solution

You have spent the last six months developing a new product for treatment of arthritis. You believe a breakthrough could occur at any time during the next eight months and that the probability of success in any given month is about 10%. If you do not succeed within that eight-month period, you have decided to abandon the project. In the event that your efforts are successful, the clinical testing required for FDA approval will take six to ten additional months from the time of development success. Based on prior experience, if development efforts are successful, there is an 80% probability that approval will be granted. Notice of approval or disapproval in any month is equally likely. If you are not successful in getting FDA approval in 10 months, then you will abandon the project (because you will NOT get FDA approval). During development, your venture has been consuming cash at an average rate of $30,000 per month. You estimate that in any given month of your clinical testing there is a 30% probability that the cost will be only $20,000 and a 20% probability that it will be $45,000 and a 50% probability costs will be $30,000 . The cost of financing the venture will be much lower once FDA approval is obtained. The problem is that you need additional financing right now.

Suppose you want to provide enough financing for the worst case successful outcome. How much money should you raise? (Simulation is not needed to address this.)