Gordon model

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The Gordon model, also called Gordon's model or the Gordon growth model is a variant of the discounted dividend 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 are currently off market. It is named after Myron Gordon, who is currently a professor at the University of Toronto.

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 which is equal to the cost of equity for that company. It involves summing the infinite series.

\sum_{t=1}^{\infty} D*\frac{(1+g)^t}{(1+k)^t}. The current price of the above security should be

P = D*\frac{1+g}{k-g}.

In practice this P is then adjusted by various factors e.g. the size of the company.

Contents

[edit] n b

let

A = \sum_{t=1}^{n} D*\frac{(1+g)^t}{(1+k)^t} = D*[\frac{(1+g)}{(1+k)} +...+ \frac{(1+g)^n}{(1+k)^n}]


A*\frac{(1+k)}{(1+g)} = D*[ \frac{(1+g)^0}{(1+k)^0}+ \frac{(1+g)}{(1+k)} +...+ \frac{(1+g)^{n-1}}{(1+k)^{n-1}} + (\frac{(1+g)^n}{(1+k)^n} - \frac{(1+g)^n}{(1+k)^n})]


A*(1+k) = D*(1+g)*(1-\frac{(1+g)^n}{(1+k)^n}) + (1+g)A

Ak = D*(1+g)*(1-\frac{(1+g)^n}{(1+k)^n}) + (1+g)A - A

A(k-g) = D*(1+g)*(1-\frac{(1+g)^n}{(1+k)^n})

A = D*\frac{(1+g)}{(k-g)}*(1-\frac{(1+g)^n}{(1+k)^n})

as,

n --> \infty and g < k

A = D*\frac{(1+g)}{(k-g)}

[edit] Problems with the model

a) The model requires one perpetual growth rate

  • greater than (negative 1) and
  • less than the cost of capital.

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 stocks, 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) Gordon's model is 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.

[edit] See also

[edit] References

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