1. Financial Management: Principles & Applications
Thirteenth Edition
Chapter 13
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Risk Analysis and Project Evaluation
Copyright © 2018, 2014, 2011 Pearson Education, Inc. All Rights Reserved

2. Learning Objectives
Explain the importance of risk analysis in the capital-budgeting decision-making process.
Use sensitivity, scenario and simulation analyses to investigate the determinants of project cash flows.
Use break-even analysis to evaluate project risk.
Describe the types of real options.

3. 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

4. 13.1 THE IMPORTANCE OF RISK ANALYSIS

5. The Importance of Risk Analysis
There are two fundamental reasons to perform a project risk analysis before making the final accept/reject decision:
Project cash flows are risky and may not be equal to the estimates of future cash flows used to compute NPV.
Forecasts are made by humans who can be either too optimistic or too pessimistic when making their cash flow forecasts.

6. 13.2 TOOLS FOR ANALYZING THE RISK OF PROJECT CASH FLOWS

7. Tools for Analyzing the Risk of Project Cash Flows
The actual cash flows an investment produces will almost never exactly equal the expected cash flows used to estimate the investment’s NPV. 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 examine the uncertainty of future cash flows and better understand the reliability of the NPV estimate.

8. Key Concepts—Expected Values and Value Drivers (1 of 3)
The cash flows used in the calculation of a project’s NPV are actually the expected values of the investment’s risky cash flows. The expected value of a future cash flow is simply a probability-weighted average of all the possible cash flows that might occur.

9. Key Concepts—Expected Values and Value Drivers (2 of 3)
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) (400) = $325

10. Key Concepts—Expected Values and Value Drivers (3 of 3)
Financial managers sometimes refer to the basic determinants of an investment’s cash flows – and consequently, its performance – as value drivers.
Value drivers for investment cash flows consist of fundamental determinants of project revenues (e.g., market size, market share, and unit price) and costs (e.g., variable costs and cash fixed costs, which exclude depreciation expense)

11. CHECKPOINT 13.1: CHECK YOURSELF
Forecasting Revenues Using Expected Values

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. Step 1: Picture the Problem (1 of 2)
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. Step 1: Picture the Problem (2 of 2)
Blank
Deep Recession
Mild Recession
Turn-Around
Probability
40%
50%
10%
High Priced Home:
Total Revenues $0
$40,000,000
$80,000,000
Medium Priced Home:
$20,000,000
$60,000,000
$120,000,000
Low-Priced Home:
Total Revenues for each Scenario
$140,000,000
$320,000,000

15. Step 2: Decide on a Solution Strategy
To compute the expected total revenue, we can proceed in three steps:
Estimate the probability of each state of the economy.
Calculate the total revenue from each category of homes for each of the three states of the economy.
Calculate a probability weighted average of the total revenues (step 2 times step 3).

16. Step 3: Solve The expected total revenues are $118,0000. Blank
Deep Recession
Mild Recession
Turn-around
Step 1
Probability
40%
50%
10%
Step 2
Total Revenues for each Scenario
$40,000,000
$140,000,000
$320,000,000
Step 3
Probability × Total Revenue
$16,000,000
$70,000,000
$32,000,000
The expected total revenues are $118,0000.

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. 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.

22. The Problem
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.

23. Step 1: Picture the Problem (1 of 2)
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. Step 1: Picture the Problem (2 of 2)
We consider the following changes:
Unit sales (−10%)
Price per unit (−10%)
Variable cost per unit (+10%)
Cash fixed costs per year (+10%)

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. Step 3: Solve (1 of 3)
Following are the projected cash flows for years 0-5:
 Blank
Year-0
Years 1-4
Year-5
Revenues
5,000,000
Less: Variable cost
$ (3,600,000.00)
Less: Depreciation expense
$ (300,000.00)
Less: Cash fixed cost
$ (400,000.00)
Net operating income
$ ,000.00
$ ,000.00
Less: Taxes
$ (210,000.00)
$ (210,000.00)
Net operating profit after tax
$ ,000.00
$ ,000.00
plus: Depreciation expense
$ ,000.00
less: CAPEX
$ (1,800,000.00)
Blank
less: change in working capital
$ (500,000.00)
$ ,000.00
Free cash flow
$ (2,300,000.00)
$ ,000.00
$ 1,590,000.00

27. Step 3: Solve (2 of 3)
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:
Year
Free Cash Flow
$ (2,300,000.00) 1
$ ,000.00 2 3 4 5
$ 1,590,000.00
NPV
$1,001,714.68
IRR
26.65%

28. Step 3: Solve (3 of 3)
The following table shows the impact on NPV of changes in the value drivers.
Value Drivers
Expected NPV
Revised NPV
% Change
Unit Sales (−10%)
$1,001,714.68
$ 648,446.62
−35%
Price per unit (−10%)
$ (259,956.99)
−126%
Variable cost (+10%)
$ 220,414.70
−78%
Cash fixed cost (+10%)
$ 900,780.95
−10%

29. Step 4: Analyze (1 of 2)
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. Step 4: Analyze (2 of 2)
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. 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.

