Fuel cell research under uncertainty

Suppose an energy company is deciding whether to undertake a five-year research project to develop fuel cells for electric vehicles. If the project goes ahead, it will cost $50 million, all of which must be paid when the project starts. (That is, the project would require a single payment of $50 million in year 0). Whether the project will succeed is uncertain. If it does, it will produce a fuel cell that could be licensed to automobile companies for $10 million a year forever starting in year 6. If it fails, it produces nothing. The probability of success is 60% and the interest rate is 10%. You may assume the firm is risk-neutral.

1. Draw the firm's cash-flow diagrams and decision tree and label everything clearly. What should the firm do? Why? Would your answer be different if the interest rate were a lot lower?
2. Now suppose it is possible to do a quick small-scale pilot study before undertaking the main project. The pilot study costs $5 million and will reveal whether or not the main project will succeed with complete accuracy. To keep the timing of things simple, imagine that the pilot study can be done in year 0 and there will still be time to begin the main project that year if it looks like a good idea. (In other words, doing the pilot study has no effect on the timing of the main project.) Draw the new decision tree and determine what the firm should do.
3. Finally, suppose the test in part (2) is not completely accurate. In particular, suppose it never indicates the main project will succeed when it will actually fail (i.e., it never returns "false positives"), but there's a 50% chance the pilot study will fail when the main project would actually succeed (a 50% chance of a "false negative"). Draw the new decision tree and determine the maximum amount the firm would be willing to pay for the imperfect pilot study.

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