Firm's HL and LL are identical except for their leverage ratios and the interest rates they pay on debt. Each has $20 million in assets, $4 million of EBIT, and is in the 40 percent federal-plus-state tax bracket. Firm HL, however, has debt ratio (D/A) of 50 percent and pays 12 percent interest on its debt, whereas LL has a 30 percent debt ratio and pays only 10 percent interest on its debt. Calculate the rate of return on equity (ROE) for HL.

16.8%

Explanation:

The computation of the rate of return on equity for HL is shown below:-

Return on Equity  = Net income ÷ Total equity

Computation of the total debt and equity for HL firm using debt ratio

For HL:

Debt ratio = Total debt ÷ Total assets

0.50 = Total debt ÷ $20,000,000

Total debt = $10,000,000

Total equity = Total assets - Total debt

$20,000,000 - $10,000,000  

= $10,000,000

Interest expense = 12% on debt

= 12% × $10,000,000

= $1,200,000

Calculate the net income for HL firm:-

Earning before interest and tax   $4,000,000

Less: Interest expense                  $1,200,000

Earning before tax                         $2,800,000

Less: Taxes at 40%                         $1,120,000

Net income                                     $1,680,000

Substitute the values in ROE formula for HL firm:

Return on Equity = Net income ÷ Total equity

$1,680,000 ÷ $10,000,000

= 0.168

or 16.8%