Suppose a firm has a net profit margin of 20%, sales of $150 million, assets of $300 million, and owner’s equity of $225 million. If the dividend payout ratio is 10%, what is the firm’s sustainable growth rate?

Question

BlackTom AI · Accepted Answer

First, extract the key financial figures: net profit margin = 20%, sales = $150 million, owner's equity = $225 million, and dividend payout ratio = 10%. 
Next, compute net income: NI = Net Margin × Sales = 0.20 × $150 million = $30 million. 
Then determine the retention ratio (the portion of earnings retained for growth): retention = 1 − payout = 1 − 0.10 = 0.90. 
Now assess profitability relative to equity to get ROE: ROE = Net Income / Shareholders' Equity = $30 million / $225 million = 0.133333... ≈ 13.33%. 
Finally, apply the sustainable growth rate formula: g = ROE × retention = 0.133333... × 0.90 = 0.12, i.e., 12%. 
Option-by-option evaluation:
- 10.43%: This would require a lower ROE or retention than computed; since ROE is ~13.33% and retention is 90%, the product is 12%, not 10.43%. 
- 12.88%: This is close but slightly higher than the calculated 12%; it would imply a marginally higher ROE or retention than given. 
- 12.00%: This matches the calculated sustainable growth rate using the given numbers (ROE ≈ 13.33% and retention 90%). 
- 9.38%: This is substantially lower than the result produced by the standard g = ROE × retention formula with the provided figures, suggesting a smaller ROE or retention than present. 
In summary, the correct approach yields g = 12%, making 12.00% the result that aligns with the data.

Suppose a firm has a net profit margin of 20%, sales of $150 million, assets of $300 million, and owner’s equity of $225 million. If the dividend payout ratio is 10%, what is the firm’s sustainable growth rate?单项选择题

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