Natsam Corporation has $$285$ million of excess cash. The firm has no debt and $494$ million shares outstanding with a current market price of $$20$ per share.$$ Natsam's board has decided to pay out this cash as a$$ one$-$time dividend.

a$.$ What is the$$ ex$-$dividend price of a share in a perfect capital$$ market?

b$.$ If the board instead decided to use the cash to do a$$ one$-$time share$$ repurchase, in a perfect capital$$ market, what is the price of the shares once the repurchase is$$ complete?

c$.$ In a perfect capital$$ market, which policy in part $($a$)$ or $($b$)$ makes investors in the firm better$$ off?