Bets and decisions · Acquisitions · difficulty 4 of 5
The winner's curse
You want to buy a company. Under its current owner it is worth V, which you only know is uniformly distributed between $0 and $100 million; the owner knows V exactly. Under your management it would be worth 1.5 × V. You make a single take-it-or-leave-it offer of $60 million. The owner accepts if your offer is at least V, and otherwise refuses and nothing happens. What is your expected profit, in millions of dollars?
Answer with an expected value. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.
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