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### FM12 Ch 13 Tool Kit

Course: FI515 FI515, Spring 2011
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Word Count: 3391

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13. 1/10/2007 Chapter Tool Kit for Real Options 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...

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13. 1/10/2007 Chapter Tool Kit for Real Options 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%. WACC= Risk-free rate = Initial cost of project= 14% 6% \$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 = Time Line Year Expected CF NPV = Figure 13-1 0 (\$50) \$22.00 1 \$22.00 2 \$22.00 \$1.08 DCF and Decision Tree Analysis for the Investment Timing Option (Millions of Dollars) Part 1. Scenario Analysis: Proceed with Project Today Future Cash Flows Now: Year 0 Year 1 Year 2 Year 3 0.25 -\$50 3 \$22.00 High 0.50 Average NPV of this Probability Scenarioc Probability x NPV \$33 \$33 \$33 \$26.61 0.25 \$6.65 \$25 \$25 \$25 \$8.04 0.50 \$4.02 \$5 \$5 \$5 -\$38.39 0.25 1.00 -\$9.60 Low 0.25 Expected value of NPVs = \$1.08 Standard Deviation = \$24.02 Coefficient of Variation = 22.32 a b Std Deviation Part 2. Decision Tree Analysis: Implement in One Year Only if Optimal Future Cash Flows Now: Year 0 Year 1 Year 2 Year 3 Year 4 0.25 High Wait Average Low 0.50 0.25 NPV of this Probability Scenariod Probability x NPV -\$50 \$33 \$33 \$33 \$23.35 0.25 \$5.84 -\$50 \$25 \$25 \$25 \$7.05 0.50 \$3.53 \$0 \$0 \$0 \$0 \$0.00 0.25 1.00 \$0.00 Expected value of NPVs = \$9.36 Standard Deviationa = \$8.57 Coefficient of Variationb = Notes: Std Deviation 0.92 a The standard deviation is calculated as in Chapter 6. b The coefficient of variation is the standard deviation divided by the expected value. 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. c Figure 13-2 Sensitivity Analysis for the Investment Timing Option Decision Tree (Millions of Dollars) 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) Now: Year 0 Year 1 Year 2 Future Cash Flows Year 3 Year 4 NPV of this Probability Scenarioc Probability x NPV -\$50 \$33 \$33 \$33 \$20.04 0.25 \$5.01 -\$50 \$25 \$25 \$25 \$3.74 0.50 \$1.87 \$0 High Average \$0 \$0 \$0 \$0.00 0.25 1.00 \$0.00 Low Expected value of NPVs = \$6.88 Standard Deviationa = \$7.75 Coefficient of Variationb = 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 2 through Year 4 Operating Cash Flows \$6.88 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 16.0% 17.0% 18.0% Notes: 3.0% \$13.11 \$11.78 \$10.50 \$9.27 \$8.09 \$6.95 \$5.85 \$4.79 \$3.77 \$2.78 \$1.83 Cost of Capital Used to Discount the Year 1 Cost 4.0% 5.0% 6.0% 7.0% \$13.46 \$13.80 \$14.14 \$14.47 \$12.13 \$12.47 \$12.81 \$13.14 \$10.85 \$11.20 \$11.53 \$11.86 \$9.62 \$9.97 \$10.30 \$10.64 \$8.44 \$8.78 \$9.12 \$9.45 \$7.30 \$7.64 \$7.98 \$8.31 \$6.20 \$6.54 \$6.88 \$7.21 \$5.14 \$5.48 \$5.82 \$6.15 \$4.12 \$4.46 \$4.80 \$5.13 \$3.13 \$3.47 \$3.81 \$4.14 \$2.18 \$2.52 \$2.86 \$3.19 8.0% \$14.79 \$13.47 \$12.19 \$10.96 \$9.78 \$8.64 \$7.54 \$6.48 \$5.45 \$4.46 \$3.51 9.0% \$15.11 \$13.78 \$12.51 \$11.28 \$10.09 \$8.95 \$7.85 \$6.79 \$5.77 \$4.78 \$3.83 The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. c The Year 2 through Year 4 operating cash flows in are discounted at the WACC of 14%. The cost in Year 1 is discounted at the risk-free rate of 6%. a b Std Deviation Real Option Analysis the project, so the time to maturity of the option is one year. If the company exercises the option, it must pay a strike price equal to the cost of implementing the project. If the company does implement the project, it gains the value of the project. If you exercise a call option, you will own a stock that is worth whatever its price is. If the company implements the project, it will gain a project, whose value is equal to the present value of its cash flows. Therefore, the present value of a project's future cash flows is analogous to the current value of a stock. The rate of return on the project is equal to its cost of capital. To find the value of a call option, we need the standard deviation of its rate of return; to find the value of this real option, we need the standard deviation of the projects expected rate of return. The first step is to find the value of the project's future cash flows, as of the time the option must be exercised. We also need the standard deviation of the project's value as of the date it must be exercised. Finally, we need the present value of the project's future cash flows. Figure 13-3 Estimating the Input for "Stock Price" in the Option Analysis of the Investment Timing Option (Millions of Dollars) Now: Year 0 Year 1 Year 2 Future Cash Flows Year 3 Year 4 PV of this Scenarioc Probability Probability x PV \$33 \$33 \$33 \$67.21 0.25 \$16.80 \$25 \$25 \$25 \$50.91 0.50 \$25.46 \$5 High Average \$5 \$5 \$10.18 0.25 1.00 Std Deviation \$2.55 Low Expected value of PVs = \$44.80 Standard Deviation = \$21.07 Coefficient of Variation = 0.47 a b Notes: a b c Figure 13-4 The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. The WACC is 14%. All cash flows in this scenario are discounted back to Year 0. 