Question

Jasmine Manufacturing wishes to maintain a sustainable growth rate of 8.25 percent a year, a debt-equity ratio of .44, and a dividend payout ratio of 30.5 percent. The ratio of total assets to sales is constant at 1.31. What profit margin must the firm achieve in order to meet its growth rate goal?

Answer 1

Answer:

Profit Margin = 10.8%

Explanation:

We know, Sustainable Growth Rate = Retention Ratio × Return on Equity

Again, we know,

Retention ratio = (1 - Dividend payout ratio)

Given,

Dividend payout ratio = 30.5%

Sustainable growth rate = 8.25%

Debt-to-Equity ratio = 0.44

Total assets to sales = (Total Assets ÷ Sales) = 1.31

Putting the value in the above formula,

Sustainable Growth Rate = (1 - Dividend payout ratio) × Return on Equity

or, 0.0825 = (1 - 0.305) × Return on Equity

or, 0.0825 = 0.695 × Return on Equity

or, 0.1187 = Return on Equity

Therefore, ROE = 11.87%

Again, ROE in DuPont Formula = Profit Margin × Total Asset Turnover × Equity Multiplier

We know, Equity Multiplier = $\frac{Total assets}{Total shareholders' Equity}$

or, Equity Multiplier = $\frac{Total Stockholders' Equity + Total debt}{Total stockholders' Equity}$

or, Equity Multiplier = 1 + Debt to asset ratio

Again, asset turnover = (1 ÷ Total assets to sales) = 1 ÷ 1.31

Putting the value in the ROE formula,

11.87% = Profit Margin × (1 ÷ 1.31) × (1 + 0.44)

or, 0.1187 = Profit Margin × 0.7634 × 1.44

or, 0.1187 = Profit Margin × 1.099296

or, Profit Margin = 0.108

Therefore, Profit Margin = 10.8%