A firm wants a sustainable growth rate of 3.38 percent while maintaining a dividend payout ratio of 32 percent and a profit margin of 6 percent. The firm has a capital intensity ratio of 2. What is the debt-equity ratio that is required to achieve the firm's desired rate of growth?

This was a question on a previous quiz. We are now given the explanation of:

Sustainable growth rate = .0338 = [ROE (1 - .32)]/{1 - [ROE (1 - .32)]}

ROE = .04808

ROE = .04808 = .06 (1/2) Equity multiplier

Equity multiplier = 1.60

Debt-equity ratio = 1.60 - 1 = .60times

Firstly, it was my understanding that the Sustainable growth rate is ROE x 0.32 / 1 - ROE x 0.32 .......... the above is different and I don't understand why?

Secondly, the ROE I understand is .06 (profit margin) x total asset turnover x Equity multiplier (1 + debt equity ratio) but how was the total asset turnover of (1/2) found? Maybe explaining the process in a different way than was given to us would help.

Thank you!