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 Time the Option Expires Now: Year 0 Year 1 PV in Year 1 for this Probability x PVYear 1 Scenarioc Probability Future Cash Flows Year 2 Year 3 Year 4 \$33 \$33 \$33 \$76.61 0.25 \$19.15 \$25 \$25 \$25 \$58.04 0.50 \$29.02 \$5 \$5 \$5 \$11.61 0.25 1.00 \$2.90 High Average Low Expected value of PVYear 1 = \$51.08 Standard Deviation of PVYear 1a = \$24.02 Coefficient of Variation of PVYear 1b = 0.47 Std Deviation Part 2. Direct Method: Use the Scenarios to Directly Estimate the Variance of the Project's Return PriceYear 0d Probability Probability x ReturnYear 1 PVYear 1e ReturnYear 1f \$76.61 71.0% 0.25 17.8% \$58.04 29.5% 0.50 14.8% \$11.61 -74.1% 0.25 1.00 -18.5% Std Deviation High \$44.80 Average Low Expected return = 14.0% Standard deviation of return = 53.6% Variance of return = 28.7% a g Part 3. Indirect Method: Use the Scenarios to Indirectly Estimate the Variance of the Project's Return Expected "price" at the time the option expiresh = Standard deviation of expected "price" at the time the option expiresi = Coefficient of variation (CV) = Time (in years) until the option expires (t) = Variance of the project's expected return = ln(CV2+1)/t = Notes: \$51.08 \$24.02 0.47 1 20.0% The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. c The WACC is 14%. The Year 2 through Year 4 cash flows are discounted back to Year 1. d The Year 0 price is the expected PV from Figure 13-3. e The Year 1 PVs are from Part 1. f The returns for each scenario are calculated as (PVYear 1 - PriceYear 0)/PriceYear 0. g The variance of return is the standard deviation squared. h The expected "price" at the time the option expires is taken from Part 1. i The standard deviation of expected "price" at the time the option expires is taken from Part 1. a b Figure 13-5 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 rRF = t= X= P= 2 = Real Option Risk-free interest rate Time until the option expires Cost to implement the project Current value of the project Variance of the project's rate of return = = = = = 6% 1 \$50.00 \$44.80 a 20.0% b d1 = d2 = N(d1)= N(d2)= { ln (P/X) + [rRF + 2 /2) ] t } / ( t1/2 ) d1 - (t 1 / 2) = = = = 0.112 -0.33 0.54 0.37 V= P[ N (d1) ] - Xe-rRF t [ N (d2) ] = \$7.04 Part 2. Sensitivity Analysis of Option Value to Changes in Variance Variance Option Value \$7.04 12.0% \$5.24 14.0% \$5.74 16.0% \$6.20 18.0% \$6.63 20.0% \$7.04 22.0% \$7.42 24.0% \$7.79 26.0% \$8.15 28.0% \$8.49 30.0% \$8.81 32.0% \$9.13 Notes: a b The current value of the project is taken from Figure 13-3. The variance of the project's rate of return is taken from Part 3 of Figure 13-4. THE GROWTH OPTION: AN ILLUSTRATION (Section 13.3) Kidco Corporation designs and produces products aimed at the pre-teen market. Most of these products have a very short life cycle, given the rapidly changing tastes of pre-teens. Kidco is considering one such project, which will cost \$30 million to implement and will last only two years. Kidco believes there is a 25 percent chance that the project will catch the fancy of pre-teens. In this scenario, it will generate cash flows of \$34 million in each of the next two years, after which pre-teen tastes are likely to change. There is a 50 percent chance of average demand for the new product, which produces expected cash flows of \$19 million annually for two years. There is a 25% chance that the pre-teens wont like the product, and it will generate cash flows of only \$3 million per year. The cost of capital for this project is 14%. WACC= Risk-free rate= Initial cost= 14% 6% \$30 DCF Analysis Expected annual cash flows (in millions): Probability Cash Flow Prob. x CF 25% \$34 \$8.50 50% \$20 \$10.00 25% \$2 \$0.50 Expected CF = Time Line Year Expected CF NPV = 0 (\$30) \$1.29 \$19.00 1 \$19.00 2 \$19.00 Figure 13-6 Scenario Analysis and Decision Tree Analysis for the Kidco Project (Millions of Dollars) Part 1. Scenario Analysis of Kidco's First Generation Project Future Cash Flows Year 1 Year 2 Now: Year 0 NPV of this Probability Scenarioc Probability x NPV \$34 \$34 \$25.99 0.25 \$6.50 \$20 \$20 \$2.93 0.50 \$1.47 \$2 -\$30 High Average \$2 -\$26.71 0.25 1.00 Std Deviation -\$6.68 Low Expected Value of NPVs = \$1.29 Standard Deviation = \$18.70 Coefficient of Variation = 14.54 a b Part 2. Decision Tree Analysis of the Growth Option Now: Year 0 Future Cash Flows Year 2d Year 3 Year 1 NPV of this Probability Scenarioe Probability x NPV Year 4 \$34 \$34 -\$30 \$34 \$34 \$42.37 0.25 \$10.59 \$20 \$20 -\$30 \$20 \$20 \$1.57 0.50 \$0.79 \$2 \$2 \$0 \$0 -\$26.71 0.25 1.00 -\$6.68 High -\$30 Average Low Expected Value of NPVs = \$4.70 Standard Deviation = \$24.62 Coefficient of Variation = 5.24 a b Notes: a b c The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. The operating cash