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Chapter 7
Risk and Real Options in
Capital Budgeting
®2002 Prentice Hall Publishing
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Quantifying Risk and its
Appraisal
• Risk is the variability of possible outcomes
• Assumption of independence
– No causative relationship between cash
flows from period to period
– Risk-free rate for discounting
• Isolate the time value of money
– Standard deviation of the probability
distribution of NPVs
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Standardizing the Dispersion
• Assess the probability of adversity
• Determining probabilities of adverse events
– Consult the normal probability
distribution table
– Express differences from the mean in
terms of standard deviations to determine
the probability
• Fundamental for a realistic assessment
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Information Generated
• Probability distribution of IRR
– Compute the mean and standard deviation
• Nonnormal distribution
• Biases in obtaining information
– Adjustment for biases
• Problems
– Over-adjustment
– Accountability
– Results depends on behavioral considerations
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Dependence of Cash Flows
(CFs) over Time
• Consequence of CFs being correlated over time
– Perfect correlation
• CFs deviate in exactly the same relative manner
• Linear function
– Moderate correlation
• Use a series of conditional probability
distributions
• Take account of the correlation of CFs over
time
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Simulation
• To approximate the standard deviation use
random sampling
• If CFs are highly correlated over time
– The risk of a project will be greater than
if they are mutually independent
• Degree of dependence of CFs is important
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Total Risk for Multiple
Investments
• Total risk
– The sum of systematic and unsystematic risk
• Standard deviation (SD)
• Correlation between projects
• Feasible combinations and dominance
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Standard Deviation
• Depends on
– Degree of correlation between various
projects
• Higher the degree of positive correlation
the greater the SD of the portfolio
– SD of possible NPVs of each project
• Greater the SD of individual projects the
greater the SD of the portfolio
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Correlation Between Projects
• Range of correlation
– Between 0 and 1.00
– Lack of negatively correlated projects
• Unrelated lines of business tend to have low
degrees of correlation
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Feasible Combination and
Dominance
• Evaluating feasible combinations
– Determine which combinations dominate
in NPV and/or SD
– Determines the efficient frontier
• Relation to existing portfolio
– Investment proposals can be eliminated
because they are dominated
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Real Options in Capital
Investments
• Valuation in general
• Types of option
– Option to vary output
– Option to abandon
– Option to postpone
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Valuation in General
• Real options
– Enhance the worth of a project
– Difficult to value
• Decision trees
• Simulations
• Ad hoc approaches
• Project worth = NPV + option value
• As the number of options increases
– Uncertainty increases
– Option value increases
– Project’s worth increases
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The Option to Expand
• Using a decision tree
– Expected NPVs for the various branches
– Sequence of decisions and chance events
– Optimal set of decisions
• Rolling back the tree
• Backward induction
– Comparing NPVs
• Optimal decision at the first decision point
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The Option to Abandon
• Provides a safety net
• Consists of
– Selling the asset
or
– Employing the asset in another area
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Economic Rationale for
Abandonment
• Same as capital budgeting
• Project worth =
NPV without abandonment
+
Value of abandonment option
• Abandon a project
– If the PV of possible future benefits >
current abandonment value
– Appears better now than in the future
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• Abandonment Option Makes Situation
Better
– A significant improvement occurs
• A portion of the downside is eliminated
when events turn unfavorable
– Abandonment is more valuable
• The greater the volatility of CFs
– Abandonment mitigates the effects of bad
outcomes
• Ongoing Abandonment Evaluations
– Optimal time to abandon
– Continual assessment of projects
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The Option to Postpone or Time
• Obtain new information
– Market
– Prices
– Cost
• Give up
– Interim CFs
– First mover advantage
• Commodity situation
• Noncommodity situation
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Final Observations on Real
Options
• Real options are different from financial options
– Cannot use risk neutrality
– Exercise price can change over time
– Volatility is difficult to measure
– Imprecise opportunity cost
– More difficult to value
• Recognition of management flexibility
• More uncertainty is a positive with real options
®2002 Prentice Hall Publishing
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