Sustainable Growth Rate

Imagine a company that starts off with EUR 1,000,000 in equity. It then generates a return on equity of 12% for the year. That means a net income of EUR 120,000. If all of these earnings are retained, then they flow into stockholder's equity.

What would happen to equity in this case?

No. There's money being made here. There's no decrease.

Exactly! That's a simple relationship. If earnings are retained, then equity grows at the rate of ROE.

No. The net income has to go somewhere, and it's being kept on the books.

But suppose now that a quarter of earnings are paid out to stockholders in a cash dividend. That's EUR 30,000 leaving the firm. The firm keeps the rest. Now how much do you think equity will increase?

No. That's the ROE, but now a quarter of that is being paid out.

That's right. EUR 30,000 is paid out, the other EUR 90,000 is kept, and that represents a 9% increase from the starting equity. In a more general sense, the proportion of earnings paid in dividends is the __dividend payout ratio__, and the proportion of earnings retained is the __retention ratio__. These add up to one. Here, the 0.25 dividend ratio means that the retention ratio, usually denoted as _b_, is 0.75.

No. That represents the portion of earnings paid out, not what is kept to increase equity.

The sustainable growth rate _g_ is then the retention rate times the ROE, just like in the example. $$\displaystyle g = b \times ROE $$ How might you state the relationship between the retention rate and the growth rate, all else equal?

No. This doesn't have to be the case, and usually is not. The dividend payout ratio and the retention rate sum to one.

No. The retention rate can increase even if ROE is constant or even declining.

Yes! The main idea here is that there is a direct relationship between these two. A higher retention rate will allow equity to grow faster; that's for sure. If ROE is constant (that's not for sure), then the growth rate should increase.

In practice, this isn't always the case. Higher retention rates should mean higher growth rates, which is called __dividend displacement of earnings__. But studies have shown that some companies pay higher dividends and yet have higher growth rates. Of course, the key here is _all else equal_, and the world is not a clean lab. Other things happen. But in theory, if only in theory, the proportion of ROE that is plowed back into the company should serve as a sustainable growth rate.

To summarize: [[summary]]

It would decrease

It would increase by 12%

It would remain unchanged

3%

9%

12%

The retention rate and the growth rate must sum to one

As the retention rate increases, the return on equity increases

A higher retention rate should correspond to a higher growth rate

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