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 they've 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 (20%), medium (47%), and low (33%)? 2. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (24%), medium (43%), and low (33%)? 3. Prepare a 5 3 table containing the estimated NPV of the decision to delay for each combination of the following: risk-free rate of interest (7%, 8%, 9%) and weighted-average cost of capital (10%, 11%, 12%, 13%, and 14%). For example, one cell in your table would be the estimated NPV of the project if the risk-free rate of interest is 7% and the weighted-average cost of capital is 10%. EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) A B D E F G H 1 J 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 2 3 Discount rate (WACC) = 15.00% 4 5 Cash Outflow Market Demand End-of-Period Cash Inflows NPV of Weighted 6 @ time 0 (Scenario) Probability 1 2 3 Scenario NPV 7 High 0.25 $70 $70 $70 $59.826 $14.956 8 $100 Medium 0.50 $50 $50 $50 $14.161 $7.081 9 Low 0.25 $5 $5 $5 ($88.584) ($22.146) 10 1.00 Expected NPV = ($0.109) 11 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 17 18 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted 19 (Scenario) Probability 1 2 3 4 Outflows* Inflows** NPV @time 0*** 20 High 0.25 ($100) $70 $70 $70 ($95.24) $138.979 21 Medium 0.50 ($100) $50 ($95.24) $99.271 $2.016 22 Low 0.25 $0 $0 $0 $0 $0.00 $0.000 $0.000 23 1.00 Expected NPV = $12.951 24 *discounted at risk-free rate of interest 25 ** discounted at WACC (weighted average cost of capital); formula for cell 120:=PV(B14,1,(PV(B14,3, E20))) 26 ***formula for cellJ20:=C20* (120+H20) 27 28 $10.94 $50 $50 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 they've 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 (20%), medium (47%), and low (33%)? 2. Holding everything else constant, what is the expected NPV of the decision if the probabilities for the three scenarios are as follows: high (24%), medium (43%), and low (33%)? 3. Prepare a 5 3 table containing the estimated NPV of the decision to delay for each combination of the following: risk-free rate of interest (7%, 8%, 9%) and weighted-average cost of capital (10%, 11%, 12%, 13%, and 14%). For example, one cell in your table would be the estimated NPV of the project if the risk-free rate of interest is 7% and the weighted-average cost of capital is 10%. EXHIBIT 12.7 Decision Trees: Real-Options Analysis (Investment-Timing Option) A B D E F G H 1 J 1 Panel A: Expected NPV--Invest in Project Today (time 0); amounts in $ millions 2 3 Discount rate (WACC) = 15.00% 4 5 Cash Outflow Market Demand End-of-Period Cash Inflows NPV of Weighted 6 @ time 0 (Scenario) Probability 1 2 3 Scenario NPV 7 High 0.25 $70 $70 $70 $59.826 $14.956 8 $100 Medium 0.50 $50 $50 $50 $14.161 $7.081 9 Low 0.25 $5 $5 $5 ($88.584) ($22.146) 10 1.00 Expected NPV = ($0.109) 11 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 17 18 Market Demand End-of-Period Cash Flows PV of Cash PV of Cash Weighted 19 (Scenario) Probability 1 2 3 4 Outflows* Inflows** NPV @time 0*** 20 High 0.25 ($100) $70 $70 $70 ($95.24) $138.979 21 Medium 0.50 ($100) $50 ($95.24) $99.271 $2.016 22 Low 0.25 $0 $0 $0 $0 $0.00 $0.000 $0.000 23 1.00 Expected NPV = $12.951 24 *discounted at risk-free rate of interest 25 ** discounted at WACC (weighted average cost of capital); formula for cell 120:=PV(B14,1,(PV(B14,3, E20))) 26 ***formula for cellJ20:=C20* (120+H20) 27 28 $10.94 $50 $50