FM12 Ch 13 Tool Kit

# FM12 Ch 13 Tool Kit - Chapter 13 Tool Kit for Real Options...

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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 0 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 St \$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

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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 St -\$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 St -\$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 \$3.83 Notes: Scenario d Standard Deviation a = Coefficient of Variation b = a The standard deviation is calculated as in Chapter 6. b The coefficient of variation is the standard deviation divided by the expected value. c The WACC is 14%. d The NPV in Part 2 is as of Year 0. Therefore, each of the project cash flows is discounted back one more year than in Part 1. Part 1. Decision Tree Analysis: Implement in One Year Only if Optimal (Discount Cost at the Risk-Free Rate and Operating Cash Flows at the WACC) Scenario c Standard Deviation a = Coefficient of Variation b = Cost of Capital Used to Discount the Year 2 through Year 4 Operating Cash Flows a The standard deviation is calculated as in Chapter 6.
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