flows are discounted by the WACC of 14%. The total cash flows in Year 2 are equal to the operating cash flows for the first generation product minus the \$30 million cost to implement the second generation product, if it is optimal to do so. d The operating cash flows in Year 1 through Year 4, which do not include the \$30 million cost of implementing the second generation project in Year 2 for the high demand and average demand scenarios, are discounted at the WACC of 14%. The implementation cost in Year 2 for the high demand and average demand scenarios is discounted at the risk-free rate of 6%. e Std Deviation Sensitivity Analysis of the Kidco Decision Tree Analysis in Figure 13-6 (Millions of Dollars) Cost of Capital Used to Discount the Year 1 Year 4 Operating Cash Flows (These do not include the \$30 million implemetation cost of the second generation project in Year 2.) Table 13-1 Cost of Capital Used to Discount the \$30 Million Implementation Cost in Year 2 of the Second Generation Project 4.0% 5.0% 6.0% 7.0% 8.0% \$11.36 \$11.76 \$12.14 \$12.51 \$12.88 \$10.01 \$10.41 \$10.79 \$11.16 \$11.52 \$8.71 \$9.10 \$9.49 \$9.86 \$10.22 \$4.70 8.0% 9.0% 10.0% 11.0% \$7.04 \$7.45 \$7.84 \$8.23 \$8.60 \$8.96 \$9.31 12.0% 13.0% 14.0% \$5.83 \$4.65 \$3.52 \$6.23 \$5.06 \$3.92 \$6.63 \$5.45 \$4.32 \$7.01 \$5.84 \$4.70 \$7.38 \$6.21 \$5.07 \$7.75 \$6.57 \$5.44 \$8.10 \$6.92 \$5.79 15.0% \$2.42 \$2.83 \$3.22 \$3.61 \$3.98 \$4.34 \$4.69 16.0% \$1.36 \$1.77 \$2.16 \$2.54 \$2.92 \$3.28 \$3.63 17.0% \$0.33 \$0.74 \$1.13 \$1.52 \$1.89 \$2.25 \$2.60 18.0% Figure 13-7 3.0% \$10.96 \$9.61 \$8.30 9.0% \$13.23 \$11.88 \$10.57 -\$0.66 -\$0.25 \$0.14 \$0.52 \$0.90 \$1.26 \$1.61 Estimating the Input for "Stock Price" in the Growth Option Analysis of the Investment Option Timing (Millions of Dollars) Now: Year 0 Year 1 Year 2 Future Cash Flows Year 3 Year 4 PV of this Scenarioc Probability Probability x PV \$34 \$34 \$43.08 0.25 \$10.77 \$20 \$20 \$25.34 0.50 \$12.67 \$2 High Average \$2 \$2.53 0.25 1.00 Std Deviation \$0.63 Low Expected value of PVs = \$24.07 Standard Deviation = \$14.39 Coefficient of Variation = 0.60 a b Notes: a b c Figure 13-8 The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. The WACC is 14%. All cash flows in this scenario are discounted back to Year 0. Estimating the Input for "Stock Return Variance" in the Growth Option Analysis (Millions of Dollars) Part 1. Find the Value and Risk of Future Cash Flows at the Time the Option Expires Now: Year 0 Year 1 PV in Year 2 for this Probability x PVYear 2 Scenarioc Probability Future Cash Flows Year 2 Year 3 Year 4 \$34 \$34 \$55.99 0.25 \$14.00 \$20 \$20 \$32.93 0.50 \$16.47 \$2 \$2 \$3.29 0.25 1.00 \$0.82 High Average Low Expected value of PVYear 2 = \$31.29 Standard Deviation of PVYear 2a = \$18.70 Coefficient of Variation of PV b Year 2 = 0.60 Std Deviation Part 2. Direct Method: Use the Scenarios to Directly Estimate the Variance of the Project's Return PriceYear 0d PVYear 2e Probability Probability x ReturnYear 2 ReturnYear 2f \$55.99 52.5% 0.25 13.1% 5.4% \$32.93 17.0% 0.50 8.5% 0.6% \$3.29 -63.0% 0.25 1.00 -15.8% 11.9% Expected return = 5.9% 17.9% Standard deviation of return = 42.3% Variance of return = 17.9% High \$24.07 Average Low a g Part 3. Indirect Method: Use the Scenarios to Indirectly Estimate the Variance of the Project's Return Expected "price" at the time the option expiresh = Standard deviation of expected "price" at the time the option expiresi = Coefficient of variation (CV) = Time (in years) until the option expires (t) = Variance of the project's expected return = ln(CV2+1)/t = Notes: \$31.29 \$18.70 0.60 2 15.3% The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. c The WACC is 14%. The Year 3 through Year 4 cash flows are discounted back to Year 2. d The Year 0 price is the expected PV from Figure 13-7. e The Year 2 PVs are from Part 1. f The returns for each scenario are calculated as (PVYear 2/ PriceYear 0)0.5 - 1. g The variance of return is the standard deviation squared. h The expected "price" at the time the option expires is taken from Part 1. i The standard deviation of expected "price" at the time the option expires is taken from Part 1. a b Figure 13-9 Estimating the Value of the of the Growth Option Using a Standard Financial Option (Millions of Dollars) Part 1. Find the Value of a Call Option Using the Black-Scholes Model rRF = t= X= P= 2 = Real Option Risk-free interest rate Time until the option expires Cost to implement the project Current value of the project Variance of the project's rate of return = = = = = 6% 2 \$30.00 \$24.07 a 15.3% b d1 = d2 = N(d1)= N(d2)= { ln (P/X) + [rRF + 2 /2) ] t } / ( t1/2 ) d1 - (t 1 / 2) = = = = 0.096 -0.46 0.54 0.32 V= P[ N (d1) ] - Xe-rRF t [ N (d2) ] = \$4.34 Part 2. Sensitivity Analysis of Option Value to Changes in Variance Variance Option Value \$4.34 11.3% \$3.60 13.3% \$3.98 15.3% \$4.34 17.3% \$4.68 19.3% \$4.99 21.3% \$5.29 23.3% \$5.57 25.3% \$5.84 27.3% \$6.10 29.3% \$6.35 