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Copyright © 2011 Pearson Prentice Hall. All rights reserved. Risk Analysis and Project Evaluation Chapter 13

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Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Risk Analysis and Project Evaluation

Chapter 13

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Slide Contents

• Learning Objectives• Principles Used in This Chapter

1.The Importance of Risk Analysis2.Tools for Analyzing the Risk of Project Cash Flows3.Break-Even Analysis4.Real Options in Capital Budgeting

• Key Terms

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Learning Objectives

1. Explain the importance of risk analysis in the capital budgeting decision-making process.

2. Understand the use of sensitivity and scenario analysis as well as simulation analysis to investigate the determinants of project cash flows.

3. Use break-even analysis to evaluate project risk.4. Explain the types of real options.

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Principles Used in This Chapter

• Principle #2: There Is a Risk-Return Tradeoff

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13.1 The Importance of Risk Analysis

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The Importance of Risk Analysis

• There are two fundamental reasons to perform a project risk analysis before making a final accept/reject decision:– Project cash flows are risky and may not be

equal to the estimates used to compute NPV.– Forecasts are made by humans who can be

either too optimistic or too pessimistic when making their cash flow forecasts. Risk analysis will help guard against such biases.

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13.2 Tools for Analyzing the Risk of Project Cash Flows

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Tools for Analyzing the Risk of Project Cash Flows

• It is reasonable to assume that the actual cash flows an investment produces will never equal the expected cash flows used to estimate the investment’s NPV as there are many possible cash flow outcomes for any project.

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Tools for Analyzing the Risk of Project Cash Flows (cont.)

• Tools such as Sensitivity analysis, Scenario analysis, and Simulation analysis provide better understanding of the uncertainty of future cash flows and, consequently, the reliability of the NPV estimate.

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Key Concepts - Expected Values and Value Drivers

• Expected Values– The expected value of a future cash flow is

given by the probability weighted average of all the possible cash flows that might occur.

– The cash flows used to calculate a project’s NPV are expected values.

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Key Concepts - Expected Values and Value Drivers (cont.)

• Example 13.1

– 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

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Checkpoint 13.1

Forecasting Revenues Using Expected ValuesMarshall Homes is a Texas homebuilder that specializes in the construction of high-end homes costing $1.5 million to $10 million each. To estimate its revenues for 2011 following the economic downturn of 2007–09, it divided its home sales into three categories based on selling price (high, medium, and low) and estimated the number of units it expects to sell under three different economic scenarios for 2011. These scenarios include a deep recession (Scenario I), a continuation of current conditions in which the economy is in a mild recession (Scenario II), and finally a turnaround in the economy and return to the economic conditions of 2004–2006 (Scenario III). What are Marshall’s expected revenues for 2011?

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Checkpoint 13.1

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Checkpoint 13.1

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Checkpoint 13.1

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Checkpoint 13.1: Check Yourself

• Consider your forecast of Marshall Home’s expected revenues for 2011 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.

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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:

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Step 1: Picture the Problem (cont.)

Deep Recession

Mild Recession Turn-Around

Probabil i ty 40% 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

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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).

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Step 3: Solve

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

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Step 3: Solve (cont.)

• Thus the expected total revenues declines from $156,000,000 to $118,0000.

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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.

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Value Drivers

• Value drivers are the basic determinants of an investment’s cash flows and consequently its performance.

• Value drivers may consist of determinants of project revenues (e.g., market share, market size, and price) and costs (e.g., variable and cash fixed costs)

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Value Drivers (cont.)

• Identification of value drivers allow the financial manager to:– Allocate more time and money toward refining

their forecasts of these key variables.– Monitor the key value drivers regularly so that

prompt corrective action can be taken in the event that the project is not proceeding as expected.

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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.

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Checkpoint 13.2

Project Risk Analysis: Sensitivity AnalysisCrainium, Inc. is considering an investment in a new plasma cutting tool to be used in cutting out steel silhouettes that will be sold through the firm’s catalog sales operations. The silhouettes can be cut into any two-dimensional shape such as a state, university mascot or logo, etc. The products are expected to sell for an average price of $25 per unit, and the company analysts expect the firm can sell 200,000 units per year at this price for a period of five years. Launching this service will require the purchase of a $1.5 million plasma cutter and materials handling system that has a residual or salvage value in five years of $250,000. In addition, the firm expects to have to invest an additional $500,000 in working capital to support the new business. Other pertinent information concerning the business venture is provided below:

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Checkpoint 13.2 Crainium’s analysts have estimated the project’s expected or base-case cash flows as well as the NPV and IRR to be the following:

Although the project is expected to have a $209,934 NPV and a 15.59% IRR (which exceeds the project’s 10% discount rate), it is risky, so the firm’s analysts want to explore the importance of uncertainty in the project cash flows. Perform a sensitivity analysis on this proposed investment.

