Determining the Cost of Capital: Weighted Average Cost of Capital

The firm's target capital structure is the mix of debt, preferred stock, and common equity the firm plans to raise funds for its future projects. The target proportions of debt, preferred stock, and common equity, along with the cost of these components, are used to calculate the firm's weighted average cost of capital $($WACC$).$ If the firm will not have to issue new common stock, then the cost of retained earnings is used in the firm's WACC calculation. However, if the firm will have to issue new common stock, the cost of new common stock should be used in the firm's WACC calculation.

Quantitative Problem: Barton Industries expects that its target capital structure for raising funds in the future for its capital budget will consist of $40\%$ debt, $5\%$ preferred stock, and $55\%$ common equity. Note that the firm's marginal tax rate is $40\%.$ Assume that the firm's cost of debt, rd$,$ is $7\mathrm{.}6\%,$ the firm's cost of preferred stock, rps$,$ is $7\mathrm{.}1\%$ and the firm's cost of equity is $11\mathrm{.}6\%$ for old equity, rs$,$ and $12\mathrm{.}34\%$ for new equity, re$.$ What is the firm's weighted average cost of capital $($WACC$1)$ if it uses retained earnings as its source of common equity? Round your answer to $3$ decimal places. Do not round intermediate calculations.

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What is the firm$$s weighted average cost of capital $($WACC$2)$ if it has to issue new common stock? Round your answer to $3$ decimal places. Do not round intermediate calculations.