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.)