Understanding the optimal capital structure Review 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 Ratio Equity Ratio rd rs WACC

$30\%70\%6\mathrm{.}02\%9\mathrm{.}40\%9\mathrm{.}71\%$

$40\%60\%6\mathrm{.}75\%9\mathrm{.}750\%9\mathrm{.}55\%$

$50\%50\%7\mathrm{.}15\%10\mathrm{.}60\%10\mathrm{.}02\%$

$60\%40\%7\mathrm{.}55\%11\mathrm{.}30\%10\mathrm{.}78\%$

$70\%30\%8\mathrm{.}24\%12\mathrm{.}80\%11\mathrm{.}45\%$

Which capital structure shown in the preceding table is Transworld Consortium Corp.$$s optimal capital structure?

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

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

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

Debt ratio $=70\%$; equity ratio $=30\%$

Debt ratio $=30\%$; equity ratio $=70\%$

Consider this case: Globo$-$Chem Co$.$ has a capital structure that consists of $30\%$ debt and $70\%$ equity. The firm$$s current beta is $1\mathrm{.}25,$ but management wants to understand Globo$-$Chem Co$.$s market risk without the effect of leverage.

If Globo$-$Chem Co$.$ has a $25\%$ tax rate, what is its unlevered beta? $1\mathrm{.}05$

$1\mathrm{.}09$

$0\mathrm{.}95$

$0\mathrm{.}86$

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 $3\mathrm{.}5\%,$ 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 firm$$s 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.$$s unlevered beta to solve for the firm$$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?

$7\mathrm{.}77\%$

$9\mathrm{.}43\%$

$10\mathrm{.}55\%$

$11\mathrm{.}10\%$