Two partners have decided to sell the manufacturing business they have been running. They have lined up five prospective buyers and have hired a consultant to help them with the bidding and the sale. The consultant, an expert in assessments of this sort, has told the partners that the business is worth $10 million.
The consultant has obtained indications that the prospective buyers would be willing to participate in a sealed-bid auction to determine who will buy the business and at what price. Under the rules of the auction, the sale price would be the highest bid.
Due to their limited information about the business, the bidders may overestimate or underestimate what the business is actually worth. After listening to some of the bidders’ preliminary thoughts, the consultant concludes that limited information will lead each of them to value the business at a minimum of $8 million and a maximum of $15 million. Their most likely value is $10 million. (We interpret this to mean that a suitable model for an individual value will be a triangular distribution.) The bidders, however, have an instinct about the Winner’s Curse, and they each plan to bid only 75 percent of their estimated value for the business. (The Winner’s Curse is a phenomenon in competitive bidding where the winner is generally the one that most overestimates the value of the prize.)
A) What is the expected price that the partners will receive for their business?
B) What is the probability that the partners will receive more than $10 million for the business?
C) Suppose the consultant asks for a fee in order to identify five more bidders to participate in the auction. How large a fee should the partners be willing to pay for this service?