# Assessing the Cost of Stocks using the Gordon Model

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## The Gordon Model

According to the Gordon growth model, the future prices of stocks that distribute dividends have little to do with current prices and more to do with expected cash flow. The idea is investors who choose these stocks do so with the expectation of ever-increasing dividend payments in addition to the company’s growth. Therefore, if you know, or can estimate, the dividend’s growth rate, you can use it along with a required rate of return to evaluate current stock prices.

The Gordon growth model formula is as follows:

Where:

• P0 is the current price of the stock
• D0 is the current year’s total dividend payment
• g is the annual dividend growth rate
• r is the required annual rate of return

The top portion of the equation, i.e., D0 (1+g) , calculates the dividend payment one year from the present (D1 ); if you already know that figure, you could reduce the formula to:

## Estimating Dividend Growth Rate (g)

A stock broker or some financial reports can provide the dividend growth rate, but you can also estimate this yourself from historical data using a derivation of the compounding interest formula:

Where:

• Do is the initial year’s total dividend payment
• Dt is the total dividend payment at time “t”
• t is the number of years between the two dividend figures.

To walk through an example, say a stock currently offers \$4 in annual dividend payments, but three years ago, it only offered \$3.50:

## The Required Rate of Return

The required rate of return is more subjective. It could be the minimum return you expect, such as an alternate investment’s anticipated yield used to assess the stock, or it might be the rate of inflation to ensure the stock outruns deterioration. You might also choose to evaluate the stock’s price based on the average yield of all stocks or the historical yield of the stock in question under the premise that it maintains historical growth. If you choose the latter, estimate the yield with the same formula used for the dividend growth rate, except replace dividend figures with stock prices.

The only caveat to this model is the required rate of return must be greater than the dividend growth rate or the formula fails. This should not, however, pose a problem, because the Gordon growth model is being used to assess the stock’s current value, given the dividend growth rate and the required rate of return. If the dividend growth rate already exceeds your required rate of return, then you know it’s a good investment, even without the formula.

## Assessing the Stock Price

To continue the previous example, say your required rate of return is 8 percent, and as presented earlier, the dividend growth rate is 0.0455 and with annual payments of \$4 presently:

Therefore, an acceptable current price for the stock would be \$121.16 with respect to your required rate of return and the dividend growth rate. If the current stock price is higher than this, give it a pass. If the price is lower, then you’re ahead of the game.

Just keep in mind stocks, by their very nature, are volatile, so even if the price is lower than this target value, it doesn’t mean the stock is infallible.

## Calculating the Stock’s Future Return (r)

By rearranging the Gordon growth model, you derive the following equation:

This enables you to calculate the stock’s anticipated return based on the dividends, dividend growth and the current price. If the previous example’s stock was currently priced at \$100, then the formula would show:

This tells you that purchasing the current stock at \$100 grants you an 8.73 percent yield, if everything continues as anticipated.