Question

A firm wishes to maintain an internal growth rate of 9.6 percent and a dividend payout ratio of 43 percent. The current profit margin is 7.7 percent, and the firm uses no external financing sources.

What must total asset turnover be?

Answer 1

Solution-

Interrnal growth rate (IGR) = 9.60%
Dividend payout ratio = 43%
Retention Ratio (b) = 1 - Dividend payout ratio
Retention Ratio (b) = 1 - 0.43
Retention Ratio (b)= 0.57
IGR = [Return on assets(ROA) * b] / [1 - (Return on assets(ROA) * b)]
0.096 = ROA*0.57/ [1 - (0.57*ROA)]

0.096[1-(0.57ROA)]=ROA*0.57

0.096*1-0.096*0.57ROA=0.57ROA
0.096 - 0.05472*ROA = 0.57*ROA

0.096=0.57ROA + 0.05472ROA
0.096= 0.62472*ROA
Return on assets(ROA)= 0.096/0.62472 = 15.37%
ROA = Profit Margin * Total Asset Turnover
0.1537 = 0.077 * Total Asset Turnover
Total Asset Turnover = 1.9961 times
So, Total Asset Turnover is 2 times (approx)