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4-1Chapter 14Chapter 14Risk and ManagerialRisk and ManagerialOptions in CapitalOptions in CapitalBudgetingBudgeting© 2001 ...
4-2Risk and ManagerialRisk and ManagerialOptions in Capital BudgetingOptions in Capital BudgetingThe Problem of Project Ri...
4-3An Illustration of TotalAn Illustration of TotalRisk (Discrete Distribution)Risk (Discrete Distribution)ANNUAL CASH FLO...
4-4Probability DistributionProbability Distributionof Year 1 Cash Flowsof Year 1 Cash Flows.40.05.25Probability-3,000 1,00...
4-5CFCF11 PP11 (CFCF11)()(PP11))$ -3,000 .05 $ -1501,000 .25 2505,000 .40 2,0009,000 .25 2,25013,000 .05 650ΣΣ=1.001.00 CF...
4-6(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -150 ( -3,000 - 5,000)22((.05.05))250 ( 1,000 - 5,000)22((.25.25))2,0...
4-7Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal AProposal A))(CFCF11)()(PP11)) ((CFCF11 -- CFCF11)...
4-8Summary ofSummary of Proposal AProposal AThe standard deviationstandard deviation =SQRT (14,400,000) = $3,795$3,795The ...
4-9An Illustration of TotalAn Illustration of TotalRisk (Discrete Distribution)Risk (Discrete Distribution)ANNUAL CASH FLO...
4-10Probability DistributionProbability Distributionof Year 1 Cash Flowsof Year 1 Cash Flows.40.05.25Probability-3,000 1,0...
4-11Expected Value of Year 1Expected Value of Year 1Cash Flows (Cash Flows (Proposal BProposal B))CFCF11 PP11 (CFCF11)()(P...
4-12(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -50 ( -1,000 - 5,000)22((.05.05))500 ( 2,000 - 5,000)22((.25.25))2,0...
4-13Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal BProposal B))(CFCF11)()(PP11)) ((CFCF11 -- CFCF11...
4-14Summary ofSummary of Proposal BProposal BThe standard deviation ofProposal BProposal B << Proposal AProposal A..(( $2,...
4-15Total Project RiskTotal Project RiskProjects have riskthat may changefrom period toperiod.Projects are morelikely to h...
4-16Probability Tree ApproachProbability Tree ApproachA graphic or tabular approach fororganizing the possible cash-flowst...
4-17Probability Tree ApproachProbability Tree ApproachBasket Wonders isexamining a project that willhave an initial costin...
4-18Probability Tree ApproachProbability Tree ApproachNode 1: 20% chance of a$1,200$1,200 cash-flow.Node 2: 60% chance of ...
4-19Probability Tree ApproachProbability Tree ApproachEach node inYear 2Year 2represents abranchbranch of ourprobabilitytr...
4-20Joint Probabilities [P(1,2)]Joint Probabilities [P(1,2)].02 Branch 1.12 Branch 2.06 Branch 3.21 Branch 4.24 Branch 5.1...
4-21Project NPV Based onProject NPV Based onProbability Tree UsageProbability Tree UsageThe probabilitytree accounts forth...
4-22NPV for Each Cash-FlowNPV for Each Cash-FlowStream at 5% Risk-Free RateStream at 5% Risk-Free Rate$ 2,238.32$ 1,331.29...
4-23NPV on the CalculatorNPV on the CalculatorRemember, we canuse the cash flowregistry to solvethese NPV problemsquickly ...
4-24Actual NPV Solution UsingActual NPV Solution UsingYour Financial CalculatorYour Financial CalculatorSolving for Branch...
4-25Actual NPV Solution UsingActual NPV Solution UsingYour Financial CalculatorYour Financial CalculatorSolving for Branch...
4-26Calculating the ExpectedCalculating the ExpectedNet Present Value (Net Present Value (NPVNPV))Branch NPVNPViiBranch 1 ...
4-27Calculating the VarianceCalculating the Varianceof the Net Present Valueof the Net Present ValueNPVNPVii$ 2,238.32$ 1,...
