Expected NPV 1177400 9 911300 1 1059660 91130 9680530 e Recommendation The

# Expected npv 1177400 9 911300 1 1059660 91130 9680530

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Expected NPV = \$1,177,400 (.9) - \$911,300 (.1) = \$1,059,660 – \$91,130 = \$968,0530 e. Recommendation: The project has a positive expected NPV, which is substantial relative to the size of the initial investment. This argues strongly for acceptance. There is substantial risk, however, since there is a modest chance of a significant loss. Most managers would probably accept this project unless the underlying business is so weak that the loss would seriously damage it. More Complex Decision Trees: Examples 12-2 and 12-3 (pages 522 and 524) 9. Work Station Inc. manufactures office furniture. The firm is interested in “ergonomic” products that are designed to be easier on the bodies of office workers’ who suffer from aliments such as back and neck pain due to sitting for long periods. Unfortunately customer acceptance of ergonomic furniture tends to unpredictable, so a wide range of market response is possible. Management has made the following two-year, probabilistic estimate of the cash flows associated with the project arranged decision tree format (\$000). Path \$7,000 1 .3 \$4,000 .7 .6 \$5,000 2 \$6,000 .4 \$3,000 3 .8 \$2,000 .2 \$2,400 4 Work Station is a relatively small company, and would be seriously damaged by any project that lost more than \$1.5 million. The firm’s cost of capital is 14%. a. Develop a probability distribution for NPV based on the forecast. I.e., calculate the project’s NPV along each path of the decision tree and the associated probability. b. Calculate the project’s expected NPV. c. Analyze your results and make a recommendation about the project’s advisability considering both expected NPV and risk SOLUTION: a. The NPV along each of the project’s four paths and the probability of each of those outcomes is calculated as follows: Path 1 NPV = -6000 + 4000(PVF 14,1 ) + 7000(PVF 14,2 ) = -6000 + 4000(.8772) + 7000(.7695) = -6000 + 3508.8 + 5386.5 = 2895.3 Probability = .6 .3 = .18 46
Risk Topics and Real Options in Capital Budgeting Path 2 NPV = -6000 + 4000(.8772) + 5000(.7695) = -6000 + 3508.8 + 3847.5 = 1356.3 Probability = .6 .7 = .42 Path 3 NPV = -6000 + 2000(.8772) + 3000(.7695) = -6000 + 1754.4 + 2308.5 = -1937.1 Probability = .4 .8 = .32 Path 4 NPV = -6000 +1754.4 + 2400(.7695) = -6000 + 1754.4 + 1846.8 = -2398.8 Probability = .4 .2 = .08 1.00 b. The expected NPV for the entire project is the sum of the products of each path’s NPV and probability. Expected NPV = 2895.3(.18) + 1356.3(.42) 1937.1(.32) – 2398.8(.08) = 521.2 + 569.6 – 619.9 – 191.9 = 279.0 c. Recommendation: The project has a positive expected NPV, which is quite small relative to the size of the initial investment. This argues weakly for acceptance. However, risk considerations tell another story. Two paths with probabilities totaling 40% have ruinously negative NPVs. That means accepting the project has as much as a 40% probability of seriously damaging or sinking the company. Most rational managers would forego such a project in spite of the positive overall expected NPV. Abandonment Options: Example 12-5 (page 528)

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