A company wishes to maintain an internal growth rate of 7.1% and a dividend payout ratio of 25% per year. The ratio of total assets to sales is constant at 0.85. What profit margin must the firm achieve

7.514%

Explanation:

Given that,

Internal growth rate = 7.1%

Dividend payout ratio = 25% per year

Total assets to sales ratio = 0.85

ROA:

= Internal growth rate : [ (1 - payout ratio) (1 + internal growth rate) ]

= 7.1% : [ (1 - 25%) (1 + 7.1%) ]

= 0.071 : (0.75 * 1.071)

= 0.071 : 0.80325

= 8.84%

ROA = Net income : Total assets

Now, we multiply and divide right hand side by sales

ROA = (Net income : sales) : (Total assets : sales)

= (Net income : sales) * (sales : total assets)

8.84% = Profit margin * (1 : 0.85)

Profit margin = 8.84% * 0.85

= 7.514%