$4.$ Determining the optimal capital structureUnderstanding the optimal capital structureReview this situation: Transworld Consortium Corp. is trying to identify its optimal capital structure. Transworld Consortium Corp. has gathered the following financial information to help with the analysis.Debt RatioEquity RatiordrsWACC$30\%70\%6\mathrm{.}02\%9\mathrm{.}40\%9\mathrm{.}71\%40\%60\%6\mathrm{.}75\%9\mathrm{.}750\%9\mathrm{.}55\%50\%50\%7\mathrm{.}15\%10\mathrm{.}60\%10\mathrm{.}02\%60\%40\%7\mathrm{.}55\%11\mathrm{.}30\%10\mathrm{.}78\%70\%30\%8\mathrm{.}24\%12\mathrm{.}80\%11\mathrm{.}45\%$Which capital structure shown in the preceding table is Transworld Consortium Corp.s optimal capital structure?Debt ratio $=40\%$; equity ratio $=60\%$Debt ratio $=30\%$; equity ratio $=70\%$Debt ratio $=60\%$; equity ratio $=40\%$Debt ratio $=70\%$; equity ratio $=30\%$Debt ratio $=50\%$; equity ratio $=50\%$Consider this case:Globo$-$Chem Co$.$ currently has a capital structure consisting of $30\%$ debt and $70\%$ equity. However, Globo$-$Chem Co$.$s CFO has suggested that the firm increase its debt ratio to $50\%.$ The current risk$-$free rate is $3\%,$ the market risk premium is $7\mathrm{.}5\%,$ and Globo$-$Chem Co$.$s beta is $1\mathrm{.}25.$If the firms tax rate is $25\%,$ what will be the beta of an all$-$equity firm if its operations were exactly the same? $$Now consider the case of another company:US Robotics Inc. has a current capital structure of $30\%$ debt and $70\%$ equity. Its current before$-$tax cost of debt is $6\%,$ and its tax rate is $25\%.$ It currently has a levered beta of $1\mathrm{.}25.$ The risk$-$free rate is $3\%,$ and the risk premium on the market is $7\mathrm{.}5\%.$ US Robotics Inc. is considering changing its capital structure to $60\%$ debt and $40\%$ equity. Increasing the firms level of debt will cause its before$-$tax cost of debt to increase to $8\%.$First, solve for US Robotics Inc.s unlevered beta. $$Use US Robotics Inc.s unlevered beta to solve for the firms 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 firms weighted average cost of capital $($WACC$)$ be if it makes this change in its capital structure?$8\mathrm{.}18\%9\mathrm{.}27\%10\mathrm{.}90\%7\mathrm{.}63\%$