Evergreen Technology is exploring the possibility of acquiring a 100% stake in a privately owned start-up, AlphaTech, which is at the forefront of next generation communication chip for $10 million. AlphaTech currently is in its final development stage of its flagship communication chip, SignalOne. The quality of the chip is measured by its latency level: Ultra-Low, Low and Medium. If the chip could achieve Ultra-Low latency, AlphaTech's valuation will increase to $100 million. If the chip could achieve Low or Medium, the AlphaTech's valuation will be $50 million and $20 million, respectively. There could also be a possibility that the chip would fail to achieve latency level and not viable to be commercialised. The followings are the probabilities for the eventual latency performance of SignalOne chip: Ultra-Low ~ 0.10 Low ~ 0.20 Medium ~ 0.40 Not viable ~ 0.30 Alternatively, Evergreen Technology could acquire a 40% stake in AlphaTech at the initial phase for $6 million while it waits for the preliminary test report on a SignalOne prototype. The preliminary test report can be positive or negative, and the probability of each is 0.5. If the preliminary test report is positive, Evergreen Technology will then proceed to acquire the remaining 60% stake for $15 million. Given the positive preliminary test result, the probabilities for the eventual latency performance of SignalOne chip will be: Ultra-Low ~ 0.25 Low ~ 0.35 Medium ~ 0.30 Not viable ~ 0.10 In the event that the preliminary test report is negative, Evergreen Technology will either sell off its 40% stake at $5 million or proceed to acquire the remaining 60% stake for $3 million. Given the preliminary test result is negative, the probabilities for the eventual latency performance of SignalOne chip will be: Ultra-Low ~ 0.01 Low ~ 0.05 Medium ~ 0.20 Not viable ~ 0.74 (a) Examine the case presented above and show the decision tree with the relevant decision nodes, chance nodes, branches and payoff values correctly indicated. (14 marks