31.3% \$6.59 Notes: a b The current value of the project is taken from Figure 13-7. The variance of the project's rate of return is taken from Part 3 of Figure 13-8. Total value = NPV of first generation project + Value of growth option Total value = 1.29 + 4.34 Total value = 5.63 Data for Std Deviation 163 24 389 577 =Variance of PV Data for Std Deviation 49 3 22 73 =Variance of PV Data for Std Deviation 43 5 12 60 =Variance of PV Data for Std Deviation 125 19 300 444 =Variance of PV Data for Std Deviation 163 24 389 577 =Variance of PV Data for Std Deviation 8.1% 1.2% 19.4% 28.7% =Variance of PV Data for Std Deviation 153 1 196 350 =Variance of NPV Data for Std Deviation 355 5 247 606 =Variance of NPV Data for Std Deviation 90 1 116 207 =Variance of PV Data for Std Deviation 153 1 196 350 =Variance of PV Data for Std Deviation =Variance of PV Web 13A: THE ABANDONMENT OPTION Intial Cost= WACC= Risk free rate = After-tax salvage value = \$26 12% 6% \$14 DCF Analysis Table 13A-1 Expected Operating Cash Flows for Project at Synapse Systems (Millions of Dollars) Demand High Average Low Probability 25% 50% 25% 2007 \$18 \$7 -\$8 Operating Cash Flow 2008 2009 \$23 \$28 \$8 \$9 -\$9 -\$10 2010 \$33 \$10 -\$12 Expected operating cash flow = \$6.00 \$7.50 \$9.00 \$10.25 Year Now: Year 0 Expected CF (\$26) Year 1 \$6.00 Year 2 \$7.50 Year 3 \$9.00 Year 4 \$10.25 Time Line NPV = Figure 13A-1 -1.74 Scenario Analysis and Decision Tree Analysis for the Synapse Project (Millions of Dollars) Part 1. Scenario Analysis of the Project (Ignoring the Option to Abandon) Now: Year 0 Year 1 Future Cash Flows Year 2 Year 3 NPV of this Probability Scenarioc Probability x NPV Year 4 \$18 \$23 \$28 \$33 \$49.31 0.25 \$12.33 \$7 \$8 \$9 \$10 -\$0.61 0.50 -\$0.31 -\$8 -\$9 -\$10 -\$12 -\$55.06 0.25 1.00 -\$13.77 High -\$26 Average Low Expected Value of NPVs = -\$1.74 Standard Deviationa = \$36.92 Coefficient of Variationb = -21.17 Part 2. Decision Tree Analysis of the Abandonment Option Future Cash Flows NPV of this Probability Now: Year 0 Year 1d Year 2e Year 3e Year 4e Scenariof Probability x NPV \$18 \$23 \$28 \$33 \$49.31 0.25 \$12.33 \$7 \$8 \$9 \$10 -\$0.61 0.50 -\$0.31 \$6 \$0 \$0 \$0 -\$19.94 0.25 1.00 -\$4.98 High -\$26 Average Low Expected Value of NPVs = Standard Deviationa = \$25.65 Coefficient of Variationb = Notes: \$7.04 3.64 The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. c The operating cash flows are discounted by the WACC of 12%. d The cash flow in Year 1 for the low demand scenario is equal to the -\$8 million operating cash flow plus the after-tax salvage value of \$14 million, since Synapse will e bandon the proejct in this scenario. a The cash flows in Years 2 though Year 4 for the low demand scenario are zero, because Synapse abandons the project immediately after the -\$8 million operating f oss in Year 1. l The operating cash flows in Year 1 though Year 4, which do not include the \$14 million after-tax salvage value, are discounted at the WACC of 12%. The \$14 million salvage value in the low demand scenario in Year 1 is discounted at the riskfree rate of 6%. a b Cost of Capital Used to Discount the Year 1 through Year 4 Operating Cash Flows (These do not include the \$14 million after-tax salvage value in Year 1.) Table 13A-2 Sensitivity Analysis of the Synapse Decision Tree Analysis in Figure 13A-1 (Millions of Dollars) \$7.04 8.0% 9.0% 10.0% 11.0% 12.0% 13.0% 14.0% 15.0% 16.0% 17.0% 18.0% Cost of Capital Used to Discount the \$14 Million After-tax Salvage Value in the Low Demand Scenario of Year 1. 3.0% 4.0% 5.0% 6.0% 7.0% 8.0% 9.0% \$10.18 \$10.15 \$10.12 \$10.08 \$10.05 \$10.02 \$9.99 \$9.38 \$9.34 \$9.31 \$9.28 \$9.25 \$9.22 \$9.19 \$8.60 \$8.57 \$8.54 \$8.50 \$8.47 \$8.44 \$8.41 \$7.85 \$7.82 \$7.79 \$7.76 \$7.73 \$7.70 \$7.67 \$7.13 \$7.10 \$7.07 \$7.04 \$7.01 \$6.98 \$6.95 \$6.44 \$6.41 \$6.38 \$6.34 \$6.31 \$6.28 \$6.25 \$5.77 \$5.74 \$5.71 \$5.67 \$5.64 \$5.61 \$5.58 \$5.13 \$5.09 \$5.06 \$5.03 \$5.00 \$4.97 \$4.94 \$4.50 \$4.47 \$4.44 \$4.41 \$4.37 \$4.34 \$4.31 \$3.90 \$3.87 \$3.84 \$3.80 \$3.77 \$3.74 \$3.71 \$3.32 \$3.29 \$3.25 \$3.22 \$3.19 \$3.16 \$3.13 Real Option Analysis Where Firm Has the Option to Abandon Break the project into two projects plus an option to abandon the second project. Project A starts at time zero and lasts one year. It has the initial cost and first-year operating cash flows of the original project. Project B begins at Year 2 and last through Year 4. It has no initial cost, but has the Year 2 through 4 operating cash flows of the original project. There is also a real option that allows you to abandon Project B if the value of B at time 1 is less than the abandonment amount. Figure 13A-2 Breaking Synapse's Project into Two Separate Projects of the Investment Timing Option (Millions of Dollars) Part 1. DCF Analysis of Project A that Lasts One Year Future Cash Flows Now: Year 0 Year 1 NPV of this Probability Scenarioc Probability x NPV \$18 -\$9.93 0.25 -\$2.48 \$7 -\$19.75 0.50 -\$9.88 -\$8 -\$33.14 0.25 1.00 -\$8.29 High -\$26 Average Low Expected value of PVs = -\$20.64 Standard Deviationa = \$8.26 Coefficient of Variationb = (0.40) Part 2. DCF Analysis of Project B that Starts at Year 1 If Project A is Already in Place Future Cash Flows NPV of this Probability Now: Year 0 Year 1 Year 2 Year 3 Year 4 Scenarioc Probability x NPV \$23 \$28 \$33 \$59.24 0.25 \$14.81 \$8 \$9 \$10 \$19.14 0.50 \$9.57 -\$9 -\$10 -\$12 -\$21.92 0.25 1.00 -\$5.48 High Average Low Expected value of PVs = Standard Deviationa = a b c Figure 13A-3 \$28.69 Coefficient of Variationb = Notes: \$18.90 1.52 The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. The WACC is 12%. All cash flows in this scenario are discounted back to Year 0. Estimating the Input for "Stock Return Variance" in the Abandonment Option Analysis (Millions of Dollars) Part 1. Find the Value and Risk of Future Cash Flows at the Time the Option Expires Now: Year 0 Year 1 Future Cash Flows Year 2 Year 3 Year 4 PV in Year 1 for this Probability c Scenario Probability x PVYear 1 \$23 \$33 \$66.35 0.25 \$16.59 \$8 \$9 \$10 \$21.44 0.50 \$10.72 -\$9 High Average \$28 -\$10 -\$12 -\$24.55 0.25 1.00 -\$6.14 Low Expected value of PVYear 1 = \$21.17 Standard Deviation of PVYear 1a = \$32.14 Coefficient of Variation of PVYear 1b = 1.518 Part 2. Direct Method: Use the Scenarios to Directly Estimate the Variance of the Project's Return PriceYear 0d PVYear 1e ReturnYear 1f Probability Probabilityx ReturnYear 1 \$66.35 High Average 0.25 62.8% \$21.44 13.4% 0.50 6.7% -\$24.55 \$18.90 251.1% -229.9% 0.25 1.00 -57.5% Low Expected return = 12.0% Standard deviation of returna = 170.0% Variance of returng = 289.2% Part 3. Indirect Method: Use the Scenarios to Indirectly Estimate the Variance of the Project's Return Expected "price" at the time the option expiresh = Standard deviation of expected "price" at the time the option expiresi = Coefficient of variation (CV) = Time (in years) until the option expires (t) = Variance of the project's expected return = ln(CV2+1)/t = Notes: \$21.17 \$32.14 1.52 1 119.5% The standard deviation is calculated as in Chapter 6. The coefficient of variation is the standard deviation divided by the expected value. c The WACC is 12%. The Year 2 through Year 4 cash flows are discounted back to Year 1. d The Year 0 price is the expected NPV from Part 2 of Figure 13-12. e The Year 1 PVs are from Part 1. f The returns for each scenario are calculated as (PVYear 1/ PriceYear 0) - 1. g The variance of return is the standard deviation squared. h The expected "price" at the time the option expires is taken from Part 1. i The standard deviation of expected "price" at the time the option expires is taken from Part 1. a b Figure 13A-4 Estimating the Value of the of the Abandonment Option Using a Standard Financial Option (Millions of Dollars) Part 1. Find the Value of a Put Option Using the Black-Scholes Model rRF = t= X= P= 2 = Real Option Risk-free interest rate Time until the option expires Salvage value if abandon Current value of the Project B Variance of Project B's rate of return d1 = d2 = N(d1)= N(d2)= V of Call = V of Put = V of Put = V of Put = = = = = = 6% 1 \$14.00 \$18.90 a 175.0% b { ln (P/X) + [rRF + 2 /2) ] t } / ( t1/2 d1 - (t 1 / 2) 0.82 0.35 = = 0.934 -0.39 P[ N (d1) ] - Xe-rRF t [ N (d2) ] = \$10.99 Call \$10.99 \$5.28 - P \$18.90 + + X e-rRF t \$13.18 Part 2. Sensitivity Analysis of Put Option Value to Changes in Variance Variance Option Value \$5.28 55.0% \$2.29 75.0% \$2.94 95.0% \$3.51 115.0% \$4.02 135.0% \$4.48 155.0% \$4.89 175.0% \$5.28 195.0% \$5.63 215.0% \$5.96 235.0% \$6.27 255.0% \$6.56 Notes: a b The current value of the project is taken from Figure 13E-7. The variance of the project's rate of return is taken from Part 3 of Figure 13E-7. Total NPV= Total NPV= Total NPV= NPV of A -\$20.64 \$3.53 + + NPV of B \$18.90 + + Value of abandonment option \$5.28 Probability Data for Std Deviation 652 1 711 1,363 Probability Data for =Variance of NPV Std Deviation 447 29 182 658 =Variance of NPV Probability Data for Std Deviation 29 0 39 68 Probability =Variance of PV Data for Std Deviation 407 0 417 823 Probability =Variance of PV Data for Std Deviation 510 0 522 1,033 =Variance of PV Data for Std Deviation 142.9% 0.0% 146.3% 289.2% =Variance of PV
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Keller Graduate School of Management - FI515 - FI515
BCDEFGHI12/20/2006123Chapter 14. Tool Kit for Financial Planning and Forecasting Financial Statements45MicroDrive's recent financial statements are shown below.67 INCOME STATEMENT200620078 (in millions of dollars)9\$2,850.0\$3,000.01
Keller Graduate School of Management - FI515 - FI515
BCDEFGH12/21/200612Note: You may get a warning from Excel that cannot calculate a formula, because the model in the AUTOMATIC3FEEDBACK worksheet intentionally has circular references. If you get this warning, go to the menu bar and click on4
Keller Graduate School of Management - FI515 - FI515
