# Gordon model (Constant-Growth Valuation Model)

The Gordon model is one of the models used in dividend valuation. It is very simple, as long as one knows the formula, which is:

P0=D1/(rs-g)

Also sometimes presented as: P = D/(k-g)

Where:

P0 or P – price of the stock

D1 or D – per share dividend expected at the end of year 1 (at the end of the next financial period)

rs or k – required return for equity investor

g – constant growth rate (expected annual growth of dividends)

Gordon model is usually used for mature companies only since it is assumed that annual growth of dividends remains constant.

It is very important to note that if you are only given the current per share dividend (D0, per share dividend received in this financial period), then you will need to adjust it for the next financial period before you can use it in the Gordon model. To do this you will need to take the current dividend and multiply it by (1 + g). The calculation is as follows:

D1=D0*(1+g)

The original equation of the Gordon model (P0=D1/(rs-g)) calculates the price of the share. However, you are looking for the cost of common stock. Therefore, you need to rearrange equation of the Gordon model as follows:

rs = (D1/Po) + g

Now you just plug in the numbers into the adjusted Gordon equation and you will be able to obtain the cost of common stock. Because common stock is paid out of the after-tax earnings, the tax adjustment is irrelevant.

Sometimes it is necessary to find the growth rate (g) first, before you can calculate the cost of the common stock (rs) with the help of the Gordon model. To do so, you need to find out what was the per share dividends applicable to common stock over the last few years (this information will be given). After obtaining this information, you can calculate the growth rate.

It is best to explain this with an example.

EXAMPLE 1:

Calculating the growth rate, which is necessary for usage of the Gordon model:

The information given below is on per share dividends applicable to common stock over the last few years. You need to find the growth rate of dividends over the given period.

Per share dividends from 2005-2010:

2010 – \$4

2009 – \$3.96

2008 – \$3.76

2007 – \$3.27

2006 – \$3.25

2005 – \$3

Now, by using a financial calculator, you can calculate the growth rate as follows:

PV = -3 (per share dividend in 2005, the first year from which per share dividend information is available)

FV = 4 (per share dividend in 2010, the per share dividend in the current period)

N = 5 (number of periods over which growth occurred)

Find I = it will be 5.92% (this number represents growth of dividends over the given period)

EXAMPLE 2:

Using the growth rate (found above) in the Gordon model:

Now, if we know that the growth of the dividends is expected to be the same into the future and the price of the stock is \$55, we can compute the cost of common stock (rs) as follows:

rs=(4*(1+0.0592)/55)+0.0592

rs=0.0770+0.0592

rs=0.1362=0.14%

The cost of common stock also represents the return that investors expect to earn from their shares. If the actual return is less – investors will sell their stock.

# Test yourself

The ordinary share is currently sold for \$40 each. The growth of shares was 10% over the last 5 years and is expected to be the same in the future. A dividend of \$3.5 dollars was paid to shareholders in the current period.

REQUIRED: What is the cost of an ordinary share?

SOLUTION:

We need to use the adjusted Gordon model. In other words, we need to use the formula: rs = (D1/Po) + g

Rs=(3.5*(1+.1)/40) +.1

Rs=(3.85/40) +.1

Rs=19.63%

Note that the dividend is adjusted for growth in the next period by multiplying the current dividend by (1+g).

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