Question

In: Accounting

A firm wishes to maintain an internal growth rate of 9.3 percent and a dividend payout...

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?

Solutions

Expert Solution

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.

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