Question

Austral & Company has a debt ratio of 0.5, a total assets turnover ratio of 0.25, and a profit margin of 10%. The Board of Directors is unhappy with the current return on equity (ROE), and they think it could be doubled. This could be accomplished (1) by increasing the profit margin to 12% and (2) by increasing debt utilization. Total assets turnover will not change. What new debt ratio, along with the new 12% profit margin, would be required to double the ROE?

Answer 1

CURRENT ROE = Profit margin * Asset turnover * Equity multiplier

                            = 10 * .25 * 2

                            = 5%

**Let Asset be 1 so debt = 1*.50 = .50 .Equity = total asset - total debt

                                  = 1 -.50 = .50

Equity multiplier = Asset /equity

                    = 1 /.50

                    = 2

Now ,Double ROE = 5 * 2 = 10%

10 = 12 * .25 *Equity multiplier

10 = 3 * EM

Equity multiplier = 10 /3 = 3.33

Let equity be 1 so Total asset = 3.33 . Therefore debt = 3.33 - 1 = 2.33

Debt ratio = 2.33/3.33

             = .70

New debt ratio = .70