# Gordon Growth Model

## What it is:

**The Gordon Growth Model**, also known as the *dividend discount model (DDM)*, is a method for calculating the intrinsic value of a stock, exclusive of current market conditions. The model equates this value to the present value of a stock's future dividends.

The model is named in the 1960s after professor Myron J. Gordon, but Gordon was not the only financial scholar to popularize the model. In the 1930s, Robert F. Weise and John Burr Williams also produced significant work in this area.

There are two basic forms of the model: the stable model and the multistage growth model.

**Stable Model**

Value of stock = D_{1}/ (k - g)

where:

D_{1} = next year's expected annual dividend per share

k = the investor's discount rate or required rate of return, which can be estimated using the Capital Asset Pricing Model or the Dividend Growth Model (see Cost of Equity)

g = the expected dividend growth rate (note that this is assumed to be constant)

**Multistage Growth Model**

When dividends are not expected to grow at a constant rate, the investor must evaluate each year's dividends separately, incorporating each year's expected dividend growth rate. However, the multistage growth model does assume that dividend growth eventually becomes constant. See the example below.

## How it works (Example):

**Stable Model**

Let's assume XYZ Company intends to pay a $1 dividend per share next year and you expect this to increase by 5% per year thereafter. Let's further assume your required rate of return on XYZ Company stock is 10%. Currently, XYZ Company stock is trading at $10 per share. Using the formula above, we can calculate that the intrinsic value of one share of XYZ Company stock is:

*$1.00/(.10-.05) = $20*

According to the model, XYZ Company stock is worth $20 per share but is trading at $10; the Gordon Growth Model suggests the stock is undervalued.

The stable model assumes that dividends grow at a constant rate. This is not always a realistic assumption for growing (or declining) companies, which gives way to the multistage growth model.

**Multistage Growth Model**

Let's assume that during the next few years XYZ Company's dividends will increase rapidly and then grow at a stable rate. Next year's dividend is still expected to be $1 per share, but dividends will increase annually by 7%, then 10%, then 12%, and then steadily increase by 5% after that. By using elements of the stable model, but analyzing each year of unusual dividend growth separately, we can calculate the current fair value of XYZ Company stock.

Here are the inputs:

D_{1} = $1.00

k = 10%

g_{1} (dividend growth rate, year 1) = 7%

g_{2} (dividend growth rate, year 2) = 10%

g_{3} (dividend growth rate, year 3) = 12%

g_{n} (dividend growth rate thereafter) = 5%

Since we have estimated the dividend growth rate, we can calculate the actual dividends for those years:

D_{1} = $1.00

D_{2} = $1.00 * 1.07 = $1.07

D_{3} = $1.07 * 1.10 = $1.18

D_{4} = $1.18 * 1.12 = $1.32

We then calculate the present value of each dividend during the unusual growth period:

$1.00 / (1.10) = $0.91

$1.07 / (1.10)2 = $0.88

$1.18 / (1.10)3 = $0.89

$1.32 / (1.10)4 = $0.90

Then, we value the dividends occurring in the stable growth period, starting by calculating the fifth year's dividend: *D _{5 }= $1.32*(1.05) = $1.39 *

We then apply the stable-growth Gordon Growth Model formula to these dividends to determine their value in the fifth year:*$1.39 / (0.10-0.05) = $27.80 *

The present value of these stable growth period dividends are then calculated:

$27.80 / (1.10)5 = $17.26

Finally, we can add the present values of Company XYZ's future dividends to arrive at the current intrinsic value of Company XYZ stock:*$0.91+$0.88+$0.89+$0.90+$17.26 = $20.84*

The multistage growth model also indicates that Company XYZ stock is undervalued (a $20.84 intrinsic value, compared with a $10 trading price).

Analysts frequently incorporate an assumed sale price and sale date into these calculations if they know the stock is not going to be held indefinitely. Also, coupon payments can be used in place of dividends when analyzing bonds.

## Why it Matters:

The Gordon Growth Model allows investors to calculate the value of a share of stock exclusive of current market conditions. This exclusion allows investors to make apples-to-apples comparisons among companies in different industries, and for this reason Gordon Growth Model is one of the most widely used equity analysis and valuation tools. However, there is some sentiment that Gordon Growth Model’s exclusion of nondividend factors tends to undervalue stocks in companies with exceptional brand names, customer loyalty, unique intellectual property, or other nondividend, value-enhancing characteristics.

Mathematically, two circumstances are required to make the Gordon Growth Model effective. First, a company must distribute dividends (however, analysts frequently apply the Gordon Growth Model to stocks that do not pay dividends by making assumptions about what the dividend would be if the company did pay dividends). Second, the dividend growth rate (g) cannot exceed the investor's required rate of return (k). If g is greater than k, the result would be negative, and stocks cannot have negative values.

The Gordon Growth Model, especially the multistage growth model, often requires users to make somewhat unrealistic and difficult estimates of dividend growth rates (g). It is important to understand that the Gordon Growth Model is highly sensitive to changes in g and k, and many analysts perform sensitivity analyses to evaluate how different assumptions change the valuation. Under the Gordon Growth Model, a stock becomes more valuable when its dividend increases, the investor's required rate of return decreases, or the expected dividend growth rate increases. The Gordon Growth Model also implies that a stock price grows at the same rate as dividends.