Answer to Question #207891 in Financial Math for Amy

Question

A firm faces a 30 percent tax rate and has $500m in assets, currently financed entirely with equity. Equity is worth $100 per share, and book value of equity is equal to market value of equity. Also, let's assume that the firm's expected EBIT is $60m. The firm is considering switching to a 25 percent debt capital structure, and has determined that they would have to pay a 10 percent yield on perpetual debt. How much will ROE change if they switch to the proposed capital structure?

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Multiple Choice

• There will be no change in the firm's ROE.
• The ROE will increase by 0.47 percent.
• The ROE will increase by 1.15 percent.

The ROE will increase by 0.82 percent.

Answer 1

Interest expense$= \$500M X 0.25 X 0.10$

$=\$12.5M$ per year

Net income$= [\$60M - \$12.5M] X (1 - 0.3)$

$= \$47.5M X 0.7$

$= \$33.25M$

Shareholder's equity $= \$500M - (25\% \space of \space \$500M)$

$= \$375M$

New return on equity $=\frac{ Net \space income}{ Shareholder's\space equity}$

$= \frac{\$33.25M}{ \$375M}$

$= 0.088666666 or 8.8666666\%$

Old return on equity$=\frac{\$60M \times (1 - 0.3) }{ \$500M}$

$= \frac{\$49M }{\$500M}$

$= 0.084\space or \space8.4\%$

Change in return on equity = New return on equity - Old return on equity

$= 8.8666666\% - 8.4\%$

$= 0.4666666\%$

The return on equity will increase by$\space 0.47\%.$