A firm wishes to maintain an internal growth rate of 4.5 percent and a dividend payout ratio of 60 percent. The current profit margin is 7.5 percent and the firm uses no external financing sources. What must the total asset turnover be?
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A firm wishes to maintain an internal growth rate of 4.5 percent and a dividend payout ratio of 60 percent. The current profit margin is 7.5 percent and the firm uses no external financing sources. What must the total asset turnover be?
To find the total asset turnover, we can use the internal growth rate formula:
Internal Growth Rate = (Return on Assets) x (Retention Ratio)
Given that the firm wants to maintain an internal growth rate of 4.5% and a dividend payout ratio of 60%, we can calculate the retention ratio:
Retention Ratio = 1 - Dividend Payout Ratio = 1 - 0.60 = 0.40
Now we need to calculate the return on assets:
Return on Assets = Profit Margin x Total Asset Turnover
Given that the profit margin is 7.5% and the retention ratio is 0.40, we can substitute these values into the internal growth rate formula:
4.5% = (7.5%) x Total Asset Turnover x (0.40)
Now we can solve for Total Asset Turnover:
Total Asset Turnover = (4.5% / (7.5% x 0.40))
Total Asset Turnover = 0.6
Therefore, the total asset turnover must be 0.6.
To find the total asset turnover, we will use the formula:
Total Asset Turnover = Internal Growth Rate / (1 - Dividend Payout Ratio)
Given:
Internal Growth Rate = 4.5%
Dividend Payout Ratio = 60%
First, we need to convert the percentages into decimal form by dividing them by 100:
Internal Growth Rate = 4.5% / 100 = 0.045
Dividend Payout Ratio = 60% / 100 = 0.6
Now we can substitute these values into the formula:
Total Asset Turnover = 0.045 / (1 - 0.6)
Next, subtract the dividend payout ratio from 1:
Total Asset Turnover = 0.045 / 0.4
Finally, divide the internal growth rate by the result:
Total Asset Turnover = 0.1125
Therefore, the total asset turnover must be 0.1125 (or 11.25%) for the firm to maintain an internal growth rate of 4.5% and a dividend payout ratio of 60%.