General Auto Corporation $($GAC$)$ is developing a new model of compact car. The car is assumed to generate sales for the next $5$ years. GAC has gathered information about the following quantities through focus groups with marketing and engineering departments:

$$ The fixed cost of manufacturing the cars is $$1\mathrm{.}9$ billion. The fixed cost is incurred at the beginning of year $1,$ before any sales are recorded.

$$ Margin per car: This is the unit selling price minus the variable cost of producing a car. GAC assumes that in year $1$ the margin will be $$5000.$ Every other year the margin will decrease by $4\%.$

$$ The demand for the car is uncertain. GAC assumes that the demand for the cars is normally distributed with mean $140,000$ and standard deviation $30,000.$ Every year after that sales decreases by $5\%$ of the sales made in the previous year.

$$ The discount rate is $15\%.$

Using a simulation model help GAC evaluate the NPV of the cash flows for this new car over the $5-$year horizon.