If a stock is assumed to produce a series of periodic growing dividend payments, then it can be valued using the present value of growing perpetuity formula. This formula shows the value today of series of periodic payments which are growing at a constant rate (g) each period. The payments are made at the end of each period, continue forever, and have a discount rate i applied.

## Formula

PV = Pmt / (i - g)

**Variables used in the formula**

PV = Present Value

Pmt = Periodic payment

i = Discount rate

g = Growth rate

## How to Find the Value of a Stock

If we treat the payment (Pmt) as the dividend at the end of the first year, the growth rate (g) as the rate at which the dividend grows each year, and the discount rate as the required rate of return for equity investors, then the present value (PV) of these cash flows must represent the price an investor is prepared to pay today for this stock.

This formula is sometimes referred to as the Gordon growth model or Gordon dividend model, and is used to calculate the value of a stock based on future dividends. It assumes that the dividends are paid at the end of every period, and that they grow at a constant rate forever.

## Example of how to Value a Stock

Suppose for example, a stock pays a dividend of 1.25 at the end of year 1 and the business plans to increase the dividend by 5% each year. If the investors required rate of return is 12%, then the price they are prepared to pay for the stock is given by the time value of money formula as follows:

Pmt = 1.25 Dividend at the end of the first year g = 5% Dividend growth rate i = 12% Rate of return for equity investors Stock Price = Pmt / (i - g) Stock Price = 1.25 / (12% - 5%) Stock Price = 17.86

As investor should be prepared to pay 17.86 for this series of cash flows, and as these represent the stock, the stock price should also be 17.86.

Because of the requirement for a constantly growing dividend payment, the model is best suited to a stable business which is expected to experience steady growth, and to pay out regular increasing dividends to shareholders.

Our stock valuation calculator can be used to carry out the calculations described above, by entering details relating to the dividend, growth rate, and investor return rate.

## About the Author

Chartered accountant Michael Brown is the founder and CEO of Plan Projections. He has worked as an accountant and consultant for more than 25 years and has built financial models for all types of industries. He has been the CFO or controller of both small and medium sized companies and has run small businesses of his own. He has been a manager and an auditor with Deloitte, a big 4 accountancy firm, and holds a BSc from Loughborough University.