The Mann Company belongs to a risk class for which the appropriate discount rate is $10$ percent. Mann currently has $164,000$ outstanding shares selling at $$130$ each. The firm is contemplating the declaration of a $$5$ 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 $($MM$)$ model, which is discussed in the text.

a$.$ What will the price of the stock be on the ex$-$dividend date if the dividend is declared? $($Omit $ sign in your response.$)$

Price of the stock $

$125$

b$.$ What will the price of the stock be at the end of the year if the dividend is not declared? $($Omit $ sign in your response.$)$

Price of the stock $

$143$

c$.$ If Mann makes $$3\mathrm{.}9$ million of new investments at the beginning of the period, earns net income of $$2\mathrm{.}8$ 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 calculations.$)$

Number of shares to be issued

$15360$

shares

d$.$ Is it realistic to use the MM model in the real world to value stock?