Since 70 percent of preferred dividends received by a corporation is excluded from taxable income,the component cost of equity for a company that pays half of its earnings out as common dividends and half as preferred dividends should,theoretically,be
Cost of equity = r_s(0.30)(0.50)+ r_s(1 − T)(0.70)(0.50).

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The formula provided seems to be a mix of variables and not a standard formula for calculating the cost of equity. The cost of equity is typically calculated using models such as the Capital Asset Pricing Model (CAPM) or the Dividend Discount Model (DDM), and the tax treatment of dividends (like the 70% exclusion for preferred dividends) affects the cost of debt or the overall cost of capital, not directly the cost of equity in the manner described.

Since 70 Percent of Preferred Dividends Received by a Corporation