4-28Summary of theSummary of theDecision Tree AnalysisDecision Tree AnalysisThe standard deviationstandard deviation =SQRT...
4-29Simulation ApproachSimulation ApproachAn approach that allows us to testthe possible results of aninvestment proposal ...
4-30Simulation ApproachSimulation ApproachMarket analysisMarket analysisMarket size, selling price, marketgrowth rate,and ...
4-31Simulation ApproachSimulation ApproachEach variable is assigned an appropriateprobability distribution. The distributi...
4-32Simulation ApproachSimulation ApproachEach proposal will generate an internal rate ofinternal rate ofreturnreturn. The...
4-33Combining projects in this manner reducesthe firm risk due to diversificationdiversification.Contribution to Total Fir...
4-34NPVP = Σ ( NPVj )NPVP is the expected portfolio NPV,NPVj is the expected NPV of the jthNPV that the firm undertakes,m ...
4-35σσPP = Σ Σ σjkσjk is the covariance between possibleNPVs for projects j and k,σσ jk = σ j σ k rr jk .σj is the standar...
4-36E: Existing ProjectsE: Existing Projects8 CombinationsEE EE + 1 EE + 1 + 2EE + 2 EE + 1 + 3EE + 3 EE + 2 + 3EE + 1 + 2...
4-37Managerial (Real) OptionsManagerial (Real) OptionsManagement flexibility to makefuture decisions that affect aproject’...
4-38Managerial (Real) OptionsManagerial (Real) OptionsExpand (or contract)Expand (or contract)Allows the firm to expand (c...
4-39Previous Example withPrevious Example withProject AbandonmentProject AbandonmentAssume thatthis projectcan beabandoned...
4-40Project AbandonmentProject AbandonmentNode 3Node 3:(500500/1.05)(.1)+(-100-100/1.05)(.5)+(-700-700/1.05)(.4)=($476.19)...
4-41Project AbandonmentProject Abandonment-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 111...
4-42Project AbandonmentProject Abandonment$ 2,238.32$ 1,331.29$ 1,059.18$ 344.90$ 72.79-$ 199.32-$ 1,280.95-$900-$900(.20....
4-43Summary of the AdditionSummary of the Additionof the Abandonment Optionof the Abandonment Option* For “True” Project c...
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Ch 14 - Risk and Managerial Options in Capital Budgeting

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Financial Management by Van Horne
Ch 14 - Risk and Managerial Options in Capital Budgeting

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  1. 1. 4-1Chapter 14Chapter 14Risk and ManagerialRisk and ManagerialOptions in CapitalOptions in CapitalBudgetingBudgeting© 2001 Prentice-Hall, Inc.Fundamentals of Financial Management, 11/eCreated by: Gregory A. Kuhlemeyer, Ph.D.Carroll College, Waukesha, WI
  2. 2. 4-2Risk and ManagerialRisk and ManagerialOptions in Capital BudgetingOptions in Capital BudgetingThe Problem of Project RiskTotal Project RiskContribution to Total Firm Risk:Firm-Portfolio ApproachManagerial Options
  3. 3. 4-3An Illustration of TotalAn Illustration of TotalRisk (Discrete Distribution)Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL APROPOSAL AState ProbabilityProbability Cash FlowCash FlowDeep Recession .05 $ -3,000Mild Recession .25 1,000Normal .40 5,000Minor Boom .25 9,000Major Boom .05 13,000ANNUAL CASH FLOWS: YEAR 1PROPOSAL APROPOSAL AState ProbabilityProbability Cash FlowCash FlowDeep Recession .05 $ -3,000Mild Recession .25 1,000Normal .40 5,000Minor Boom .25 9,000Major Boom .05 13,000
