1. Lecture 1
Du Pont Identity

2. Financial ratios ROA = NI / A ROE = NI / E where
ROA = Return on Assets
ROE = Return on Equity
NI = Net Income
A = Total Assets
E = Total Equity

3. 1. Du Pont Identity (DPI) for ROA
Start with ROA = NI/A Multiply and divide the right-hand-side by S/S:

4. Numerical Example
Information given: NI/S = 0.1 S/A = 2

5. What is S/A?

6. 2. DPI for ROE
ROE = NI/E Multiply and divide the right-hand-side by S/S Multiply and divided the right-hand-side by (A/A)

7. Variables in ROE

8. One step further
Balance Sheet Identity: A = D + E where A = Total Assets D = Total Debt E = Total Equity

9. One step further (cont.)

10. Summary
ROA Du Pont Identities: 1. ROA = NI/A 2. ROA = (NI/S) x (S/A) 3. ROA = Profit margin x Asset use efficiency

11. Summary ROE Du Pont Identities: ROE = NI/E ROE = (NI/S) x (S/E)
ROE = (NI/S) x (S/A) x (A/E)
ROE = Profit margin x Asset use efficiency x Equity multiplier
ROE = ROA x (A/E)
ROE = (NI/S) x (S/A) x (1 + D/E)
ROE = Profit margin x Asset use efficiency x (1 + Debt-equity ratio)

12. What does it mean?
ROA = Profit margin x Asset use efficiency x (1 + Debt-equity ratio)

13. Numerical Example ROA calculation Given the following information:
Net Income = $1,000
Total Assets = $10,000
Sales = $15,000
Calculate the return on assets.

14. Numerical Example ROE calculation Given the following information:
Profit margin = 8%
Sales = $20,000
Total Assets = $50,000
Total Equity = $30,000
Net Income = $1,600
What is the return on equity?

15. Numerical Example Calculation of missing variables given ROE
Given the following information:
Profit margin = 8%
Total equity = $30,000
Net Income = $5,000
ROE = 16.67%
Asset use efficiency = 0.5
What is total debt, D?

16. Missing variable

17. Practice, Practice, Practice
Information given: Net Income = $5,000 Sales = $62,500 Total Assets = $125,000 Total Equity = $30,000 Total Debt = $95,000 ROE = 16.67%