A firm wishes to maintain an internal growth rate of 9 percent and a dividend payout ratio of 66 percent. The ratio of total assets to sales is constant at 1, and the profit margin is 8.1 percent. If the firm also wishes to maintain a constant debt-equity ratio, what must it be

the constant debt-equity ratio is 2.580

Explanation:

Given:

dividend payout ratio of 66 percent= 0.66

Sustainable Growth rate of 9 percent = 0.09

profit margin is 8.1 percent= 0.081

total assets to sales is constant at 1

We need to calculate the Retention Ratio first,

which gives the percentage of a company's earnings that are not paid out in dividends but credited to retained earnings. It can be calculated using below expression,

Retention Ratio = 1 - Dividend pay-out ratio

Retention Ratio = 1 - 0.66 = 0.34

ROE i.e the return on equity which is a measure of the profitability of a business in relation to the equity can be calculated as;

Sustainable Growth rate = (ROE * Retention Ratio)/(1 - ROE*Retention Ratio)

0.09 = (ROE * 0.34/(1 - ROE*0.34)

0.09 (1 - 0.34ROE) = 0.34ROE

0.09 - 0.0306ROE = 0.34ROE

0.3094ROE = 0.09

ROE = 0.09/0.3094

ROE = 0.290 or 2.90%

debt-equity ratio can now be calculated as;

Return on Equity = Profit Margin×Total Assets to sales ratio×(1+D/E)

0.290 = 0.081*1*(1+D/E)

1 + D/E = 0.290/0.081

1 + D/E = 3.580

D/E = 3.580 - 1 = 2.580

Therefore, the constant debt-equity ratio is 2.580