# Internal Growth Rate

Internal growth rate is the maximum rate of growth in sales and assets that a company can achieve using only retained earnings. It is the rate of growth up to which the company might not need any external financing. A growth rate target higher than the internal growth rate must be financed by external sources of capital i.e. debt or equity.

An associated concept is the sustainable growth rate, a growth rate that can achieved by maintaining the existing mix of debt and equity in the company’s capital structure.

## Formula

Internal growth rate can be calculated using the following formula:

Internal Growth Rate = Retention Ratio × ROA

Internal Growth Rate = (1 - Dividend Payout Ratio) × ROA

### Understanding the Math

Every dollar of earnings reinvested becomes a dollar of assets. In other words, increase in assets (the internal growth rate) equals the reinvested earnings expressed as a percentage of assets:

 Internal Growth Rate = Reinvested Earnings Total Assets

Let us multiply and divide the right-hand side with net income and rearrange:

 Internal Growth Rate = Reinvested Earnings × Net Income Net Income Total Assets

The first term on the right-hand side equals the retention ratio, i.e. the percentage of earnings reinvested, and the second expression equals return on assets (ROA).

Internal Growth Rate = Retention Ratio × Return on Assets (ROA)

Retention ratio is also called plow-back ratio. It equals 1 minus the dividend payout ratio. The above equation can also be expressed as follows:

Internal Growth Rate = (1 − Dividend Payout Ratio) × ROA

## Example

A company earnings \$15 million last year, 60% of which was paid out as dividends. The company’s closing total assets stood at \$100 million and its equity amounted to \$40 million. Calculate the internal growth rate of the company and see how it is different from the sustainable growth rate.

### Solution

Internal growth can be calculated if we know the return on assets and retention ratio or dividend payout ratio.

We already have the dividend payout ratio, but we need to work out the return on assets.

 Return on Assets = \$15 million = 15% \$100 million

At ROA of 15% and dividend payout ratio of 60%, internal growth rate is 6%:

Internal Growth Rate = (1 - 60%) × 15% = 6%

The company can achieve a 6% increase in sales and assets without obtaining any external funding. However, the company’s investors might not be satisfied with just 6% growth. The management might want to raise external finance. If they raise external money such that its financial leverage (i.e. debt ratio) remains the same, it can achieve a growth rate up to the sustainable growth rate.

To calculate sustainable growth rate, we need retention ratio (or dividend payout ratio) and return on equity (ROE).

 Return on Equity (ROE) = \$15 million = 37.5% \$40 million

We can work out sustainable growth rate as follows:

Sustainable Growth Rate = (1 - 60%) × 37.5% = 15%

You can see that the sustainable growth rate is higher than the internal growth rate.

## Internal Growth Rate vs Sustainable Growth Rate

Since sustainable growth rate allows for external financing but only in the proportion of its current capital mix, the sustainable growth rate is higher than the internal growth rate. This is evident from the example above.

But let us see how internal growth rate is related to sustainable growth rate mathematically.

Let us multiply and divide the expression for internal growth rate with equity and rearrange:

 Internal Growth Rate = RI × NI × Equity NI Equity Assets

The first two expressions on the right-hand side are the definition of sustainable growth rate. With this, we reach the following expression:

 Internal Growth Rate = Sustainable Growth Rate × Equity Assets