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Gates Appliances has a return-on-assets (investment) ratio of 13 percent. a. If the debt-to-total-assets ratio is 25 percent, what is the return on equity? (Input your answer as a percent rounded to 2 decimal places.) b. If the firm had no debt, what would the return-on-equity ratio be? (Input your answer as a percent rounded to 2 decimal places.)

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Answer:

a. Return on Equity refers to how much income the company earned per dollar of investment. One formula for the Return on Equity is;

Return on Equity = Return on Assets * [tex]\frac{Total Assets}{ 1 - ( Debt/Assets)}[/tex]

Assuming assets are $1 this can be calculated by;

= 13% * [tex]\frac{1}{1 - 0.25}[/tex]

= 17.33%

b. If there is no debt then the Return on Investment will be the same as the return on Equity. However, proving it with the formula gives;

Return on Equity = Return on Assets * [tex]\frac{Total Assets}{ 1 - ( Debt/Assets)}[/tex]

= 13% * [tex]\frac{1}{1 -0}[/tex]

= 13%

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