The firms HL and LL are identical except for their debt-to-total-assets ratios a

Question

The firms HL and LL are identical except for their debt-to-total-assets ratios and interest rates on debt. Each has $20 million in assets, earned $4 million before interest and taxes in 2005, and has a 40 percent marginal tax rate. Firm HL, however, has a debt-to-total-assets ratio (D/TA) of 50 percent and pays 12 percent interest on its debt, whereas LL has a 30 percent debt-to-total-assets ratio and pays only 10 percent interest on debt.

a. Calculate the rate of return on equity (net income/equity) for each firm. (1.5%)

Explanation / Answer

According to the given information,

Assets = $20 million

EBIT = $4 million

tax rate = 40%

Debt -to-total assets for HL = 50%

Interest rate = 12%

Debt -to-total assets for LL = 30%

Interest rate = 10%

Calculating the return on equity for HL:

Return on equity = Net income / Total equity

First, we have to calculate Net income using EBIT.

Interst rate should be calculated on the total value of debt. The value of debt for HL is calculated as

Debt-to-total assets = Total value of debt / Total assets

                      50% = Total value of debt / $20,000,000

Total value of debt = 50% * $20,000,000

                            = $10,000,000

Therefore, the total value of debt for HL is $10,000,000

The value of debt for LL is calculated as

Debt-to-total assets = Total value of debt / Total assets

                      30% = Total value of debt / $20,000,000

Total value of debt = 30% * $20,000,000

                            = $6,000,000

Therefore, the total value of debt for LL is $6,000,000

Interest amount for HL = 12% ($10,000,000)

                                   = $1,200,000

Interest amount for LL = 10% ($6,000,000)

                                   = $600,000

Therefore, the net income for HL is $1,680,000

Equity for HL = Assets - debt

                    = $20,000,000 - $10,000,000

                    = $10,000,000

Equity for LL = Assets - Debt

                    = $20,000,000 - $6,000,000

                    = $14,000,000

ROE for HL = $1,680,000 / $10,000,000

                  = 0.168 or 16.8%

ROE for LL = $2,040,000 / $14,000,000

                 = 0.1457or 14.57%

Income statement Dollars EBIT $4,000,000 (-) Interest rate@12% $1,200,000 Earnings before taxes $2,800,000 (-)Taxes @ 40% $1,120,000 Net income $1,680,000

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