a firm finances with only debt and common equity, and if its equity multiplier is 3.0, then its debt ratio must be 0.667.

Question

Quizplus · Accepted Answer

The equity multiplier is calculated as:
Equity Multiplier = Total Assets / Total Equity
Since the firm finances with only debt and equity, Total Assets would equal Total Debt + Total Equity. Therefore, we can rearrange the equation to solve for Total Debt:
Total Debt = Equity Multiplier x Total Equity - Total Equity
Simplify the equation by factoring out Total Equity:
Total Debt = Total Equity x (Equity Multiplier - 1)
Substitute in the given equity multiplier of 3.0:
Total Debt = Total Equity x (3.0 - 1) = 2 x Total Equity
The debt ratio is calculated as:
Debt Ratio = Total Debt / Total Assets
Substitute in the equation for Total Debt:
Debt Ratio = (2 x Total Equity) / (Total Equity + 2 x Total Equity) = 2 / 3
Therefore, the debt ratio is 0.667, which means answer A is true.

A Firm Finances with Only Debt and Common Equity, and If