The Mann Company belongs to a risk class for which the appropriate discount rate is $12$ percent. The company currently has $237,000$ outstanding shares selling at $$144$ each. The firm is contemplating the declaration of a $$3$ dividend at the end of the fiscal year that just began. Assume there are no taxes on dividends. Answer the following questions based on the Miller and Modigliani model, which is discussed in the text.

a$.$ What will be the price of the stock on the ex$-$dividend date if the dividend is declared?

$($Do not round intermediate calculations.$)$

b$.$ What will be the price of the stock at the end of the year if the dividend is not declared? $($Do not round intermediate calculations.$)$

c$.$ If the company makes $$6\mathrm{.}2$ million of new investments at the beginning of the period, earns net income of $$3\mathrm{.}6$ million, and pays the dividend at the end of the year, how many shares of new stock must the firm issue to meet its funding needs? $($Do not round intermediate colculations and round your answer to the nearest whole number, e$.$g$.,32.)$

$\backslash$table$[[$a$.$ Price of the stock$],[$b$.$ Price of the stock$],[$c$.$ Number of shares$]]$