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Chapter 7 Risk and Real Options in Capital Budgeting ®2002 Prentice Hall Publishing 1 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 ®2002 Prentice Hall Publishing 2 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 ®2002 Prentice Hall Publishing 3 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 ®2002 Prentice Hall Publishing 4 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 ®2002 Prentice Hall Publishing 5 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 ®2002 Prentice Hall Publishing 6 Total Risk for Multiple Investments • Total risk – The sum of systematic and unsystematic risk • Standard deviation (SD) • Correlation between projects • Feasible combinations and dominance ®2002 Prentice Hall Publishing 7 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 ®2002 Prentice Hall Publishing 8 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 ®2002 Prentice Hall Publishing 9 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 ®2002 Prentice Hall Publishing 10 Real Options in Capital Investments • Valuation in general • Types of option – Option to vary output – Option to abandon – Option to postpone ®2002 Prentice Hall Publishing 11 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 ®2002 Prentice Hall Publishing 12 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 ®2002 Prentice Hall Publishing 13 The Option to Abandon • Provides a safety net • Consists of – Selling the asset or – Employing the asset in another area ®2002 Prentice Hall Publishing 14 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 ®2002 Prentice Hall Publishing 15 • 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 ®2002 Prentice Hall Publishing 16 The Option to Postpone or Time • Obtain new information – Market – Prices – Cost • Give up – Interim CFs – First mover advantage • Commodity situation • Noncommodity situation ®2002 Prentice Hall Publishing 17 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 18