You have the opportunity to purchase a facility that manufactures laptops. If you purchase this facility,

you expect to sell $2$M laptops per year for the next $10$ years. The profit per laptop is $$250,$ and the annual

fixed cost of operating the facility is $$150$M$.$ After $10$ years, there is a $50\%$ probability that you will sell

$0\mathrm{.}25$M laptops per year in perpetuity starting at t$=11,$ and a $50\%$ probability that you will sell $2\mathrm{.}5$M laptops

per year in perpetuity starting at t$=11.$ The profit per laptop and annual fixed cost of operating the facility

always remain the same. The purchase price of the facility is $$1,800$M$.$ Assume a discount rate of $12\mathrm{.}5\%.$

a$)$ What is the NPV of the facility?

Assume that in exactly ten years $($t$=10),$ you learn whether you will sell $0\mathrm{.}25$M or $2\mathrm{.}5$M laptops per year in

perpetuity $($from t$=11$ onward$).$ You now have the option to abandon the facility at t$=10$ after learning

how many laptops you will sell going forward. Abandoning the facility means that you get a payoff of zero.

b$)$ Calculate the present value at t$=10$ of future cash flows if you learn that you will sell $0\mathrm{.}25$M laptops

per year going forward, and explain why you would abandon the facility in this case.

c$)$ Calculate the present value at t$=10$ of future cash flows if you learn that you will sell $2\mathrm{.}5$M laptops

per year going forward, and explain why you would not abandon the facility in this case.

d$)$ From the perspective of t$=0,$ calculate the NPV of the facility under the assumptions that you will

abandon the facility at t$=10$ if you learn at t$=10$ that you will sell $0\mathrm{.}25$M laptops per year from t$=11$

onward, and that you will choose at t$=10$ to continue operating the facility if you learn at t$=10$

that you will sell $2\mathrm{.}5$M laptops per year from t$=11$ onward.