Governor of State X is considering investing on a 100-mile highway connecting state's two cities: A and B. Today, governor is presented with three options:
Option I: Asphalt, costs $200,000 per mile and lasts for 8 years after which it has to be replaced. It has an annual maintenance cost of 20,000 per mile. Option II: Concrete, costs $1,200,000 per mile lasts 20 years and needs to be maintained every 5 years at a cost of $240,000. Option III: New material, not fully tested for long term durability. It costs 1,294,400 per mile. It will last 16 years with 80% chance and 10 years with 20% chance. Due to weight considerations, option I will not be able to accommodate heavy commercial vehicles which is estimated to cost $12,00,000 per year to state X.
MARR is 10%. a) Which option should the governor choose (draw the complete decision tree)? b) What is the risk of choosing the third option measured by its standard deviation? c) If pretesting the third option is available to remove the uncertainty completely today, before any selection is made and any cost is dispersed, would the governor pay for this test? What is the maximum amount that she would pay?