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Checkpoint 13.2

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Checkpoint 13.2

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Checkpoint 13.2: Check Yourself

• 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.

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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).

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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%)

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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.

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Step 3: Solve

• Following are the projected cash flows for years 0-5:

Year-0 Years 1-4 Year-5

Revenues 5,000,000 5,000,000

Less: Variable Cost $(3,600,000.00) $(3,600,000.00)

Less: Depreciation Expense $(300,000.00) $(300,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $700,000.00 $700,000.00

Les: Taxes $(210,000.00) $(210,000.00)

Net operating profit after tax $490,000.00 $490,000.00

Plus: Depreciation Expense $300,000.00 $300,000.00

Less: CAPEX $(1,800,000.00) $300,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,300,000.00) $790,000.00 $1,590,000.00

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Step 3: Solve (cont.)

• Given the free cash flows for years 0-5, we can compute the NPV and IRR on excel, which gives us the following results:

Year Free Cash Flow

0 $(2,300,000.00)

1 $790,000.00

2 $790,000.00

3 $790,000.00

4 $790,000.00

5 $1,590,000.00

NPV $1,001,714.68

IRR 26.65%

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Step 3: Solve (cont.)

• What if sales drop by 10%?Year-0 Years 1-4 Year-5

Revenues 4,500,000 4,500,000

Less: Variable Cost $(3,240,000.00) $(3,240,000.00)

Less: Depreciation Expense $(300,000.00) $(300,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $560,000.00 $560,000.00

Les: Taxes $(168,000.00) $(168,000.00)

Net operating profit after tax $392,000.00 $392,000.00

Plus: Depreciation Expense $300,000.00 $300,000.00

Less: CAPEX $(1,800,000.00) $300,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,300,000.00) $692,000.00 $1,492,000.00

NPV $648,446.62

IRR 21.59%

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Step 3: Solve (cont.)• What if variable costs increase by 10%?

Year-0 Years 1-4 Year-5

Revenues 5,000,000 5,000,000

Less: Variable Cost $(3,960,000.00) $(3,960,000.00)

Less: Depreciation Expense $(300,000.00) $(300,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $340,000.00 $340,000.00

Les: Taxes $(102,000.00) $(102,000.00)

Net operating profit after tax $238,000.00 $238,000.00

Plus: Depreciation Expense $300,000.00 $300,000.00

Less: CAPEX $(1,800,000.00) $300,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,300,000.00) $538,000.00 $1,338,000.00

NPV $220,414.70

IRR 15.19%

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Step 3: Solve (cont.)• What if price per unit drops by 10%

Year-0 Years 1-4 Year-5

Revenues 4,500,000 4,500,000

Less: Variable Cost $(3,600,000.00) $(3,600,000.00)

Less: Depreciation Expense $(300,000.00) $(300,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $200,000.00 $200,000.00

Les: Taxes $(60,000.00) $(60,000.00)

Net operating profit after tax $140,000.00 $140,000.00

Plus: Depreciation Expense $300,000.00 $300,000.00

Less: CAPEX $(1,800,000.00) $300,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,300,000.00) $440,000.00 $1,240,000.00

NPV ($259,956.99)

IRR 8.02%

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Step 3: Solve (cont.)• What if fixed costs increase by 10%?

Year-0 Years 1-4 Year-5

Revenues 5,000,000 5,000,000

Less: Variable Cost $(3,600,000.00) $(3,600,000.00)

Less: Depreciation Expense $(300,000.00) $(300,000.00)

Less: Cash Fixed Cost $(440,000.00) $(440,000.00)

Net Operating Income $660,000.00 $660,000.00

Les: Taxes $(198,000.00) $(198,000.00)

Net operating profit after tax $462,000.00 $462,000.00

Plus: Depreciation Expense $300,000.00 $300,000.00

Less: CAPEX $(1,800,000.00) $300,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,300,000.00) $762,000.00 $1,562,000.00

NPV $900,780.95

IRR 25.22%

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Step 3: Solve (cont.)

• 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%) $1,001,714.68 $(259,956.99) -126%

Variable Cost (+10%) $1,001,714.68 $220,414.70 -78%

Cash Fixed Cost (+10%) $1,001,714.68 $900,780.95 -10%

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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%.

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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. Furthermore, once the project is implemented, these two value drivers must be closely monitored.

