The Profit margin that must be achieved is 12.74%.
First step
Return on equity= Growth rate /(1 + Growth rate) Ă— Retention ratio
Return on equity=12.8% / (1 + 12.8%) Ă— (100%-40%)
Return on equity= 0.128/(1 +0.128) Ă— 0.60
Return on equity= 0.128/1.128 Ă— 0.60
Return on equity= 0.128/0.6768Ă—100
Return on equity= 18.91%
Second step
Now the profit margin is:
Profit margin= ROE / Asset turnover Ă— Equity Multiplier
Profit margin= 18.91% / {(1/.94) Ă— 1.4}
Profit margin= 0.1891 / 1.06 Ă— 1.4
Profit margin= 12.74%
Inconclusion the Profit margin that must be achieved is 12.74%.
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