  4. 4. 4-4Probability DistributionProbability Distributionof Year 1 Cash Flowsof Year 1 Cash Flows.40.05.25Probability-3,000 1,000 5,000 9,000 13,000Cash Flow ($)Proposal AProposal A
  5. 5. 4-5CFCF11 PP11 (CFCF11)()(PP11))$ -3,000 .05 $ -1501,000 .25 2505,000 .40 2,0009,000 .25 2,25013,000 .05 650ΣΣ=1.001.00 CFCF11=$5,000$5,000CFCF11 PP11 (CFCF11)()(PP11))$ -3,000 .05 $ -1501,000 .25 2505,000 .40 2,0009,000 .25 2,25013,000 .05 650ΣΣ=1.001.00 CFCF11=$5,000$5,000Expected Value of Year 1Expected Value of Year 1Cash Flows (Cash Flows (Proposal AProposal A))
  6. 6. 4-6(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -150 ( -3,000 - 5,000)22((.05.05))250 ( 1,000 - 5,000)22((.25.25))2,000 ( 5,000 - 5,000)22((.40.40))2,250 ( 9,000 - 5,000)22((.25.25))650 (13,000 - 5,000)22((.05.05))$5,000$5,000(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -150 ( -3,000 - 5,000)22((.05.05))250 ( 1,000 - 5,000)22((.25.25))2,000 ( 5,000 - 5,000)22((.40.40))2,250 ( 9,000 - 5,000)22((.25.25))650 (13,000 - 5,000)22((.05.05))$5,000$5,000Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal AProposal A))
  7. 7. 4-7Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal AProposal A))(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22*(*(PP11))$ -150 3,200,000250 4,000,0002,000 02,250 4,000,000650 3,200,000$5,000$5,000 14,400,00014,400,000(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22*(*(PP11))$ -150 3,200,000250 4,000,0002,000 02,250 4,000,000650 3,200,000$5,000$5,000 14,400,00014,400,000
  8. 8. 4-8Summary ofSummary of Proposal AProposal AThe standard deviationstandard deviation =SQRT (14,400,000) = $3,795$3,795The expected cash flowexpected cash flow = $5,000$5,000
  9. 9. 4-9An Illustration of TotalAn Illustration of TotalRisk (Discrete Distribution)Risk (Discrete Distribution)ANNUAL CASH FLOWS: YEAR 1PROPOSAL BPROPOSAL BState ProbabilityProbability Cash FlowCash FlowDeep Recession .05 $ -1,000Mild Recession .25 2,000Normal .40 5,000Minor Boom .25 8,000Major Boom .05 11,000ANNUAL CASH FLOWS: YEAR 1PROPOSAL BPROPOSAL BState ProbabilityProbability Cash FlowCash FlowDeep Recession .05 $ -1,000Mild Recession .25 2,000Normal .40 5,000Minor Boom .25 8,000Major Boom .05 11,000
  10. 10. 4-10Probability DistributionProbability Distributionof Year 1 Cash Flowsof Year 1 Cash Flows.40.05.25Probability-3,000 1,000 5,000 9,000 13,000Cash Flow ($)Proposal BProposal B
  11. 11. 4-11Expected Value of Year 1Expected Value of Year 1Cash Flows (Cash Flows (Proposal BProposal B))CFCF11 PP11 (CFCF11)()(PP11))$ -1,000 .05 $ -502,000 .25 5005,000 .40 2,0008,000 .25 2,00011,000 .05 550ΣΣ=1.001.00 CFCF11=$5,000$5,000CFCF11 PP11 (CFCF11)()(PP11))$ -1,000 .05 $ -502,000 .25 5005,000 .40 2,0008,000 .25 2,00011,000 .05 550ΣΣ=1.001.00 CFCF11=$5,000$5,000
  12. 12. 4-12(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -50 ( -1,000 - 5,000)22((.05.05))500 ( 2,000 - 5,000)22((.25.25))2,000 ( 5,000 - 5,000)22((.40.40))2,000 ( 8,000 - 5,000)22((.25.25))550 (11,000 - 5,000)22((.05.05))$5,000$5,000(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -50 ( -1,000 - 5,000)22((.05.05))500 ( 2,000 - 5,000)22((.25.25))2,000 ( 5,000 - 5,000)22((.40.40))2,000 ( 8,000 - 5,000)22((.25.25))550 (11,000 - 5,000)22((.05.05))$5,000$5,000Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal BProposal B))