34. 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 $ 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?

35. Step 1: Picture the Problem
We are given the following revised estimates for two scenarios:
Blank 
Scenario 1
Scenario 2
Unit sales
175,000.00
100,000.00
Price per unit
$24.50
$35
Rest of the information is the same as Checkpoint 13.2

36. 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.

37. Step 3: Solve (1 of 2) Scenario 1 cash flow and NPV/IRR estimates NPV
 Blank
Year 0
Years 1-4
Year-5
Revenues
Blank
$ 4,287,500.00
Less: Variable cost
$ (3,500,000.00)
Less: Depreciation expense
$ (250,000.00)
Less: Cash fixed cost
$ (400,000.00)
Net operating income
$ ,500.00
$ ,500.00
Less: Taxes
$ (41,250.00)
Net operating profit after tax
$ ,250.00
plus: Depreciation expense
$ ,000.00
less: CAPEX
$ (1,500,000.00)
less: change in working capital
$ (500,000.00)
$ ,000.00
Free cash flow
$ (2,000,000.00)
$ 346,250.00
$ 1,096,250.00
NPV
($326,276.10)
IRR
6.29%

38. Step 3: Solve (2 of 2) Scenario 2 cash flow and NPV/IRR estimates
 Blank
Year 0
Years 1-4
Year-5
Revenues
Blank
$ 3,500,000.00
Less: Variable cost
$ (2,000,000.00)
Less: Depreciation expense
$ (250,000.00)
Less: Cash fixed cost
$ (400,000.00)
Net operating income
$ 850,000.00
Less: Taxes
$ (255,000.00)
Net operating profit after tax
$ 595,000.00
plus: Depreciation expense
$ 250,000.00
less: CAPEX
$ (1,500,000.00)
less: change in working capital
$ (500,000.00)
$ 500,000.00
Free cash flow
$ 845,000.00
$ 1,595,000.00
NPV = $1,471,606 IRR = 36%

39. 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.

40. Simulation Analysis (1 of 3)
Scenario analysis provides the analyst with a discrete number of project NPV estimates for a limited number of cases or scenarios. Simulation analysis generates thousands of NPV estimates that are built on thousands of values for each of the investment’s value drivers. These different values arise out of each value driver’s individual probability distribution.

41. Simulation Analysis (2 of 3)
Simulation process involves the following five steps:
Select appropriate probability distribution for each of the investment’s key value drivers.
Randomly select one value for each of the value drivers from its respective probability distributions.
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.

42. Simulation Analysis (3 of 3)
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.
Use the stored values of the project NPV to construct a histogram or probability distribution of NPV.

43. Figure 13-1 Probability Distribution of NPVs for the Marketing of Longhorn’s Brake Lights

44. 13.3 BREAK—EVEN ANALYSIS

45. 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 (NOI) equals zero.

46. Accounting Break—Even Analysis
Accounting break-even analysis involves determining the level of sales necessary to cover total costs – that is, both cash fixed costs and depreciation and variable cost
We decompose production costs into two components: fixed costs and variable costs.

47. Fixed Costs
Fixed costs (or indirect costs) do not vary directly with sales revenue but instead remain constant despite any change to the business; they can be divided into fixed operating costs before depreciation and depreciation itself.
As the number of units sold increases, fixed cost per unit decreases, because the fixed costs are spread over larger quantities of output.

48. Variable Costs
Variable costs (or direct costs) are those 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. If zero units are produced, total variable costs will be equal to zero.

49. Calculating the Accounting Break—Even Point
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.

50. Figure 13-2 Accounting Break—Even Analysis (1 of 2)

51. Figure 13-2 Accounting Break—Even Analysis (2 of 2)

54. 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 values for the worst-case scenario 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.

55. Step 1: Picture the Problem (1 of 3)
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

56. Step 1: Picture the Problem (2 of 3)
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

57. Step 1: Picture the Problem (3 of 3)
The following table shows the break-up of total costs for four units of output.
Units of Output
Variable Costs
Fixed Costs
Total Costs
50,000.00
$ 1,050,000.00
$700,000.00
$ 1,750,000.00
100,000.00
$ 2,100,000.00
$ 2,800,000.00
150,000.00
$ 3,150,000.00
$ 3,850,000.00
200,000.00
$ 4,200,000.00
$ 4,900,000.00

58. Step 2: Decide on a Solution Strategy
To determine the accounting breakeven quantity, we can use the following equation:
QBreak-even = F ÷ (P−V)
Where F = total fixed costs
P = Sale price per unit
V = Variable cost per unit

59. Step 3: Solve (1 of 2)
QBreak-even = F ÷ (P−V) = $700,000 ÷ ($23−$21) = $700,000 ÷ $2 = 350,000 units

60. Step 3: Solve (2 of 2)
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.
Units of Output
Variable Costs
Fixed Costs
Total Costs
Revenue
Profit
50,000.00
$ 1,050,000.00
 $700,000.00
$1,750,000.00
1,150,000.00
(600,000.00)
100,000.00
$ 2,100,000.00
$2,800,000.00
2,300,000.00
(500,000.00)
150,000.00
$ 3,150,000.00
$3,850,000.00
3,450,000.00
(400,000.00)
200,000.00
$ 4,200,000.00
$4,900,000.00
4,600,000.00
(300,000.00)
350,000.00
$ 7,350,000.00
$8,050,000.00
8,050,000.00 $0

61. 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.

