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?
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?
To determine the maximum amount that the person should be willing to pay the consultant for the information, we need to assess the expected value of the project with and without the consultant's information. The expected value can help us understand the average outcome of a scenario by multiplying the financial gain or loss by the corresponding probabilities.
Here are the steps to calculate the expected value:
1. Without the consultant's information:
- If the project succeeds, the person will gain $15 million with a 20% probability.
- If the project fails, the person will lose $3 million with an 80% probability.
Expected value without the consultant's information:
(0.20 * $15 million) + (0.80 * -$3 million) = $3 million - $2.4 million = $0.6 million
2. With the consultant's information:
- If the consultant confirms that the project will succeed, the outcome is certain, and the person will gain $15 million.
- If the consultant confirms that the project will fail, the outcome is certain, and the person will lose $3 million.
Expected value with the consultant's information:
If the person knows the outcome with certainty, the expected value becomes the actual value of the outcome, which is either $15 million or -$3 million, depending on the consultant's information.
Now, to determine the maximum amount the person should be willing to pay, we compare the expected value with and without the consultant's information. The person should be willing to pay up to the amount that would make the expected value with the consultant equal to the expected value without the consultant.
If we assume x as the maximum amount the person is willing to pay, the equation will be:
x + (0.20 * $15 million) + (0.80 * -$3 million) = $0.6 million
Simplifying the equation:
x + $3 million - $2.4 million = $0.6 million
x = $0.6 million - $3 million + $2.4 million
x = $0.6 million - $0.6 million
x = $0
Therefore, the most the person should be willing to pay the consultant for the information is $0, as the expected value with the consultant's information matches the expected value without it.
In this case, the person should not pay anything to the consultant, as the information they provide does not change the expected value of the project.