  13. 13. 4-13Variance of Year 1Variance of Year 1Cash Flows (Cash Flows (Proposal BProposal B))(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -50 1,800,000500 2,250,0002,000 02,000 2,250,000550 1,800,000$5,000$5,000 8,100,0008,100,000(CFCF11)()(PP11)) ((CFCF11 -- CFCF11))22((PP11))$ -50 1,800,000500 2,250,0002,000 02,000 2,250,000550 1,800,000$5,000$5,000 8,100,0008,100,000
  14. 14. 4-14Summary ofSummary of Proposal BProposal BThe standard deviation ofProposal BProposal B << Proposal AProposal A..(( $2,846$2,846 << $3,795$3,795 ))The standard deviationstandard deviation =SQRT (8,100,000) = $2,846$2,846The expected cash flowexpected cash flow = $5,000$5,000
  15. 15. 4-15Total Project RiskTotal Project RiskProjects have riskthat may changefrom period toperiod.Projects are morelikely to havecontinuous, ratherthan discretedistributions.CashFlow($)11 22 33Year
  16. 16. 4-16Probability Tree ApproachProbability Tree ApproachA graphic or tabular approach fororganizing the possible cash-flowstreams generated by aninvestment. The presentationresembles the branches of a tree.Each complete branch representsone possible cash-flow sequence.
  17. 17. 4-17Probability Tree ApproachProbability Tree ApproachBasket Wonders isexamining a project that willhave an initial costinitial cost today of$900$900. Uncertaintysurrounding the first yearcash flows creates threepossible cash-flowscenarios in Year 1Year 1.-$900-$900
  18. 18. 4-18Probability Tree ApproachProbability Tree ApproachNode 1: 20% chance of a$1,200$1,200 cash-flow.Node 2: 60% chance of a$450$450 cash-flow.Node 3: 20% chance of a-$600-$600 cash-flow.-$900-$900(.20) $1,200$1,200(.20) -$600-$600(.60) $450$450Year 1Year 1112233
  19. 19. 4-19Probability Tree ApproachProbability Tree ApproachEach node inYear 2Year 2represents abranchbranch of ourprobabilitytree.Theprobabilitiesare said to beconditionalconditionalprobabilitiesprobabilities.-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) -$ 700-$ 700Year 2Year 2
  20. 20. 4-20Joint Probabilities [P(1,2)]Joint Probabilities [P(1,2)].02 Branch 1.12 Branch 2.06 Branch 3.21 Branch 4.24 Branch 5.15 Branch 6.02 Branch 7.10 Branch 8.08 Branch 9-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) -$ 700-$ 700Year 2Year 2
  21. 21. 4-21Project NPV Based onProject NPV Based onProbability Tree UsageProbability Tree UsageThe probabilitytree accounts forthe distributionof cash flows.Therefore,discount all cashflows at only therisk-freerisk-free rate ofreturn.The NPV for branch iNPV for branch i ofthe probability tree for twoyears of cash flows isNPV = Σ (NPVNPVii)(PPii)NPVNPVii =CFCF11(1 + RRff )11(1 + RRff )22CFCF22- ICOICO+i = 1z
  22. 22. 4-22NPV for Each Cash-FlowNPV for Each Cash-FlowStream at 5% Risk-Free RateStream at 5% Risk-Free Rate$ 2,238.32$ 1,331.29$ 1,059.18$ 344.90$ 72.79-$ 199.32-$ 1,017.91-$ 1,562.13-$ 2,106.35-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) -$ 700-$ 700Year 2Year 2
  23. 23. 4-23NPV on the CalculatorNPV on the CalculatorRemember, we canuse the cash flowregistry to solvethese NPV problemsquickly andaccurately!