62. Cash Break—Even Analysis
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.

63. NPV Break—Even Analysis
The NPV break-even analysis identifies the level of sales necessary to produce an NPV of zero. It differs from accounting break-even analysis in that NPV break-even focuses on cash flows, not accounting profits, and also accounts for Principle 1: Money Has a Time Value.

64. Figure 13-3 NPV Break—Even
Blank
Worst-Case Scenario
Price per unit
$ 190
Variable cost per unit
$ (160)
Cash fixed costs per year
$(285,000)

65. Operating Leverage and the Volatility of Project Cash Flows (1 of 3)
The composition of fixed and variable costs vary by firm. The mix of fixed and variable operating costs not only affects the break-even output but also determines the operating leverage.
Operating leverage, which tends to be higher for firms with more fixed costs, measures the sensitivity of changes in operating income to changes in sales.

66. Operating Leverage and the Volatility of Project Cash Flows (2 of 3)
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. Thus, if DOL is 3.0 and there is a 5% change in sales, NOI will increase by 15% (3.0 × 5%)

67. +20% = $3.6 million/$3.0 million − 1
Table 13-1 How Operating Leverage Affects NOI for a 20% Increase in Longhorn’s Sales
Blank
Base Sales Level for Year t
Forecast Sales Level for Year t +1
Percentage Change in Sales and NOI
Unit sales
15,000
18,000
Sales
$3,000,000
$3,600,000
+20% = $3.6 million/$3.0 million − 1
Less: Total variable costs
2,250,000
2,700,000
Revenue before fixed costs
$ 750,000
$ 900,000
Less: Total fixed costs
375,000
NOI (or EBIT)
$ 375,000
$ 525,000
+40% = $525,000/$375,000 − 1

68. −20% = $2.4 million/$3.0 million − 1
Table 13-2 How Operating Leverage Affects NOI for a 20% Decrease in Longhorn’s Sales
Blank
Base Sales
Level for Year t
Forecast Sales
Level for Year t +1
Percentage Change in Sales and NOI
Unit sales
15,000
12,000
Sales
$3,000,000
$2,400,000
−20% = $2.4 million/$3.0 million − 1
Less: Total variable costs
2,250,000
1,800,000
Revenue before fixed costs
$ 750,000
$ 600,000
Less: Total fixed costs
375,000
NOI or (EBIT)
$ 375,000
$ 225,000
−40% = $225,000/$375,000 − 1

69. Operating Leverage and the Volatility of Project Cash Flows (3 of 3)
We can summarize operating leverage as follows:
Operating leverage is higher if fixed operating costs are high relative to variable operating costs.
Higher operating costs increases the sensitivity of operating income to changes in sales.
DOL is an indication of the firm’s use of operating leverage. The DOL is not a constant but decreases as the level of sales increase beyond break-even point.
Operating leverage is a double-edged sword; it magnifies both profits and losses, helping in good times and causing pain in the bad times.

70. 13.4 REAL OPTIONS IN CAPITAL BUDGETING

71. Real Options in Capital Budgeting (1 of 2)
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:
Timing Options - the option to delay a project until estimated future cash flows are more favorable.

72. Real Options in Capital Budgeting (2 of 2)
Expansion Options - the option to increase the scale and scope of an investment in response to realized demand; and
Contract, Shut-down, and Abandonment options - the options to slow down production, halt production temporarily, or stop production permanently (abandonment).

73. CHECKPOINT 13.5: CHECK YOURSELF
Analyzing Real Options:
Option to Expand

74. 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?

75. Step 1: Picture the Problem
Build 1 smooth-Thru at a cost of $2.4 million
Build 10 more restaurants
NPV = 10 × $800,000
Don’t build any more restaurants
NPV = −$1,600,000
P(favorable)
= .4
P(Unfavorable)
= .6

76. 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.

77. Step 3: Solve (1 of 3)
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%

78. Step 3: Solve (2 of 3)
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

79. Step 3: Solve (3 of 3)
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

80. 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.

81. Key Terms (1 of 3) Accounting break-even analysis Break-even analysis
Cash break-even point
Contribution margin
Degree of operating leverage (DOL)
Direct cost
Expected value

82. Key Terms (2 of 3) Fixed cost Indirect cost NPV break-even analysis
Operating leverage
Real options
Scenario analysis
Sensitivity analysis

83. Key Terms (3 of 3)
Simulation analysis
Value drivers
Variable costs

84. Copyright