A sealed-bid auction is going to be held in the near future for Medex Pharmaceuticals. You represent one of two companies expected to enter bids. The basic data available to your firm consist of an estimate of the value of Medex and some information on the uncertainty surrounding that value. Your task is to prepare a quantitative bidding strategy for this auction. The attached letter from your boss explains his thinking about the problem and offers some suggestions for your approach.
TO: ............... Susan Morganstern
FROM: .............Vaughn Newman
RE: ...............Bidding for Medex
As promised, I am following up our conversation of a few days ago with more information. You mentioned that your staff group might be able to help us prepare our bid for Medex Pharmaceuticals. Here are some of the details you asked about.
First of all, I don't want you to get the impression that our primary objective is simply to win the bid. We'd like to own Medex, of course, but only if the net effect is to increase our shareholder value. One of my big concerns is that we might win the bid but overestimate the value of Medex. That would not be a success.
Second, I'm confident that my Valuation Committee is doing its best to determine how much Medex is worth, but, as you said, we have to recognize the uncertainty we're dealing with. Medex might be worth a lot more or a lot less than our estimate-it really depends on how their R&D division does and on what happens to the market for the new drug they just got approved. I looked back at some of our previous work, and it looks like we've been high or low in our assessment by as much as 50 percent.
That's a lot of uncertainty, but it just seems to be the nature of the situations we've been in.
Third, I am pretty sure that the only other bidder for Medex will be National, in which case we'll have only one rival to worry about. Somehow, this ought to make things simpler than if there were several bidders out there.
Finally, as a corporation, National resembles us closely, and whichever one of us gets Medex should be able to extract the same value from the assets. National's access to information is about the same as ours, so their level of uncertainty should be the same. In addition, National has had some experience in this sort of bidding, and they're not naive about bidding strategy. Judging from their track record, they'll want to avoid overbidding, too. In essence, I guess I'm saying that they are likely to analyze the deal pretty much the way we are.
Any insight you could give us on how we should approach the bidding would be appreciated. The sealed bid is due at Morgan Stanley next Friday.
Here are some guidelines for your analysis:
Your boss has provided an estimate, based on his past experience, of the range of errors that are likely to be made in valuing companies such as Medex. Errors up to 50 percent above and below the true value are possible. If we assume that the true value is $100 million, we could represent the range of possible estimates by a uniform probability distribution with a minimum value of $50 million and a maximum value of $150 million. Other probability models would also be plausible.
We know that our competitor, National, is similar to our company in all important ways. Thus, we may assume that their probability distribution for the value of Medex is the same as ours.
Bidding theory suggests that we should bid less than our estimated value in a common-value auction such as this. Formulate your strategy in terms of a bid level, which is the percentage of our estimated value we will bid.
We clearly cannot know for certain what bid level National will choose. But we can determine what our bid level should be for any given bid level they might choose.
Although your boss has specified the problem rather precisely, you should explore the sensitivity of your results to your assumptions, including the range of uncertainty, the form of the probability distribution, and the number of bidders.