  24. 24. 4-24Actual NPV Solution UsingActual NPV Solution UsingYour Financial CalculatorYour Financial CalculatorSolving for Branch #3:Step 1: Press CF keyStep 2: Press 2ndCLR Work keysStep 3: For CF0 Press -900 Enter ↓ keysStep 4: For C01 Press 1200 Enter ↓ keysStep 5: For F01 Press 1 Enter ↓ keysStep 6: For C02 Press 900 Enter ↓ keysStep 7: For F02 Press 1 Enter ↓ keys
  25. 25. 4-25Actual NPV Solution UsingActual NPV Solution UsingYour Financial CalculatorYour Financial CalculatorSolving for Branch #3:Step 8: Press ↓ ↓ keysStep 9: Press NPV keyStep 10: For I=, Enter 5 Enter ↓ keysStep 11: Press CPT keyResult: Net Present Value = $1,059.18You would complete this for EACH branch!
  26. 26. 4-26Calculating the ExpectedCalculating the ExpectedNet Present Value (Net Present Value (NPVNPV))Branch NPVNPViiBranch 1 $ 2,238.32Branch 2 $ 1,331.29Branch 3 $ 1,059.18Branch 4 $ 344.90Branch 5 $ 72.79Branch 6 -$ 199.32Branch 7 -$ 1,017.91Branch 8 -$ 1,562.13Branch 9 -$ 2,106.35P(1,2)P(1,2) NPVNPVii * P(1,2)P(1,2).02 $ 44.77.12 $159.75.06 $ 63.55.21 $ 72.43.24 $ 17.47.15 -$ 29.90.02 -$ 20.36.10 -$156.21.08 -$168.51Expected Net Present ValueExpected Net Present Value = -$ 17.01-$ 17.01
  27. 27. 4-27Calculating the VarianceCalculating the Varianceof the Net Present Valueof the Net Present ValueNPVNPVii$ 2,238.32$ 1,331.29$ 1,059.18$ 344.90$ 72.79-$ 199.32-$ 1,017.91-$ 1,562.13-$ 2,106.35P(1,2)P(1,2) ((NPVNPVii - NPVNPV )2[P(1,2)P(1,2)].02 $ 101,730.27.12 $ 218,149.55.06 $ 69,491.09.21 $ 27,505.56.24 $ 1,935.37.15 $ 4,985.54.02 $ 20,036.02.10 $ 238,739.58.08 $ 349,227.33VarianceVariance = $1,031,800.31$1,031,800.31
  28. 28. 4-28Summary of theSummary of theDecision Tree AnalysisDecision Tree AnalysisThe standard deviationstandard deviation =SQRT ($1,031,800) = $1,015.78$1,015.78The expected NPVexpected NPV = -$ 17.01-$ 17.01
  29. 29. 4-29Simulation ApproachSimulation ApproachAn approach that allows us to testthe possible results of aninvestment proposal before it isaccepted. Testing is based on amodel coupled with probabilisticinformation.
  30. 30. 4-30Simulation ApproachSimulation ApproachMarket analysisMarket analysisMarket size, selling price, marketgrowth rate,and market shareInvestment cost analysisInvestment cost analysisInvestment required, useful life offacilities, and residual valueOperating and fixed costsOperating and fixed costsOperating costs and fixed costsFactors we might consider in a model:
  31. 31. 4-31Simulation ApproachSimulation ApproachEach variable is assigned an appropriateprobability distribution. The distribution forthe selling price of baskets created byBasket Wonders might look like:$20 $25 $30 $35 $40 $45 $50.02 .08 .22 .36 .22 .08 .02The resulting proposal value is dependenton the distribution and interaction ofEVERY variable listed on slide 14-30.
