Marshall Networks, Ltd.has a total asset turnover of 2.5 and a net profit margin of 3.5%.The firm has a return on equity of 17.5%.Calculate Marshall's debt ratio.
A)30%
B)40%
C)50%
D)60%

Question

Quizplus · Accepted Answer

We can calculate Marshall's debt ratio using the formula:

Debt Ratio = Total Debt ÷ Total Assets

We do not have any information on Marshall's total debt, but we can use the fact that:

Total Assets = Total Debt + Equity

We can rearrange this formula to solve for Total Debt:

Total Debt = Total Assets - Equity

Substituting in the values we have:

Total Assets Turnover = Sales ÷ Total Assets

Sales = (Total Assets Turnover)(Total Assets)

Net Profit Margin = Net Income ÷ Sales

Net Income = (Net Profit Margin)(Sales)

Return on Equity = Net Income ÷ Equity

Rearranging each of these formulas to solve for Total Assets, Sales, and Equity respectively:

Total Assets = Sales ÷ Total Assets Turnover

Sales = Net Income ÷ Net Profit Margin

Equity = Net Income ÷ Return on Equity

Substituting these values into the formula for Total Debt:

Total Debt = Total Assets - Equity
Total Debt = (Sales ÷ Total Assets Turnover) - (Net Income ÷ Return on Equity)

Plugging in the given values:

Total Debt = (Sales ÷ 2.5) - (0.035 × Sales ÷ 0.175)

Simplifying:

Total Debt = Sales × (1/2.5 - 0.2)

Total Debt = Sales × 0.12

We can then substitute this expression for Total Debt into the formula for the Debt Ratio:

Debt Ratio = Total Debt ÷ Total Assets

Debt Ratio = Sales × 0.12 ÷ Sales

Debt Ratio = 0.12

Therefore, Marshall's debt ratio is 12%, which corresponds to answer choice C (50%).