Firms HD and LD are identical except for their level of debt and the interest rates they pay on debt⎯HD has more debt and pays a higher interest rate on that debt. Based on the data given below, what is the difference between the two firms' ROEs?

Question

Quizplus · Accepted Answer

ROE = Net Income / Equity
Let's assume that both firms have the same level of assets and operating income.
Since HD has more debt, its equity will be lower compared to LD. Therefore, even if both firms have the same net income, HD's ROE will be higher because the denominator (equity) will be lower. However, HD also pays a higher interest rate on its debt, which will result in lower net income compared to LD.
Let's calculate the ROE for each firm using the given data:
ROE HD = 10 / (50+200) = 4.00%
ROE LD = 8 / (100+200) = 2.67%
The difference between the two ROEs is:
ROE HD - ROE LD = 4.00% - 2.67% = 1.33%
However, we also need to consider the difference in interest expense, which directly affects net income:
Interest expense HD = 200 * 0.11 = $22
Interest expense LD = 200 * 0.08 = $16
The difference in interest expense is:
Interest expense HD - Interest expense LD = $22 - $16 = $6
This means that HD has $6 less in net income compared to LD. To account for this difference, we need to adjust the numerator in the ROE calculation:
ROE HD = (10 - 6) / (50+200) = 1.33% / 25% = 5.32%
Now we can calculate the difference between the adjusted ROEs:
ROE HD - ROE LD = 5.32% - 2.67% = 2.65%
Therefore, the closest answer choice is C) 2.41%.

Firms HD and LD Are Identical Except for Their Level