Chapter 9: Stocks And Their Valuation Models

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This document discusses the valuation models used to assess the worth of stocks, primarily focusing on discounted cash flow analysis and dividend valuation models. It covers the fundamental principles of stock valuation, including the discounted dividend model, constant growth stocks, and the valuation of non-constant growth stocks, along with preferred stock valuation. The discussion emphasizes the importance of estimating future dividends, growth rates, and required returns to determine stock prices accurately. Additionally, the document explores the sensitivity of stock prices to various factors and the scenarios where traditional valuation models may not be applicable.

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Stock valuation is a critical aspect of financial analysis and investment decision-making, underpinning strategies for equity investment and portfolio management. The core premise of stock valuation involves determining the present value of expected future cash flows generated by the stock. These cash flows are typically in the form of dividends paid to shareholders or free cash flows attributable to equity holders. Understanding the various models of valuation is essential for investors, analysts, and managers to assess whether a stock is overvalued, undervalued, or fairly valued based on current market prices.

The discounted cash flow (DCF) method serves as the foundation for most stock valuation techniques. The DCF approach involves projecting the future cash flows generated by the stock and discounting them to their present value using an appropriate discount rate, which reflects the riskiness of those cash flows. In the context of stocks, two primary valuation approaches emerge: the dividend discount model (DDM) and the valuation based on free cash flows.

The dividend discount model, especially the Gordon Growth Model, simplifies stock valuation by assuming that dividends grow at a constant rate indefinitely. This model posits that the intrinsic value of a stock is the present value of all expected future dividends, which can be expressed mathematically as:

P₀ = D₁ / (r_s – g)

where P₀ is the current stock price, D₁ is the dividend expected next year, r_s is the required rate of return, and g is the constant growth rate of dividends.

This model assumes that the firm’s dividends will grow at a steady rate, which is reasonable for mature, stable companies. For example, if a company just paid a dividend of $1.15, and dividends are expected to grow at 8.3%, with a required return of 13.7%, the stock’s intrinsic value can be estimated as follows:

D₁ = D₀ × (1 + g) = $1.15 × 1.083 ≈ $1.245

Then,

P₀ = $1.245 / (0.137 – 0.083) ≈ $43.12

This calculation illustrates how sensitive stock prices are to assumptions about the dividend growth rate and required return. Changes in these parameters can lead to significant variations in the valuation, emphasizing the importance of accurate estimates and scenario analysis in practice. The relationships among dividends, growth rates, and required returns are nonlinear, and small changes can lead to exponential effects on the computed stock price.

Furthermore, the expected rate of return on a stock, calculated via:

r_s = (D₁ / P₀) + g

represents the combination of the dividend yield and the capital gains yield, encapsulating the dual role of dividends and stock appreciation in investor returns.

Valuation becomes more complex when dividends do not grow at a constant rate, necessitating the use of multi-stage models. In such cases, analysts estimate a short-term non-constant growth rate until a horizon date, followed by a constant growth assumption thereafter. The stock’s value at the horizon can be calculated as the present value of the projected dividends during the non-constant growth period plus the discounted horizon or continuing value, which accounts for the perpetuity of dividends beyond the horizon.

Non-constant growth models are particularly relevant for companies experiencing rapid growth, restructuring, or industry shifts. For instance, a firm might have a high growth rate for a few years before stabilizing, requiring valuation techniques that can accommodate such dynamics. The horizon value or terminal value, calculated at the horizon date, forms a critical component of this process. For example, if a company’s dividend grows at 30% for three years, then at 8% afterward, the valuation involves calculating the present value of the immediate dividends and the terminal value derived from the perpetuity formula:

Horizon Value = Dₙ₊₁ / (r_s – g_long-term)

Preferred stock, which pays a fixed dividend and has no growth, can be valued similarly to perpetuity formulas used in bond valuation:

V_p = D / r_p

For a preferred stock paying a $10 annual dividend with a required return of 10.3%, the value is:

V_p = $10 / 0.103 ≈ $97.09

When preferred stock has a finite maturity, its valuation incorporates the present value of all future dividends and the face value at maturity, discounted at the appropriate rate, similar to fixed-income securities. Variations in required returns impact these valuations significantly, as demonstrated through sensitivity analyses, where factors such as dividend levels, growth rates, and required returns influence market prices. These models assume the stability of estimates and are most accurate for firms with predictable dividend policies and stable growth environments.

In conclusion, stock valuation models serve as essential tools for measuring intrinsic value and informing investment decisions. While the dividend discount models are straightforward and suitable for mature companies, more complex models are required to handle growth variability and other real-world complexities. Accurate valuation hinges on reliable estimates of future dividends, growth rates, and discount rates, with sensitivity analysis aiding in understanding possible valuation ranges. These models collectively form a cornerstone of financial analysis, emphasizing the importance of diligent forecasting and scenario analysis to navigate the uncertainties inherent in equity valuation.

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