ABC’s return on equity is above the industry average. At the same time, both its profit margin
and its debt ratio are below the industry average. Which of the following statements is
CORRECT?
Its total assets turnover must be above the industry average.
Its return on assets must equal the industry average.
Its TIE ratio must be below the industry average.
Its total assets turnover must be below the industry average.
Its total assets turnover must equal the industry average.
Its total assets turnover must be above the industry average.
Its return on assets must equal the industry average.
Its TIE ratio must be below the industry average.
Its total assets turnover must be below the industry average.
Its total assets turnover must equal the industry average.
Solution
According to Dupont Analysis
Return on Equity, ROE = Profit Margin (Profit/Sales) * Total Asset Turnover (Sales/Assets) *
Equity Multiplier (Assets/Equity)
Equity Multiplier, EM = (Debt(D) + Equity(E))/ Equity(E)
(as Asset(A) = D+E)
EM =1 + D/E => D/E = EM - 1
Debt Ratio(DR) = D/A => 1/DR = A/D = (D+E)/D = 1 + E/D = 1 + 1/(D/E) = 1 + 1/(EM-1)
1/DR = (EM -1 + 1)/(EM-1) = EM/(EM-1) => DR = (EM-1)/EM
So EM = 1/(1-DR)
So ROE = Profit Margin(PM) * Total Asset Turnover * 1/(1-DR)
So Total Asset Turnover = ROE/(PM * 1/(1-DR)) = ROE*(1-DR)/PM
So Total Asset Turnover will increase if ROE is high; DR is low & PM is low which is the case
in this question
So Option 1 is correct..
ABC’s return on equity is above the industry average. At the same ti.pdf
1. ABC’s return on equity is above the industry average. At the same time, both its profit margin
and its debt ratio are below the industry average. Which of the following statements is
CORRECT?
Its total assets turnover must be above the industry average.
Its return on assets must equal the industry average.
Its TIE ratio must be below the industry average.
Its total assets turnover must be below the industry average.
Its total assets turnover must equal the industry average.
Its total assets turnover must be above the industry average.
Its return on assets must equal the industry average.
Its TIE ratio must be below the industry average.
Its total assets turnover must be below the industry average.
Its total assets turnover must equal the industry average.
Solution
According to Dupont Analysis
Return on Equity, ROE = Profit Margin (Profit/Sales) * Total Asset Turnover (Sales/Assets) *
Equity Multiplier (Assets/Equity)
Equity Multiplier, EM = (Debt(D) + Equity(E))/ Equity(E)
(as Asset(A) = D+E)
EM =1 + D/E => D/E = EM - 1
Debt Ratio(DR) = D/A => 1/DR = A/D = (D+E)/D = 1 + E/D = 1 + 1/(D/E) = 1 + 1/(EM-1)
1/DR = (EM -1 + 1)/(EM-1) = EM/(EM-1) => DR = (EM-1)/EM
So EM = 1/(1-DR)
So ROE = Profit Margin(PM) * Total Asset Turnover * 1/(1-DR)
So Total Asset Turnover = ROE/(PM * 1/(1-DR)) = ROE*(1-DR)/PM
So Total Asset Turnover will increase if ROE is high; DR is low & PM is low which is the case
in this question
So Option 1 is correct.