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Scenario Analysis

• Sensitivity analysis involves changing one value driver at a time and analyzing its effect on the investment NPV.

• Scenario analysis considers the effect of multiple changes in value drivers on the NPV. For example, the scenarios could be Expected or base-case, Worst-case and Best-case.

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Checkpoint 13.3

Project Risk Analysis: Scenario AnalysisThe analysts performing the risk analysis on the plasma cutting tool being considered by Crainium, Inc. (described in Checkpoint 13.2) now want to evaluate the project risk using scenario analysis. Specifically, they now want to evaluate thE project’s risk using scenario analysis aimed at evaluating the project’s NPV under worst- and best-case scenarios for the project’s value drivers.

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Checkpoint 13.3

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Checkpoint 13.3

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Checkpoint 13.3: Check Yourself

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?

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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

Scenario 1 Scenario 2

Unit Sales $175,000.00 $100,000.00

Price per unit $24.50 $35

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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.

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Step 3: Solve• Scenario 1 cash flow and NPV/IRR estimates

Year-0 Years 1-4 Year-5

Revenues $4,287,500.00 $4,287,500.00

Less: Variable Cost $(3,500,000.00) $(3,500,000.00)

Less: Depreciation Expense $(250,000.00) $(250,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $137,500.00 $137,500.00

Les: Taxes $(41,250.00) $(41,250.00)

Net operating profit after tax $96,250.00 $96,250.00

Plus: Depreciation Expense $250,000.00 $250,000.00

Less: CAPEX $(1,500,000.00) $250,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,000,000.00) $346,250.00 $1,096,250.00

NPV $326,276.10

IRR 6.29%

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Step 3: Solve (cont.)• Scenario 2 cash flow and NPV/IRR estimates

Year-0 Years 1-4 Year-5

Revenues $3,500,000.00 $3,500,000.00

Less: Variable Cost $(2,000,000.00) $(2,000,000.00)

Less: Depreciation Expense $(250,000.00) $(250,000.00)

Less: Cash Fixed Cost $(400,000.00) $(400,000.00)

Net Operating Income $850,000.00 $850,000.00

Les: Taxes $(255,000.00) $(255,000.00)

Net operating profit after tax $595,000.00 $595,000.00

Plus: Depreciation Expense $250,000.00 $250,000.00

Less: CAPEX $(1,500,000.00) $250,000.00

Less: Change in Working Capital $(500,000.00) $500,000.00

Free Cash Flow $(2,000,000.00) $845,000.00 $1,595,000.00

NPV $1,471,606.03

IRR 36.10%

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Step 4: Analyze

• Examination of the two scenarios reveals that this is a risky opportunity as there is a wide divergence in the two NPV estimates. The NPV could be as high as $1,491,606 or as low as a negative $326,276.

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Simulation Analysis

• Scenario analysis provides the analyst with a discrete number of estimates of project NPVs for a limited number of cases or scenarios.

• 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.

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Simulation Analysis (cont.)

• Simulation process involves the following steps:1. Estimate the probability distributions for

each of the investment’s key value drivers.2. Randomly select one value for each of the

value drivers from their respective 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.

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Simulation Analysis (cont.)

4. Store or save the calculated value of the NPV and repeat Steps 2 and 3. Computer softwares can 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.

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13.3 Break-Even Analysis

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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 i.e. to break even.

• In most cases, break-even sales is defined as the level of sales for which net operating income equals zero.

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Accounting Break-Even Analysis

• Accounting break-even analysis involves determining the level of sales necessary to cover total fixed costs (both cash fixed costs and depreciation).

• To compute the accounting break-even point, we need to decompose the costs into two components: fixed costs and variable costs.

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Accounting Break-Even Analysis (cont.)

• Fixed costs are costs that 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, as fixed costs are spread over larger quantities of output.

• Fixed costs are also known as indirect costs.

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Accounting Break-Even Analysis (cont.)

• Variable costs are costs that vary directly with the level of sales. Hence, they are also referred to as direct costs. For example, hourly wages, cost of materials used, sales commission.

• Variable costs per unit remain the same regardless of the level of output.

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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.

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Checkpoint 13.4

Project Risk Analysis: Accounting Break-Even AnalysisThe new plasma cutting tool that Crainium, Inc. is considering investing in as described in Checkpoint 13.2 has the following value driver estimates of fixed and variable costs:

Company analysts are evaluating the project’s risks and want to estimate the accounting break-even for the project’s annualrevenues and expenses. What is the break-even level of units?

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Checkpoint 13.4

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Checkpoint 13.4

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Checkpoint 13.4

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Checkpoint 13.4

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Checkpoint 13.4: Check Yourself

• 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.

