$1.$ You possess a small manufacturing facility making $$2$ million annually. Depending on a long$-$ term government contract decision, next year, your revenue could either rise by $20\%$ or drop by $25\%,$ both outcomes having an equal chance, and maintaining that level for the plant's operational duration. Additional costs tally up to $$1\mathrm{.}6$ million per year. You can sell the plant at any time to a large conglomerate for $$5$ million and your cost of capital is $10\%.$ Companies sometimes proceed with capital projects despite their negative NPV$.$ Critically discuss what drives this decision. $(40$ marks$).$