Question

Explain how the Du Pont system of analysis breaks down return on assets. Also explain how it breaks down return on stockholders’ equity

Short answer

With the Du Pont system of analysis,the return on assets is calculated by multiplying the net profit margin with the total assets turnover. Andthe return on the stockholder’s equity is calculated by multiplying the return on the asset with the equity multiplier.

Step-by-step solution

Step: Definition 

The Du Pont analysis breaks down the equation of Return on Equity (ROE) into three parts:

• Profitability is measured by the profit margin(Net income/Revenue)
• Asset efficiency is measured by asset turnover(Revenue/Average Total Assets)
• Financial leverage is measured by the equity multiplier(Average Total Assets/Average Total Equity)

Step: By the Du Pont system, return on assets is broken down as 

$$\begin{gathered} \mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{A}\mathit{s}\mathit{s}\mathit{e}\mathit{t}\mathit{s}\mathbf{}\mathbf{\left(}\mathit{R}\mathit{O}\mathit{A}\mathbf{\right)} \\ \mathbf{=}\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{}\mathit{m}\mathit{a}\mathit{r}\mathit{g}\mathit{i}\mathit{n}\mathbf{\times }\mathit{A}\mathit{s}\mathit{s}\mathit{e}\mathit{t}\mathbf{}\mathit{t}\mathit{u}\mathit{n}\mathit{o}\mathit{v}\mathit{e}\mathit{r} \\ \mathbf{=}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{S}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{s}}\mathbf{\times }\frac{\mathbf{S}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{s}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{A}\mathbf{s}\mathbf{s}\mathbf{e}\mathbf{t}\mathbf{s}} \\ \mathbf{=}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{A}\mathbf{s}\mathbf{s}\mathbf{e}\mathbf{t}\mathbf{s}} \end{gathered}$$

Step: By the Du Pont system, the return on stockholder’s equity is broken down as 

$$\begin{gathered} \mathit{R}\mathit{e}\mathit{t}\mathit{u}\mathit{r}\mathit{n}\mathbf{}\mathit{o}\mathit{n}\mathbf{}\mathit{e}\mathit{q}\mathit{u}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathbf{\left(}\mathit{R}\mathit{O}\mathit{E}\mathbf{\right)} \\ \mathbf{=}\mathit{P}\mathit{r}\mathit{o}\mathit{f}\mathit{i}\mathit{t}\mathbf{}\mathit{m}\mathit{a}\mathit{r}\mathit{g}\mathit{i}\mathit{n}\mathbf{\times }\mathit{A}\mathit{s}\mathit{s}\mathit{e}\mathit{t}\mathbf{}\mathit{t}\mathit{u}\mathit{n}\mathit{o}\mathit{v}\mathit{e}\mathit{r}\mathbf{\times }\mathit{E}\mathit{q}\mathit{u}\mathit{i}\mathit{t}\mathit{y}\mathbf{}\mathit{M}\mathit{u}\mathit{l}\mathit{t}\mathit{i}\mathit{p}\mathit{l}\mathit{i}\mathit{e}\mathit{r} \\ \mathbf{=}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{S}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{s}}\mathbf{\times }\frac{\mathbf{S}\mathbf{a}\mathbf{l}\mathbf{e}\mathbf{s}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{A}\mathbf{s}\mathbf{s}\mathbf{e}\mathbf{t}\mathbf{s}}\mathbf{\times }\frac{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{A}\mathbf{s}\mathbf{s}\mathbf{e}\mathbf{t}\mathbf{s}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{E}\mathbf{q}\mathbf{u}\mathbf{i}\mathbf{t}\mathbf{y}} \\ \mathbf{=}\frac{\mathbf{N}\mathbf{e}\mathbf{t}\mathbf{}\mathbf{i}\mathbf{n}\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{e}}{\mathbf{A}\mathbf{v}\mathbf{e}\mathbf{r}\mathbf{a}\mathbf{g}\mathbf{e}\mathbf{}\mathbf{T}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}\mathbf{}\mathbf{E}\mathbf{z}\mathbf{u}\mathbf{i}\mathbf{t}\mathbf{y}} \end{gathered}$$