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Equity Valuation: Concepts and Basic Tools

Equity

Categories of Equity Valuation Models

Learning Outcome Statement:

describe major categories of equity valuation models

Summary:

Equity valuation models are essential tools used by analysts to estimate the intrinsic value of securities. These models fall into three primary categories: present value models, multiplier models, and asset-based valuation models. Each category uses different methodologies and inputs to assess the value of a security, and analysts often employ multiple models to enhance the accuracy and reliability of their valuations.

Key Concepts:

Present Value Models

Present value models, also known as discounted cash flow models, calculate the intrinsic value of a security based on the present value of expected future benefits, such as dividends or free cash flows to equity. These models range from simple to complex, with examples including the Gordon growth model and two-stage dividend discount models.

Multiplier Models

Multiplier models, or market multiple models, derive the intrinsic value of a security from price multiples or enterprise value multiples of fundamental variables like earnings, sales, or book value. These models use ratios such as price-to-earnings (P/E) and enterprise value-to-EBITDA to compare relative values across companies.

Asset-Based Valuation Models

Asset-based valuation models estimate the value of a security by determining the net market value of a company's assets minus its liabilities and preferred shares. This approach is based on the concept that a business's value is equivalent to the sum of its assets' values.

Formulas:

Price to Earnings (P/E) Ratio

P/E=Share PriceEarnings Per Share (EPS)\text{P/E} = \frac{\text{Share Price}}{\text{Earnings Per Share (EPS)}}

The P/E ratio is used to assess the relative value of a company's shares by comparing its share price to its earnings per share.

Variables:
P/EP/E:
Price to Earnings ratio
SharePriceShare Price:
Current market price of the share
EPSEPS:
Earnings per share
Units: dimensionless

Background for the Dividend Discount Model

Learning Outcome Statement:

describe regular cash dividends, extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases

Summary:

The Dividend Discount Model (DDM) is a present value model that values equity based on the present value of expected future dividends. It considers various forms of dividends and corporate actions that affect shareholders, such as regular and extra dividends, stock dividends, stock splits, reverse stock splits, and share repurchases. Each of these elements plays a role in the valuation of stocks and the overall understanding of equity investment returns.

Key Concepts:

Regular Cash Dividends

These are dividends paid out regularly at known intervals, such as quarterly or annually, depending on the geographic location and company policy.

Extra Dividends

Also known as special dividends, these are paid by companies that do not follow a regular dividend schedule or are issued in addition to regular dividends, often seen in cyclical industries or during corporate restructuring.

Stock Dividends

These are dividends paid in the form of additional shares rather than cash, affecting the number of outstanding shares but not the total market value of the company.

Stock Splits

A corporate action where a company divides its existing shares into multiple shares to boost the liquidity of the shares, though it does not affect the market capitalization.

Reverse Stock Splits

This corporate action reduces the number of shares outstanding by consolidating shares, typically to increase the market price per share.

Share Repurchases

A transaction where a company buys back its own shares from the marketplace, reducing the number of outstanding shares, often seen as a method to return wealth to shareholders.

Dividend Payment Chronology

Involves several key dates including the declaration date, ex-dividend date, holder-of-record date, and payment date, which dictate when dividends are announced, when they are accounted for, and when they are paid.

Formulas:

Dividend Discount Model (DDM)

V0=∑t=1∞Dt(1+r)tV_0 = \sum_{t=1}^{\infty} \frac{D_t}{(1 + r)^t}

This formula calculates the present value of expected future dividends, assuming dividends continue indefinitely.

Variables:
V0V_0:
Present value of the stock
DtD_t:
Expected dividend in year t
rr:
Required rate of return
tt:
Time in years
Units: currency

Perpetual Preferred Stock Valuation

V0=D0rV_0 = \frac{D_0}{r}

Used to calculate the value of a non-callable, non-convertible perpetual preferred stock, assuming constant dividends over time.

Variables:
V0V_0:
Present value of the preferred stock
D0D_0:
Annual dividend payment
rr:
Required rate of return
Units: currency

Enterprise Value

Learning Outcome Statement:

describe enterprise value multiples and their use in estimating equity value

Summary:

Enterprise Value (EV) is a comprehensive measure used to estimate the total value of a company, often considered in the context of a potential takeover. It includes market capitalization, preferred stock, and debt, but subtracts cash and investments. EV multiples, particularly EV/EBITDA, are popular for comparing companies with different capital structures and are useful even when traditional P/E ratios are not applicable due to negative earnings.

Key Concepts:

Enterprise Value (EV)

Enterprise value is calculated as the sum of market capitalization, market value of preferred stock, and market value of debt, minus cash and cash equivalents. It represents the total value of the company as if it were to be taken over.

