Question

Problem 4-29 Constraints on Growth [LO3] Sig, Inc., wishes to maintain a growth rate of 12 percent per year and a debt-equity ratio of .3. The profit margin is 6 percent, and the ratio of total assets to sales is constant at 1.57 What dividend payout ratio is necessary to achieve this growth rate under these constraints? (A negative answer should be indicated by a minus sign. Do not round Intermediate calculations and enter your answer as a percent rounded to the nearest whole number, e.g., 32.) Payout ratio Is this growth rate possible? Yes An

Answer 1

Answer to Part 1.

Equity Multiplier = 1 + Debt Equity Ratio
Equity Multiplier = 1 + 0.30
Equity Multiplier = 1.30

ROE = Profit Margin * Total Asset Turnover * Equity Multiplier
ROE = 0.06 * 1.57 * 1.30
ROE = 0.12246 or 12.246%

Sustainable Growth Rate = [ROE * b] / [1 – (ROE * b)]
0.12 = [0.12246 * b]/ [1 – (0.12246 * b)]
0.12 = [0.12246 * b] / [1 – 0.12246 * b]
0.12 – 0.0146952* b = 0.12246 * b
0.12 = 0.1371552 * b
b = 0.8749
or b = 87.49%

b = Retention Ratio = 87.49%

Retention Ratio = 1 - Payout Ratio
0.8749 = 1 - Payout Ratio
Payout Ratio = 0.1251
or Payout Ratio = 12.51%

Answer to Part 2.

Yes, this growth rate is possible is the company maintains a payout ratio of 12.51%

Answer to Part 3.

Maximum growth rate can be achieve if the company retains all the profit i.e., if retention ratio is 100%

Sustainable Growth Rate = [ROE * b] / [1 – (ROE * b)]
Sustainable Growth Rate = [0.12246 * 1]/ [1 – (0.12246 * 1)]
Sustainable Growth Rate = 0.12246 / 0.87754
Sustainable Growth Rate = 13.95%