Answer:
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
