The manufacture of polysyllabic acid is a competitive industry. Most plants have an annual output of $270,000$ tons. Operating costs are $$1\mathrm{.}07$ a ton, and the sales price is $$1\mathrm{.}17$ a ton. A $270,000-$ton plant costs $$270,000$ and has an indefinite life. Its current scrap value of $$68,000$ is expected to decline to $$65,900$ over the next two years.

Phlogiston Incorporated proposes to invest $$270,000$ in a plant that employs a new low$-$cost process to manufacture polysyllabic acid. The plant has the same capacity as existing units, but operating costs are $$0\mathrm{.}98$ a ton. Phlogiston estimates that it has two years$$ lead over each of its rivals in use of the process but is unable to build any more plants itself before year $2.$ Also, it believes that demand over the next two years is likely to be sluggish and that its new plant will therefore cause temporary overcapacity.

You can assume that there are no taxes and that the cost of capital is $12\%.$

a$.$By the end of year $2,$ the prospective increase in acid demand will require the construction of several new plants using the Phlogiston process. What is the likely NPV of such plants?

b$.$What does that imply for the price of polysyllabic acid in year $3$ and beyond?

Note: Do not round intermediate calculations. Round your answer to $2$ decimal places.

c$.$Calculate the minimum price at which the existing plant would be scrapped.

Note: Do not round intermediate calculations.

d$.$The acid plants of United Alchemists Incorporated have been fully depreciated. Can it operate them profitably after year $2?$

e$.$ Acidosis Incorporated purchased a new plant last year for $$100,000$ and is writing it down by $$10,000$ a year. Should it scrap this plant in year $2?$

f$.$What would be the NPV of Phlogiston$$s venture?

Note: Do not round intermediate calculations. Round your answer to the nearest whole dollar number.