Firm A and firm B have debt-total asset ratios of 35% and 30% and ROA of 12% and 11%, respectively. Which firm has a greater ROE?
I think that it is firm B since it has more equity financing its assets.
correct!
More Equity means higher denominator. Higher denominator, lower percentage, lower ROE
To determine which firm has a greater Return on Equity (ROE), we need to calculate the ROE for both firms.
The formula for ROE is:
ROE = ROA * Equity Multiplier
The Equity Multiplier is calculated as:
Equity Multiplier = 1 / (1 - Debt-to-Asset Ratio)
Let's calculate the ROE for both Firm A and Firm B:
For Firm A:
Given: Debt-to-Asset Ratio = 35%, ROA = 12%
Equity Multiplier = 1 / (1 - 0.35) = 1 / 0.65 = 1.5385
ROE for Firm A = 0.12 * 1.5385 = 0.1846 or 18.46%
For Firm B:
Given: Debt-to-Asset Ratio = 30%, ROA = 11%
Equity Multiplier = 1 / (1 - 0.30) = 1 / 0.70 = 1.4286
ROE for Firm B = 0.11 * 1.4286 = 0.1571 or 15.71%
Therefore, based on the calculations, Firm A has a greater ROE (18.46%) than Firm B (15.71%).