Clover Park Racing Team has developed a new Formula One car, "VelocityX" (Model # 4065), which claims to have groundbreaking aerodynamics and fuel efficiency, potentially revolutionizing the racing experience. "VelocityX" has not yet demonstrated its performance in official races and is undergoing phase I testing to evaluate the efficacy of its new design. Despite the lack of racing data to support the claims of Clover Park Racing, the prominent racing company, Toble Motorsports, is interested in acquiring the rights to manufacture and distribute model #4065 provided it passes three sequential stages of performance testing. The development of a new Formula One car is often a long and failure-ridden process. Typically, it takes an average of 10-15 years to bring a car model from initial design to the racing track. On average, for every model that reaches competitive racing, 5,000 to 10,000 designs are explored in the development phase. Toble Motorsports, early this month, approached Clover Park Racing with an offer to purchase the rights to Model #4065 for $30 million. If "VelocityX" manages to pass all three phases of performance testing, the commercialization of "VelocityX" would be very lucrative for Toble Motorsports. If "VelocityX" could be marketed as having superior aerodynamics and fuel efficiency, it is forecasted that the model would have a market value of $510 million (this and all subsequent market values are stated at the present value). If "VelocityX" was approved for superior aerodynamics only, the present market value would be $430 million, and $50 million for superior fuel efficiency only. Phase I of performance testing for Model # 4065 has been underway for nearly 10 months. To date, there have been no critical failures or safety issues in the test runs with a team of 150 skilled drivers. Based on the development notes provided by Clover Park Racing, and Toble Motorsports' experience with the testing and development process, Toble Motorsports estimates that Model # 4065 has a 60% chance of successfully completing Phase I testing and 40% chance of failing phase I testing. If Toble Motorsports were to purchase the rights to Model # 4065, the cost to the company would be an additional $5 million to complete phase I testing. If Model #4065 were to pass Phase I, the next step would be to proceed to Phase II testing. If Model # 4065 were to pass Phase II, the next step would be to proceed to Phase III testing. Phase II testing involves rigorous track testing with several hundred skilled drivers to determine the model's performance in aerodynamics and fuel efficiency as well as to document any mechanical issues. Tobel Motorsports estimates that there is a 10% chance that Model #4065 would show superior performance in aerodynamics only, a 10% of superior fuel efficiency only, and a 30% chance of excelling in both areas simultaneously. Phase II of testing would require two years to complete and would cost $40 million. Phase III of testing requires that the car be tested in multiple racing scenarios over a multi-year time horizon. The cost and success of Phase III testing depends on the results of Phase II testing. If Phase II testing indicated that Model # 4065 excelled in aerodynamics only, the Phase III test would cost $50 million and have a 75% chance of meeting international racing standards. If it is excellent in fuel efficiency only, the Phase III test would also cost $50 million and have a 70% chance of meeting international racing standards. However, if Phase II testing showed superiority in both areas, the required Phase III testing would cost $140 million and have a 60% chance of meeting international racing standards sufficient to demonstrate superiority in both aerodynamics and fuel efficiency, a 15% chance for aerodynamics only, and a 10% chance for fuel efficiency only. a) Draw the corresponding decision tree for the above scenario. (20 Points) b) From the perspective of Toble Motorsports, what is the expected payoff of the decision whether to purchase the rights to "VelocityX" (i.e., Model # 4065) ? Show your work. (10 points) c) If you were the CEO of Toble Motorsports, would you recommend purchasing the rights to "VelocityX" (i.e., Model # 4065) ? Why or why not? (3 points)