Question

Ramble On Co. wishes to maintain a growth rate of 11.4 percent per year, a debt-equity ratio of 1.5, and a dividend payout ratio of 30 percent. The ratio of total assets to sales is constant at .87.

What profit margin must the firm achieve? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

SGR = ROE x R / (1 - ROE x R)

Where SGR = Sustainable growth rate = 11.4%

R = Retention ratio = 1 - DPR = 1 - 30% = 70%

Hence, 11.4% = ROE x 70% / (1 - ROE x 70%)

Hence, ROE = 11.4% / (70% + 11.4% x 70%) = 14.62%

Also, ROE = Profit margin x Sales to total assets ratio x (1 + D/E)

Or, 14.62% = Profit margin x 1/0.87 x (1 + 1.5)

Hence, Profirt margin = 5.09%