Hello again,

Back to reality after the events of last week in the Premier League and last night in the Champions League with some … accounting, in a sense.

The CFA Level I curriculum has a lot of question about ratios and a lot of questions ask how the return on equity ROE is affected by different properties of the firm. Let’s first look at the basic formula for ROE:

$$\text{ROE} = \frac{\text{net income}}{\text{equity}}$$

Ok that’s quite intuitive, but it doesn’t really provide a lot of insight on how different properties of the company will affect the ROE. This is where DuPont analysis is useful. The idea is pretty simple, we will introduce factors in the formula which will cancel out each other but will help us understand what is happening underneath the ROE. Let’s look at the traditional DuPont equation:

$$\text{ROE} = \frac{\text{net income}}{\text{sales}}\frac{\text{sales}}{\text{assets}}\frac{\text{assets}}{\text{equity}}$$

We now have a multiplication of three ratios, respectively:

- Net Profit Margin
- Assets Turnover
- Leverage Ratio

This decomposition is very useful to answer questions. Indeed, you know that if ROE is low, it is because either the net profit margin is poor or because the asset turnover is poor or because the firm is under-leveraged.

An easy way to remember the formula is just to remember two of the terms (for me, I remembered net profit margin and financial leverage); the third term can be found again using simple math.

Now there is an extended DuPont equation which further decomposes the net profit margin as follows:

$$\text{ROE} = \frac{\text{net income}}{\text{EBT}}\frac{\text{EBT}}{\text{EBIT}} \frac{\text{EBIT}}{\text{sales}} \frac{\text{sales}}{\text{assets}}\frac{\text{assets}}{\text{equity}}$$

Again, you see ratios coming up:

- Tax Burden
- Interests Burden
- EBIT Margin
- Asset Turnover
- Leverage Ratio

You can perform an analysis on how the ROE would change by having a look at each ratio.

Finally, there is an interesting thing about ROE that also comes up in the Corporate Finance topic of the CFA Level I curriculum: it is related to growth and dividend payout ratio. Indeed, we have the following relation:

$$ \text{g} = \text{ROE} \cdot (1-\text{dividend payout ratio}) = \text{ROE} \cdot \text{retention rate}$$

This is quite simple to understand and it allows you to solve questions when the growth rate is not explicitly given. The growth rate is in fact determined as the amount of return on equity that is not given away to shareholders as dividends. This amounts allows the company to grow and produce more net income in the following period.

That’s it for today. I’ll try to add more content soon!

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