An auto plant that costs $$160$ million to build can produce a line of flex$-$fuel cars that will produce cash flows with a present value of $$250$ million if the line is successful but only $$60$ million if it is unsuccessful. You believe that the probability of success is only about $52\%.$ You will learn whether the line is successful immediately after building the plant.

a$-1$a$-2.$ Would you build the plant?

b$-1.$ Suppose that the plant can be sold for $$90$ million to another automaker if the auto line is not successful.

Calculate the expected NPV$.$

b$-2.$ Would you build the plant?