Gordon Growth Model Formulas | Constant Growth and Zero Growth Rate

Valuation Tutorials

Gordon Growth Model Formula

Gordon Growth Model Formula is used to find the intrinsic value of the company by discounting the future dividend payouts of the company.

There are two formulas of Growth Growth Model

#1 – Gordon Growth in Future Dividends
#2 – Zero Growth in Future Dividends

We will look at both the formulas one by one

#1 – Gordon Growth Model Formula with Constant Growth in Future Dividends

The Gordon growth model formula that with the constant growth rate in future dividends is as per below.

Let’s have a look at the formula first –

Here,

P₀= Stock Price;
Div₁= Estimated dividends for the next period;
r = Required Rate of Return;
g = Growth Rate

Explanation of Constant Gordon Growth Model Formula

In the above formula, we have two different components.

The first component of the formula is the estimated dividends for the next period. To find out the estimated dividends, you need to look at the historical data and find out the past growth rate. You can also take help from financial analysts and the projections they make. The estimated dividends won’t be accurate, but the idea is to predict something that is closer to the actual future dividends.

The second component has two parts – the growth rate and required rate of return.

To find out the growth rate, we need to use the following formula –

As you already know, if we divide the retained earnings by net income, we would get the retention ratio or else, we can also use (1 – Dividend Payout Ratio) to find out the retention ratio.

And ROE is the return on equity (net income/shareholders’ equity)

To find out the required rate of return, we can use the following formula –

In other terms, we can find out the required rate of return just by adding a dividend yield and the growth rate.

Use of Constant Rate Gordon Growth Model Formula

By using this formula, we will be able to understand the present stock price of a company. If we look at both of the components in the formula, we will see that we are using the similar present value method to find out the stock price.

First, we are calculating the estimated dividends. Then, we are dividing it by the difference between the required rate of return and the growth rate. That means the discounting rate in this regard is the difference between the required rate of return and the growth rate. By dividing the same, we can easily find out the present value of stock price.

Example of Gordon Growth Model Formula with Constant Growth

Hi-Fi Company has the following information –

Estimated dividends for the next period – $40,000
Required rate of return – 8%
Growth rate – 4%

Find out the stock price of Hi-Fi Company.

In the above example, we know the estimated dividends, growth rate, and also required a rate of return.

By using the stock – PV with constant growth formula, we get –

P₀= Div₁/ (r – g)
Or, P₀ = $40,000 / (8% – 4%)
Or, P₀ = $40,000 / 4%
Or, P₀ = $40,000 * 100/4 = $10, 00,000.

By simply using the above formula, we will be able to find out the present stock price. It can be a great tool for the investors and the management of any company. One thing we should notice here is that the stock price is the total stock price since we assumed the estimated dividends for all the shareholders. By simply taking the number of shares into account, we would be able to find out the stock price per share.

Gordon Growth Model Calculator

You can use the following Stock – PV with Constant Growth Calculator.

Div₁
r
g
P_O =

P_O =

Div₁
	=
(r − g)

0
	=	0
(0 − 0)

Gordon Growth Model Formula in Excel (with excel template)

Let us now do the same example above in Excel. This is very simple. You need to provide the three inputs of Dividends, Rate of Return and Growth Rate.

You can easily find out the stock price of the company in the template provided.

You can download this Gordon Growth Model Formula template here – Gordon Growth Model Formula with Constant Growth Excel Template

#2 – Gordon Growth Formula with Zero Growth in Future Dividends

The only difference in this formula is the “Growth factor”.

Here’s the formula –

Here, P = Price of the Stock; r = required rate of return

Explanation of Zero Growth Formula

This formula is based on the dividend discount model.

Thus, we place the estimated dividends in the numerator and the required rate of return in the denominator.

Since we are calculating with zero growth, we will skip the growth factor. And as a result, the required rate of return would be the discounting rate. For example, if we assume that a company would pay $100 as a dividend in the next period, and the required rate of return is 10%; then the price of the stock would be $1000.

One thing we should keep in mind while calculating the formula is the period we use for the calculation. The period of the dividends should be similar to the period of the required rate of return.

So, if you consider the annual dividends, you need to also take annual required rate of return to maintain the integrity in the calculation. For calculating the required rate of return, we will take dividend yield into consideration (r = Dividends / Price). And that we can find out by using the historical data. The required rate of return is the minimum rate that the investors would accept.

Use of Gordon Growth Model Formula (Zero Growth)

In this formula, it is estimated dividends for the next period. And the discounting rate is the required rate of return i.e. the rate of return that the investors accept. There are various methods by using which the investors and the financial analysts can find out the present value of the stock, but this formula is the most fundamental of all.

Thus, before investing in the company, every investor should use this formula to find out the present value of the stock.

Example of Gordon Growth Model Formula (Zero Growth)

Let’s take an example to illustrate Gordon Growth Model Formula with Zero Growth Rate

Big Brothers Inc. has the following information for every investor –

The estimated dividends for the next period – $50,000
The required rate of return – 10%

Find out the price of the stock.

By using the Stock – PV with Zero Growth Formula, we get –

P = Dividend / r
Or, P = $50,000 / 10% = $500,000.
The stock price would $500,000.

One thing you should notice here is that $500,000 is the total market price of the stock. And depending on the number of outstanding shares, we would find out the price per share.

In this case, let’s say that the number of outstanding shares is 50,000.

That means the stock price would be = ($500,000 / 50,000) = $10 per share.

Gordon Zero Growth Calculator

You can use the following Gordon Zero Growth Rate Calculator

First Value
Second Value
Formula =

Formula =

First Value
	=
Second Value

0
	=	0
0

Gordon Zero Growth Formula in Excel (with excel template)

Let us now do the same example above in Excel. This is very simple. You need to provide the two inputs of Dividend and Rate of Return.

You can easily find out the price of the stock in the template provided.

You can download this Gordon Zero Growth template here – Gordon Zero Growth Rate template Excel Template

Gordon Growth Model Formula

Gordon Growth Model Formula