Miller and Modigliani's dividend policy irrelevance theorem suggests that, in perfect markets with certain assumptions $($such as perfect information, no taxes, and no transaction costs$),$ dividend policy does not affect firm value. Investors are indifferent between receiving dividends and capital gains, as they can create their desired cash flow through portfolio adjustments. However, in real$-$world scenarios with imperfections such as taxes, signaling effects, and investor preferences, dividend policy decisions may still have practical implications.

Discuss the factors that might lead real$-$world firms to deviate from the theorem's predictions. How might factors such as taxation, signaling effects, and investor preferences influence a firm's dividend policy decisions, despite the theorem's assertion of dividend irrelevance in perfect markets?"

$(10$ MARKS$)$