# TheLogicValue, an improvement of Gordon Shapiro valuation model

The dividend discount model (DDM) is a method of valuing a company’s stock price based on the theory that its stock is worth the sum of all of its future dividend payments, discounted back to their present value. In other words, it is used to value stocks based on the net present value of the future dividends.

The model sums the infinite series which gives the current price P. The equation most widely used is called the Gordon growth model. It is named after Myron J. Gordon of the University of Toronto, who originally published it along with Eli Shapiro in 1956 and made reference to it in 1959; although the theoretical underpin was provided by John Burr Williams in his 1938 text “The Theory of Investment Value”. The Gordon Model is as important to valuation theory as Bayes Theorem is to decision theory. The variables are:

• P = Target price
• D1= is the value of the next year’s dividends. D1= ( 1 + g ) x D0
• r = Cost of Equity = riskfree rate + Unlevered beta * (1 + Debt / Market Cap)
• g = is the constant growth rate in perpetuity expected for the dividends.

Problems with the model

Because the model simplistically assumes a constant growth rate, it is generally only used for mature companies (or broad market indices) with low to moderate growth rates. Some well known drawbacks of this model are:

• The presumption of a steady and perpetual growth rate less than the cost of capital may not be reasonable.
• 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 D1 with earnings per share. However, this requires the use of earnings growth rather than dividend growth, which might be different. This approach is especially useful for computing a residual value of future periods.
• The stock price resulting from the Gordon model is hyper-sensitive to the growth rate “g” chosen
• As the growth rate is important cost of equity term. How for calculation r we use riskfree rate, unlevered beta and the levered, the model is very sensitive to changes in these variables.

# Comparison of TheLogicValue with Gordon Model

In TheLogicValue model we use the same variables that the Gordon Model because it is a mix of:

• Dividend Discount Model
• Earning Yield Gap
• Price Earning Ratio
• Replace dividend by EPS

The growth rate in the long term (g) is the main problem of the Gordon Model. For its part, TheLogicValue model

gets a more consistent result using EPS instead. A comparation between models is shown in the following charts.  When we change unlevered beta the movement in price is relevant when the range is below 0,9, an usual number in equity markets. However TheLogicValue has a more natural movement with low beta.

The Gordon model shows great sensitivity to variations in the unlevered  beta, specially when the beta value is below 0.9, a usual value in the financial markets. In contrast, TheLogicValue Model has a more natural movement with low beta values. The companies are levered or unlevered (with cash the levered is negative), and it is relevant for the valuation of the company. The Gordon Shapiro model has a when used in companies that are not leveraged or that have a high cash ratio. With positive debt both models present the same results. Again, TheLogicValue model has a more logic movement in the target price. The riskfree rate is a very important variable in valuation, and the price in Gordon Model has a high sensitivity with low rates. However, TheLogicValue model has smoother results that allow to obtain stable predictions even with very low risk free rates. The Equity Premium Risk usually is within the range of 2,5% and 4,5%. In this case, the sensitivity of the Gordon Model is relatively high, as we can see in the chart. We can say that TheLogicValue is a robust mathematical model with that responds consistently to changes in variables. This allows us to use a standardized method in a large number of countries using the same criteria for all listed companies.

We conclude that the model we use in TheLogicValue is an improvement in the stock selection process comparing with dividend discount model.

We conclude that, compared with dividend discout model, TheLogicValue model  is an improvement in the stock selection process.