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Question 1 of 3

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A private equity firm is considering whether to take over another firm, called the “target.” The target has several projects in the pipeline so no one is certain exactly what the target is worth, but estimates are that it is worth anywhere between $0 and $100, with each value equally likely. Although the value of the target is uncertain, the private equity firm knows that the target is currently ill managed and that in their hands they could increase the target’s value by 50%, that is, multiply the target’s value by a factor of 3/2. If the firm is currently worth $60, for example, it would be worth $60 × (3/2) = $90 after new management is installed.

Which of the following would be a mutually profitable price for this acquisition, that is, a price such that, on average or in expectation, the owners of both the target and the private equity firm expect to profit? (Hint: It helps to know that, when any outcome between a and b is equally likely, the expected or average outcome is a + (b −a)/2, as illustrated in the diagram. (If you have taken statistics, this is a property of the uniform distribution.)
Correct! Since each outcome is equally likely, where the lowest value (a) is 0 and the highest possible value (b) is $150, then using [a + (b −a)/2] we arrive at the price of [$0 + ($150 − $0)/2] = 75.
Sorry! If each outcome is equally likely, then think about what the lowest value (a) and highest value (b) might be, then calculate the average value using [a + (b −a)/2]. To review asymmetric information, please see the section “Signaling as a Response to Asymmetric Information.”
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      Now assume that the current owners of the target know whether the projects in the pipeline are going well or not and so they know the current value of the firm. Only the outsider buyer, the private equity firm, is uncertain about the value of the target, which they continue to estimate is worth between $0 and $100, with each value equally likely. Until the target is bought, information about its true value cannot be credibly communicated to the potential buyer. Naturally, the current owners will sell only if the private equity firm offers them at least as much or more than the current value. Notice that we have transformed a problem of uncertain but symmetric information into a problem of asymmetric information.

      The mutually profitable price that you arrived at in Question 1 mutually profitable since . In this new situation, the mutually profitable price .

      Correct! Question 1 is based on uncertain but symmetric information compared to Question 2. In Question 2, the current owners know the value of the firm, so assuming there will be multiple round of negotiations between them and the prospective buyers, it would make sense for the buyers to offer less than $75 to account for the possibility that the lower values of the [$0-$150] scale are more likely. If the offer is too low and thus rejected, then the buyers could continually increase the offer until a mutually profitable price is agreed upon.
      Sorry! In Question 1 each outcome was equally likely. Is that still the case in Question 2? To review asymmetric information, please see section “Signaling as a Response to Asymmetric Information.”

      Which of the following would be an appropriate comment on asymmetric information and trade?