  32. 32. 4-32Simulation ApproachSimulation ApproachEach proposal will generate an internal rate ofinternal rate ofreturnreturn. The process of generating many, manysimulations results in a large set of internalrates of return. The distributiondistribution might look likethe following:INTERNAL RATE OF RETURN (%)PROBABILITYOFOCCURRENCE
  33. 33. 4-33Combining projects in this manner reducesthe firm risk due to diversificationdiversification.Contribution to Total Firm Risk:Contribution to Total Firm Risk:Firm-Portfolio ApproachFirm-Portfolio ApproachCASHFLOWTIME TIMETIMEProposal AProposal A Proposal BProposal BCombination ofCombination ofProposalsProposals AA andand BB
  34. 34. 4-34NPVP = Σ ( NPVj )NPVP is the expected portfolio NPV,NPVj is the expected NPV of the jthNPV that the firm undertakes,m is the total number of projects inthe firm portfolio.Determining the ExpectedDetermining the ExpectedNPV for a Portfolio of ProjectsNPV for a Portfolio of Projectsmj=1
  35. 35. 4-35σσPP = Σ Σ σjkσjk is the covariance between possibleNPVs for projects j and k,σσ jk = σ j σ k rr jk .σj is the standard deviation of project j,σkis the standard deviation of project k,rjk is the correlation coefficient betweenDetermining PortfolioDetermining PortfolioStandard DeviationStandard Deviationmj=1mk=1
  36. 36. 4-36E: Existing ProjectsE: Existing Projects8 CombinationsEE EE + 1 EE + 1 + 2EE + 2 EE + 1 + 3EE + 3 EE + 2 + 3EE + 1 + 2 + 3AA, BB, and CC aredominatingdominating combinationsfrom the eight possible.Combinations ofCombinations ofRisky InvestmentsRisky InvestmentsABCEStandard DeviationExpectedValueofNPV
  37. 37. 4-37Managerial (Real) OptionsManagerial (Real) OptionsManagement flexibility to makefuture decisions that affect aproject’s expected cash flows, life,or future acceptance.Project Worth = NPV +Option(s) Value
  38. 38. 4-38Managerial (Real) OptionsManagerial (Real) OptionsExpand (or contract)Expand (or contract)Allows the firm to expand (contract) productionif conditions become favorable (unfavorable).AbandonAbandonAllows the project to be terminated early.PostponePostponeAllows the firm to delay undertaking a project(reduces uncertainty via new information).
  39. 39. 4-39Previous Example withPrevious Example withProject AbandonmentProject AbandonmentAssume thatthis projectcan beabandoned atthe end of thefirst year for$200$200.What is theprojectprojectworthworth?-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) -$ 700-$ 700Year 2Year 2
  40. 40. 4-40Project AbandonmentProject AbandonmentNode 3Node 3:(500500/1.05)(.1)+(-100-100/1.05)(.5)+(-700-700/1.05)(.4)=($476.19)(.1)+-($ 95.24)(.5)+-($666.67)(.4)=-($266.67)-($266.67)-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) --$ 700$ 700Year 2Year 2
  41. 41. 4-41Project AbandonmentProject Abandonment-$900-$900(.20.20) $1,200$1,200(.20.20) -$600-$600(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(.10) $ 500$ 500(.50) -$ 100-$ 100(.40) -$ 700-$ 700Year 2Year 2The optimaldecision at theend of Year 1Year 1is to abandonthe project for$200$200.$200$200 >-($266.67)-($266.67)What is the“new”“new” projectvalue?
  42. 42. 4-42Project AbandonmentProject Abandonment$ 2,238.32$ 1,331.29$ 1,059.18$ 344.90$ 72.79-$ 199.32-$ 1,280.95-$900-$900(.20.20) $1,200$1,200(.20.20) -$400*-$400*(.6060) $450$450Year 1Year 1112233(.60) $1,200$1,200(.30) $ 900$ 900(.10) $2,200$2,200(.35) $ 900$ 900(.40) $ 600$ 600(.25) $ 300$ 300(1.0) $ 0$ 0Year 2Year 2*-$600 + $200 abandonment
  43. 43. 4-43Summary of the AdditionSummary of the Additionof the Abandonment Optionof the Abandonment Option* For “True” Project considering abandonment optionThe standard deviation*standard deviation* =SQRT (740,326) = $857.56$857.56The expectedexpected NPV*NPV* = $$ 71.8871.88NPV*NPV* = Original NPV +Abandonment OptionAbandonment OptionThus,Thus, $71.88$71.88 = -$17.01 + OptionOptionAbandonment OptionAbandonment Option = $ 88.89$ 88.89
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