EV/EBITDA Multiple

This multiple is a valuation metric that compares the enterprise value of a company to its earnings before interest, taxes, depreciation, and amortization (EBITDA). It is useful for assessing companies with different capital structures and is less affected by accounting practices.

Market Value of Debt

When market quotations are not available, the market value of debt can be estimated using bond values from similar maturity, sector, and credit characteristics, or by using a discount rate applied to future debt payments.

Formulas:

Enterprise Value (EV)

EV=Market Capitalization+Market Value of Preferred Stock+Market Value of Debt−Cash and InvestmentsEV = \text{Market Capitalization} + \text{Market Value of Preferred Stock} + \text{Market Value of Debt} - \text{Cash and Investments}

This formula calculates the total takeover value of a company, accounting for its equity, debt, and liquid assets.

Variables:
EVEV:
Enterprise Value
MarketCapitalizationMarket Capitalization:
Total market value of the company's outstanding shares
MarketValueofPreferredStockMarket Value of Preferred Stock:
Total market value of the company's outstanding preferred shares
MarketValueofDebtMarket Value of Debt:
Total market value of the company's debt
CashandInvestmentsCash and Investments:
Total cash and cash equivalents held by the company
Units: currency (e.g., USD, EUR)

EV/EBITDA Multiple

EV/EBITDA=Enterprise Value (EV)EBITDA\text{EV/EBITDA} = \frac{\text{Enterprise Value (EV)}}{\text{EBITDA}}

This ratio provides a measure of how many times EBITDA a company is valued at in the market, useful for comparing companies with different levels of debt and tax structures.

Variables:
EV/EBITDAEV/EBITDA:
Enterprise Value to EBITDA ratio
EnterpriseValue(EV)Enterprise Value (EV):
Total value of the company as calculated above
EBITDAEBITDA:
Earnings before interest, taxes, depreciation, and amortization
Units: ratio

Method of Comparables and Valuation Based on Price Multiples

Learning Outcome Statement:

explain the rationale for using price multiples to value equity, how the price to earnings multiple relates to fundamentals, and the use of multiples based on comparables; calculate and interpret the following multiples: price to earnings, price to an estimate of operating cash flow, price to sales, and price to book value; explain advantages and disadvantages of each category of valuation model

Summary:

The Method of Comparables and Valuation Based on Price Multiples involves comparing the relative values of stocks using various financial ratios known as multiples. These multiples, such as P/E, P/S, and P/B, help determine if a stock is fairly valued, undervalued, or overvalued compared to a benchmark. This method is grounded in the economic principle that identical assets should sell for the same price. Analysts use these multiples to make relative valuations and identify potential investment opportunities.

Key Concepts:

Price to Earnings (P/E) Ratio

The P/E ratio is a valuation multiple that compares the price of a stock to its earnings per share (EPS). It is used to determine if a stock is overvalued or undervalued relative to its earnings.

Price to Sales (P/S) Ratio

The P/S ratio compares the price of a stock to its revenue per share. It is useful during economic downturns or high growth periods as it is less affected by earnings volatility.

Price to Book (P/B) Ratio

The P/B ratio compares the market value of a stock to its book value per share. It indicates how much shareholders are paying for the net assets of a company.

Price to Cash Flow (P/CF) Ratio

The P/CF ratio compares the price of a stock to its operating cash flow per share. It provides an indication of the value of a stock relative to the cash it generates.

Enterprise Value (EV)

Enterprise value is a comprehensive measure of a company's total value, often used as the basis for more complex valuation multiples like EV/EBITDA. It includes market capitalization, debt, preferred stock, and subtracts cash and cash equivalents.

Formulas:

Price to Earnings Ratio

P/E=Market Price per ShareEarnings per Share (EPS)P/E = \frac{\text{Market Price per Share}}{\text{Earnings per Share (EPS)}}

This formula is used to determine how much investors are willing to pay per dollar of earnings, which helps in comparing the relative value of companies.

Variables:
P/EP/E:
Price to Earnings Ratio
MarketPriceperShareMarket Price per Share:
Current market price of the company's stock
EarningsperShare(EPS)Earnings per Share (EPS):
Company's net earnings divided by the number of outstanding shares
Units: dimensionless

Price to Sales Ratio

P/S=Market Price per ShareRevenue per ShareP/S = \frac{\text{Market Price per Share}}{\text{Revenue per Share}}

This ratio is used to compare the price of a company's stock to its revenue generation capability per share.

Variables:
P/SP/S:
Price to Sales Ratio
MarketPriceperShareMarket Price per Share:
Current market price of the company's stock
RevenueperShareRevenue per Share:
Total revenue divided by the number of outstanding shares
Units: dimensionless

Price to Book Ratio

P/B=Market Price per ShareBook Value per ShareP/B = \frac{\text{Market Price per Share}}{\text{Book Value per Share}}

This ratio helps investors understand the market valuation of a company relative to its book value.

