|

# Constant Growth (Gordon) Model

Gordon Model is used to determine the current price of a security. The Gordon model assumes that the current price of a security will be affected by the dividends, the growth rate of the dividends, and the required rate of return by shareholders. Use the Gordon Model Calculator below to solve the formula.

### Constant Growth (Gordon) Model Definition

Constant Growth Model is used to determine the current price of a share relative to its dividend payments, the expected growth rate of these dividends, and the required rate of return by investors in the market

### Variables

Current Annual Dividends=Annual dividends paid to investors in the last year
K=Required rate of return by investors in the market
G=Expected constant growth rate of the annual dividend payments
Current Price=Current price of stock

### Gordon Model

The Gordon Model, also known as the Constant Growth Rate Model, is a valuation technique designed to determine the value of a share based on the dividends paid to shareholders, and the growth rate of those dividends.

Dividends

Dividends are the most crucial to the development and implementation of the Gordon Model.  Investors buy shares in a company, and have two possible ways of receiving a financial benefit, they either receive dividends from the company, or they sell their shares and receive a capital gain if the price received is higher than the price paid.

Assuming that a share will continue to exist in perpetuity, and that the company intends to pay dividends for as long as its shares are outstanding, we can logically develop a valuation technique based solely on the dividends paid.

Although a particular investor can make a capital gain as well as receiving dividend payments, the Gordon model assumes that once the share is sold by one investor, it is bought by another investor.  When this happens, the new shareholder will expect to receive dividends while owning the share.  If we assume that this process will repeat itself, we find that the stream of dividends is in fact infinite.

Each new investor will value the share based on the expected dividend stream, and the future sale price.  Yet the future sale price of the share will be based on the future dividend stream.  So if we can understand the price relationship to this dividend stream, then we can calculate the price today, as well as the price at any time in the future.

If a firm pays an infinite stream of dividends, and the amount of each dividend payment never changes, then the perpetuity formula will provide a current price of the share.  All we need is to know size of the annual dividends and the required rate of return by investors in the market.  The price of the share will simply be the dividend payment divided by the required rate of return.  Since the dividend payment is constant, the only factor that affects the share price is the required rate of return.

This is a very unrealistic property for common shares.  In the long run, companies that pay out dividends to their shareholders will naturally tend to grow these dividends.  There are many reasons, the most basic being simply inflation.  As the price level grows, so will revenues, costs, and profits.  As these profits grow, so would the dividend payouts, even if the purchasing power of these dividends remains the same.  Another reason for this is that companies tend to mature in the long run, and will no longer need to retain the same level of earnings for growth.  At this stage, the dividend payout tends to grow faster than the rate of inflation for successful companies.

The Gordon Model includes the growth rate of dividends into the share price model.  The Constant Dividend Growth Model determines the price by analyzing the future value of a stream of dividends that grows at a constant rate.

Dividend Growth Rate

The Gordon Model is particularly useful since it includes the ability to price in the growth rate of dividends over the long term.  It is important to remember that the price result of the Constant Dividend Growth Model assumes that the growth rate of the dividends over time will remain constant.  This is a difficult assumption to accept in real life conditions, but knowing that the result is dependent on the growth rate allows us to conduct sensitivity analysis to test the potential error should the growth rate be different than anticipated.

By keeping the dividend growth rate constant, we can determine the share price at any time in the future, so long as we know the current dividend amount, the growth rate, and the required rate of return at the future time.  Since the dividend stream continues and grows perpetually, we simply input the dividend amount and recalculate.

The Gordon Model

Now that we have an understanding of dividends, and the constant growth rate of those dividends, we can develop a model to price a share based on the dividend payment and the growth rate.  We know that the current share price according to the Gordon Model is going to be determined by a series of dividend payments.  We can express this series mathematically below.

D=Current Annual Dividends
G=Dividend Growth Rate
K=Required Rate of Return

This formula goes on indefinitely.  We can simplify the formula a bit by factoring out D.

This equation can be further simplified to produce a simple Gordon Model Formula

The Constant Dividend Growth Model is a simple derivation of a perpetual stream of growing dividend payments relative to the required rate of return in the market.