DuPont Identity Components for Merritt Stoneworks

Question:

Merritt Stoneworks is all-equity financed and has net sales of $217,800, a taxable income of $32,600, a return on assets of 11.5 percent, a tax rate of 21 percent, and a total debt of $63,700. What are the values for the three components of the DuPont Identity?

Answer Description:

To find the values for the three components of the DuPont Identity for Merritt Stoneworks, follow these steps:

1. Net Profit Margin:
   • Formula: Net Profit Margin = Net Income/Net Sales
   • Net Income Calculation:
     • Taxable Income = $32,600
     • Tax Rate = 21%
     • Net Income = Taxable Income × (1 – Tax Rate) = $32,600 × (1 – 0.21) = $32,600 × 0.79 = $25,774
   • Net Profit Margin Calculation:
     • Net Profit Margin = $25,774 / $217,800 = 0.1181 or 11.81%
2. Total Asset Turnover:
   • Formula: Total Asset Turnover = Net Sales/Total Assets
   • Total Assets Calculation:
     • Since the company is all-equity financed, Total Assets = Total Equity.
     • To find Total Equity, we need the total debt and the fact that the company is all-equity financed. This implies no debt, so total assets should be computed directly. Given that total debt is $63,700, and it’s all-equity financed, Total Assets = Net Assets = Total Debt (in this case).
   • Total Asset Turnover Calculation:
     • Given Return on Assets (ROA) = 11.5%
     • ROA = Net Income / Total Assets
     • Total Assets = Net Income / ROA = $25,774 / 0.115 = $224,300
     • Total Asset Turnover = $217,800 / $224,300 = 0.971 or 97.1%
3. Return on Equity (ROE):
   • Formula: Return on Equity = Net Income/Total Equity​
   • Return on Equity Calculation:
     • Given that Total Equity = Total Assets (all-equity financed), Total Equity = $224,300.
     • ROE = Net Income / Total Equity = $25,774 / $224,300 = 0.115 or 11.5%

DuPont Identity Components:

1. Net Profit Margin: 11.81%
2. Total Asset Turnover: 97.1%
3. Return on Equity (ROE): 11.5%