# Gordon (Constant) Growth Dividend Discount Model and Two-stage Dividend Discount Model

## Gordon (Constant) Growth Dividend Discount Model

As the name implies, the Gordon (constant) growth dividend discount model assumes dividends grow indefinitely at a constant rate.

$$V_0=\frac{D_1}{r-g}$$

Where:

D1 = expected dividends in year 1

Note that this is of the utmost importance in your calculation. If you are given the dividend today, you would multiply D0 by (1+r) to have the dividend in one year.

r = required rate of return

g = growth rate

Analysts may use the following equation to estimate a company’s sustainable growth rate:

g = b × ROE

b = earnings retention rate or (1 – dividend payout ratio)

ROE = return on equity

## Multistage Dividend Discount Model

The two-stage dividend discount model is a bit more complicated than the Gordon model as it involves using both a short-term and a long-term growth rate to estimate a company’s current value. The two-stage DDM assumes that the company will pay dividends that grow at a constant rate at some point, but dividends are currently growing at an elevated and unsustainable rate. The intrinsic value of a share of stock using this model can be estimated as follows:

$$V_0=\sum_{t=1}^n\frac{D_0(1+g_s)^t}{(1+r)^t}+\frac{D_{n+1}/(r-g_L)}{(1+r)^n}$$

Where:

Dn+1 = D0(1 + gS)n(1 + gL)

This means that the long-term dividend is the dividend today, multiplied by one plus the short-term dividend for a number of periods n, then multiplied by one plus the long-term growth rate

n = years of short-term growth

gS = short-term growth rate

gL = long-term growth rate

While several equations are involved, the two-stage DDM calculation boils down to the sum of the discounted short-term dividends and the discounted long-term dividends. The short-term dividends have to be rolled back to the present (t = 0), while the value of the long-term dividends must first be calculated at the time of transition from short-term to long-term (t = n).

The number of stages used in valuation should not be solely based on the company’s age, as many long-established companies can experience periods of above-average or below-average growth.

### Question

Using the Gordon (constant) growth dividend discount model and assuming that r > g > 1%, what would be the effect of a 1% decrease in both the required rate of return and the constant growth rate on the stock’s current valuation? Assume there is no change to current dividend payment (D0).

1. Current valuation would increase.
2. Current valuation would decrease.
3. Current valuation would remain unchanged.

Solution

If both the required rate of return and growth rate are decreased by the same amount, the denominator should remain unchanged. However, to calculate the current value, the current dividend must be rolled ahead one year by multiplying D0 by (1+g). While the current dividend payment is unchanged in this instance, Dwill decrease slightly when g is decreased by 1% thus making the current valuation lower than it was previously.

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