# Sustainable Growth Rate and the Du-Pont Analysis (PRAT Model)

We now have a basic understanding of the concept of sustainable growth rate and how it related to the valuation of any given firm. In this article, we will dig deeper in the same formula in an attempt to connect it with the famous Du-Pont model which is used worldwide to predict the Return On Equity or the ROE number.

Let’s look at this concept in greater detail in this article:

### The Sustainable Growth Rate Formula:

The sustainable growth rate formula is pretty straightforward. It is derived based on two factors. One of those factors is the retention rate of earnings or “b” and the other is the Return on Equity or ROE. Hence, the ROE number is an important determinant of the formula.

However, in real life, it is very difficult to predict what the ROE number for the future periods will be. It is for this reason that Du-Pont analysis had been created in the first place. Since ROE is a determinant of the sustainable growth rate, Du-Pont analysis is also intertwined with the concept of sustainable growth rate. This article will explain the correlation

### Breaking Down the ROE – The PRAT model:

The formula for sustainable growth rate is

SGR = b * ROE

Where b represents the retained earnings i.e. (net income – dividends)/ net income

And ROE represents the return on equity which can be broken down into its 3 component ratios with the Du Point analysis

SGR = | (net income – dividends) | X | (net income) | X | (Sales) | X | (Total assets) |

Net income | Sales | Total Assets | Equity |

We can see that the Du-Pont analysis has been further developed in this model. Just like the Du-Pont ratio is internally made up of 3 ratios, similarly the sustainable growth rate ratio is also internally made up of 4 ratios viz, P, R, A and T

Where:

*P represents profit margin*

*R represents retention rate*

*A represents Asset Turnover*

*And surprisingly T represents Financial Leverage *

Note that leverage is not represented by L. Rather it is represented by T

**Example:**

**If a company has a profit margin of 14%, asset turnover of 2, leverage ratio of 1/2 and pays out 60% of its earnings as dividends, then what is the rate at which this company can grow indefinitely? **

Answer:

Since 60% of the earnings are paid out, the balance 40% are retained.

Therefore SGR = 14% * 0.4 *2 *0.5

= 5.6%

Hence as per the above inputs the company can continue to grow at a rate of 5.6% indefinitely. However, obviously the underlying assumption states that the capital structure policy and the dividend policy remain unchanged!

The PRAT model is important from an exam point of view. This is because it helps us calculate the Sustainable Growth Rate even though the components of sustainable growth rate may not be explicitly stated in the question paper.

### Analysis: The Financing Factors:

From an analysis point of view, we can see that two out of the four factors in the PRAT model are directly linked to the financing policy of the company. These two factors are retention rate and asset turnover. Thus, while creating the financing policy companies must take into account the fact that they could be changing the valuation of their firm for better or for worse.

However, since these factors are within the direct control of the company, the prediction pertaining to these two components shows less error and tends to be more accurate.

### The Performance Factors:

The other two factors viz. the profit margin and the asset turnover are performance driven. This means that they are not under the direct and unilateral control of the organization. There are factors beyond the reach of the company which can affect these components of the ROE and hence the sustainable growth rate number. The predictions pertaining to these components have a higher possibility of error and hence less accuracy.

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