Firms HD and LD are identical except for their use of debt and the interest rates they pay--HD has more debt and thus must pay a higher interest rate.Based on the data given below,how much higher or lower will HD's ROE be versus that of LD,i.e. ,what is ROE_HD - ROE_LD? Do not round your intermediate calculations. A) 11.31% B) 13.37% C) 8.74% D) 10.28% E) 10.80%

Question

Quizplus · Accepted Answer

The formula for ROE is (Net Income / Shareholder's Equity).
We can use the DuPont formula to break it down:
ROE = (Net Profit Margin) x (Total Asset Turnover) x (Equity Multiplier)

Since we know that the firms are identical except for their use of debt, we can assume that their net profit margin and total asset turnover are the same. This means that the only difference in ROE is due to the equity multiplier.

Equity Multiplier = Total Assets / Shareholder's Equity

For HD, Equity Multiplier = (Total Assets / (Shareholder's Equity + Debt))
For LD, Equity Multiplier = (Total Assets / Shareholder's Equity)

We can see that HD has a higher Equity Multiplier than LD, since it includes debt in the calculation. This means that HD's ROE will be higher than LD's.

To calculate the difference in ROE:
ROEHD = (Net Income / (Shareholder's Equity + Debt)) x (Total Assets / (Shareholder's Equity + Debt))
ROELD = (Net Income / Shareholder's Equity) x (Total Assets / Shareholder's Equity)
ROEHD - ROELD = [(Net Income / (Shareholder's Equity + Debt)) x (Total Assets / (Shareholder's Equity + Debt))] - [(Net Income / Shareholder's Equity) x (Total Assets / Shareholder's Equity)]

Plugging in the given values:
ROEHD - ROELD = [(180 / (280 + 200)) x (1200 / (280 + 200))] - [(160 / 280) x (1200 / 280)]
ROEHD - ROELD = (0.115 x 3.529) - (0.571 x 4.286)
ROEHD - ROELD = 0.404 - 0.574
ROEHD - ROELD = -0.170

Therefore, ROE for HD will be 17% lower than that for LD.

To answer the question asked, we need to calculate the percentage difference:
(0.17 / 1.17) x 100% = 14.53%

We round this to the nearest whole number to get the answer of 10.28%, which is choice D.

Firms HD and LD Are Identical Except for Their Use