Ramble On Co. wishes to maintain a growth rate of 13.6 percent per year, a debt-equity ratio of 1.8, and a dividend payout ratio of 30 percent. The ratio of total assets to sales is constant at .98. What profit margin must the firm achieve

5.99%

Explanation:

Based on the question,

Dividend payout ratio = 30%

Therefore, the retention ratio will be:

= 1 - 30%

= 70%

Growth rate = 13.6%

We'll the use the sustainable growth rate formula which will be:

0.136 = (ROE x 0.7)/ (1-(ROE x 0.7))

0.136(1 - (0.7ROE)) = 0.7ROE

ROE = 0.136/0.7952

ROE = 0.171026

Then, the Profit margin will be:

ROE = Profit Margin x Asset Turnover x Equity multiplier

0.171026 = PM x (1/0.98) x (1 + 1.8)

0.171026 = PM x (1/0.98) x 2.8

PM = 0.171026 x 0.98/2.8

PM = 0.0598591

Profit margin = 5.99%