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? Applicable to Both Firms Firm HD's Data Firm LD's Data Assets $200 Debt ratio 50% Debt ratio 30% EBIT $40 Interest rate 12% Interest rate 10% Tax rate 35%

2.41%

Explanation:

The difference between the two firms' ROEs is shown below:-

Particulars          Firm HD                             Firm LD

Assets $200      Debt ratio 50%            Debt ratio 30%

EBIT $40            Interest rate 12%          Interest rate 10%

Tax rate 35%

Debt                            $100                              $60

Interest                        $12                                  $6

                          ($100 × 12%)                       ($60 × 10%)      

Taxable income         $28                                 $36

                               ($40- $12)                          ($40 - $6)

Net income                $18.2                                $22.1

                       $28 × (1 - 0.35)                     $36 × (1 - 0.35)

Equity                          $100                                $140

                              ($200 - $100)                   ($200 - $60)

ROE                              18.2%                               15.79%

                           ($18.2 ÷ $100)                   ($22.1 ÷ $140)

Taxable income = EBIT - Interest

Net income = Income - Taxable income

Equity = Assets - Debt

ROE = Net income ÷ Equity

Difference in ROE = ROE Firm HD - ROE Firm LD

= 18.2% - 15.79%

= 2.41%

So, for computing the difference between the two firms' ROEs we simply deduct the ROE firm LD from ROE firm HD.

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