posted by Devon .
A person must decide whether or not to proceed with a particular investment project. If the project succeeds, She will gain $15 million. If the project fails, she will lose $3 million. She estimates there is a 20% chance that the project will succeed and an 80% chance it will fail.
There is a consultant that could tell her with certainty if the project succeed or fail, but only for a fee. What is the most that she should be willing to pay the consultant for the information? Explain. Assume that she correctly estimated the probabilities of the project’s likely success and failure.
I AM LOST on this one - can anyone please help?
First, lets assume the person is RISK NEUTRAL -- where the change in utility from an expected dollar loss is equal to the change in utility from an expected dollar gain.
That said, this is simply a comparison of the expected return on the person's investment. Without the consultant, there is a 20% chance she gets 15M and an 80% chance she loses 3M.
E(return) = .2*15 - .8*3 = 0.6
If she hires the consultant, she will only make the investment if its a win. However, taking into account of the fee, her expected return must greater than what she could do without the consultant. So:
E(return) = .2*(15 - F) - .8*F - 0.6
I get the Fee=2.4