1b7eae1d3b3785ea333fc191502c1b480470cbb0.xlsCorporate Valuation12/22/2006Chapter 15. Tool Kit for Corporate Valuation,Value-Based Management, and Corporate GovernanceThis spreadsheet has two major components, one for Corporate Valuation and one for V
Keller Graduate School of Management - FI515 - FI515
A1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253545556575859606162BCDEFGH1/31/2007IChapter 16. Tool Kit for Capital Structure Decisio
Keller Graduate School of Management - FI515 - FI515
A1234567891011121314151617181920212223242526272829303132333435363738394041424344454647484950515253BCDEFGH1/1/2007Chapter 17. Tool Kit for Capital Structure Decisions: ExtensionsCAPITAL STRUCTU
Keller Graduate School of Management - FI515 - FI515
1/2/2007Chapter 18. Tool Kit for Distributions to Shareholders: Dividends and RepurchasesTHE LEVEL OF DISTRIBUTIONS AND FIRM VALUE (Section 18.1) DIVIDEND THEORIESMM Dividend Irrelevance Theory Proposed by Merton Miller and Franco Modigliani, this theo
Keller Graduate School of Management - FI515 - FI515
A 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63BCDEFGHIREFUNDING OPERATIONS (Section 19.8)T his example examines the
Keller Graduate School of Management - FI515 - FI515
1/4/2007Chapter 20. Tool Kit for Lease FinancingTYPES OF LEASES (Section 20.1)Leasing provides firms with a flexible alternative when it comes to acquiring productive assets. Instead of buying fixedassets and having them on the balance sheet, companie
Keller Graduate School of Management - FI515 - FI515
A12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849505152BCDEFGHI1/11/2007Chapter 21. Tool Kit for Hybrid Financing: Preferred Stock, Warrants, and Conver
Keller Graduate School of Management - FI515 - FI515
A12345678910111213141516171819202122232425262728293031323334353637383940BCDEFGH1/12/2007IJKChapter 22. Model for Working Capital ManagementTwo useful tools for working capital management are (1) the cas
Keller Graduate School of Management - FI515 - FI515
b7d940feeeeaa66ea6d473bfe281d35f9c2aab32.xlsChapter1/14/2007Chapter 23. Tool Kit for Derivatives and Risk ManagementA derivative is a security whose values are determined by the market price or interest rate of some other asset. Derivatives are aprim
Keller Graduate School of Management - FI515 - FI515
A123456789101112131415161718192021222324252627282930313233BCDEF9/8/2006Chapter 24. Tool Kit for Bankruptcy, Reorganization, and LiquidationREORGANIZATION IN BANKRUPTCY (Section 24.5)Columbia Software Company is a
Keller Graduate School of Management - FI515 - FI515
1/16/2007Chapter 25. Tool Kit for Mergers, LBOs, Divestitures, and Holding CompaniesIn theory, merger analysis is quite simple. The acquiring firm performs an analysis to value the target company. The acquiring firm then seeks to buy thefirm at prefera
Keller Graduate School of Management - FI515 - FI515
2/25/2007Chapter 26. Tool Kit for Multinational Financial ManagementAt the beginning of this textbook, we stated that one of the driving forces in financial management today is globalization. Thischapter explores the unique challenges of a multinationa
Keller Graduate School of Management - FI515 - FI515
A123456789BCDEFGHChapter 27. Tool Kit for Providing and Obtaining CreditIn Chapter 22, we addressed the topic of working capital management with a brief discussion of trade credit. In thischapter, we extend those analyses to several mor
Keller Graduate School of Management - FI515 - FI515
A1234789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172DEFGHI9/20/2006In Chapters 22 and 27, we ad
Keller Graduate School of Management - FI515 - FI515
Tool Kit for Chapter 29: Pension Plan ManagementPENSION FUND MATHEMATICS: DEFINED BENEFIT PLANS (Section 29.4)The calculation of the present value of expected future benefits is of primary importance for defined benefit pension plans. Thiscalculation d
Keller Graduate School of Management - FI515 - FI515
2c3bbab94ebdfc4afa80fc2a9c0f7f2b05500117.xlsChapter 77.4The expected return on the portfolio is the weighted average of the expected returns onasset A and asset B.^^^r p = w A r A + (1 w A ) r BThe standard deviation of the portfolio, p, is not a
Keller Graduate School of Management - FI515 - FI515
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week1Lab2-9aenter N = 1, I/YR = 6, PV = -500, PMT = 0, and FV = ?IPMTPVFV6%0-500\$530.00N1bN2Enter N = 2, I/YR = 6, PV = -500, PMT = 0, and FV = ? Solve fIPMTPVFV6%0-500\$561.80cN1aPMT0PVFV(\$471.70) \$500.00N
Keller Graduate School of Management - FI515 - FI515
52N=12;I/YR=YTM=9%;PMT=0.081,000=80;FV=1000;PV=VB=?N12I/YR9%PMT80FV1000PV(\$928.39)55rT10=6%;rC10=9%;LP=0.5%;DRP=?64Probabilityof RateofreturnifDemandforthethisdemand thisdemandcompany'sproduct occurringoccursweek0.1belowaveragre0.2
Keller Graduate School of Management - FI515 - FI515
101rd13%0%Tax rateAfter tax cost of debt =A-T rd =A-T rd =10.7(1-Tax rate)100%13%20%13%35%(rd)xxAfter tax cost of debt =13%13.0%WACC=(wd)(rd(1T)+(wps)(rps)+(wce)(rs)wd =wp =ws =30%rd =6.0%5%65%rp =rs =5.8%12.0%tax rate =
