We are trying to determine the proper capacity level for a new electric car. A unit of capacity gives us the potential to produce one car per year. It costs $10,000 to build a unit of capacity, and the cost is charged equally over the next 5 years. It also costs $400 per year to maintain a unit of capacity (whether or not it is used). Each car sells for $14,000 and incurs a variable production cost of $10,000. The annual demand for the electric car during each of the next 5 years is believed to be normally distributed with mean 500,000 and standard deviation 100,000. The demands during different years are assumed to be independent. Profits are discounted at a 10% annual interest rate. We are working with a 5-year planning horizon. Capacity levels of 300,000, 400,000, 500,000, 600,000, and 700,000 are under consideration.
a. Assuming we are risk neutral, use simulation to find the optimal capacity level.
b. Using the answer to part a, there is a 5% chance that the actual discounted profit will exceed what value?
c. Using the answer to part a, there is a 5% chance that the actual discounted profit will be less than what value?
d. If we are risk averse, how might the optimal capacity level change?