###### Value at Risk (VaR)

Value at Risk (VaR) measures the probability of underperformance by providing a statistical... **Read More**

Sustainable growth rate (SGR) is the growth rate of dividends (and earnings) that a company can maintain for a given return on equity (ROE), assuming that the capital structure remains unchanged, and no additional common stock is issued. The SGR can be used as an input in the Gordon Growth Model.

Sustainable growth rate (SGR) can be calculated as:

$$\text{g}=\text{b}\times\text{ROE}$$

Where:

\(\text{g}=\) Dividend growth rate.

\(\text{b}=\) earnings retention rate (1 − Dividend payout ratio).

The higher the return on equity, the higher the sustainable dividend/earnings growth rate. The higher the earnings retention rate, the higher the sustainable dividend/earnings growth rate. This relationship is known as the dividend displacement of earnings.

The SGR equation can be expanded to examine what drives ROE:

$$\text{ROE}=\frac{\text{Net income}}{\text{Shareholder’s equity}}$$

ROE can be related to return on assets (ROA) and the extent of financial leverage (equity multiplier):

$$\text{ROE}=\frac{\text{Net income}}{\text{Total assets}}\times\frac{\text{Total assets}}{\text{Shareholders’ equity}}$$

A company can therefore increase its ROE either by increasing ROA or using leverage.

The ROE equation can be expanded further by breaking ROA into two components, profit margin and turnover (efficiency):

$$\text{ROE}=\frac{\text{Net income}}{\text{Sales}}\times\frac{\text{Sales}}{\text{Total assets}}\times\frac{\text{Total assets}}{\text{Shareholders’ equity}}$$

The first term is the company’s profit margin. A high-profit margin will result in a high ROE. The second term calculates total asset turnover, which is the company’s efficiency. A high turnover will result in high ROE. The third term is the equity multiplier.

This relationship is widely known as the DuPont model. The PRAT model is a method to calculate the sustainable growth rate using the DuPont model. By combining these equations, the dividend growth rate can be calculated as:

$$ \begin{align*} \text{g}&=\text{Profit margin}\times\text{Retention rate}\times\text{Asset turnover}\times\text{Financial leverage} \\ \\ &=\frac{\text{Net income}-\text{Dividends}}{\text{Net income}}\times\frac{\text{Net income}}{\text{Sales}}\times\frac{\text{Sales}}{\text{Totals assets}}\times\frac{\text{Total assets}}{\text{Shareholders’ equity}} \end{align*} $$

Where:

\(\frac{\text{Net income}-\text{Dividends}}{\text{Net income}}\) is the retentio ratio.

And the rest of the equation is the ROE.

Consider the following information:

- Profit margin = 4%.
- Total asset turnover = 1.2.
- Equity multiplier = 1.75.
- Retention ratio = 65%.

The sustainable growth rate (SGR) is *closest* to:

$$\begin{align*}\text{g}&=\frac{\text{Net income}}{\text{Sales}}\times\frac{\text{Net income}-\text{Dividends}}{\text{Net income}}\times\frac{\text{Sales}}{\text{Totals assets}}\times\frac{\text{Total assets}}{\text{Shareholders’ equity}}\\&=0.65\times4\%\times1.2\times1.75\\&=5.46\%\end{align*}$$

A company with a higher earnings retention and higher financial leverage (equity multiplier) will have a higher sustainable dividend growth rate.

## Question

Consider two companies with the following information:

$$\small{\begin{array}{l|c|c|c}{}& \textbf{ROA} & \textbf{Retention rate} & \textbf{Equity multiplier}\\ \hline\text{Blue Enterprises} & 13\% & 30\% & 1.3 \\ \hline\text{Green Enterprises} & 13\% & 40\% & 1.8\\ \end{array}}$$

Given the above information, the sustainable growth rate for Blue and Green are

closestto:

- 3.9% and 5.2%, respectively.
- 5.07% and 9.36%, respectively.
- 3.9% and 7.2%, respectively.
## Solution

The correct answer is B:The formula for the sustainable growth rate is:

$$\text{g}=\text{b}\times\text{ROE}$$

For Blue:

$$\text{g}=13\%\times30\%\times1.3=5.07\%$$

For Green:

$$\text{g}=13\%\times40\%\times1.8=9.36\%$$

Reading 23: Discounted Dividend Valuation

*LOS 23 (o) Calculate and interpret the sustainable growth rate of a company and demonstrate the use of DuPont analysis to estimate a company’s sustainable growth rate.*