Stencil, Inc., wishes to expand its facilities. The company currently has $8$ million shares outstanding and no debt. The stock sells for $$31$ per share, but the book value per share is $$12.$ Net income is currently $$4\mathrm{.}8$ million. The new facility will cost $$45$ million, and it will increase net income by $$820,000.$ Assume a constant price$-$earnings ratio.

a$-1.$ Calculate the new book value per share. $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-2.$ Calculate the new total earnings. $($Do not round intermediate calculations.$)$

a$-3.$ Calculate the new EPS. $($Do not round intermediate calculations and round your answer to $4$ decimal places, e$.$g$.,32\mathrm{.}1616.)$

a$-4.$ Calculate the new stock price. $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

a$-5.$ Calculate the new market$-$to$-$book ratio. $($Do not round intermediate calculations and round your answer to $4$ decimal places, e$.$g$.,32\mathrm{.}1616.)$

b$.$ What would the new net income for the company have to be for the stock price to remain unchanged?