Question

Firm A and Firm B have debt-total assets ratios of 65 percent and 45 percent, respectively, and returns on total assets of 5% and 7%, respectively. Which firm has a greater return on equity

Answer 1

Answer:

Firm A

Step-by-step explanation:

D = Debt

A= Asset

E = Equity

ROA = Return on assets

ROE = Return on equity

For Firm A:

$\frac{D}{A}=0.65\\\frac{E}{A}=1-0.65=0.35\\ROA = 0.05\\ROE=\frac{ROE}{\frac{E}{A}}=\frac{0.05}{0.35} \\ROE=0.1429=14.29\%$

For Firm B:

$\frac{D}{A}=0.45\\\frac{E}{A}=1-0.45=0.55\\ROA = 0.07\\ROE=\frac{ROE}{\frac{E}{A}}=\frac{0.07}{0.55} \\ROE=0.1273=12.73\%$

Therefore, Firm A has a greater return on equity.