Gordon model
Encyclopedia
The Gordon growth model is a variant of the discounted cash flow
model, a method for valuing a stock
or business. Often used to provide difficult-to-resolve valuation issues for litigation, tax planning, and business transactions that don't have an explicit market value. It is named after Myron J. Gordon
, who originally published it in 1959. It assumes that the company issues a dividend
that has a current value of D that grows at a constant rate g. It also assumes that the required rate of return for the stock remains constant at k>g which is equal to the cost of equity for that company. It involves summing the infinite series which gives the value of price current P.
Summing the infinite series we get,
In practice this P is then adjusted by various factors e.g. the size of the company.
k denotes expected return = yield + expected growth.
It is common to use the next value of D given by :
, thus the Gordon's model can be stated as
Note that the model assumes that the earnings growth
is constant for perpetuity. In practice a very high growth rate cannot be sustained for a long time. Often it is assumed that the high growth rate can be sustained for only a limited number of years. After that only a sustainable growth rate
will be experienced. This corresponds to the terminal case of the Discounted cash flow
model. Gordon's model is thus applicable to the terminal case.
.
Write this as
so the return k is the dividend divided by the price.
b) When g is very close to k, the price is very high, approaching infinity as "g" approaches "k".
The model requires one perpetual growth rate
But for many growth stocks, the current growth rate can vary with the cost of capital significantly year by year. In this case this model should not be used.
b)
If the stock does not currently pay a dividend, like many growth stock
s, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Miller-Modigliani hypothesis
of dividend irrelevance is true, and therefore replace the stocks's dividend D with E earnings per share.
But this has the effect of double counting
the earnings. The model's equation recognizes the trade off between paying dividends and the growth realized by reinvested earnings. It incorporates both factors. By replacing the (lack of) dividend with earnings, and multiplying by the growth from those earnings, you double count.
c)
The results of the Gordon model are sensitive if k is close to g. For example, if
Say the
So the price of the stock
The difference determined in valuation is relatively small.
Now say the
So the price of the stock
The difference determined in valuation is large.
Discounted cash flow
In finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...
model, a method for valuing a stock
Stock
The capital stock of a business entity represents the original capital paid into or invested in the business by its founders. It serves as a security for the creditors of a business since it cannot be withdrawn to the detriment of the creditors...
or business. Often used to provide difficult-to-resolve valuation issues for litigation, tax planning, and business transactions that don't have an explicit market value. It is named after Myron J. Gordon
Myron J. Gordon
Myron J. Gordon was an American economist. He was Professor Emeritus of Finance at Rotman School of Management of the University of Toronto. In 1959, Gordon published a method for valuing a stock or business, now known as Gordon growth model.Gordon held a B.A. from the University of...
, who originally published it in 1959. It assumes that the company issues a dividend
Dividend
Dividends are payments made by a corporation to its shareholder members. It is the portion of corporate profits paid out to stockholders. When a corporation earns a profit or surplus, that money can be put to two uses: it can either be re-invested in the business , or it can be distributed to...
that has a current value of D that grows at a constant rate g. It also assumes that the required rate of return for the stock remains constant at k>g which is equal to the cost of equity for that company. It involves summing the infinite series which gives the value of price current P.
-
.
Summing the infinite series we get,
-
，
In practice this P is then adjusted by various factors e.g. the size of the company.
-
，
k denotes expected return = yield + expected growth.
It is common to use the next value of D given by :
, thus the Gordon's model can be stated as -
.
Note that the model assumes that the earnings growth
Earnings growth
Earnings growth is the annual rate of growth of earnings from investments.-Overview:Generally, the greater the earnings growth, the better.When the dividend payout ratio is the same, the dividend growth rate is equal to the earnings growth rate....
is constant for perpetuity. In practice a very high growth rate cannot be sustained for a long time. Often it is assumed that the high growth rate can be sustained for only a limited number of years. After that only a sustainable growth rate
Sustainable growth rate
According to PIMS an important lever of business success is growth. Among 37 variables, growth is mentioned as one of the most important variables for success: market share, market growth, marketing expense to sales ratio or a strong market position.The question how much growth is sustainable is...
will be experienced. This corresponds to the terminal case of the Discounted cash flow
Discounted cash flow
In finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...
model. Gordon's model is thus applicable to the terminal case.
Some properties of the model
a) When the growth g is zero,.Write this as
so the return k is the dividend divided by the price.
b) When g is very close to k, the price is very high, approaching infinity as "g" approaches "k".
Problems with the model
a)The model requires one perpetual growth rate
- greater than (negative 1) and
- less than the cost of capitalCost of capitalThe cost of capital is a term used in the field of financial investment to refer to the cost of a company's funds , or, from an investor's point of view "the shareholder's required return on a portfolio of all the company's existing securities"...
.
But for many growth stocks, the current growth rate can vary with the cost of capital significantly year by year. In this case this model should not be used.
b)
If the stock does not currently pay a dividend, like many growth stock
Growth stock
In finance, a growth stock is a stockof a company that generates substantial and sustainable positive cash flow and whose revenues and earnings are expected to increase at a faster rate than the average company within the same industry...
s, more general versions of the discounted dividend model must be used to value the stock. One common technique is to assume that the Miller-Modigliani hypothesis
Modigliani-Miller theorem
The Modigliani–Miller theorem forms the basis for modern thinking on capital structure. The basic theorem states that, under a certain market price process , in the absence of taxes, bankruptcy costs, agency costs, and asymmetric information, and in an efficient market, the value of a firm is...
of dividend irrelevance is true, and therefore replace the stocks's dividend D with E earnings per share.
But this has the effect of double counting
Double counting (accounting)
Double counting in accounting is an error whereby a transaction is counted more than once, for whatever reason. But in social accounting it also refers to a conceptual problem in social accounting practice, when the attempt is made to estimate the new value added by Gross Output, or the value of...
the earnings. The model's equation recognizes the trade off between paying dividends and the growth realized by reinvested earnings. It incorporates both factors. By replacing the (lack of) dividend with earnings, and multiplying by the growth from those earnings, you double count.
c)
The results of the Gordon model are sensitive if k is close to g. For example, if
- dividend = $1.00
- cost of capital = 8%
Say the
- growth rate = 1% - 2%
So the price of the stock
- assuming 1% growth= $14.43 = 1.00(1.01/.07)
- assuming 2% growth= $17.00 = 1.00(1.02/.06)
The difference determined in valuation is relatively small.
Now say the
- growth rate = 6% - 7%
So the price of the stock
- assuming 6% growth= $53 = 1.00(1.06/.02)
- assuming 7% growth= $107 = 1.00(1.07/.01)
The difference determined in valuation is large.
See also
- Discounted cash flowDiscounted cash flowIn finance, discounted cash flow analysis is a method of valuing a project, company, or asset using the concepts of the time value of money...
- Stock valuationStock valuationIn financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally potential market prices, and thus to profit from price movement – stocks that are judged...
- Time value of moneyTime value of moneyThe time value of money is the value of money figuring in a given amount of interest earned over a given amount of time. The time value of money is the central concept in finance theory....
- Net present valueNet present valueIn finance, the net present value or net present worth of a time series of cash flows, both incoming and outgoing, is defined as the sum of the present values of the individual cash flows of the same entity...