You are a turnaround artist, specializing in identifying underperforming companies, buying them, improving their performance and stock price, and then selling them. You have found such a prospect, Sicco. This company’s marketing department is mediocre; you believe that if you take over the company, you will increase its value by 75% of whatever it was before. But its accounting department is very good; it can conceal assets, liabilities, and transactions to a point where the company’s true value is hard for outsiders to identify. (But insiders know the truth perfectly.) You think that the company’s value in the hands of its current management is somewhere between $10 million and $110 million, uniformly distributed over this range. The current management will sell the company to you if, and only if, your bid exceeds the true value known to them.

(a) If you bid $110 million for the company, your bid will surely succeed. Is your expected profit positive?

(b) If you bid $50 million for the company, what is the probability that your bid succeeds? What is your expected profit if you do succeed in buying the company? Therefore, at the point in time when you make your bid of $50 million, what is your expected profit? (Warning: In calculating this expectation, don’t forget the probability of your getting the company.)

(c) What should you bid if you want to maximize your expected profit? (Hint: Assume it is X million dollars. Carry out the same analysis as in part (b) above, and find an algebraic expression for your expected profit as seen from the point in time when you are making your bid. Then choose X to maximize this expression.)