12.5. Widget production and sales take place over a oneyear cycle. For simplicity, assume that all costs

(revenues) are paid (received) at the end of the one-year cycle.
A factory with a life of three years (from today)
has a capacity to produce 1 million widgets each year (which are to be sold at the end of each year of production). Widgets produced within the last year have just been sold.
Each year, production costs can either rise or decline by 50 percent from the previous year’s cost. Over the coming year, widgets will be produced at a cost of $2 per widget. Unlike production costs, which vary from year to year, the revenue from selling widgets is stable. Assume that in the coming year and in all future years the widget selling price is $4 per widget.
The performance of a portfolio of stocks in the widget industry depends entirely on expected future production costs. When widget production costs increase by 50 percent from date t to date t 1, the return on the industry portfolio over the same interval of time is assumed to be 30 percent. If the production costs decline by 50 percent, the industry portfolio return is assumed to be 40 percent over that time period.
Assume that the factory producing the widgets is to be closed down and sold for its salvage value whenever the cost of extraction per widget exceeds the selling price of a widget. This closure occurs at the beginning of the production year.
Value the factory, assuming that its salvage value is zero and that the risk-free return is 12 percent per year.