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**Unformatted text preview: **1/10/2007 Chapter 13. Tool Kit for Real Options WACC= 14% Risk-free rate = 6% Initial cost of project= $50 DCF Analysis Expected annual cash flows (in millions): Probability Cash Flow Prob. x CF 25% $33 $8.25 50% $25 $12.50 25% $5 $1.25 Expected CF = $22.00 Time Line Year 1 2 3 Expected CF ($50) $22.00 $22.00 $22.00 NPV = $1.08 Figure 13-1 DCF and Decision Tree Analysis for the Investment Timing Option (Millions of Dollars) Part 1. Scenario Analysis: Proceed with Project Today Future Cash Flows NPV of this Probability Now: Year 0 Year 1 Year 2 Year 3 Probability x NPV S $33 $33 $33 $26.61 0.25 $6.65 High-$50 Average $25 $25 $25 $8.04 0.50 $4.02 Low $5 $5 $5-$38.39 0.25-$9.60 1.00 Expected value of NPVs = $1.08 $24.02 22.32 THE INVESTMENT TIMING OPTION: AN ILLUSTRATION (Section 13.2) Murphy Systems is considering a project that will create a new type of hand-held device for connecting to the Internet. The cost of the project is $50 million, but the future cash flows are uncertain. Murphy estimates a 25% probability that the new Internet device will be very popular in which case the project will generate cash flows of $30 million each year for three years. There is a 50% probability generating cash flows of $25 million each year for three years. Unfortunately, there is a 25% chance that the Internet device will not be popular, which means that the project will generate only $5 million per year in cash flows. The cost of capital for this project is 14%. Scenario c Standard Deviation a = Coefficient of Variation b = 0.25 0.25 0.50 Part 2. Decision Tree Analysis: Implement in One Year Only if Optimal Future Cash Flows NPV of this Probability Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability x NPV S-$50 $33 $33 $33 $23.35 0.25 $5.84 High Wait Average-$50 $25 $25 $25 $7.05 0.50 $3.53 Low $0 $0 $0 $0 $0.00 0.25 $0.00 1.00 Expected value of NPVs = $9.36 $8.57 0.92 Notes: Figure 13-2 Sensitivity Analysis for the Investment Timing Option Decision Tree (Millions of Dollars) Future Cash Flows NPV of this Probability Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability x NPV S-$50 $33 $33 $33 $20.04 0.25 $5.01 High Average-$50 $25 $25 $25 $3.74 0.50 $1.87 Low $0 $0 $0 $0 $0.00 0.25 $0.00 1.00 Expected value of NPVs = $6.88 $7.75 1.13 Part 2. Sensitivity Analysis of NPV to Changes in the Cost of Capital Used to Discount Cost and Cash Flows Cost of Capital Used to Discount the Year 1 Cost $6.88 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% 8.0% $13.11 $13.46 $13.80 $14.14 $14.47 $14.79 $15.11 9.0% $11.78 $12.13 $12.47 $12.81 $13.14 $13.47 $13.78 10.0% $10.50 $10.85 $11.20 $11.53 $11.86 $12.19 $12.51 11.0% $9.27 $9.62 $9.97 $10.30 $10.64 $10.96 $11.28 12.0% $8.09 $8.44 $8.78 $9.12 $9.45 $9.78 $10.09 13.0% $6.95 $7.30 $7.64 $7.98 $8.31 $8.64 $8.95 14.0% $5.85 $6.20 $6.54 $6.88 $7.21 $7.54 $7.85 15.0% $4.79 $5.14 $5.48 $5.82 $6.15 $6.48 $6.79 16.0% $3.77 $4.12 $4.46 $4.80 $5.13 $5.45 $5.77 17.0% $2.78 $3.13 $3.47 $3.81 $4.14 $4.46 $4.78 18.0% $1.83 $2.18 $2.52 $2.86 $3.19 $3.51$3....

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