Q$1.$ Decision Tree $(22$ marks$)$:

XYZ company is considering to decide whether to tender for an infrastructure project for the local government or not. The cost of preparing the bid is estimated to be $$20,000.$ It is a two$-$stage bidding procedure: Bidders first submit the technical proposals in accordance with the specifications but without prices. If XYZ decides to bid, the probability of becoming a candidate for the second stage is around $60\%.$ Once becoming the candidate, company XYZ then has to submit further detailed documents $($with additional costs of $$8,000)$ but it still can choose to abandon bidding.

At this stage, their bid will either be accepted or rejected. Company XYZ estimates that the labor and material costs associated with the contract are $$300,000.$ Three possible bid prices of $$350,000,$$$375,000,$ and $$400,000$ are proposed, and the estimated probability of these bids being accepted $($second stage$)$ is $0\mathrm{.}85,0\mathrm{.}70,$ and $0\mathrm{.}35$ respectively.

$($a$)$ What is the Expected Monetary Value $($EMV$)$ for each option? Illustrate the calculations with a decision tree, and identify the final option.

$(12$ marks$)$

$($b$)$ Explain why do$-$nothing option should be included in the decision analysis.

$(2$ marks$)$

$($c$)$ One of the consultants advises that decision$-$tree method may not be adequate. He suggests that Sensitivity Analysis and Influence Diagram may also be considered in the evaluation. Explain the key differences between these methods, and how these tools can be used in what circumstances.

$(4$ marks$)$

$($d$)$ Explain what are the functions of $($i$)$ Risk Register and $($ii$)$ Contingency Reserve in risk management, respectively.

$(4$ marks$)$