Question

company ABC has a profit margin of 8.5% a capital intensity ratio of .8, debt equity ratio of .6 net income of $31,000 in dividends paid to $15,810 what is a sustainable rate of growth

9.94 percent

9.58

9.42

9.09

9.93

Answer 1

Solution:
	Answer is 4th option 9.09 percent
Working Notes:
Notes:	We compute sustainable growth rate with below formula
	Sustainable growth rate = (ROE × b) / [1 – (ROE × b)]
	Where b = retention ratio
	ROE = return on Equity
	We will get b retention ratio with below formula
	b= retention ratio = 1 - (dividend/net income)
	Using the DuPont identity to calculate ROE
	Return on Equity (ROE) = (Profit margin)(total asset turnover)(Equity multiplier)
	Where
	Profit margin = 8.5% already given
	Total asset turnover =(1/capital intensity ratio)
	Equity multiplier = 1+ debt equity ratio
So	Now will compute the sustainable growth rate
	b= retention ratio = 1 - (dividend/net income)
	b= retention ratio = 1 - (15810/31000)
	b= retention ratio = 0.49
	Return on Equity (ROE) = (Profit margin)(total asset turnover)(Equity multiplier)
	= (Profit margin)(total asset turnover)(Equity multiplier)
	= (Profit margin)(1/capital intensity ratio)(1+ debt equity ratio)
	= (8.5%) x (1/0.8) x (1+ 0.6)
	=0.17
	=17%
At last	Sustainable growth rate = (ROE x b) / (1 - (ROE x b))
	Sustainable growth rate = (0.17 x 0.49) / (1 - (0.17 x 0.49))
	Sustainable growth rate =0.090869423
	Sustainable growth rate =9.0869423%
	Sustainable growth rate =9.09%
Please feel free to ask if anything about above solution in comment section of the question.