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Week8-Ch25 Toolkit

# Week8-Ch25 Toolkit - 4/11/2010 Chapt er 25 Tool Kit for...

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4/11/2010 Chapter 25. 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 T ime Line Year 0 1 2 3 Expected CF (\$50) \$22.00 \$22.00 \$22.00 NPV = \$1.08 Figure 25-1 DCF and Decision Tree Analysis for the Investment Timing Option (Millions of Dollars) Part 1. Scenario Analysis: Proceed with Project T oday Future Cash Flows NPV of this Probability Data for Now: Year 0 Year 1 Year 2 Year 3 Probability x NPV Std Deviation \$33 \$33 \$33 \$26.61 0.25 \$6.65 163 High -\$50 Average \$25 \$25 \$25 \$8.04 0.50 \$4.02 24 Low \$5 \$5 \$5 -\$38.39 0.25 -\$9.60 389 1.00 577 =Variance of PV Expected value of NPVs = \$1.08 \$24.02 22.32 Part 2. Decision-T ree Analysis: Implement in One Year Only If Optimal Future Cash Flows NPV of this Probability Data for Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability x NPV Std Deviation -\$50 \$33 \$33 \$33 \$23.35 0.25 \$5.84 49 High Wait Average -\$50 \$25 \$25 \$25 \$7.05 0.50 \$3.53 3 Low \$0 \$0 \$0 \$0 \$0.00 0.25 \$0.00 22 1.00 73 =Variance of PV Expected value of NPVs = \$9.36 \$8.57 0.92 Notes: Figure 25-2 Sensitivity Analysis for the Investment Timing Option Decision Tree (Millions of Dollars) Future Cash Flows NPV of this Probability Data for Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability x NPV Std Deviation -\$50 \$33 \$33 \$33 \$20.04 0.25 \$5.01 43 High Average -\$50 \$25 \$25 \$25 \$3.74 0.50 \$1.87 5 Low \$0 \$0 \$0 \$0 \$0.00 0.25 \$0.00 12 1.00 60 =Variance of PV Expected value of NPVs = \$6.88 \$7.75 1.13 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 \$3.83 Notes: Real Option Analysis Figure 25-3 Estimating the Input for "Stock Price" in the Option Analysis of the Investment Timing Option (Millions of Dollars) Future Cash Flows PV of this Probability Data for Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability x PV Std Deviation \$33 \$33 \$33 \$67.21 0.25 \$16.80 125 High Average \$25 \$25 \$25 \$50.91 0.50 \$25.46 19 Low \$5 \$5 \$5 \$10.18 0.25 \$2.55 300 1.00 444 =Variance of PV Expected value of PVs = \$44.80 \$21.07 0.47 Notes: Figure 25-4 Estimating the Input for "Stock Return Variance" in the Option Analysis of the Investment Timing Option (Millions of Dollars) Part 1. Find the Value and Risk of Future Cash Flows at the T ime the Option Expires PV in Year 1 Future Cash Flows for this Probability Data for Now: Year 0 Year 1 Year 2 Year 3 Year 4 Probability Std Deviation \$33 \$33 \$33 \$76.61 0.25 \$19.15 163 High Average \$25 \$25 \$25 \$58.04 0.50 \$29.02 24 Low \$5 \$5 \$5 \$11.61 0.25 \$2.90 389 1.00 577 =Variance of PV \$51.08 \$24.02 0.47 Part 2. Direct Method: Use the Scenarios to Directly Estimate the Variance of the Project's Return Probabilit y Data for Probabilit y Std Deviation \$76.61 71.0% 0.25 17.8% 8.1% High \$44.80 Average \$58.04 29.5% 0.50 14.8% 1.2% Low \$11.61 -74.1% 0.25 -18.5% 19.4% 1.00 Expected return = 14.0% 28.7% =Variance of PV 53.6% 28.7% Part 3. Indirect Method: Use the Scenarios to Indirectly Estimate the Variance of the Project's Return \$51.08 \$24.02 Coefficient of variation (CV) = 0.47 T ime (in years) until the option expires (t) = 1.00 20.0% Notes: Figure 25-5 Estimating the Value of the of the Investment Timing Option Using a Standard Financial Option (Millions of Dollars) Part 1. Find the Value of a Call Option Using the Black-Scholes Model Real Option Risk-free interest rate = 6% t =

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