QUESTION 5 ROA ROE INTERNAL SUSTAINABLE GROWTH RATE Direct

QUESTION 5: ROA, ROE & INTERNAL, SUSTAINABLE GROWTH RATE Direct Calculation: . DJ\'s has a total sales of $155,940, an Debt-to-Equity ratio of 0.46, a profit margin of 5.28 percent, a retention ratio of.74, and total assets of $138,000. What is ROA, ROE, and sustainable growth rate? Reverse Calculation: DJ\'s has a total sales of S155,940, an Debt-to-Equity ratio of 0.46, a profit margin of 5.28 percent, and total assets of $138,000. . The sustainable growth rate is 6.9%. What is retention rte and dividend payout ratio?

Solution

Answer a.

Assets Turnover = Total Sales / Total Assets
Assets Turnover = $155,940 / $138,000
Assets Turnover = 1.13

Equity Multiplier = 1 + Debt-to-Equity Ratio
Equity Multiplier = 1 + 0.46
Equity Multiplier = 1.46

ROA = Profit Margin * Assets Turnover
ROA = 5.28% * 1.13
ROA = 5.97%

ROE = ROA * Equity Multiplier
ROE = 5.97% * 1.46
ROE = 8.72%

Retention Ratio, b = 0.74

Sustainable Growth Rate = [ROE * b] / [1 - ROE * b]
Sustainable Growth Rate = [0.0872 * 0.74] / [1 - 0.0872 * 0.74]
Sustainable Growth Rate = 0.064528 / 0.935472
Sustainable Growth Rate = 0.0690
Sustainable Growth Rate = 6.90%

Answer b.

Assets Turnover = Total Sales / Total Assets
Assets Turnover = $155,940 / $138,000
Assets Turnover = 1.13

Equity Multiplier = 1 + Debt-to-Equity Ratio
Equity Multiplier = 1 + 0.46
Equity Multiplier = 1.46

ROE = Profit Margin * Assets Turnover * Equity Multiplier
ROE = 5.28% * 1.13 * 1.46
ROE = 8.71%

Retention Ratio = b

Sustainable Growth Rate = [ROE * b] / [1 - ROE * b]
0.069 = [0.0871 * b] / [1 - 0.0871 * b]
0.069 - 0.00601 * b = 0.0871 * b
0.069 = 0.09311 * b
b = 0.74

Retention Ratio = 0.74

Dividend Payout Ratio = 1 - Retention Ratio
Dividend Payout Ratio = 1 - 0.74
Dividend Payout Ratio = 0.26