A company is trying to determine the proper capacity level for its new electric car. A unit of capacity provides 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 five 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 five years is believed to be normally distributed with mean 50,000 and standard deviation 10,000. The demands during different years are assumed to be independent. Profits are discounted at a 10% annual interest rate. The company is working with a five-year planning horizon.
Capacity levels of 30,000, 40,000, 50,000, 60,000, and 70,000 are under consideration. You can assume that the company never produces more than demand, so there is never any inventory to carry over from year to year.
a. Assuming that the company is 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, and there is a 5% chance that the actual discounted profit will be less than what value?
c. If the company is risk averse, how might the optimal capacity level change?