Percy's has a plowback ratio of 75% and a sustainable growth rate of 6 percent. The capital intensity ratio is 1.4 and the debt-equity ratio is .6. What is the proﬁt margin?

Question

Quizplus · Accepted Answer

The formula for sustainable growth rate is: 
sustainable growth rate = (profit margin x retention ratio) / (1 - (profit margin x retention ratio) x capital intensity ratio)

Given: 
plowback ratio = 75% or retention ratio = 0.75 
sustainable growth rate = 6% 
capital intensity ratio = 1.4 
debt-equity ratio = 0.6

We need to find the profit margin. Rearranging the above formula:

profit margin = (sustainable growth rate x (1 - (profit margin x retention ratio) x capital intensity ratio)) / retention ratio

Substituting the given values:

profit margin = (0.06 x (1 - (profit margin x 0.75) x 1.4)) / 0.75

Multiplying by 0.75 on both sides:

0.75 x profit margin = 0.045 - 0.105 x profit margin

1.105 x profit margin = 0.045

profit margin = 0.045 / 1.105 = 0.0407 or 4.07%

Therefore, the closest answer choice is (C) 6.60%.

Percy's Has a Plowback Ratio of 75% and a Sustainable