2. ®2002 Prentice Hall Publishing 1 Chapter 7 Risk and Real Options in Capital Budgeting

3. ®2002 Prentice Hall Publishing 2 Quantifying Risk and its Appraisal Risk is the variability of possible outcomesRisk is the variability of possible outcomes Assumption of independenceAssumption of independence –No causative relationship between cash flows from period to period –Risk-free rate for discounting Isolate the time value of moneyIsolate the time value of money –Standard deviation of the probability distribution of NPVs

4. ®2002 Prentice Hall Publishing 3 Standardizing the Dispersion Assess the probability of adversityAssess the probability of adversity Determining probabilities of adverse eventsDetermining 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 assessmentFundamental for a realistic assessment

5. ®2002 Prentice Hall Publishing 4 Information Generated Probability distribution of IRRProbability distribution of IRR –Compute the mean and standard deviation Nonnormal distributionNonnormal distribution Biases in obtaining informationBiases in obtaining information –Adjustment for biases ProblemsProblems –Over-adjustment –Accountability –Results depends on behavioral considerations

6. ®2002 Prentice Hall Publishing 5 Dependence of Cash Flows (CFs) over Time Consequence of CFs being correlated over timeConsequence of CFs being correlated over time –Perfect correlation CFs deviate in exactly the same relative mannerCFs deviate in exactly the same relative manner Linear functionLinear function –Moderate correlation Use a series of conditional probability distributionsUse a series of conditional probability distributions Take account of the correlation of CFs over timeTake account of the correlation of CFs over time

7. ®2002 Prentice Hall Publishing 6 Simulation To approximate the standard deviation use random samplingTo approximate the standard deviation use random sampling If CFs are highly correlated over timeIf 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 importantDegree of dependence of CFs is important

8. ®2002 Prentice Hall Publishing 7 Total Risk for Multiple Investments Total riskTotal risk –The sum of systematic and unsystematic risk Standard deviation (SD)Standard deviation (SD) Correlation between projectsCorrelation between projects Feasible combinations and dominanceFeasible combinations and dominance

9. ®2002 Prentice Hall Publishing 8 Standard Deviation Depends onDepends on –Degree of correlation between various projects Higher the degree of positive correlation the greater the SD of the portfolioHigher 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 portfolioGreater the SD of individual projects the greater the SD of the portfolio

10. ®2002 Prentice Hall Publishing 9 Correlation Between Projects Range of correlationRange of correlation –Between 0 and 1.00 –Lack of negatively correlated projects Unrelated lines of business tend to have low degrees of correlationUnrelated lines of business tend to have low degrees of correlation

11. ®2002 Prentice Hall Publishing 10 Feasible Combination and Dominance Evaluating feasible combinationsEvaluating feasible combinations –Determine which combinations dominate in NPV and/or SD –Determines the efficient frontier Relation to existing portfolioRelation to existing portfolio –Investment proposals can be eliminated because they are dominated

12. ®2002 Prentice Hall Publishing 11 Real Options in Capital Investments Valuation in generalValuation in general Types of optionTypes of option –Option to vary output –Option to abandon –Option to postpone

13. ®2002 Prentice Hall Publishing 12 Valuation in General Real optionsReal options –Enhance the worth of a project –Difficult to value Decision treesDecision trees SimulationsSimulations Ad hoc approachesAd hoc approaches Project worth = NPV + option valueProject worth = NPV + option value As the number of options increasesAs the number of options increases –Uncertainty increases –Option value increases –Project’s worth increases

14. ®2002 Prentice Hall Publishing 13 The Option to Expand Using a decision treeUsing a decision tree –Expected NPVs for the various branches –Sequence of decisions and chance events –Optimal set of decisions Rolling back the treeRolling back the tree Backward inductionBackward induction –Comparing NPVs Optimal decision at the first decision pointOptimal decision at the first decision point

15. ®2002 Prentice Hall Publishing 14 The Option to Abandon Provides a safety netProvides a safety net Consists ofConsists of –Selling the asset or or –Employing the asset in another area

16. ®2002 Prentice Hall Publishing 15 Economic Rationale for Abandonment Same as capital budgetingSame as capital budgeting Project worth =Project worth = NPV without abandonment NPV without abandonment + Value of abandonment option Value of abandonment option Abandon a projectAbandon a project –If the PV of possible future benefits > current abandonment value –Appears better now than in the future

17. ®2002 Prentice Hall Publishing 16 Abandonment Option Makes Situation BetterAbandonment Option Makes Situation Better –A significant improvement occurs A portion of the downside is eliminated when events turn unfavorableA portion of the downside is eliminated when events turn unfavorable –Abandonment is more valuable The greater the volatility of CFsThe greater the volatility of CFs –Abandonment mitigates the effects of bad outcomes Ongoing Abandonment EvaluationsOngoing Abandonment Evaluations –Optimal time to abandon –Continual assessment of projects

18. ®2002 Prentice Hall Publishing 17 The Option to Postpone or Time Obtain new informationObtain new information –Market –Prices –Cost Give upGive up –Interim CFs –First mover advantage Commodity situationCommodity situation Noncommodity situationNoncommodity situation

19. ®2002 Prentice Hall Publishing 18 Final Observations on Real Options Real options are different from financial optionsReal 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 flexibilityRecognition of management flexibility More uncertainty is a positive with real optionsMore uncertainty is a positive with real options