Vigo Vacations has an equity multiplier of 2.5. The company’s assets are financed with some combination of long-term debt and common equity. What is the company’s debt ratio?
The correct answer and explanation is:
To calculate the debt ratio, we start with the equity multiplier formula: Equity Multiplier=Total AssetsTotal Equity\text{Equity Multiplier} = \frac{\text{Total Assets}}{\text{Total Equity}}
The equity multiplier given is 2.5, so: Total AssetsTotal Equity=2.5\frac{\text{Total Assets}}{\text{Total Equity}} = 2.5
This implies that for every dollar of equity, there are $2.50 of assets. Rewriting this: Total Assets=2.5×Total Equity\text{Total Assets} = 2.5 \times \text{Total Equity}
The relationship between assets, equity, and debt is: Total Assets=Total Equity+Total Debt\text{Total Assets} = \text{Total Equity} + \text{Total Debt}
Substituting Total Assets=2.5×Total Equity\text{Total Assets} = 2.5 \times \text{Total Equity}: 2.5×Total Equity=Total Equity+Total Debt2.5 \times \text{Total Equity} = \text{Total Equity} + \text{Total Debt}
Rearranging to solve for debt in terms of equity: Total Debt=2.5×Total Equity−Total Equity\text{Total Debt} = 2.5 \times \text{Total Equity} – \text{Total Equity} Total Debt=1.5×Total Equity\text{Total Debt} = 1.5 \times \text{Total Equity}
Now, the debt ratio formula is: Debt Ratio=Total DebtTotal Assets\text{Debt Ratio} = \frac{\text{Total Debt}}{\text{Total Assets}}
Substitute Total Debt=1.5×Total Equity\text{Total Debt} = 1.5 \times \text{Total Equity} and Total Assets=2.5×Total Equity\text{Total Assets} = 2.5 \times \text{Total Equity}: Debt Ratio=1.5×Total Equity2.5×Total Equity\text{Debt Ratio} = \frac{1.5 \times \text{Total Equity}}{2.5 \times \text{Total Equity}} Debt Ratio=1.52.5=0.6 or 60%\text{Debt Ratio} = \frac{1.5}{2.5} = 0.6 \, \text{or} \, 60\%
Explanation:
The equity multiplier of 2.5 indicates that the company has $2.50 in assets for every $1.00 of equity. The remaining portion of the assets is financed through debt. By breaking down the relationship between assets, equity, and debt, we determined that 60% of the company’s assets are financed through debt, while the remaining 40% are financed through equity.
The debt ratio of 60% shows that the company relies significantly on debt to finance its operations. A higher debt ratio can indicate greater financial leverage, which may boost returns in good times but also increases risk during downturns.