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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

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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

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Step 1: Picture the Problem (cont.)

• 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 $700,000.00 $2,800,000.00

150,000.00 $3,150,000.00 $700,000.00 $3,850,000.00

200,000.00 $4,200,000.00 $700,000.00 $4,900,000.00

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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 unitV = Variable cost per unit

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Step 3: Solve

• QBreak-even = F ÷ (P-V)

= $700,000 ÷ ($23-$21)= $700,000 ÷ $2= 350,000 units

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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.

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 $700,000.00 $2,800,000.00 2,300,000.00 (500,000.00)

150,000.00 $3,150,000.00 $700,000.00 $3,850,000.00 3,450,000.00 (400,000.00)

200,000.00 $4,200,000.00 $700,000.00 $4,900,000.00 4,600,000.00 (300,000.00)

350,000.00 $7,350,000.00 $700,000.00 $8,050,000.00 8,050,000.00 $0

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Step 4: Analyze

• Break-even analysis indicates the number of units the firm must sell in order to cover total fixed and variable costs resulting in net operating income of zero.

• 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.

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Calculating the Cash Break-Even Point

• The cash break-even point computes the level of sales where cash fixed costs (ignoring depreciation) are covered and as a result, cash flow is equal to zero.

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NPV Break-Even Analysis

• The NPV break-even analysis identifies the level of sales necessary to produce a zero level of NPV.

• NPV break-even focuses on cash flows, not accounting profits.

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Operating Leverage and the Volatility of Project Cash Flows

• The composition of fixed and variable costs vary by firm. For example, a manufacturing firm is likely to have a higher fixed cost component compared to service firm.

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Operating Leverage and the Volatility of Project Cash Flows (cont.)

• Most businesses may have some flexibility in their cost structure and maybe able to alter the composition of fixed and variable costs, at least marginally.

• The mix of fixed and variable costs will impact the breakeven output and also the operating leverage.

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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) measures the firm’s operating leverage for a particular level of sales.

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Operating Leverage and the Volatility of Project Cash Flows (cont.)

• DOL indicates by what percentage the NOI will change for a given percentage change in sales.

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Operating Leverage and the Volatility of Project Cash Flows (cont.)

• We can make the following 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.

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Operating Leverage and the Volatility of Project Cash Flows (cont.)

– The degree of operating leverage is an indication of the firm’s use of operating leverage. The DOL is not a constant but decreases as the level of sales increases beyond the breakeven point.

– Operating leverage is a double-edged sword, magnifying both profits and losses.

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13.4 Real Options in Capital Budgeting

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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 Option – the option to delay a project

until expected cash flows are more favorable.

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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 option – the option to slow down production, halt production temporarily, or stop production permanently (abandonment).

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Checkpoint 13.5

Analyzing Real Options: Option to ExpandYou are considering introducing a new drive-in restaurant called Smooth-Thru featuring high protein and vitamin-laced smoothies along with other organic foods. The initial outlay on this new restaurant is $2.4 million and the present value of the free cash flows (excluding the initial outlay) is $2 million, such that the project has a negative expected NPV of$400,000. Looking closer, you find that there is a 50% chance that this new restaurant will be well received and will produce annual cash flows of $320,000 per year forever (a perpetuity), while there is a 50% chance of it producing a cash flow of only $80,000 per year forever (a perpetuity) if it isn’t received well. The required rate of return you use to discount the project cash flows is 10%. However, if the new restaurant is successful, you will be able to build 4 more of them and they will have costs and cash flows similar to the successful restaurant’s cash flows. If your new restaurant is not received favorably, you will not expand. Ignoring the fact that there would be a time delay in building additional new restaurants if the project is favorably received, determine the project’s NPV.

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Checkpoint 13.5

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Checkpoint 13.5

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Checkpoint 13.5 – Check Yourself

• 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?

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Step 1: Picture the Problem

P(favorable)=.4

P(Unfavorable)=.6

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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.

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Step 3: Solve

• We are given the following information (per Restaurant):

• Perpetual annual cash flow (if favorably received) = $320,000

• Perpetual annual cash flow (if not favorably received) = $80,000

• Probability of being favorably received = 40%• Discount rate = 10%

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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

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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

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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.

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Key Terms

• Accounting break-even analysis• Break-even analysis• Cash break-even point• Contribution margin• Degree of operating leverage• Direct cost• Expected value

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Key Terms (cont.)

• Fixed cost• Indirect cost• NPV break-even analysis• Operating leverage• Real options• Scenario analysis• Sensitivity analysis

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Key Terms (cont.)

• Simulation analysis• Value drivers• Variable costs