# Divided Earning Growth Rate Return Ipo Value Formula ## Present Value of Growth Opportunities, Earnings Retention Rate, and Dividend Payout Ratio

Whether a company pays out its earnings as dividends or retains its earnings to reinvest in its business depends on its return on equity (ROE) and on investors' required rate of return, which is dependent on the perceived riskiness of the company's stock.

If a company's ROE is greater than the market's required rate of return, or capitalization rate (k), then it would benefit the company's stock price if the company reinvested its earnings in more growth and distribute little or no earnings as dividends. If its investment opportunities are limited, and its return on investment is less than the capitalization rate, then it would pay the company to distribute its earnings as dividends rather than reinvest it.

## Company Growth Rates Depend on its ROE and Earnings Retention Rate

The growth of dividends and the stock price is dependent on company growth, which, in itself, is difficult to project even to the next year, since analysts frequently get it wrong. However, 2 factors obviously related to the company's growth rate are its ROE and the company's earnings retention rate (aka plowback ratio), which is the amount of earnings that the company reinvests in its business rather than distributing it to shareholders as a dividend.

Since the retention rate plus the dividend payout ratio, which is the fraction of company earnings paid out as dividends, equals 1, it follows that:

Earnings Retention Rate = 1 – Dividend Payout Ratio

Hence, if a company distributes 60% of its earnings as dividends, then its retention rate is 40%.

How much a company grows based on the reinvested earnings is commensurate with its ROE multiplied by the retention rate:

Company Growth Rate = ROE × Retention Rate

So if the company's retention rate is 40% and its return on stockholders' equity is projected to be 50%, then its growth for the coming year should be 20% (.4 × .5 = .2 = 20%).

## Present Value of Growth Opportunities (PVGO)

For investors, company growth is desirable only if it increases their return on investment—either its stock price and/or its dividends increase. According to the dividend discount model, it is possible for a company to grow while its stock price declines. A company's stock price will increase only if the company can reinvest the money and earn a higher rate of return than the required rate of return demanded by investors.

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The additional growth of a company's earnings has net present value of growth opportunities (PVGO).

PVGO = ROE – Required Rate of Return

If its ROE is greater than the required rate of return, then its PVGO exceeds zero, and the stock price will increase if the company reinvests some of its earnings for further growth. If the PVGO is zero, meaning that the ROE equals the capitalization rate, then it makes no difference to the stock price if earnings are reinvested or not; however, an earnings retention rate greater than that necessary to maintain liquidity will lower the dividend without increasing the stock price.

## Growth Rate in the Present Value of Stock Formula

If PVGO is negative, then the company will still grow, but its overall ROE will decline, and with it, its stock price. Therefore, the company should distribute most of its earnings as dividends, since that will yield the greatest return for stockholders.

Each scenario can be evaluated by calculating the intrinsic value of the stock using the dividend discount model, but with different return on equity rates and different plowback ratios.

## How To Calculate Growth Rates

The company growth rate, g, is determined by its ROE and by the earnings retention rate (RR):

g = ROE × RR

Consider a stock that pays a \$4 annual dividend, and the required rate of return demanded by investors is 12%.

If the company was paying all its earnings as dividends, then the company is not experiencing growth, so its stock price is determined solely by its dividend and its capitalization rate (k). The constant-growth dividend discount model calculates the stock price (P) as:

 D1 P = (k – g) D1 = Next Year's Dividend Amountk = capitalization rateg = company growth rate

For a no-growth company, g = 0, and the above equation reduces to:

P = D1/k = \$4/0.12 = \$33.33

Now suppose that the company earns 20% on its reinvested earnings and it reduces it dividend to \$2 per share, and reinvests the other \$2, for an earnings retention rate of 50%:

g = ROE × RR = 0.20 × 0.50 = 0.10 = 10%

Since the company's ROE is higher than its capitalization rate of 12%, the additional growth has a net present value for stockholders, so the stock price should rise:

P = D1/k – g = \$2/(0.12-0.10) = \$2/0.02 = \$100.00

As you can see, the stock price is much higher even though the dividend was cut in half.

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Remember, this is a hypothetical scenario. In the real world, companies usually have an earnings retention rate of 100% in their early, fast-growing phase; then as they grow larger they start paying out a dividend. The dividend payout ratio increases as the company's size increases and its growth prospects decline. In the real world, stock prices usually decline substantially after a dividend cut, but this is only because it usually indicates that the company is having financial trouble, and if it is, then its required rate of return increases to compensate investors for the increased risk, in addition to other factors causing a stock price decline.

Returning to our hypothetical scenarios, now suppose the company's ROE is only equal to its capitalization rate of 12%, then a 50% retention rate would give the company a 6% growth:

P = \$2/0.06 = \$33.33

Note that this price is equal to the no-growth price, because the company's return on equity is equal to its capitalization rate; but note also that the dividend is only half what it was in the scenario where the dividend payout ratio was 100%.

Hence, with a ROE equal to its capitalization rate, the company can maximize the benefit to its shareholders by distributing all its earnings as dividends.

## What is Gordon Growth Model?

(Note: companies usually retain some earnings to maintain liquidity.)

For the final scenario, suppose the company's return on equity is only 10%, then, with a 50% retention rate, its growth rate is 10% × 50% = 5%, which means the stock price is:

P = \$2/(0.12 - 0.05) = \$2/0.07 = \$28.57

As you can see, the company grew, but the stock price declined!

Note that the price declined even though the dividend was cut in half from the 1st scenario above!

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Hence, in this scenario, with a negative net present value, both the stock price and the dividend are lower.

But if the company decides to pay out all its earnings as dividends, then it earnings retention rate is 0% and its dividend payout ratio is 100%, and the stock price increases:

P = \$4/0.12 = \$33.33

Hence, a company in this position—sometimes referred to as a cash cow, because such a company is best milked for its dividends—will maximize its return to investors by paying out all its earnings as dividends.

In fact, if a cash cow doesn't pay out all or most of its earnings as dividends, then it could become a takeover target—major investors will buy it out at the lower stock price for management control, then increase the dividend payout ratio to 100%, which would increase its stock price to its highest intrinsic value, then sell the stock for a profit.

Based on the preceding discussion, it can be seen that the stock price can be equated to the no-growth value per share plus the present value of growth opportunities:

Stock Price = No-Grow Value per Share + Present Value of Growth Opportunities

With this formula, it is easier to see that when the PVGO is positive, it increases the stock price, when it is 0, it makes no contribution to the stock price, but will lower the dividend if any of it is reinvested, and when it is negative, as it is when the company's ROE is less than the required rate of return demanded by investors, then the stock price declines, even with reinvested earnings.