Assume that it costs $32,000 to build a widget factory and that the current cost of capital is 10%. In addition, we sell only one widget per year, with the first sale occurring in the year in which you build the factory. The current cash flow of a widget is $4,000. While we know the current cash flow for widgets, we are uncertain about the future cash flows.Marketing reports indicate that there is a 50% chance that cash flows will go up to $6,000 next period (and remain there forever), however, there is also a 50% chance that cash flows will go down to $2,000 (and remain there forever).

(a)If you build the factory now, evaluate the project with discounted cash flow analysis, and provide the net present value (NPV) of this investment.

(b) Now suppose that you have the option of waiting one year in order to find out whether the cash flow goes up or down. Two different scenarios can occur. The first possibility with a chance of 50% is that one year from now you are informed that the cash flow goes up $6,000 (and remains there forever). The second possibility with a chance of 50% is that one year from now you are informed that the cash flow goes down to $2,000 (and remains there forever).Calculate the expected NPV of the two scenarios combined.