Finance Quiz on Sustainable Growth Rate

Chapter 6: Common Stock Valuation

• The chapter aims to explore methods used by financial analysts to determine the economic value of common stocks.
• These methods are categorized into four types: Dividend discount models, Residual Income models, Free Cash Flow models, and Price ratio models.
• Warren Buffett stated, "If a business is worth a dollar and I can buy it for 40 cents, something good may happen to me."
• Niels Bohr noted, "Prediction is difficult, especially about the future."
• Learning objectives include understanding and differentiating between different security valuation methods. These include the basic dividend discount model, the two-stage dividend growth model, the residual income model and free cash flow model, and price ratio analysis.

The Stock Market

• The stock market is a complex system, making future predictions challenging.
• Fundamental analysis involves studying company financials and economic factors to estimate a stock's value. The goal is to find undervalued and overvalued stocks. However, stocks may already be properly valued for reasons not readily apparent.

The Dividend Discount Model (DDM)

• The DDM is a method to estimate the value of a stock by discounting expected future dividend payments.
• The basic DDM equation is: P₀ = (D₁ / (1+k)) + (D₂ / (1+k)²) + ... + (Dₜ / (1+k)ᵗ), where:
• P₀ = the present value of all future dividends at time 0.
• Dₜ = the dividend to be paid at time t.
• k = the appropriate risk-adjusted discount rate

Example: The Dividend Discount Model

• Example: A stock is expected to pay three 100annualdividends.Therisk−adjusteddiscountrate(k)is15100 annual dividends. The risk-adjusted discount rate (k) is 15%. The current stock value (P₀) is 100annualdividends.Therisk−adjusteddiscountrate(k)is15228.32.

The Constant Growth Rate Model

• Assumes dividends grow at a constant rate (g).
• The dividend in the next period, (t + 1), is: Dₜ₊₁ = Dₜ × (1 + g)
• For constant dividend growth for "T" years, the DDM formula is: P₀ = D₀ × (1 + g) ^ t / (k-g) , where:
• P₀ = the current stock value.
• D₀ = the current dividend.
• g =constant dividend growth rate.
• k = the appropriate risk-adjusted discount rate

Example: The Constant Growth Rate Model

• Example: Given a current dividend of 10,a1010, a 10% growth rate, 20 yearly dividends, and an 8% discount rate, the stock value (P₀) is 10,a10243.86.

The Constant Perpetual Growth Model

• Assumes dividends grow at a constant rate (g) forever.
• The DDM formula for constant perpetual dividend growth is: P₀ = D₁ / (k – g), where:
• P₀ = the current stock value.
• D₁ = the next dividend.
• g = the constant dividend growth rate.
• k = the appropriate risk-adjusted discount rate.

Example: Constant Perpetual Growth Model

• Example: In 2019, DTE Energy's (DTE) dividend was 3.78.Usingadiscountrate(k)of53.78. Using a discount rate (k) of 5% and a growth rate (g) of 2%, the estimated DTE value is 3.78.Usingadiscountrate(k)of5128.52.

The Dividend Discount Model: Estimating the Growth Rate

• Estimating the growth rate in dividends (g) can be done through methods such as using historical average, industry median, or sustainable growth rate.

The Historical Average Growth Rate

• Example: The Broadway Joe Company's dividend history is used to calculate the arithmetic and geometric average growth rates.

The Sustainable Growth Rate

• The sustainable growth rate is ROE × Retention Ratio = ROE × (1 − Payout Ratio)
• ROE= Net Income / Equity
• Payout Ratio = Proportion of earnings paid out as dividends
• Retention Ratio = Proportion of earnings retained for investment.

Example: Calculating and Using the Sustainable Growth Rate

• Example: American Electric Power (AEP) had an ROE of 10.5%, 3.97inearningspershare,and3.97 in earnings per share, and 3.97inearningspershare,and2.68 dividend per share. The Retention rate is 32.5%; sustainable growth rate is 3.41%.

Example: Calculating and Using the Sustainable Growth Rate, II.

• Example: The actual early-2019 stock price of AEP was $73.05. Using the Sustainable Growth Rate to value the stock gives an extremely poor estimate. A detailed analysis would look into the values of g and k.

Analyzing ROE

• To estimate a sustainable growth rate you need a relatively stable dividend payout ratio and ROE. Changes in sustainable growth rate often come from changes in ROE.
• The DuPont formula breaks down ROE into profit margin, asset turnover, and equity multiplier.
• Managers can increase the sustainable growth rate by a number of possible measures

The Two-Stage Dividend Growth Model

• This model assumes two stages of dividend growth. The first stage experiences a growth rate g₁ for T years, then a perpetual second stage with growth rate g₂.
• The model's formula is given as: P₀ = Do (1+g₁)^t / (k-g₁) + Do (1+g₁)^t (1+g₂)/(1+k)^t × (1 / (k-g₂))

Using the Two-Stage Dividend Growth Model, I. & II.

