# 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 mightn’t 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. 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.

## Formula

Reinvested earnings will cause an increase in assets equivalent to total amount of reinvested earnings. This relationship can be expressed in percentage terms as follows:

$$ Internal\ Growth\ Rate\\=\frac{Reinvested\ Earnings}{Total\ Assets} $$

Let’s multiply and divide the right-hand side with net income:

$$ Internal\ Growth\ Rate\\=\frac{Reinvested\ Earnings}{Net\ Income}\times\frac{Net\ Income}{Total\ Assets} $$

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

$$ Internal\ Growth\ Rate\\=Retention\ Rate\times Return\ on\ Assets\ (ROA) $$

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

$$ Internal\ Growth\ Rate\\=(1−Dividend\ Payout\ Ratio)\times Return\ on\ Assets\ (ROA) $$

## 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.

$$ Internal\ Growth\ Rate\\=(1−60\%)\times\frac{$15\ million}{$100\ million}=6% $$

The company can achieve a 6% increase in sales and assets without obtaining any external funding. However, the company’s investors mightn’t 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 which is calculated as follows:

$$ Sustainable\ Growth\ Rate\\=(1−Dividend\ Payout\ Ratio)\times ROE\\=(1−60\%)\times\frac{$15\ million}{$40\ million}=15\% $$

Internal growth rate can be expressed as follows:

$$ Internal\ Growth\ Rate\\=\frac{Reinvested\ Earnings}{Net\ Income}\times\frac{Net\ Income}{Equity}\times\frac{Equity}{Assets} $$

$$ Internal\ Growth\ Rate\\=Sustainable\ Growth\ Rate\times\frac{Equity}{Assets} $$

Written by Obaidullah Jan