Question

Decision Tree

A company is trying to decide whether to bid for a certain contract or not. They estimate that merely preparing the bid will cost $10,000. If their company bids, then they estimate that there is a 50% chance that their bid will be put on the “short-list”, otherwise their bid will be rejected. Once “short-listed”, the company will have to supply further detailed information (entailing costs estimated at $5,000). After this stage, their bid will either be accepted or rejected. The company estimate that the labor and material costs associated with the contract are $127,000. They are considering three possible bid prices, namely $155,000, $170,000 and $190,000. They estimate that the probability of these bids being accepted (once they have been short-listed) is 0.90, 0.75 and 0.35 respectively. What should the company do and what is the expected monetary value of your suggested course of action?

NOTE:

1-To answer this question, please draw the company’s decision tree and evaluate it according to the expected value criterion.
​​​​​​​2- Please show the calculations.

Answer 1

Expected value at node 4 = 0.1*(-$5k)+0.9*$23k = $20.2k

Expected value at node 5 = 0.25*(-$5k)+0.75*$38k = $27.25k

Expected value at node 6 = 0.65*(-$5k)+0.35*$58k = $17.05k

Expected value at node 3 = Max($20.2k,$27.25k,$17.05k) = $27.25k

Expected value at node 2 = 0.5*$0 + 0.5*$27.25k = $13.625k

Expected value at node 1 = max(($13.625k-$10k),0) = $3.625k

So company should bid $170k and expected monetary value of your suggested course of action = $3.625k