Dividend Discount Model: Gordon Growth Rate

In the previous article, we became aware that the value of a stock can be split into two parts. One part is the horizon period i.e. the period chosen by the analyst for which they believe they can accurately forecast the financials of the company and therefore its dividends. This part remains the same when the calculation is done as per Gordon Growth model as well.

The second part is the terminal value. This is where the Gordon growth formula becomes important. The Gordon growth model simply assumes that the dividends of a stock keep of increasing forever at a given constant rate. Let us understand this with the help of an example.

Example:

Let’s say that an analyst wants to forecast the value of a given stock. He is using the dividend discount model to do so. He selects a 5 year horizon period for which he will project the most accurate possible dividend projections. Beyond that he will consider the stock to be perpetuity.

Calculation under Dividend Discount Model:

Let’s assume that the firm will pay dividends of $4, $5, $6, $7 and $8 in each of the 5 years of the horizon period. The normal dividend discount model will assume that the firm will continue paying, let’s say $10 dividend from the 6th year to perpetuity. This means that the dividends being forecasted are constant.

Calculation under Dividend Discount Model using Gordon Growth Rate:

In this case too, we will assume that the firm pays 4, $5, $6, $7 and $8 in each of the 5 years of the horizon period. This is the part where both the models remain the same. However, instead of assuming that the dividend from 6th year onwards will remain constant at $10, the Gordon growth model assumes that the dividend will keep on increasing at a constant rate. So, if this rate was 10%, then the dividend for the 7th year will be $11 and that of the 8th year will be $12.21. It then calculates the terminal value as a growing perpetuity instead of it being an ordinary perpetuity.

This assumption is obviously more viable given the fact that dividends do actually grow year on year. Hence, instead of assuming that they will stop growing instantly we can assume that they will grow at a given constant rate till eternity.

The Gordon Growth Formula:

According to the Gordon growth model, the value of the stock is derived from two parts:

Value = Present Value of Horizon + Terminal Value

The terminal value is then calculated as a growing perpetuity. There is some complex mathematics behind the derivation of this formula. However, that is not what we are concerned with.

The formula simply is:

Terminal Value = (D1/(r-g)) where:

• D1 is the dividend expected to be received at the end of Year 1
• R is the rate of return expected by the investor and
• G is the perpetual growth rate at which the dividends are expected to grow

Calculation:

For instance, in the above case, the terminal value can be calculated as follows, if the rate of return expected by the investors is 12%

D1 = $11, r = 12% and g = 10%

Therefore, the terminal value for the above stock is $550

Important Point to Note:

The Gordon model only works if the rate of return expected by the investors i.e. r is greater than the constant growth rate that is assumed by the investor i.e. “g”. Hence, r always has to be greater than g. g could even be a negative number implying that dividends are declining at a steady rate. However, it cannot be equal to or greater than r.

Also, not that we did not take the first value from the terminal period i.e. the dividend of 6th year i.e. $10. For our purpose, that should be considered D0. We need to use the value of the second dividend that is paid in the terminal period i.e. D1. Alternatively, we could use D0*(1+g) which is the same thing as D1