Question

A firm wishes to maintain an internal growth rate of 9.3 percent and a dividend payout ratio of 39 percent. The current profit margin is 6.4 percent, and the firm uses no external financing sources. What must total asset turnover be?

Answer 1

Solution:
	Total asset turnover =2.18 times
Working Notes:
	Retention ratio (b) = 1- payout ratio
	b= 1-0.39 = 0.61
	b=61%
	Internal growth rate = (ROA x b) /(1-(ROA x b))
	Retention ratio (b) =61% = 0.61
	ROA (Return on Assets)=??
	Internal growth rate=9.3%=0.093
	Internal growth rate = (ROA x b) /(1-(ROA x b))
	0.093 = (ROA x 0.61)/(1-(ROAx0.61))
	0.093 (1-(ROA x 0.61)) = ROA x 0.61
	0.093 - ROA x 0.61 x 0.093 = ROA x0.61
	0.093 = 0.61 x ROA + 0.05673 x ROA
	ROA = 0.093/(0.61+0.05673)
	ROA = 0.093/0.66673
	ROA = 0.13948674875
	ROA = Profit margin x Total assets turnover
	0.13948674875 = 0.064 x Total assets turnover
	Total assets turnover = 0.13948674875/0.064
	Total assets turnover = 2.179480449
	Total assets turnover = 2.18 times
Please feel free to ask if anything about above solution in comment section of the question.