$11\mathrm{.}38$ Paye's Panes manufactures insulated windowpanes. The company's CFO has asked you to assess a

new manufacturing plant she is considering. The initial cost will be $$475,000.$ While for tax purposes the

plant can be depreciated straight$-$line to zero book value over $10$ years, the CFO expects that the firm

will sell the plant at the end of Year $5.$ At that time, the CFO estimates that there is a $20$ percent chance

that the plant can be sold for $$80,000,$ a $30$ percent chance it can be sold for $$70,000,$ and a $50$ percent

chance that it can be sold for $$25,000.$ The initial investment in working capital of $$30,000$ will be

recovered when the machine is sold. Additional revenues from the plant are expected to be $$205,000$

per year, and additional operating costs will be $$73,000$ per year. The firm has a marginal tax rate of $23$

percent and a $9$ percent cost of capital. $($a$)$ What is the NPV of the new plant? $($b$)$ You complete your

analysis and read in the Wall Street Journal that a new process for making insulated window will be

available five years from today. You believe that this will lower the Year $5$ sales price of the plant

dramatically. To the nearest dollar, what is the lowest amount that you can sell the plant for and still

recommend to your CFO that she undertake the investment?