The Winner’s Curse

Acquiring a company

Company A is considering acquiring Company T. The value of Company T depends on an uncertain oil exploration outcome, ranging from $0 to $100 (each value equally likely) per share under current management, and 50% higher under Company A’s management. Company T will learn the outcome before deciding whether to accept the offer (and will only accept if the offer meets or exceeds its realized value). What per-share price should Company A offer to Company T?

  • In the following exercise, you will represent Company A (the acquirer) which is currently considering acquiring Company T (the target) by means of a tender offer.

    You plan to tender in cash for 100% of Company T's shares but are unsure how high a price to offer. The main complication is this: the value of the company depends directly on the outcome of a major oil exploration project it is currently undertaking.

    The very viability of Company T depends on the exploration outcome. In the worst case (if the exploration fails completely), the company under current management will be worth nothing — $0/ share. In the best case (a complete success), the value under current management could be as high as $100/share. Given the range of exploration outcomes, all share values between $0 and $100 per share are considered equally likely.

    By all estimates the company will be worth considerably more in the hands of Company A than under current management. In fact, whatever the value under current management, the company will be worth 50% more under the management of Company A than under Company T. If the exploration project generates a $50/share value under Company T, the value under Company A is $75/share. Similarly, a $100/share value under Company T implies a $150/share value under Company A, and so on.

    However, in the worst case if exploration fails completely, the company is worth $0/share under either management.

    The board of directors of Company A has asked you to determine the price they should offer for Company T's shares. This offer must be made now, before the outcome of the drilling project is known. From all indications, Company T would be happy to be acquired by Company A, provided it is at a profitable price.

    You expect Company T to delay a decision on your bid until the results of the project are in, then accept or reject your offer before releasing the news of the drilling results to the press.

    Thus, you (Company A) will not know the results of the exploration project when submitting your price offer, but Company T will know the results when deciding whether or not to accept your offer. In addition, Company T is expected to accept any offer by Company A that is greater or equal to the (per share) value of the company under its own management.

    As the representative of Company A, you are deliberating over price offers in the range $0/share (this is tantamount to making no offer at all) to $150/share. What price offer per share would you tender for Company T's stock?

  • Mean offer: 50.64

  • Over 50% of participants make offers in the range between $50 and $75.

  • Intuition: the expected value of Company T is $50, meaning this is worth $75 to me (Company A). So, it should be profitable to suggest a bid between $50 and $75.

Suppose you bid $60. The firm will reject your bid if it’s worth more than that, so it must be that it’s worth at most $60. Since, by assumption, all possible values are equally likely, Company T is worth $30 on average (and $45 to you). Hence, if you bid $60, your expected loss is $15.

Make this calculation for some other values. What conclusion do you reach?

…For any positive bid, the outcome is an expected loss equal to 25% of the bid!

But 89.58% of participants make positive offers!

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