Calculating the weighted average of the cost of equity

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We find the cost of capital by calculating the weighted average of the cost of equity, debt, and preferred stock.  Different sources of funds have different costs. Debt is almost always cheaper than equity, but using debt increases risk in terms of default risk to lenders and higher earnings volatility for equity investors. Thus using more debt can increase value for some firms and decrease value for others. 

If the firm's objective is the maximization of firm value, how does choosing the financing mix for the firm help management to achieve that?  In other words, what should the financing mix look like? 

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