- Last Updated: Wednesday, 06 September 2017 19:16

Generally, investors buy common stocks for two reasons: they offer a cash dividend, and they also have the potential to provide a capital gain. In this article, we will present a method for calculating stock prices based on a constant growth model, leveraging a discounted cash flows approach which considers both dividends and capital gains.

Since investors buy stocks for both the dividends they pay today, as well as the possibility of a gain when selling the stock in the future, the expected return can be expressed by the following calculation:

Expected Return = (Dividends Paid + Capital Gain) / Price of Stock

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This expected return for a stock is also known as the market capitalization rate or discount rate. We're going to use all three terms interchangeably throughout our calculations and explanations in this article. Let's look at a quick example of how this formula works.

Listed below are the starting assumptions:

- Price of Stock A is currently $100.00 per share or (P0).
- Dividends are expected to be $3.00 per share (Div).
- The price of Stock A is expected to be $105.00 per share in one year's time (P1). Therefore, our capital gain is expected to be $105.00 - $100.00 or $5.00 per share.

In this example:

Expected Return, or R = ($3.00 + $5.00) / $100.00 = 8.0%

We can now use this expected return to calculate the price of a stock in the same risk class as Stock A using the following formula:

Stock Price = (Dividends Paid (Div) + Expected Price (P1)) / (1 + Expected Return (R))

Proving this calculation with our example information above, we have:

Stock Price = ($3.00 + $105) / (1 + 0.08) = $108.00 / 1.08 = $100

Some individuals may recognize this stock price calculation as the beginnings of a discounted cash flow formula. Essentially, the price of a stock is the cash flows gained by the stockholder, divided by the discount rate or market capitalization rate.

The stock prices just calculated are only short term values - a one year horizon. But let's think about the value of a stock over a nearly infinite timeline. Let's say a stockholder plans to sell their stock in 100 years. In this example, the value of the stock would be all the dividends received each year, plus the capital gain of the stock in 100 years.

We know from our prior example the investor's expected return was 8.0%, and the growth rate of the stock was 5.0%. In 100 years, the stock's price would then be:

$100 x (1.05)^{100} = $13,150.13

If we discount this selling price by the expected return, or discount rate, we find:

$13,150.13 / (1.08)^{100} = $13,150.13 / 2,119.76 = $5.98

The above information tells us the current price of a stock has very little to do with the future price of the stock. The net present value of the stock's price increase 100 years from now is only $5.98! While it's possible to run through the calculations, it's clear that $100.00 - $5.98, or $94.02 of the stock's price is derived from the present value of the dividends received each year.

In fact, when taken to the extreme (an infinite timeline), the price of stock today has no relationship to a future capital gain. It is a function of the dividend stream, divided by the rate of return that can be derived from stocks of similar risk. This allows us to simplify our stock pricing formula:

Stock Price = Sum of Dividends (Div) in each Time (T) / (1 + R)^{T}

Students and investors might recognize this formula as the discounted cash flow formula, where stock dividends are substituted for cash flows.

It's possible to further simplify this stock price formula by applying a constant growth model to the company's dividends. This is similar to simplifications used when evaluating returns in perpetuity. Using this model, our stock price formula then becomes:

Stock Price = Dividends (Div) / (Expected Return (R) - Dividend Growth Rate (G))

Or

Stock Price = Div / (R - G)

This constant growth stock pricing model does not mean the stock's dividends will remain the same over time; the assumption is the growth rate is constant over a long period of time. Closely examining this stock pricing formula reveals that it only works when the expected return, or discount rate, is greater than the dividend growth rate. An assumption that is quite logical.

Now that we have a simple formula to calculate a stock's price, we need to figure out how to calculate all the individual variables in that formula. Specifically, we need to calculate the projected growth rate in dividends and the market capitalization rate (discount rate or expected return).

An estimate of a company's dividend growth rate can be made by examining a company's projected earnings growth rate. This estimate assumes the return on equity for a company and its payout ratio remains constant. Dividend growth can then be estimated using the following calculation:

Dividend Growth (G) = Plowback Ratio x Return on Equity

Where:

- Plowback Ratio = 1 - Payout Ratio, and
- Payout Ratio = Dividends Paid / Earnings per Share, and
- Return on Equity = Earnings per Share / Book Equity per Share

These variables can be easily calculated when researching a stock. In fact, they are often calculated by many of the online stock research tools. We explain the significance of many of these variables in our article on financial ratios.

Sticking with our example, if Stock A has a payout ratio of 60%, which means they pay out 60% of earnings in terms of dividends, their plowback ratio is 1 - 60%, or 40%. Let's also assume the company's return on equity is 10.0%. That means their estimated dividend growth rate is:

Dividend Growth (G) = 40% x 10% = 4.0%

If we go back to our simplified stock price formula, we can use that same calculation to develop an estimate of the discount rate (or market capitalization rate). Rearranging this formula we have:

Discount Rate (R) = (Dividends (Div) / Stock Price (P0)) + Dividend Growth Rate (G)

If we are going to develop estimated prices for stocks, then we're going to need to figure out the proper discount rate (expected stockholder return), based on stocks of equivalent risk. We've already discussed how the dividend growth rate can be calculated, so we only need to solve for this portion of the discount rate equation:

Dividends / Stock Price

Fortunately, this metric is a commonly published stock ratio, and is known as the dividend yield. In this example, we are examining a stock of equivalent risk to Stock A. Let's assume that Stock B has:

- Dividend Yield of 7.0%
- Payout Ratio of 45%
- Return on Equity of 12%

First, solving for the dividend growth rate:

Dividend Growth (G) = 55% x 12% = 6.6%

Finally, solving for the discount rate:

Discount Rate (R) = 7.0% + 6.6% = 13.6%

We now have a method for calculating a stock's price based on some fundamental information about the stock itself and information for stocks of equivalent risk. That is, we've explained how to calculate all the variables in our stock pricing formula:

Stock Price = Div / (R - G)

The simple discounted cash flow approach to pricing stocks is extremely useful in valuing and evaluating stocks. Whenever estimating stock prices, the analyst or investor should carefully examine the output of all calculations.

For example, the value of the discount rate is very important, and needs to be made for stocks of equivalent risk. The estimate should be based on a reasonably high (ten plus) number of stocks.

Analysts also need to pay careful attention to the growth rates being used. If the company being evaluated has a relatively high growth rate, the analyst needs to think about the sustainability of that rate over time.

Finally, keep in mind the stock market is very efficient. If the stock prices calculated are very different than the actual market prices, then it's a good idea to revisit the assumptions. There is no such thing as easy money when it comes to picking stocks. If there was, we'd all be rich.

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