objectives 1.Explain the importance of risk analysis in the capital budgeting decision-making process. 2.Use sensitivity, scenario and simulation analyses to investigate the determinants of project cash flows. 3.Use break-even analysis to evaluate project risk. 4.Describe the types of real options.

4. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-4 Principles Applied in This Chapter Principle 1: Money has a Time Value Principle 2: There Is a Risk-Return Tradeoff Principle 3:Cash Flows are the Source of Value

5. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-5 13.1 THE IMPORTANCE OF RISK ANALYSIS

6. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-6 The Importance of Risk Analysis There are two main reasons to perform a project risk analysis before making the final decision: –Project cash flows are risky and may not be equal to the estimates used to compute NPV. –Forecasts made by humans can be biased, either too optimistic or too pessimistic.

7. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-7 13.2 TOOLS FOR ANALYZING THE RISK OF PROJECT CASH FLOWS

8. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-8 Tools for Analyzing the Risk of Project Cash Flows There are many possible cash flow outcomes for any risky project. The analyst uses tools such as Sensitivity analysis, Scenario analysis, and Simulation analysis to better understand the uncertainty of future cash flows.

9. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-9 Key Concepts - Expected Values and Value Drivers Expected Values –The cash flows used to calculate a project’s NPV are expected values of the investment’s risky cash flows. The expected value of a future cash flow is a probability-weighted average of all the possible cash flows that might occur.

10. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-10 Key Concepts - Expected Values and Value Drivers (cont.) Example What is the expected cash value if there are two possible cash flows, $100 and $400 and the probabilities of these cash flows are 25% and 75%. Expected cash value =.25 ( 100) +.75 (400) = $325

11. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-11 CHECKPOINT 13.1: CHECK YOURSELF Forecasting Revenues Using Expected Values

12. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-12 The Problem Consider your forecast of Marshall Home’s expected revenues for 2014 where the probability of entering a deep recession increases to 40%, the probability of mild recession drops to 50%, and the probability of a turn-around declines to only 10%. You may assume that the estimates of the number of units sold and the selling price of each remain unchanged.

13. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-13 Step 1: Picture the Problem The following table lays out the number of units the firm’s manager estimate they will sell in each of three home categories for each of the three possible states of the economy:

14. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-14 Step 1: Picture the Problem (cont.) Deep Recession Mild RecessionTurn-Around Probability40%50%10% High Priced Home: Total Revenues $0$40,000,000$80,000,000 Medium Priced Home: Total Revenues $20,000,000$60,000,000$120,000,000 Low-Priced Home: Total Revenues $20,000,000$40,000,000$120,000,000 Total Revenues for each Scenario $40,000,000$140,000,000$320,000,000

15. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-15 Step 2: Decide on a Solution Strategy To compute the expected total revenue, we can proceed in three steps: 1.Estimate the probability of each state of the economy. 2.Calculate the total revenue from each category of homes for each of the three states of the economy. 3.Calculate a probability weighted average of the total revenues (step 2 times step 3).

16. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-16 Step 3: Solve Deep Recession Mild Recession Turn- around Step 1Probability40%50%10% Step 2Total Revenues for each Scenario $40,000,00 0 $140,000,0 00 $320,000,0 00 Step 3Probability × Total Revenue $16,000,00 0 $70,000,00 0 $32,000,00 0 The expected total revenues declines from $156,000,000 to $118,0000.

17. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-17 Step 4: Analyze The table in step 3 shows that there can be wide variation in revenue based on the future economic scenario. The table only shows the revenues. To get a more realistic picture, we should also consider the impact on expenses and consequently, profits and cash flows.

18. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-18 Value Drivers Value drivers for investment cash flows consist of the fundamental determinants of project revenues (e.g., market share, market size, and price) and costs (e.g., variable costs and cash fixed costs, which are fixed costs other than depreciation).

19. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-19 Value Drivers (cont.) Identification of value drivers allow the financial manager to: –Focus on refining forecasts of these key variables. –Monitor the key value drivers throughout the life of the project, so that timely corrective action can be taken.

20. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-20 Sensitivity Analysis Sensitivity analysis occurs when a financial manager evaluates the effect of each value driver on the investment’s NPV. It helps identify the variable that has the most impact on NPV.

21. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-21 CHECKPOINT 13.2: CHECK YOURSELF Project Risk Analysis: Sensitivity Analysis

22. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-22 The Problem After a careful cost analysis of the costs for making the silhouettes, Cranium’s management has determined that it will be possible to reduce the variable cost per unit down to $18 per unit by purchasing an additional option for the equipment that will raise its initial cost to $1.8 million (the residual or salvage value for this configuration is estimated to be $300,000). All other information remains the same as before. For this new machinery configuration, analyze the sensitivity of the project NPV to the same percent changes analyzed above.

23. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-23 Step 1: Picture the Problem To evaluate the sensitivity of the project’s NPV and IRR to uncertainty surrounding the project’s value drivers, we need to analyze the effects of the changes in the value drivers (unit sales, price per unit, variable cost per unit, and annual fixed operating cost other than depreciation).

24. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-24 Step 1: Picture the Problem (cont.) We consider the following changes: –Unit sales (-10%) –Price per unit (-10%) –Variable cost per unit (+10%) –Cash fixed costs per year (+10%)

25. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-25 Step 2: Decide on a Solution Strategy The objective of this analysis is to explore the effects of the prescribed changes in the value drivers on the project’s NPV. We will need to estimate the base-case NPV based on given information and then compute the NPV based on assumed changes to the value drivers.

26. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-26 Step 3: Solve Following are the projected cash flows for years 0-5:

27. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-27 Step 3: Solve (cont.) Given the free cash flows for years 0-5, we can compute the NPV and IRR on Excel spreadsheet, which gives us the following results:

28. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-28 Step 3: Solve (cont.) The following table shows the impact on NPV of changes in the value drivers.

29. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-29 Step 4: Analyze Here we observe that a 10% adverse change in value drivers has a significant impact on NPV. If the price per unit drops by 10%, the project turns negative with the value of NPV declining by 126%.

30. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-30 Step 4: Analyze (cont.) The results also show that NPV is most sensitive to changes in the selling price and variable cost. Thus management must be doubly sure that the estimates on these value drivers are accurate and that these two value drivers are closely monitored.

31. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-31 Scenario Analysis Sensitivity analysis involves changing one value driver at a time and analyzing its effect on the investment NPV. Scenario analysis allows the financial manager to simultaneously consider the effects of changes in the estimates of multiple value drivers on the investment opportunity’s NPV.

32. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-32 CHECKPOINT 13.3: CHECK YOURSELF Project Risk Analysis: Scenario Analysis

33. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-33 The Problem The deepening recession that characterized the economy caused Cranium’s management to reconsider the base-case scenario for the project by lowering their unit sales estimates to 175,000 at revised price per unit of $24.50. Based on these projections, is the project still viable? What if Longhorn followed a higher price strategy of $35 per unit but only sold 100,000 units? What would you recommend Longhorn do?

34. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-34 Step 1: Picture the Problem We are given the following revised estimates for two scenarios: Rest of the information is the same as Checkpoint 13.2

35. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-35 Step 2: Decide on a Solution Strategy Our objective is to determine the sensitivity of NPV to the two scenarios. We can estimate the free cash flows as before and then compute the NPVs for the two scenarios and compare.

36. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-36 Step 3: Solve Scenario 1 cash flow and NPV/IRR estimates NPV($326,276.10) IRR6.29%

37. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-37 Step 3: Solve (cont.) Scenario 2 cash flow and NPV/IRR estimates

38. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-38 Step 4: Analyze Examination of the two scenarios reveals that this is a risky opportunity as there is a wide divergence in the NPV estimates. The NPV could be as high as $1,491,606 or as low as a negative $326,276.

39. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-39 Simulation Analysis Simulation analysis generates thousands of estimates of NPV that are built upon thousands of values for each of the investment’s value drivers. These different values arise out of each value driver’s individual probability distribution.

40. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-40 Simulation Analysis (cont.) Simulation process involves the following steps: 1.Estimate the probability distributions for each of the key value drivers. 2.Randomly select one value for each of the value drivers from their probability distributions. 3.Combine the values selected for each of the values drivers to estimate project cash flows for each year of the project’s life and calculate the project’s NPV.

41. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-41 Simulation Analysis (cont.) 4.Store or save the calculated value of the NPV and repeat Steps 2 and 3. Computer softwares allows one to easily repeat Steps 2 and 3 thousands of times. 5.Use the stored values of the project NPV to construct a histogram or probability distribution of NPV.

42. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-42 Figure 13-1 Probability Distribution of NPVs for the Marketing of Longhorn’s Brake Lights

43. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-43 13.3 BREAK-EVEN ANALYSIS

44. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-44 Break-Even Analysis Break-even analysis determines the minimum level of output or sales that the firm must achieve in order to avoid losing money – that is, to break even. In most cases, break-even sales is defined as the level of sales for which net operating income equals zero.

45. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-45 Accounting Break-Even Analysis Accounting break-even analysis involves determining the level of sales necessary to cover total fixed costs – that is, both cash fixed costs and depreciation. We decompose production costs into: fixed costs and variable costs.

46. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-46 Accounting Break-Even Analysis (cont.) Fixed costs (or indirect costs) do not vary directly with sales revenue. For example, insurance premiums, administrative salaries. As the number of units sold increases, fixed cost per unit decreases, because the fixed costs are spread over larger quantities of output.

47. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-47 Accounting Break-Even Analysis (cont.) Variable costs (or direct costs) are costs that vary with firm sales. For example, hourly wages, cost of materials used, sales commission. Variable costs per unit remain the same regardless of the level of output.

48. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-48 Figure 13-2 Accounting Break-Even Analysis

49. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-49 Figure 13-2 Accounting Break-Even Analysis (cont.)

50. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-50 Accounting Break-Even Analysis (cont.) The accounting break-even point is the level of sales that is necessary to cover both variable and total fixed costs, such that the net operating income is equal to zero.

51. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-51 CHECKPOINT 13.4: CHECK YOURSELF Project Risk Analysis: Accounting Break-Even Analysis

52. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-52 The Problem Crainium, Inc.’s analysts have estimated the accounting break-even for the project to be 130,000 units and now want to consider how the worst-case scenario value driver values would affect the accounting break-even. Specifically, consider a unit price of $23, variable cost per unit of $21, and total fixed costs of $700,000.

53. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-53 Step 1: Picture the Problem The new investment that Crainium, Inc. is planning to invest is described in Checkpoint 13.2 with the following revised estimates: –Price per unit =$25 –Variable cost per unit = $23 –Total fixed cost per year = $700,000

54. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-54 Step 1: Picture the Problem (cont.) The annual costs consists of total fixed costs and variable costs that vary by the level of output. Total costs = Variable cost (# of units) + Total fixed costs

55. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-55 Step 1: Picture the Problem (cont.) The following table shows the break-up of total costs for four units of output.

56. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-56 Step 2: Decide on a Solution Strategy To determine the accounting breakeven quantity, we can use the following equation: Q Break-even = F ÷ (P-V) –Where F = total fixed costs P = Sale price per unit V = Variable cost per unit

57. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-57 Step 3: Solve Q Break-even = F ÷ (P-V) = $700,000 ÷ ($23-$21) = $700,000 ÷ $2 = 350,000 units

58. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-58 Step 3: Solve (cont.) The table below shows that at 350,000 units of output, total costs = total revenue i.e. the firm breaks even or accounting profits are equal to zero.

59. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-59 Step 4: Analyze Break-even point sets the lower limit on the level of sales, from an accounting perspective. Note projects that merely break even in an accounting sense have negative NPVs and results in a loss of shareholder value.

60. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-60 Calculating the Cash Break-Even Point The cash break-even point tells us the level of sales where we have covered our cash fixed costs (ignoring depreciation) and as a result our cash flow is zero.

61. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-61 NPV Break-Even Analysis The NPV break-even analysis identifies the level of sales necessary to produce a zero level of NPV. It differs from accounting break- even analysis in that NPV break-even focuses on cash flows, not accounting profits.

62. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-62 Figure 13-3 NPV Break-Even

63. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-63 Operating Leverage and the Volatility of Project Cash Flows The composition of fixed and variable costs vary by firm. The mix of fixed and variable operating costs determines operating leverage.

64. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-64 Operating Leverage and the Volatility of Project Cash Flows (cont.) Operating leverage results from the use of fixed costs in the operations of the firm and measures the sensitivity of changes in operating income to changes in sales. Degree of operating leverage (DOL) tells us when there is a percent change in sales, how that is reflected in a percent change in NOI.

65. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-65 Operating Leverage and the Volatility of Project Cash Flows (cont.)

66. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-66 Table 13-1 How Operating Leverage Affects NOI for a 20% Increase in Longhorn’s Sales Table 13-2 How Operating Leverage Affects NOI for a 20% Decrease in Longhorn’s Sales

67. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-67 Operating Leverage and the Volatility of Project Cash Flows (cont.) We can make the following summary observations about operating leverage: –Operating leverage results from substitution of fixed operating costs for variable operating costs. –The effect of operating leverage is to increase the effect of changes in sales on operating income.

68. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-68 Operating Leverage and the Volatility of Project Cash Flows (cont.) –The degree of operating leverage (DOL) is an indication of the firm’s use of operating leverage. The DOL decreases as the level of sales increases beyond the break-even point. –Operating leverage is a double-edged sword, magnifying both profits and losses, helping in the good times and causing pain in the bad times.

69. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-69 13.4 REAL OPTIONS IN CAPITAL BUDGETING

70. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-70 Real Options in Capital Budgeting Opportunities to alter the project’s cash flow stream after the project has begun are referred to as real options. The most common sources of flexibility or real options that can add value to an investment opportunity include: 1.Timing Options. The option to delay a project until estimated future cash flows are more favorable.

71. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-71 Real Options in Capital Budgeting (cont.) 2.Expansion Options. The option to increase the scale and scope of an investment in response to realized demand; and 3.Contract, Shut-down, and Abandonment options. The options to slow down production, halt production temporarily, or stop production permanently (abandonment).

72. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-72 CHECKPOINT 13.5: CHECK YOURSELF Analyzing Real Options: Option to Expand

73. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-73 The Problem If you thought there was a 40% chance that this project would be favorably received and 60% chance that the project would be unfavorably received, what would be the NPV of the project if you were to introduce 10 additional restaurants if it is well received?

74. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-74 Step 1: Picture the Problem Build 1 smooth- Thru at a cost of $2.4 million Build 10 more restaurants NPV =10 x $800,000 Don’t build any more restaurants NPV = -$1,600,000 P(favorable) =.4 P(Unfavorable) =.6

75. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-75 Step 2: Decide on a Solution Strategy We need to determine the NPV of this project assuming we will build 10 restaurants if the project is favorably received and will not build any additional restaurants if it is not favorably received.

76. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-76 Step 3: Solve We are given the following information (per Restaurant): Perpetual annual cash flow: –if favorably received = $320,000 –if not favorably received = $80,000 Probability of being favorably received = 40% Discount rate = 10%

77. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-77 Step 3: Solve (cont.) We use the PV of perpetuity equation (given by CF/i) to determine the present value of cash flows. NPV (if favorably received) –=($320,000 ÷.10) - $2,400,000 = $800,000 NPV (if not favorably received) –= ($80,000 ÷.10) - $2,400,000 = -$1,600,000

78. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-78 Step 3: Solve (cont.) Assuming we will open 10 restaurants if it is favorably received and only one if it is unfavorably received, we can determine the expected NPV as follows: Expected NPV = 10 (.4)($800,000) + 1(.60)(-1,600,000) = $2,240,000

79. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-79 Step 4: Analyze Without the option to expand, this project would have had a NPV of -$640,000. NPV = $800,000(.4) + (-$1,600,000)(.6) = -$640,000 However, by considering the option to expand, the project has a positive NPV.

80. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-80 Key Terms Accounting break-even analysis Break-even analysis Cash break-even point Contribution margin Degree of operating leverage Direct cost Expected value

81. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-81 Key Terms (cont.) Fixed cost Indirect cost NPV break-even analysis Operating leverage Real options Scenario analysis Sensitivity analysis

82. Copyright ©2014 Pearson Education, Inc. All rights reserved.13-82 Key Terms (cont.) Simulation analysis Value drivers Variable costs