Question

A firm wants a sustainable growth rate of 3.33 percent while maintaining a 31 percent dividend...

A firm wants a sustainable growth rate of 3.33 percent while maintaining a 31 percent dividend payout ratio and a profit margin of 5 percent. The firm has a capital intensity ratio of 2. What is the debt-equity ratio that is required to achieve the firm's desired rate of growth?

Sustainable Growth Rate = 3.33%
Dividend payout ratio = 31%

Retention Ratio, b = 100% - Dividend payout ratio
Retention Ratio, b = 100% - 31%
Retention Ratio, b = 69%

Sustainable Growth Rate = [ROE * b] / [1 - ROE * b]
0.0333 = [ROE * 0.69] / [1 - ROE * 0.69]
0.0333 - ROE * 0.0230 = ROE * 0.69
0.0333 = ROE * 0.713
ROE = 0.0467
ROE = 4.67%

ROE = Profit Margin * (1 / Capital intensity ratio) * Equity Multiplier
0.0467 = 0.05 * (1 / 2) * Equity Multiplier
Equity Multiplier = 1.868

Debt-equity Ratio = 1 - Equity Multiplier
Debt-equity Ratio = 1 - 1.868
Debt-equity Ratio = 0.868 or 0.87

So, required debt-equity ratio is 0.87 in order to achieve the desired rate of growth.