13 - Asset Pricing III - Equity Valuation

Asset Pricing III: Equity Valuation

Overview

• Understanding how equity (stock) is priced using a uniform annuity framework.

• Focus on expected cash flow structures derived from stock ownership.

Agenda

• Analyze Cash Flow Stream (CFS) for equity holders.

• Treat dividend payments as deterministic cash flows (approximating reality).

• Apply growth annuity formula to dividend payments.

• Use classical asset pricing theory to derive equity share price.

Cash Flow from Ownership of Stock

• Right to Future Profits: Ownership provides access to future profits through dividends and potential selling price.

• Cash Flow Components:

  • Dividends received during holding period.

  • Selling Price upon liquidation after collecting final dividend.

• Deterministic Discounting: This cash flow stream requires discounting to derive current investment value.

Addressing Uncertainty in Future Values

• Problem Statement: Unknown future dividend values and selling price complicate pricing equity.

• Simplifying Assumptions: Simplifying assumptions necessary to adapt deterministic cash flow models to equity.

Cash Flow Structures

• Buy and Hold Scenario: CFS for holding stock generated over periods:

  • Period 0: Cash flow CFS=(−0,1,2,…,+)

  • Sell after k periods: CFS=(−,+1,+2,…,+ + +)

  • This evolving flow must be analyzed further as ownership transfers.

Classical Theory Application

• CFS Analysis: Consider CFS expressions of different holders to understand valuation through time.

• Fundamental relations using classical theory:

  • Present value reflects discounted future cash flows.

  • CFS perpetuates over time, even if individual holders change.

Equities as Perpetuities

• Perpetual Cash Flow: Price of equity reflects expected future dividends modeled as perpetual cash flows.

• Challenges: Still face uncertainty regarding future dividends.

• Assumption Adjustments: Adopt deterministic frameworks to find usable equity pricing strategies despite growth ambiguity.

Growth Annuity Concepts

• Constant Growth Assumption: Assume dividends grow at a constant geometric growth rate:

  • (D_t = D_{t-1} (1 + g))

  • Enables simplification of valuation through consistent growth expectations.

Equity Valuation Methodology

• Pricing CFS with Growth Rate: Integrate expected growth into dividend valuation:

  • (PV = D_1 / (r - g))

  • CFS considered as summation of present values influenced by growth.

Numerical Example

• Example Problem: Calculating share price with known answers using growth dividend discount model:

  • Initial dividend: $1, growth rate: 3%, interest: 5%.

    • Calculated Price = $51.50 for expected dividend of $1.03.

Back Calculating Implied Growth Rate

• Valuation Scenario: Given Company X’s proposed fair price of $55, backwards resolution of implied growth from known parameters yielding:

  • (g = \frac{55 \times 0.05 - 1}{55 + 1})

Conclusions and Cautions

• Constant geometric growth assumption forms basis for analysis.

• DDM helpful in conceptualizing stock valuation effects.

  • Factors Increasing Price: Higher expected future dividends increase stock prices.

  • Factors Decreasing Price: Higher opportunity costs (interest) decrease stock prices.

• Cautions: This model is simplistically applied; better valuation models exist for practical valuation.