Q$2.$ The Developer Company, HKChem, is considering of bidding for an urban renewal project to be awarded by the Hong Kong Government. HKChem has decided to put up a bid price of $$1100$ million. The company estimates that it has a $50\%$ chance of winning the contract with this bid. If the company wins the contract, it can choose one of three design alternatives for the urban renewal project. The outcomes arising from these alternatives are given as follows:

Alternative I:

$\backslash$table$[[$Outcomes$,$Probability,Profit $($$ millions$)],[$Great Success,$0\mathrm{.}30,6000],[$Moderate Success,$0\mathrm{.}60,3000],[$Failure$,0\mathrm{.}10,-1000]]$

Alternative II:

$\backslash$table$[[$Outcomes$,$Probability,Profit $($$ millions$)],[,,],[$Great Success,$0\mathrm{.}50,3000],[$Moderate Success,$0\mathrm{.}30,2000],[$Failure$,0\mathrm{.}20,-400]]$

Alternative III:

Outcomes Probability Profit $($$ millions$)$

Moderate Success

$1\mathrm{.}00$

$2500$

The cost of preparing the contract proposal is $$20$ million. If the company does not make a bid, it will invest in an alternative investment option with a guaranteed profit of $$300$ million.

$($a$)$ Construct a sequential decision tree for representing this decision situation.

$(9$ marks$)$

$($b$)$ Determine whether the company should make a bid.

$(10$ marks$)$

$($c$)$ Determine whether your decision would be the same if the outcomes for Alternatives I, II and III can be realized in $5,2,1$ years from the period when the initial decision was made respectively. With aid of Table $2-1,$ use $10\%$ discount rate in your calculation. List all the major assumptions in arriving at your assumptions.

$(6$ marks$)$