Keller Graduate School of Management - FI515 - FI515
122Operating Cash Flows for the first year of Project's LifeSales revenueOperating costsDepreciationOper. income before taxes (EBIT)Taxes on operating income (40%)Net operating profit after taxes (NOPAT)Add back depreciationOperating cash flow\$1
Keller Graduate School of Management - FI515 - FI515
22-2The two principal reasons for holding cash are for transactions and compensatingbalances. The target cash balance is not equal to the sum of the holdings for eachreason because the same money can often partially satisfy both motives.22-4The four
Keller Graduate School of Management - FI515 - FI515
Arvo Corporation is trying to choose between three alternative investments.The three securities that the company is considering are as follows:Tax-free municipalTheXYZCorporationhas of 8.8%.bonds with a returnWooli Corporation \$1000,000whichitplans of
Keller Graduate School of Management - FI515 - FI515
5.2nfv12pmnt1000pv100i-85012.48%5.3nfv7pmnt1000current yeildpvi90 (\$1,052.06)8%8.55%5.4r* = 4%; I1 = 2%; I2 = 4%; I3 = 4%; MRP = 0; rT-2 = ?; rT-3 = ?r = r* + IP + DRP + LP + MRP.Since these are Treasury securities, DRP = LP = 0.
Keller Graduate School of Management - FI515 - FI515
Midterm ExamNameCORPORATE VALUATIONSpring 2004Multiple Choice - Circle the letter of the BEST answer (3 points each)1. Which of the following statements is most correct about a stock which has a beta of 1.2?a. If the stocks beta doubles, its expecte
Keller Graduate School of Management - FI515 - FI515
Keller Graduate School of Management - FI515 - FI515
Keller Graduate School of Management - FI515 - FI515
Keller Graduate School of Management - FI515 - FI515
Keller Graduate School of Management - FI515 - FI515
FIN303Exam-type questionsChapter 11.Which of the following statements is most correct?a.b.c.d.2.One advantage of forming a corporation is that you have limited liability. *Corporations face fewer regulations than sole proprietorships.One disad
Keller Graduate School of Management - FI515 - FI515
FIN303Exam-type questionsFor Midterm 2Chapter 21. Suppose you have \$2,000 and plan to purchase a 3-year certificate of deposit (CD) thatpays 4% interest, compounded annually. How much will you have when the CDmatures?a.b.c.d.\$2,324.89\$2,591.45
Keller Graduate School of Management - FI515 - FI515
iPractice for final testWhich of the following statements is most correct?.a. The rate of depreciation will often affect operating cashflows, even though depreciation is not a cash expense.b. Corporations should fully account for sunk costs when mak
Keller Graduate School of Management - FI515 - FI515
PRACTICE FINAL EXAM (Answers provided at practice tests end)The following questions are worth 3 points each. Provide the single best response.1. The primary goal of a publicly-owned firm interested in serving its stockholders should be toa. Maximize ex
Keller Graduate School of Management - FI515 - FI515
CHAPTER 3RISK AND RETURN: PART IIOVERVIEWIn Chapter 2 we presented the key elements ofrisk and return analysis. There we saw thatmuch of the risk inherent in a stock can beeliminated by diversification, so rationalinvestors should hold portfolios o
Keller Graduate School of Management - FI515 - FI515
CHAPTER 7STOCKS AND THEIR VALUATION(Difficulty: E = Easy, M = Medium, and T = Tough)Multiple Choice: ConceptualEasy:Required returnAnswer: d Diff: E1.If the expected rate of return on a stock exceeds the required rate,a.b.c.d.e.The stock is
Keller Graduate School of Management - FI515 - FI515
Assignment 3exQuestion 1Assume that you are comparing two mutually exclusive projects. Which of the following statements is mostcorrect?Answer2. Normal projects C and D are mutually exclusive. Project C has a higher net present value if the WACC isl
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week1Lab.6%1-1a. A proprietorship, or sole proprietorship, is a business owned by one individual.The individual proprietor has the right to all the profits from the business and alsoresponsibility for all the firm's liabilities. If the
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week2Lab3-2The four financial statements contained in most annual reports are the balance sheet, incomestatement, statement of retained earnings, and statement of cash flows.3-3When a company reports \$20 million of retained earnings on
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week3Lab.docx5-1a.A bond is a promissory note issued by a business or a governmental unit.Treasury bonds, sometimes referred to as government bonds, are issued by the Federal governmentand are not exposed to default risk.Corporate bond
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week5Lab10-1a. The weighted average cost of capitalWACC is the weighted average of the after-tax component costs of capital-debt, preferredstock, and common equity. Each weighting factor is the proportion of that type of capital in theo
