Which of the following statements is false?

a$)$ The $$bird$-$in$-$the$-$hand$$ theory suggests that a $100\%$ payout ratio is optimal.

b$)$ The dividend irrelevance theory is based upon the concept that the free cash flow that a firm can produce for its equity shareholders is the basis upon which the common shares are valued, whether or not that cash is paid to the investors in the form of dividends.

c$)$ The tax preference theory suggests that low payout ratios are optimal.

d$)$ The signaling effect theory says that the value of a firm is not likely to be affected by the decision of the Board of Directors to increase the dividend.