A pharmaceutical company is conducting a clinical trial for a new drug to treat a rare disease. The company has invested $10 million in the research and development of the drug, and the estimated cost of the clinical trial is $30 million. The company estimates that there is a 25% probability that the clinical trial will fail, in which case the company will lose the entire $40 million investment. The company is considering two risk management options: (1) purchase insurance to cover the potential loss in case of clinical trial failure and (2) invest in a backup research project that has a 50% chance of generating a profit of $20 million in case the clinical trial fails. The backup project will cost $5 million to develop. Assuming that the company is risk-neutral and only interested in maximizing expected value, which option should the company choose? Show all the calculations and assumptions.

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