Some of the most common types of intrinsic economic valuation model.

Instead of estimating each cash flow for each time period using a general-purpose DCF model that can be used for any investment asset, we can make reasonable simplifying assumptions for different kinds of specific investments in order to develop formulas by which these estimates can be made.

• These formulas provide shortcuts to operationalize the theory, and represent different types of the dividend discount model (DDM). 
• In each model type, dividends or free-cash-flow continue forever, but a terminal price may be assumed to simplify the analysis. 
• These model types can be given names so as to emphasize their specific simplifying assumptions.

Some of the most common types of intrinsic economic valuation model are

• constant dividend in perpetuity,
• constant dividend growth rate in perpetuity, e.g., decline (negative growth), slow growth, and fast growth,
• constant multistage dividend growth rates, e.g., two-stage and three-stage,
• variable logistic (LOGIT) dividend growth rates,
• free-cash-flow (FCF) used to estimate the cash distributions to equity owners, e.g., free-cash-flow with constant financial leverage (debt/equity ratio) and free-cash-flow with increasing financial leverage (rising debt/equity ratio), which in turn can be used either in a general DCF model or in a specific DDM model,
• special situations handled by a general-purpose DCF model that is customized to fit the circumstances of each investment case, e.g., rapid growth by external merger or acquisition (M&A) or by internal sudden expansion. Relatively complex M&A models are available elsewhere. In such cases the capital gains component of total return can greatly dominate the dividend component, especially when the number of years of dividends in the analysis is small.

Following the example of John Burr Williams (1938), four types of models of investment valuation and four types of dividend forecasts are illustrated below.

• The vertical axis is cash flow, and the scale is log-linear except for FCF forecasts which is linear. 
• The horizontal axis is time in years, and it continues to infinity. 
• A company lives forever, but its estimate of dividends or cash flow can have a finite life with a capital gain at the end of the forecast period.

Types of Growth
Models of Investment Valuation
Declining DDM	Constant DDM	Slow Growth DDM	Fast Growth DDM
Forecasts of Dividends or Free Cash Flow
Logit Growth DDM	2-Stage Growth DDM	FCF Constant D/E	FCF Rising D/E

• Slow and fast growth are relative to current average growth rates, historical precedents and the discount rate used in the model.
• Fast growth includes speculative growth. 
• LOGIT growth is a special case of S-curve growth for rapid followed by slower growth phases. 
• These growth patterns may be used in multi-stage models with different patterns for different stages of growth. See theory for the mathematics behind these models.

These models have been implemented in DCF Valuator, a free online web-based application that estimates intrinsic value per share, goal implied value, range of value with Monte Carlo simulation scenarios, and rate of return on investment for any common stock in any currency. For a walk-through tour of the DCF Valuator, click here and invoke any of the model types in the table.

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