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# nov_4 - this case the NPV of the project would be(note that...

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Example Ford plans to produce and sell “smart cars” for the next 10 years. An opti- mistic forecast is after-tax cash ﬂows of \$3 million per year, and a pessimistic forecast is after-tax cash ﬂows of \$500,000 per year. These are the only two possibilities, and each scenario is equally likely. Ford will know which sce- nario has been realized at the end of the year. The project requires an initial investment of \$9 million today for equipment which will be worth \$4 million in one year. The discount rate is 15%, and the equipment does not qualify for CCA. Is this a good project? Solution The optimistic NPV is - 9 + 3 . 15 ± 1 - (1 . 15) - 10 ² = 6 . 056 and the pessimistic NPV is - 9 + 0 . 5 . 15 ± 1 - (1 . 15) - 10 ² = - 6 . 491 Since each scenario is equally likely, the expected NPV of the project is E [ NPV ] = ( . 5)(6 . 056) - ( . 5)(6 . 491) = - 0 . 2175 Based on this calculation, this does not look like a good project and we would be tempted to reject it. However , if the pessimistic scenario is realized, Ford can decide to abandon the project and sell the equipment for \$4 million. In
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Unformatted text preview: this case, the NPV of the project would be (note that we are including the ﬁrst year’s cash ﬂow of \$500,000)-9 + 4 . 5 1 . 15 =-5 . 087 This is higher than the NPV from continuing the project under the pes-simistic scenario (i.e. Ford loses less by abandoning than by continuing), so if this scenario is realized, Ford should abandon the project. Thus, the correct expected NPV is E [ NPV ] = ( . 5)(6 . 056)-( . 5)(5 . 087) = 0 . 4845 Incorporating the option to abandon in our NPV calculation reveals that the project actually looks good, and should be accepted. Note that without the option to abandon, the (expected) NPV of the project is -0.2175, and with the option to abandon, the NPV of the project is 0.4845. For this reason, we call 0 . 4845-(-. 2175) = 0 . 701822 the value of the option to abandon. 1...
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