Final answer:
The sustainable growth rate for a company can be calculated by multiplying the return on equity (ROE) by the retention rate (1 - dividend payout ratio). With a profit margin of 6%, total asset turnover of 1.4, equity multiplier of 1.5, and dividend payout ratio of 32%, the sustainable growth rate calculation yields an answer of 8.568%, which is not among the provided options.
Step-by-step explanation:
The question involves calculating the sustainable growth rate for the Green Giant company using the given financial ratios. The formula for the sustainable growth rate is the return on equity (ROE) multiplied by the retention rate (which is 1 minus the dividend payout ratio). The ROE itself can be calculated from the profit margin, the total asset turnover, and the equity multiplier by the relation ROE = Profit Margin × Total Asset Turnover × Equity Multiplier. Using the given data:
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- Profit Margin = 6%
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- Total Asset Turnover = 1.4 times
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- Equity Multiplier = 1.5 times
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- Dividend Payout Ratio = 32%
First, we find the ROE:
ROE = Profit Margin × Total Asset Turnover × Equity Multiplier = 0.06 × 1.4 × 1.5 = 0.126 or 12.6%
Then, we calculate the retention rate:
Retention Rate = 1 - Dividend Payout Ratio = 1 - 0.32 = 0.68 or 68%
Finally, the sustainable growth rate (SGR) is:
SGR = ROE × Retention Rate = 0.126 × 0.68 = 0.08568 or 8.568%
Since this value is not listed in the multiple-choice options, we might need to recheck our calculations or consider that the values given were not the same as those used to calculate the choices provided.