1. As per Modigliani and Miller's perfect world - A lower dividend payout doesn't reduce company's cost of capital.

2. However, as per the Dividend capitalization model (Cost of Equity = (Dividend per Share/ Current Market Value of Stock) + Growth Rate of Dividend), the cost of equity goes down if dividend is lowered (since dividend is at numerator in this formula).

In this formula, there is no tax or agency cost considered. Isn't there a contradiction between #1 and #2?

Is there a list of steps available by Modigliani and Miller that indicates that lower dividend payout doesn't reduce company's cost of capital.