# Dividend Discount Model Formula | Gordon Growth Model

When investors buy shares, they expect to get (either or both of) two types of cash flows – dividend, during the period for which they hold the share, and capital appreciation based on an expected price at the end of the holding period.

The **Dividend Discount Model** is premised on the assumption that price of a share is determined by the discounted sum of all of its future dividend payments (i.e. net present value of all future dividends). **Dividend Discount Model** is the simplest model for valuing equity.

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**Dividend Discount Model Formula**

Where,

P_{0} = Current price of the stock

D_{t }=Dividend expected to be paid at the end of year t

r = required rate of return for equity investors

If dividends are expected to grow at a constant rate of g percent per year, then the above equation becomes:

This simplifies to:

This equation is referred to as the **Dividend Discount Model **or the **Gordon growth model** as it was proposed by Myron J. Gordon. It relates the value of a stock to its expected future dividends, the cost of equity and the expected growth rate in dividends. This model can be used to value a firm that is in 'steady state' with dividends growing at a rate that can be sustained forever.

This formula can be used only when the expected rate of return (r) is greater than the growth rate (g) otherwise the denominator would become zero yielding a result in infinity (a mathematical error) . Even in a real world context, in general, it is not expected that a stock’s dividend will grow at a rate g, which is greater than r for an infinite period.

### Example

For example, Company X has paid a dividend of Rs. 10 per share last year (D) and its dividend is expected to grow at 5 % every year. If an investor’s expected rate of return from Company X share is 7 %, what will be the market price of the share as per the dividend discount model?

D_{0} = 10; g = 5% or 0.05; r = 7% or 0.07

D_{1 }= D_{0 }* (1 +g) = 10 * 1.05 = 10.50

The market price of Company X share as per the **dividend discount model** with constant growth rate is Rs. 525.

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**Calculating Cost of Equity using Gordon Growth Model:**

If we know the market price of the share, the dividend amount and the dividend growth rate, then we can compute the expected rate of return (r) by using the following formula:

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