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Decision Tree and Statistics

I need some help with this question containing a decision tree and analysis:
Bob is a second year MBA student contemplating his employment situation. He has three prospects:
• He has a "standing" offer from Company A for $65K. This offer does not expire.
• He has an "exploding" offer from Company B for $75K. This offer expires in 1 week.
• He interviewed with Company C but hasn't heard from them about their decision. They will inform him about their decision in 2 weeks. He assigns a 30% chance of getting an offer from them. If he does get an offer, he assigns a 30% chance that it will be for $70K, a 40% chance it will be for $80K, and a 30% chance it will be for $90K.

Bob talked to company B to try and negotiate an extension for the offer expiration date. They will not extend it. However, they did tell him if he declines the current offer, but he is still interested later, they will offer it to him again if the position is still open. Bob assigns only a 25% chance that the "B" offer will still be available after he has heard form Company C.

Bob thinks the salary growth prospects, benefits and lifestyle of each of these firms are equivalent and there fore he wants to make his choice to maximize expected initial salary.

A.) Draw a decision tree for bob's decision. If Bob wants to maximize the expected value of his initial salary what should he do?
B.) How much does the expiration date on the offer from Company B cost him (in terms of initial salary)? In other words, what is the most he should be willing to give up in initials salary to extend the deadline on the offer from Company B until after he hears from company C? (Hint: Deadline extension means that the B offer is available with probability 1 after he hears form Company C)
C.) How much would it be worth in terms of initial salary to know now whether or not the B position will still be available in two weeks?
D.) Bob has a contact at company C that can give him some inside information about whether or not he will get the offer there. The information would come now, before he has to decide about the offer from Company B. The contact would tell him his "prospects are good" or his "prospects are bad". This information is imperfect: the probability that the contact says "prospects are good" given the she will get the offer is equal to p where 0<p<1. Assume that the contact is equally reliable in detecting the negative outcomes, that is: P ("prospects are good"| offer) = P ("prospects are bad" | no offer) = p.

Create a plot that shows the value of this contact's information as a function of p. Use increments of .05 or smaller on your chart. Write a sentence interpreting the chart.

Solution Summary

This in-depth solution contains four decision trees and their analysis for Bob's job prospects in the four different scenarios. It also interprets the information of the decision tree and provides advice to Bob on what his job prospects are.

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