Chapter 6 Notes: Common Stock Valuation

Common Stock Valuation

Introduction

  • The Stock Market

    • Warren Buffett quote: "If a business is worth a dollar and I can buy it for 40 cents, something good may happen to me."

    • Niels Bohr quote: "Prediction is difficult, especially about the future."

Learning Objectives

  • Aimed at developing a good understanding of security valuation methods:

    1. The basic dividend discount model.

    2. The two-stage dividend growth model.

    3. The residual income model and free cash flow model.

    4. Price ratio analysis.

Common Stock Valuation

  • Objective: Examine methods used by financial analysts for assessing the economic value of common stocks, categorized into:

    1. Dividend discount models

    2. Residual income model

    3. Free cash flow model

    4. Price ratio models

Security Analysis

Fundamental Analysis

  • Definition: The study of a company’s accounting statements and other financial and economic information to estimate the economic value of its stock.

  • Aim: Identify "undervalued" stocks to buy and "overvalued" stocks to sell.

  • Caution: Stocks thought to be undervalued may be correctly priced due to reasons not immediately evident. Simpler models demand more caution from analysts.

The Dividend Discount Model (DDM)

Overview

  • Definition: The value of a stock equals the present value of its future cash flows.

  • Purpose: Estimate the value of a share of stock by discounting all expected future dividend payments.

  • Basic DDM equation:
    P<em>0=racD</em>1(1+k)+racD<em>2(1+k)2+…+racD</em>T(1+k)TP<em>0 = rac{D</em>1}{(1 + k)} + rac{D<em>2}{(1 + k)^2} + … + rac{D</em>T}{(1 + k)^T}

  • Where:

    • $P_0$ = present value of future dividends

    • $D_t$ = dividend to be paid in year $t$

    • $k$ = risk-adjusted discount rate

  • Key Insight: The final expression in this equation typically consists of the majority of a stock’s value.

Example: The DDM Calculation

  • Scenario: Stock pays three annual dividends of $100, with a discount rate $k$ of 15%.

  • Calculation:
    P0=rac100(1.15)1+rac100(1.15)2+rac100(1.15)3=228.32P_0 = rac{100}{(1.15)^1} + rac{100}{(1.15)^2} + rac{100}{(1.15)^3} = 228.32

The Constant Growth Rate Model

Model Description

  • Assumes dividends will grow at a constant growth rate $g$.

  • Formula adjustments for growth:

    • $D{t+1} = Dt imes (1 + g)$

    • $D1 = D0 imes (1 + g)$

    • $D2 = D0 imes (1 + g)^2$

DDM Formula for Constant Growth

  • When dividends grow at a constant rate for $T$ years:
    P<em>0=racD</em>0(1+g)k−gP<em>0 = rac{D</em>0 (1 + g)}{k - g}

Example: Constant Growth Rate Calculation

  • Parameters: Current dividend $D_0 = 10$, growth rate $g = 10%$, discount rate $k = 8%$.

  • Calculation:
    P0=rac10imes(1+0.10)0.08−0.10P_0 = rac{10 imes (1 + 0.10)}{0.08 - 0.10}

The Constant Perpetual Growth Model

Model Description

  • Assumes dividends grow indefinitely at a constant rate $g$.

  • DDM formula for perpetual growth:
    P<em>0=racD</em>0(1+g)k−gP<em>0 = rac{D</em>0 (1 + g)}{k - g}

  • Note: Must hold that $g < k$.

Example: Constant Perpetual Growth Calculation

  • Context: DTE Energy dividends of $3.78, $k = 5%, $g = 2%.

  • Resulting estimated value:
    P0=rac3.78(1+0.02)0.05−0.02=128.52P_0 = rac{3.78(1 + 0.02)}{0.05 - 0.02} = 128.52

Estimating Growth Rate

Methods to Estimate Growth Rate $g$:

  1. Historical average dividend growth rate.

  2. Industry median or average growth rate.

  3. Sustainable dividend growth rate.

Historical Average Growth Rate Example

  • Broadway Joe Company dividends:

    • 2019: $2.20, 2018: $2.00, 2017: $1.80, 2016: $1.75, 2015: $1.70, 2014: $1.50.

  • Calculated percentage changes and average rates.

Sustainable Growth Rate

  • Definition: The growth rate consistent with the company's earnings.

  • Calculating sustainable growth using:

    • Payout Ratio = Proportion of earnings paid out as dividends.

    • Retention Ratio = Proportion of earnings retained for reinvestment.

  • Formula:
    SustainableextGrowthextRate=ROEimesRetentionextRatioSustainable ext{ } Growth ext{ } Rate = ROE imes Retention ext{ } Ratio

  • Essential Parameter:
    ROE=racNetextIncomeEquityROE = rac{Net ext{ } Income}{Equity}

Two-Stage Dividend Growth Model

Model Overview

  • Assumes a firm will grow at rate $g1$ for $T$ years, then at rate $g2$ perpetually thereafter.

  • Formula:
    P<em>0=racD</em>0(1+g<em>1)(1+k)T+racD</em>T(1+g<em>2)(k−g</em>2)(1+k)TP<em>0 = rac{D</em>0(1 + g<em>1)}{(1 + k)^T} + rac{D</em>T(1 + g<em>2)}{(k - g</em>2)(1 + k)^T}

Example of Two-Stage Model

  • Parameters: D0 = $5, g1 = -10%, g2 = 4%, k = 10%.

  • Calculation of present values of both growth stages.

Price Ratio Analysis

Key Ratios

  1. Price-Earnings Ratio (P/E):

    • Current stock price per share divided by annual EPS.

    • High P/E stocks often termed growth stocks, low P/E as value stocks.

  2. Price-Cash Flow Ratio (P/CF):

    • Current stock price divided by cash flow per share (net income + depreciation).

    • Cash flow can provide better insights than net income.

  3. Price-Sales Ratio (P/S):

    • Current stock price divided by annual sales per share.

    • High P/S suggests high growth; low suggests slow growth.

  4. Price-Book Ratio (P/B):

    • Market value divided by book (accounting) value of equity.

    • A ratio > 1 indicates value creation for shareholders.

Conclusion

Strategic Insights

  • Analysts face challenges in security valuation due to varied subjective interpretations of financial data.

  • Understanding multiple models aids in enhancing confidence in assessments while recognizing inherent subjectivity in valuations.

Chapter Reviews

  • Covered content: Security Analysis, Dividend Discount Models, Residual Income Model, Free Cash Flow Model, and Price Ratio Analysis.