Chapter 13
Risk Analysis and
Project Evaluation
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Slide Contents
• Learning Objectives
• Principles Used in This Chapter
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
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13-2
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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13-3
Principles Used in This Chapter
• Principle #2: There Is a Risk-Return
Tradeoff
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13-4
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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13-6
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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13-8
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
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= .25 ( 100) + .75 (400)
= $325
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Checkpoint 13.1
Forecasting Revenues Using Expected Values
Marshall 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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13-13
Checkpoint 13.1
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13-14
Checkpoint 13.1
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13-15
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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13-16
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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13-17
Step 1: Picture the Problem (cont.)
Deep Recession
Probability
Mild Recession
Turn-Around
40%
50%
10%
$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
High Priced Home:
Total Revenues
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13-18
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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13-19
Step 3: Solve
Deep
Recession
Mild
Recession
40%
50%
Step 1
Probability
Step 2
Total Revenues
for each
Scenario
$40,000,000
Step 3
Probability ×
Total Revenue
$16,000,000
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Turn-around
10%
$140,000,000 $320,000,000
$70,000,000
$32,000,000
13-20
Step 3: Solve (cont.)
• Thus the expected total revenues declines
from $156,000,000 to $118,0000.
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13-21
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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13-23
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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13-24
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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13-25
Checkpoint 13.2
Project Risk Analysis: Sensitivity Analysis
Crainium, 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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13-26
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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13-27
Checkpoint 13.2
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13-28
Checkpoint 13.2
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13-29
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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13-30
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
Revenues
Years 1-4
Year-5
5,000,000
5,000,000
$(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)
$700,000.00
$700,000.00
$(210,000.00)
$(210,000.00)
Net operating profit after tax
$490,000.00
$490,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Net Operating Income
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(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
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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
Revenues
Year-5
4,500,000
4,500,000
$(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)
$560,000.00
$560,000.00
$(168,000.00)
$(168,000.00)
Net operating profit after tax
$392,000.00
$392,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Net Operating Income
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$692,000.00
NPV
$648,446.62
IRR
21.59%
$1,492,000.00
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Step 3: Solve (cont.)
• What if variable costs increase by 10%?
Year-0
Years 1-4
Revenues
Year-5
5,000,000
5,000,000
$(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)
$340,000.00
$340,000.00
$(102,000.00)
$(102,000.00)
Net operating profit after tax
$238,000.00
$238,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Net Operating Income
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$538,000.00
NPV
$220,414.70
IRR
15.19%
$1,338,000.00
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Step 3: Solve (cont.)
• What if price per unit drops by 10%
Year-0
Years 1-4
Revenues
Year-5
4,500,000
4,500,000
$(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
$300,000.00
Less: Variable Cost
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$440,000.00
NPV
($259,956.99)
IRR
8.02%
$1,240,000.00
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Step 3: Solve (cont.)
• What if fixed costs increase by 10%?
Year-0
Years 1-4
Revenues
Year-5
5,000,000
5,000,000
$(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)
$660,000.00
$660,000.00
$(198,000.00)
$(198,000.00)
Net operating profit after tax
$462,000.00
$462,000.00
Plus: Depreciation Expense
$300,000.00
$300,000.00
Less: Variable Cost
Net Operating Income
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,800,000.00)
$300,000.00
$(500,000.00)
$500,000.00
$(2,300,000.00)
$762,000.00
NPV
$900,780.95
IRR
25.22%
$1,562,000.00
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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
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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Revised NPV
% Change
13-40
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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13-41
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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13-42
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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13-43
Checkpoint 13.3
Project Risk Analysis: Scenario Analysis
The 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 worstand best-case scenarios for the project’s value drivers.
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13-44
Checkpoint 13.3
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13-45
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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13-47
Step 1: Picture the Problem
• We are given the following revised
estimates for two scenarios:
Scenario 1
Unit Sales
Price per unit
Scenario 2
$175,000.00
$100,000.00
$24.50
$35
• Rest of the information is the same as
Checkpoint 13.2
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13-48
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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13-49
Step 3: Solve
• Scenario 1 cash flow and NPV/IRR estimates
Year-0
Years 1-4
Revenues
Year-5
$4,287,500.00
$4,287,500.00
$(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)
$96,250.00
$96,250.00
$250,000.00
$250,000.00
Less: Variable Cost
Net operating profit after tax
Plus: Depreciation Expense
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,500,000.00)
$250,000.00
$(500,000.00)
$500,000.00
$(2,000,000.00)
$346,250.00
NPV
$326,276.10
IRR
6.29%
$1,096,250.00
13-50
Step 3: Solve (cont.)
• Scenario 2 cash flow and NPV/IRR estimates
Year-0
Years 1-4
Revenues
Year-5
$3,500,000.00
$3,500,000.00
$(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)
$850,000.00
$850,000.00
$(255,000.00)
$(255,000.00)
Net operating profit after tax
$595,000.00
$595,000.00
Plus: Depreciation Expense
$250,000.00
$250,000.00
Less: Variable Cost
Net Operating Income
Les: Taxes
Less: CAPEX
Less: Change in Working Capital
Free Cash Flow
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$(1,500,000.00)
$250,000.00
$(500,000.00)
$500,000.00
$(2,000,000.00)
$845,000.00
NPV
$1,471,606.03
IRR
36.10%
$1,595,000.00
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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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13-52
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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13-53
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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13-54
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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13-55
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13-56
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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13-58
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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13-59
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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13-60
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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13-61
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13-62
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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13-63
Checkpoint 13.4
Project Risk Analysis: Accounting Break-Even Analysis
The 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 annual
revenues and expenses. What is the break-even level of units?
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13-64
Checkpoint 13.4
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13-65
Checkpoint 13.4
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13-66
Checkpoint 13.4
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13-67
Checkpoint 13.4
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13-68
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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13-69
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 unit
V = 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 Expand
You 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
Build 1 smoothThru at a cost of
$2.4 million
P(Unfavorable)
=.6
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Build 10 more
restaurants
NPV =10 x
$800,000
Don’t build any
more restaurants
NPV = -$1,600,000
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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
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