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week5Lab10-1a. The weighted average cost of capitalWACC is the weighted average of the after-tax component costs of capital-debt, preferredstock, and common equity. Each weighting factor is the proportion of that type of capital in theo
Keller Graduate School of Management - FI515 - FI515
AnhNguyenFI515Week6Lab.doc12-1a. Cash flow, which is the relevant financial variable, represents the actual flow ofcash.Accounting income, on the other hand, reports accounting data as defined by GenerallyAccepted Accounting Principles (GAAP).b. Inc
Keller Graduate School of Management - FI515 - FI515
Effective annual rateAnswer: b Diff: E24.Which of the following bank accounts has the highest effective annualreturn?a. An accountpounding.b. An accountpounding.c. An accountpounding.d. An accountpounding.e. All of thewhich pays 10 percent n
Keller Graduate School of Management - FI515 - FI515
Time Remaining:1. (TCO C)On its 1999 balance sheet, Sherman Books showed a balance of retained earnings equal to \$510 million. On its2000 balance sheet, the balance of retained earnings was also equal to \$510 million. Which of the followingstatements
Keller Graduate School of Management - FI515 - FI515
Towson UniversityDepartment of FinanceFin331Dr. M. Rhee2010 SpringNAME:ID#:1.If APR = 10%, what is the EAR (effective annual rate) for quarterly compounding?a. 10.00%b. 10.38%c. 12.36%d. 13.36%e. 15.52%Answer: bAPR = Nominal ratePeriods/yr
Keller Graduate School of Management - FI515 - FI515
Time Remaining:1. (TCO B) Which of the following statements is most correct?(Points: 10)a. If a project with normal cash flows has an IRR which exceeds the cost ofcapital, then the project must have a positive NPV.b. If the IRR of Project A exceeds t
E. Stroudsburg - ECON - 550
Week 3: Working Capital ManagementChapter 3 ProblemsProblem 3: Calculate the future Valve of \$2,000 inA Five years at an interest of 5%NPERRatePVGiven55.00%-5,000PMT0FV\$6,381.41Amount of Interest Earned\$1,381.41B Ten years at an interest
E. Stroudsburg - ECON - 550
Week 5 Discussion Chapter 11 - Problem 15Problem 13 Gentry Can Company's latest annual dividend of \$1.25 a share was paid yesterday andmaintained its historic 7% annual rate of growth. You plan to purchase the stock todaybecause you believe that the di
E. Stroudsburg - ECON - 550
Week 5 Discussion Chapter 10, Problem 2 &amp; Problem 3Problem 2 Three companies have the following reuslts during the recent periodNet Profit MarginTotal Assets turnoverTotal assets/equityK0.042.202.40L0.062.002.20M0.101.401.50A Derive for e
E. Stroudsburg - ECON - 550
Chapter11Problem13 Computearecentfiveyearaverageofthefollowingratiosforthreecompaniesofyourchoice.Category RetentionRate NetProfitMargin EquityTurnoverTotalAssestTurnoverTotalAssets/Equity GrowthRateCompaniesApple80.2%16.1%1.861.131.634.62%HP8
E. Stroudsburg - ECON - 550
YearIntial InvestmentRevenuesVariable CostsFixed CostsIntial Working CapitalDepreciationPre Tax ProfitTaxes 38%Net ProfitSalvage ValueOperating Cash FlowsIntial Investment Cost0-1,700,000123413,475,000 13,475,000 13,475,00012,100,000 1
LSU - BIOL - 2051
Chapter2ObservingtheMicrobialCellSIZEOFPROKARYOTESProkaryotesaregenerallysmallerthaneukaryotesSmallsizeallowsnutrientstoreachallpartsofcellquicklyProkaryoticcellscanbeassmallas0.2m.Thesmallesteukaryoticcellsare2m.Cocci(spherical)typicallyhavediamet
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Sports in MoviesSports in MoviesJoel L. SmithAshford UniversitySociology of SportsSOC318Brian FreelandFebruary 01, 20101Sports in MoviesAs with many social issues, sports were at the front of the segregation issue. This paperwill discuss this i
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Running head: AFFIRMATIVE ACTION1Affirmative ActionJoel L. SmithAshford UniversityEnglish CompositionENG 122Dr. Jill D. Mosley, PHDNovember 21, 2008Affirmative ActionThis paper will discuss the different views on affirmative action. I will go ov
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Running head: AMAZON MARKETING MIXAmazon Marketing MixJoel SmithTexas A &amp; M University - CommerceMarketing EnvironmentMKT 501Dr. Sonia TanejaSeptember 14, 20101Amazon Marketing MixThe business world is full of companies who are successfully comp
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Running head: ATTRIBUTION THEORY1Attribution TheoryJoel SmithTexas A &amp; M - CommerceCrisis ManagementMGT 597 02WProfessor Zhang LongApril 24, 2011Attribution TheoryWithin the field of crisis management, there are several theories that experts use
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CommunicationRunning head: COMMUNICATIONCommunicationJoel L. SmithAshford UniversityInterpersonal CommunicationCOM 200Kennedy Kelechi HalamsApril 27, 20091CommunicationIn this paper, we will discuss communication. Communication is one of the mo
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