• Examples with formulas and calculations to illustrate the two-stage model, including handling dividends that shrink and later grow, along with different discount rates are provided. These examples detail the sum of present values of the dividends.

Using the DDM to Value a Firm Experiencing "Supernormal" Growth, I and II, III

• Example of a firm experiencing phenomenal growth (30% per year for three years, then 10% thereafter).
• Calculations detail how the value is determined.

The H-Model, I and II

• The H-Model assumes a linear decline in growth rate (example, from 30% to 10% over 3 years).

Discount Rates for Dividend Discount Models

• The discount rate for a stock can be estimated using the Capital Asset Pricing Model (CAPM). This formula is: Discount rate = U.S. T-bill Rate + (Stock Beta X Stock Market Risk Premium).

Observations on Dividend Discount Models, I and II

• These sections include critical observations on the applicability and limitations of constant growth perpetual models and two-stage models, addressing factors like unrealistic constant growth assumptions, dividend-paying companies, sensitivities to the choice of growth and discount rates, and the difficulty in precisely estimating g and k.

Residual Income Model (RIM), I, II, and III

• The RIM model finds value for companies that don't pay dividends, using the clean surplus relationship.
• The change in book value per share is equal to earnings per share minus dividends.
• An equivalent formula for the Residual Income Model (RIM) is provided. Given inputs that include earnings per share at time 0, book value per share at time 0, earnings growth rate g, and discount rate k, two equivalent formulas for the Residual Income Model are provided in RIM III

Using the Residual Income Model

• Example with Quackenbush, Inc. (DUCK), illustrating how to use the RIM and its inputs to value the company when it does not pay dividends and the stock market price is provided.

The Growth of DUCK

• Example showing calculating a growth rate (g) from given data to arrive at the market price for DUCK

Free Cash Flow, I, II, and III

• Addresses valuing companies that don't pay dividends using free cash flow (FCF).
• Explains how depreciation impacts earnings and cash flows
• Provides a formula for calculating FCF: FCF = EBIT(1 – Tax Rate) + Depreciation − Capital Spending - Change in Net Working Capital
• Illustrative example comparing two companies, Twiddle-Dee and Twiddle-Dum, with the same cash flow but different depreciation schedules.

DDMs Versus FCF

• DDMs calculate equity value only; FCF models calculate firm value.
• FCF can go to both debt holders and stockholders.
• Given FCF, calculates equity value, then subtracts the debt value to determine the total value of the equity.
• Asset betas are needed to account for risk, not equity betas.

Asset Betas

• Asset Betas measure industry-wide risk.
• Converting reported equity betas to asset betas is necessary for company valuation as investors use debt to adjust risk portfolios.
• A formula for converting equity betas to asset betas is provided.

The FCF Approach, Example

• Lists necessary inputs for estimating FCF including net income, depreciation, capital expenditures, the growth rate in FCF, the required discount rate, tax rate, debt/equity ratio, and equity beta.
• This is used with a modified DDM formula (using Free Cash Flow instead of dividends)

Valuing Landon Air: A New Airline

• Example of a company valuation using free cash flow and the capital asset pricing model.

Price Ratio Analysis, I, II, and III

• P/E ratio, Earnings yield, and the relationship between high/low P/E ratios and growth/value stocks (e.g., Intel Corp data).
• P/CF ratio: a relationship between current stock price and current cash flow per share.
• P/S ratio, P/B ratio

Price/Earnings Analysis, Intel

• Example of determining expected stock prices from historical P/E ratios and projected EPS, using Intel corp. for illustrative data

Price/Cash Flow Analysis, Intel

• Example of using historical P/CF ratios to determine stock prices, using Intel corp. for illustrative data

Price/Sales Analysis, Intel

• Example of using historical P/S ratios to determine stock prices, using Intel corp. for illustrative data

Enterprise Value Ratios, Overview and Example

• Explains the enterprise value (EV) to EBITDA ratio with an example, using Kourtney's Kayaks.
• Explains the meaning of EBITDA

Using Enterprise Value Ratio to Estimate Stock Price

• Provides an example using the EV/EBITDA ratio to estimate stock prices, using Qwerty Corporation

An Analysis of CVS Health Corporation (multiple sections)

• Examines how to value CVS using various methods, including calculating sustainable growth rate, CAPM discount rate, using and interpreting different financial quotes, and comparing different valuation estimates using multiple models.

Final Thoughts: CVS

• Highlights the high degree of subjectivity in financial valuation and the usefulness and limitations of different valuation modelling techniques. The wide range of possible values found when using various models for pricing is highlighted.
• Different models produce variable estimates, so the lesson here is to select models with confidence and the subjective nature of valuation is critical.

Chapter Review, I and II

• Summary of the common stock valuation models covered.

Test your understanding of concepts related to the sustainable growth rate, the DuPont formula, and dividend growth models. This quiz covers essential financial metrics and their implications for management decisions. Dive into key definitions and calculations that shape effective financial strategies.