Question: This problem I need help to understand. Robotics desires a sustainable growth rate of 9.5 percent while maintaining a 30 percent dividend payout ratio and
This problem I need help to understand. "Robotics desires a sustainable growth rate of 9.5 percent while maintaining a 30 percent dividend payout ratio and a 12 percent profit margin. The company has a capital intensity ratio of .95. What equity multiplier is required to achieve the company's desired rate of growth?" Retention ratio=1-payout ratio =(1-0.3)=0.7 Growth rate=(ROE*Retention ratio)/[1-(ROE*Retention ratio)] 0.095=(ROE*0.7)/[1-0.7ROE] 0.095(1-0.7ROE)=0.7ROE 0.095-0.0665=0.7ROE ROE=0.095/(0.7+0.0665) =0.123939987 capital intensity ratio=Total assets/Sales Total assets=0.95Sales Total assets turnover=Sales/Total assets =(1/0.95) ROE=Total assets turnover*Profit margin* equity multiplier equity multiplier =(0.123939987*0.95)/0.12 =0.98(Approx). I do not understand the solution. Please explain.
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