Present Value of Growth Opportunities, Earnings Retention Rate, and Dividend Payout Ratio

Stock prices depends on the company’s return on equity, which depends on net earnings. But some companies pay most of their earnings as dividends, other companies reinvest all of their earnings, and the remaining companies reinvest some of their earnings but pay the rest out as dividends. The problem for the investor is how to compare the rates of return for different companies when those returns may be manifested as higher stock prices, dividends, or combination of both. And how can a company maximize the return on equity for its investors? And what will happen to the stock price in the future? Will it rise, fall, or stay the same? An easy way to compare investment returns among different assets is to measure their capitalization rate.

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 depends on the perceived riskiness of the company's stock and on how its rate of return compares with other investments. If a company's ROE exceeds 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 for 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.

The capitalization rate is most often used in real estate as a way to measure the return on investment on the purchase of different properties that changes with the market value of the property. For real estate:

Capitalization Rate = Net Income from Property / Current Market Value of Property

The current market value of the property is used instead of the purchase price to determine if the property continues to be the best use of funds. For instance, suppose you had $100,000 that you want to invest, deciding between the stock market or real estate, both yielding about 10%. You decide to buy real estate where you earn a net income of $10,000 annually. Both the return on investment and your capitalization rate is 10%. Then a business, with a much better use for your property, offers to buy it from you for $200,000. How would you decide? You’re still earning the 10% that you expected, but now your property is worth $200,000, so your capitalization rate drops to only 5%, much less than what you can earn in the stock market. By selling for $200,000, you can invest that money in the stock market to earn $20,000 annually instead of just $10,000.

So you can think of the capitalization rate as the return on investment for each successive period, such as annually: the annual return on investment if the investment was purchased at the start of each new year. The capitalization rate measures the ongoing value of the investment.

For the stock investor:

Capitalization Rate = Company Earnings-Per-Share / Current Share Price = Earnings Yield

But the stock investor realizes the earnings yield in the form of dividends or capital gains earned during a certain time period, usually 1 year:

Capitalization Rate = (Dividends + Capital Gains) / Share Price at Start of Period

The stock investor profits from their investment either through higher stock prices, through dividends, or through a combination of both. Trying to measure the rate of return from the investment of different stocks is made more difficult because some stocks pay dividends and others do not. While the earnings yield shows the earnings-per-share, how it affects the future price of the stock will depend on whether the earnings are paid out as dividends or reinvested by the company. If the ROE exceeds the current earnings yield, then investors will earn a higher return if the company reinvests all of its earnings. If ROE is less than the current earnings yield, then the stock price will be maximized if the earnings are paid out as dividends. If a company can earn a higher ROE on some projects, but not enough to use all of its earnings, then the company can maximize its stock price by reinvesting some of its earnings for the higher ROE projects, while distributing the rest as dividends. However, if the company mismanages its use of funds, such as by reinvesting in projects with an ROE lower than its earnings yield, then its investors' capitalization rate will decline, and if it does, then those investors should sell the stock to buy other stocks or to invest in other assets with a higher capitalization rate.

Company Growth Rates Depend on its ROE and Earnings Retention Rate

The growth of dividends and the stock price depends 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), the amount of earnings 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 — as an increase in either its stock price and/or its dividends. 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. The additional growth of a company's earnings comes from its present value of growth opportunities (PVGO).

PVGO = ROE – Required Rate of Return

(In corporate finance, this is sometimes called the net present value of growth opportunities (NPVGO). To decide whether a project is worthwhile pursuing, the company will determine whether the NPVGO exceeds their cost of capital. If it does, then the project may be worth pursuing. The company determines this by adding the present value of all projected income from the project and subtracting the present value of all projected expenses or capital outlays for the project, yielding a net present value. But this is a quibble. The net present value of a project is simply its present value. However, even if NPVGO exceeds the company’s cost of capital, if the NPVGO is less than the rate of return demanded by investors, then the company’s stock price may decline.)

If its ROE exceeds the required rate of return, then its PVGO exceeds zero, and the stock price will increase if the company reinvests its earnings for further growth. If the PVGO is zero, meaning that the ROE = the required rate of return, then it makes no difference to the stock price if earnings are reinvested or not; however, an earnings retention rate exceeding that necessary to maintain liquidity will lower the dividend without increasing the stock price. If PVGO is negative, then the company may 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. The company growth rate, g, is determined by its ROE and by the earnings retention rate (RR):

g = ROE × RR

Consider a stock paying 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 will not grow, 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:

Stock Price According to Constant-Growth Dividend Discount Model
D1
P =
(k – g)
  • D1 = Next Year's Dividend Amount
  • k = capitalization rate
  • g = company growth rate

Note that this equation is valid only when k > g. If g > k, then g - k would yield a negative number, even though P would actually be positive in such a case. For a no-growth company, g = 0, and the above equation reduces to:

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

If the actual stock price is higher than $33.33, then the stock investors’ capitalization rate will be less than 12%, so they will sell the stock to reinvest in other assets with a higher capitalization rate or rate of return, equivalent to the scenario where you sold your real estate for $200,000 to reinvest the money for a higher return.

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 / (kg) = $2 / (0.120.10) = $2 / 0.02 = $100.00

As you can see, the stock price is much higher even though the dividend was cut in half. 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 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 usually because it indicates financial trouble for the company, which, in turn, requires a higher rate of return 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 = 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 = the no-growth price, because the company's return on equity = its capitalization rate; but note also that the dividend is only half what it was, when 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. (Note: companies usually retain some earnings to maintain liquidity, to pay current expenses.)

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%, so 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! 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 called 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.

Granted, it is difficult for investors to quantify the PVGO for companies, so how can an investor determine project future stock prices for the company?

Remember that many factors determine stock prices, but the capitalization rate and the present value of growth opportunities offer a few nuggets of information that may yield a better picture of future stock prices for a particular company.