# Should stock price and P/E ratio increase when dividends increase?

In private conversation, someone told me that an increase in dividends should always increase stock price and P/E ratio, if all other factors remain unchanged. The "proof" involves the Dividend Discount Model (DDM) or the Gordon Growth Model (GGM):

P = D / (r - g)

where P is the current stock price, D is the dividend per share paid by the company at the end of the first period, r is the required rate of return, and g is the perpetual growth rate of the dividend.

As the story goes, if companies increase D, then P will increase.

Another way to look at the formula:

P / E = (D / E) / (r - g)

Since (D / E) is the payout ratio:

P / E = payout ratio / (r - g)

As the story goes, if companies increase their dividend payout ratio, then the P/E ratio will increase.

This does not seem correct. I don't think it is true that companies are able influence their stock price to such a large extent by simply altering the amount of cash dividends that they pay. What is the flaw in the "proof" provided above?

• That simplified formula and ceteris paribus requirement reeks of Perfectly Spherical Cow In A Frictionless Vacuum. Commented Nov 6, 2022 at 6:56

Be careful with the Gordon growth model. It is a simplification and makes lots of assumptions. It says for example that a company which grows faster than the required return, has a negative value. Why would such a marvelous company have a negative value? So if for example Berkshire Hathaway would have paid 0.00001% dividend every year, its share would have a negative value -- but fortunately, Berkshire Hathaway doesn't pay dividend so its share has a value of zero, right?

My opinion is that the format in which you present Gordon growth model is not useful. You should rearrange the equation:

P = D/(r-g)
r-g = D/P
r = g + D/P

What does this equation now tell you? It tells that the rate of return is the growth plus the dividend yield. Here I'm reinterpreting r as the true rate of return, not the rate of return that investors demand.

For the entire stock market, the equation is very accurate. Dividends have been historically at a level of about 3.7% between 1929-2021 average (according to multpl.com which has historical statistics for dividend yield). Nominal GDP we can get from https://www.thebalancemoney.com/us-gdp-by-year-3305543 and in 1929 it was \$0.105 trillion and in 2021 \$22.996 trillion. So nominal GDP has been growing at a rate of 6.03%. So we get 9.73% total annual return.

According to https://www.officialdata.org/us/stocks/s-p-500/1929?amount=100&endYear=2021 the return has been 9.84% annual (from \$100 to \$560387.36). Pretty accurate, isn't it? Only 0.11% error!

However, for an individual stock this doesn't tell anything. A company could yield a lot of return, or it could go bankrupt. If you use the Gordon formula for an individual company, never use it in the "fair price is" variant (which you specified), but always use it in the "total return is" variant (which is my rearranged form of the equation).

And in the total return variant, you shouldn't use the current dividend. You should use a fair dividend, something that the company can continue paying (and continue growing it every year at a rate of g) without getting into financial trouble.

So, to use the formula, you must estimate what amount of earnings / cash flow the company needs to finance growth. The rest can be paid as dividends. The dividend payout ratio differs between companies and between fields. A company that grows a lot needs to finance the growth, so you can expect lower dividend payout ratios from companies that are growing quickly.

So for example a company which doesn't have any loans, and pays 3% dividend, and goes to a bank to finance paying 20% dividend, doesn't really increase in value due to such a stupid decision. Actually, doing something as stupid will probably negatively affect the company, because investors' view of the reckless behavior increases the rate of return they demand from that risky company, thus decreasing the fair price of the share (because the sustainable dividend still is 3% of the old share price, and the company's growth prospects are unchanged, so to get more return, the only thing that can change is the share price -- it reduces, increasing dividend yield).

Then, about companies that currently pay no dividend. A company paying no dividend will someday in the future have a hard time of using all that earned money. If a company is 0.01% of the GDP, and the rest of the market grows at a rate of 4% paying 4% dividend yield, but that company grows at a rate of 8%, its share of GDP in percentage will be in N years:

1.08^N/1.04^N * 0.01 %

...so in 245 years, that company makes more than 100% of the world economy. That's a mathematical impossibility. So companies like Berkshire Hathaway that currently pay no dividend, should still be considered to eventually pay a dividend, and the value of that company is only determined by that eventual dividend. More about this.

There are many fundamental reasons why dividends do not automatically increase stock price, but the main flaw in your logic regarding the Growth Model is that if the company gives out more cash in dividends, it has less cash on which to grow the company, so the growth rate declines, more than offsetting the increase in dividend rate