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You work for a small company and must decide whether to go forward with an investment project. The company will gain 5 million dollars if the project is successful, but will loose 1 million dollars if not. you believe that probability of success is 0.2 and the likelihood of failure 0.8. What would be the expected value of perfect info to the company, assuming that it is risk-neutral? What would be the expected value of perfect info to you, assuming that you will receive a bonus of $250,000 if the project succeeds?

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With homework type problems, you should first show your own work. –  GEdgar Sep 3 '12 at 17:13
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2 Answers

For information about the value of perfect information, see this.

The expected value for the company if you invest is $0.2\cdot 5+0.8\cdot(-1)=0.2$ million dollars. If you have perfect information, you will invest in a succcessful project, but not in a failure. The expected value of the project given perfect information is thus $0.2\cdot 5+0.8\cdot 0=1$ million dollars. The value of perfect information is then $1-0.2=0.8$ million dollars, given risk neutrality.

If your bonus for a successful project is $250{,}000$ dollars, if you get nothing for a failure, and if you only care about your bonus, your expected bonus will be $0.2\cdot 250{,}000+0.8\cdot 0= 50{,}000$ dollars. This is true with or without perfect information, since it makes no difference to you if the company invests in a failure, or if it decides not to invest at all. The value to you of perfect information is therefore zero.

The (nonmathematical) moral of the exercise is that with a poorly designed bonus scheme, manageres may not have incentives to avoid failures.

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the expected value is 5M*.2 - 1M*.8 = .2M. I don't know the jargon but I assume the value of perfect info would be the expected loss for failure, which would be .8M. I don't think the bonus affects the value of perfect info.

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