Refer to the XYZ Company example in the chapter and the results in Panels A and B of Exhibit 12.7. On the basis of this information, management of the company has decided to delay the implementation of the project for 1 year. Those managers are now interested in knowing how sensitive this decision is with respect to the assumptions theyve made regarding the basic analysis. Therefore, they have asked you to prepare some supplementary analyses regarding Panel B of Exhibit 12.7.
Required:
1. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (21%), medium (55%), and low (24%)?
2. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (42%), medium (34%), and low (24%)?
EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) F G H I J E 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 3 Discount rate (WACC) = 15.00% Cash Outflow @time 0 Market Demand (Scenario) High Medium Low End-of-Period Cash Inflows NPV of Weighted 2 3 Scenario NPV $70 $70 $70 $59.826 $14.956 $50 $50 $50 $14.161 $7.081 $5 $5 $5 ($88.584) ($22.146) Expected NPV = L ($0.109) Probability 0.25 0.50 0.25 1.00 $100 12 Panel B: Expected NPV--Delay Investment by One Year, Only if NPV is increased, amounts in $ millions 13 14 Discount rate (WACC)= 15.00% 15 Risk-free rate = 5.00% 16 Cash outflow one year from the presenet (?) = $100 2 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted (Scenario) Probability 4 Outflows Inflows** NPV @time 0*** High 0.25 ($100) $70 ($95.24) $138.979 $10.94 Medium 0.50 ($100) $50 $50 ($95.24) $99.271 $2.016 Low 0.25 $0.00 $0.000 $0.000 1.00 Expected NPV = $12.951 discounted at risk-free rate of interest **discounted at WACC (weighted average cost of capital); formula for cell 120: =PV(B14,1,(PV(B14,3,E20))) ***formula for cellJ20:=C20"(120+H20) $0 $0 EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) F G H I J E 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 3 Discount rate (WACC) = 15.00% Cash Outflow @time 0 Market Demand (Scenario) High Medium Low End-of-Period Cash Inflows NPV of Weighted 2 3 Scenario NPV $70 $70 $70 $59.826 $14.956 $50 $50 $50 $14.161 $7.081 $5 $5 $5 ($88.584) ($22.146) Expected NPV = L ($0.109) Probability 0.25 0.50 0.25 1.00 $100 12 Panel B: Expected NPV--Delay Investment by One Year, Only if NPV is increased, amounts in $ millions 13 14 Discount rate (WACC)= 15.00% 15 Risk-free rate = 5.00% 16 Cash outflow one year from the presenet (?) = $100 2 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted (Scenario) Probability 4 Outflows Inflows** NPV @time 0*** High 0.25 ($100) $70 ($95.24) $138.979 $10.94 Medium 0.50 ($100) $50 $50 ($95.24) $99.271 $2.016 Low 0.25 $0.00 $0.000 $0.000 1.00 Expected NPV = $12.951 discounted at risk-free rate of interest **discounted at WACC (weighted average cost of capital); formula for cell 120: =PV(B14,1,(PV(B14,3,E20))) ***formula for cellJ20:=C20"(120+H20) $0 $0 EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) F G H I J E 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 3 Discount rate (WACC) = 15.00% Cash Outflow @time 0 Market Demand (Scenario) High Medium Low End-of-Period Cash Inflows NPV of Weighted 2 3 Scenario NPV $70 $70 $70 $59.826 $14.956 $50 $50 $50 $14.161 $7.081 $5 $5 $5 ($88.584) ($22.146) Expected NPV = L ($0.109) Probability 0.25 0.50 0.25 1.00 $100 12 Panel B: Expected NPV--Delay Investment by One Year, Only if NPV is increased, amounts in $ millions 13 14 Discount rate (WACC)= 15.00% 15 Risk-free rate = 5.00% 16 Cash outflow one year from the presenet (?) = $100 2 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted (Scenario) Probability 4 Outflows Inflows** NPV @time 0*** High 0.25 ($100) $70 ($95.24) $138.979 $10.94 Medium 0.50 ($100) $50 $50 ($95.24) $99.271 $2.016 Low 0.25 $0.00 $0.000 $0.000 1.00 Expected NPV = $12.951 discounted at risk-free rate of interest **discounted at WACC (weighted average cost of capital); formula for cell 120: =PV(B14,1,(PV(B14,3,E20))) ***formula for cellJ20:=C20"(120+H20) $0 $0 EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) F G H I J E 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 3 Discount rate (WACC) = 15.00% Cash Outflow @time 0 Market Demand (Scenario) High Medium Low End-of-Period Cash Inflows NPV of Weighted 2 3 Scenario NPV $70 $70 $70 $59.826 $14.956 $50 $50 $50 $14.161 $7.081 $5 $5 $5 ($88.584) ($22.146) Expected NPV = L ($0.109) Probability 0.25 0.50 0.25 1.00 $100 12 Panel B: Expected NPV--Delay Investment by One Year, Only if NPV is increased, amounts in $ millions 13 14 Discount rate (WACC)= 15.00% 15 Risk-free rate = 5.00% 16 Cash outflow one year from the presenet (?) = $100 2 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted (Scenario) Probability 4 Outflows Inflows** NPV @time 0*** High 0.25 ($100) $70 ($95.24) $138.979 $10.94 Medium 0.50 ($100) $50 $50 ($95.24) $99.271 $2.016 Low 0.25 $0.00 $0.000 $0.000 1.00 Expected NPV = $12.951 discounted at risk-free rate of interest **discounted at WACC (weighted average cost of capital); formula for cell 120: =PV(B14,1,(PV(B14,3,E20))) ***formula for cellJ20:=C20"(120+H20) $0 $0
