Understanding the optimal capital structure

Review this situation: Universal Exports Inc. is trying to identify its optimal capital structure. Universal Exports Inc. has gathered the following financial information to help with the analysis.

Debt Ratio

Equity Ratio

EPS

DPS

Stock Price

$30\%70\%1\mathrm{.}550\mathrm{.}3422\mathrm{.}35$

$40\%60\%1\mathrm{.}670\mathrm{.}4524\mathrm{.}56$

$50\%50\%1\mathrm{.}720\mathrm{.}5125\mathrm{.}78$

$60\%40\%1\mathrm{.}780\mathrm{.}5727\mathrm{.}75$

$70\%30\%1\mathrm{.}840\mathrm{.}6226\mathrm{.}42$

Which capital structure shown in the preceding table is Universal Exports Inc.$$s optimal capital structure?

a$-$ Debt ratio $=30\%$; equity ratio $=70\%$ b$-$ Debt ratio $=70\%$; equity ratio $=30\%$

Debt ratio $=50\%$; equity ratio $=50\%$

Debt ratio $=40\%$; equity ratio $=60\%$

Debt ratio $=60\%$; equity ratio $=40\%$

Consider this case:

Globex Corp. currently has a capital structure consisting of $30\%$ debt and $70\%$ equity. However, Globex Corp.$$s CFO has suggested that the firm increase its debt ratio to $50\%.$ The current risk$-$free rate is $3\mathrm{.}5\%,$ the market risk premium is $8\%,$ and Globex Corp.$$s beta is $1\mathrm{.}15.$

If the firm$$s tax rate is $25\%,$ what will be the beta of an all$-$equity firm if its operations were exactly the same?

Now consider the case of another company:

US Robotics Inc. has a current capital structure of $30\%$ debt and $70\%$ equity. Its current before$-$tax cost of debt is $10\%,$ and its tax rate is $25\%.$ It currently has a levered beta of $1\mathrm{.}15.$ The risk$-$free rate is $3\mathrm{.}5\%,$ and the risk premium on the market is $8\%.$ US Robotics Inc. is considering changing its capital structure to $60\%$ debt and $40\%$ equity. Increasing the firm$$s level of debt will cause its before$-$tax cost of debt to increase to $12\%.$

First, solve for US Robotics Inc.$$s unlevered beta.

Use US Robotics Inc.$$s unlevered beta to solve for the firm$$s levered beta with the new capital structure.

Use US Robotics Inc.$$s levered beta under the new capital structure, to solve for its cost of equity under the new capital structure.

What will the firm$$s weighted average cost of capital $($WACC$)$ be if it makes this change in its capital structure?

$8\mathrm{.}89\%$

$12\mathrm{.}70\%$

$10\mathrm{.}16\%$

$10\mathrm{.}80\%$