You work for the CEO of a new company that plans to manufacture and sell a new product,a watch that has an embedded TV set and a magnifying glass crystal.The issue now is how to finance the company,with only equity or with a mix of debt and equity.Expected operating income is $510,000.Other data for the firm are shown below.How much higher or lower will the firm's expected ROE be if it uses some debt rather than all equity,i.e. ,what is ROE_L - ROE_U? Do not round your intermediate calculations. $\begin{array}{lrr}&0 \% \text { Debt, U }&60 \% \text { Debt, L }\\\hline\text { Oper income (EB IT) } & \$ 510,000 & \$ 510,000 \\\text { Required investment } & \$ 2,500,000 & \$ 2,500,000 \\\% \text { Debt } & 0.0 \% & 600.0 \% \\\$ \text { of Debt } & \$ 0.00 & \$ 1,500,000 \\\$ \text { of Common equity } & \$ 2,500,000 & \$ 1,000,000 \\\text { Interest rate } & \mathrm{NA} & 10.00 \% \\\text { Tax rate } & 35 \% & 35 \%\end{array}$
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Question

You work for the CEO of a new company that plans to manufacture and sell a new product,a watch that has an embedded TV set and a magnifying glass crystal.The issue now is how to finance the company,with only equity or with a mix of debt and equity.Expected operating income is $510,000.Other data for the firm are shown below.How much higher or lower will the firm's expected ROE be if it uses some debt rather than all equity,i.e. ,what is ROE_L - ROE_U? Do not round your intermediate calculations.

\begin{array}{lrr}&0 \% \text { Debt, U }&60 \% \text { Debt, L }\\\hline\text { Oper income (EB IT) } & \$ 510,000 & \$ 510,000 \\\text { Required investment } & \$ 2,500,000 & \$ 2,500,000 \\\% \text { Debt } & 0.0 \% & 600.0 \% \\\$ \text { of Debt } & \$ 0.00 & \$ 1,500,000 \\\$ \text { of Common equity } & \$ 2,500,000 & \$ 1,000,000 \\\text { Interest rate } & \mathrm{NA} & 10.00 \% \\\text { Tax rate } & 35 \% & 35 \%\end{array}

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Quizplus · Accepted Answer

To calculate the difference in Return on Equity (ROE) between using some debt (leveraged, L) versus using all equity (unleveraged, U), we first need to calculate the ROE for both scenarios.For the unleveraged scenario (U):$$ \text{ROE}_U = \frac{\text{Net Income}}{\text{Equity}} $$Since there's no debt, the entire operating income is available to equity holders after taxes:$$ \text{Net Income}_U = \text{EBIT} \times (1 - \text{Tax Rate}) = \$510,000 \times (1 - 0.35) = \$331,500 $$$$ \text{ROE}_U = \frac{\$331,500}{\$2,500,000} = 0.1326 \text{ or } 13.26\% $$For the leveraged scenario (L):$$ \text{ROE}_L = \frac{\text{Net Income}}{\text{Equity}} $$First, calculate the interest expense and then the net income:$$ \text{Interest Expense} = \$1,500,000 \times 0.10 = \$150,000 $$$$ \text{Net Income}_L = (\text{EBIT} - \text{Interest Expense}) \times (1 - \text{Tax Rate}) $$$$ \text{Net Income}_L = (\$510,000 - \$150,000) \times (1 - 0.35) = \$234,000 $$$$ \text{ROE}_L = \frac{\$234,000}{\$1,000,000} = 0.234 \text{ or } 23.4\% $$The difference in ROE between using some debt versus all equity:$$ \text{ROE}_L - \text{ROE}_U = 23.4\% - 13.26\% = 10.14\% $$

You Work for the CEO of a New Company That