Suppose SG Cowen is deciding between Sanchez and Goldstein. Based on his success at PWC, the bankers feel Goldstein is a very safe hire: they feel certain his productivity will be $500,000 per year. Sanchez's background (successful entrepreneur with low GPA) makes him a riskier hire. They believe his annual productivity is high ($900,000) with probability p = 1/2, and low ($100,000) with probability 1-p = 1/2. After one year, they will know if Sanchez is high or low productivity. Both Goldstein and Sanchez can be expected to work for ten years and the bank is risk neutral. Answer the following questions mathematically. Show your work.
A. First, assume the salary is $200,000 and termination costs are zero. Is Goldstein or Sanchez a better hire? Show your work
B. In reality, SG Cowen does not know with such precision that there is a 50% chance that Sanchez will be a star. What is the lowest probability of being a star that will still lead to the company taking a chance on him?