Variables:
P/BP/B:
Price to Book Ratio
MarketPriceperShareMarket Price per Share:
Current market price of the company's stock
BookValueperShareBook Value per Share:
Total book value of the company divided by the number of outstanding shares
Units: dimensionless

Price to Cash Flow Ratio

P/CF=Market Price per ShareCash Flow per ShareP/CF = \frac{\text{Market Price per Share}}{\text{Cash Flow per Share}}

This ratio indicates how much investors are paying for each dollar of cash flows generated by the company.

Variables:
P/CFP/CF:
Price to Cash Flow Ratio
MarketPriceperShareMarket Price per Share:
Current market price of the company's stock
CashFlowperShareCash Flow per Share:
Operating cash flow divided by the number of outstanding shares
Units: dimensionless

The Gordon Growth Model

Learning Outcome Statement:

calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate

Summary:

The Gordon Growth Model is a dividend discount model (DDM) that assumes dividends grow indefinitely at a constant rate, making it suitable for companies in mature growth phases or with stable dividend growth histories. The model calculates the intrinsic value of a stock based on expected future dividends, adjusted for a constant growth rate and a required rate of return. The model is sensitive to the growth rate and required return assumptions and is typically used for companies that consistently pay dividends.

Key Concepts:

Gordon Growth Model

A method to estimate the intrinsic value of a stock by assuming dividends grow at a constant rate indefinitely. It is particularly useful for companies with stable growth and consistent dividend payments.

Dividend Growth Rate

The rate at which dividends are expected to increase over time. In the Gordon Growth Model, this rate is assumed to be constant.

Required Rate of Return

The minimum rate of return investors expect to receive from an investment, used to discount the future dividends to their present value.

Sensitivity to Growth and Return Assumptions

The intrinsic value calculated by the Gordon Growth Model is highly sensitive to the assumptions about dividend growth rate and required rate of return, making accurate estimation crucial.

Sustainable Growth Rate

A rate that can be maintained indefinitely without having to increase financial leverage or equity. It is calculated as the product of the retention rate and the return on equity.

Formulas:

Gordon Growth Model Formula

V0=D0(1+g)r−gV_0 = \frac{D_0 (1 + g)}{r - g}

This formula calculates the present value of an infinite series of future dividends that are expected to grow at a constant rate.

Variables:
V0V_0:
Present value of the stock
D0D_0:
Current dividend per share
gg:
Constant growth rate of dividends
rr:
Required rate of return
Units: currency units

Sustainable Growth Rate Formula

g=b×ROEg = b \times \text{ROE}

This formula estimates the growth rate that a company can sustain by reinvesting its earnings back into the business.

Variables:
gg:
Sustainable growth rate
bb:
Earnings retention rate (1 - Dividend payout ratio)
ROEROE:
Return on equity
Units: percentage

Preferred Stock Valuation

Learning Outcome Statement:

calculate the intrinsic value of a non-callable, non-convertible preferred stock

Summary:

Preferred stock valuation involves calculating the intrinsic value of preferred shares, which are a type of equity that typically have priority over common stock in dividend payments and asset claims during liquidation. The valuation can be done using the present value of a perpetuity formula for perpetual preferred stocks or a more complex formula that accounts for maturity and dividend payments for term preferred stocks.

Key Concepts:

Perpetual Preferred Stock

Perpetual preferred stock has no maturity date, and dividends are paid indefinitely. The value of such stock can be calculated using the present value of a perpetuity formula, assuming a constant dividend and required rate of return.

Term Preferred Stock

Term preferred stock has a specified maturity date. Its value is calculated by discounting the expected dividends and the par value at maturity, reflecting the time value of money and the risk associated with the stock.

Required Rate of Return

The required rate of return is crucial in discounting future cash flows. It can be estimated using models like the Capital Asset Pricing Model (CAPM), which considers the risk-free rate, the stock's beta, and the market risk premium.

Formulas:

Present Value of a Perpetuity

V0=D0rV_0 = \frac{D_0}{r}

This formula calculates the value of a perpetual preferred stock by dividing the annual dividend by the required rate of return.

Variables:
V0V_0:
Present value of the preferred stock
D0D_0:
Constant annual dividend
rr:
Required rate of return
Units: currency

Value of Term Preferred Stock

V0=∑t=1nDt(1+r)t+F(1+r)nV_0 = \sum_{t=1}^{n} \frac{D_t}{(1 + r)^t} + \frac{F}{(1 + r)^n}

This formula calculates the value of a term preferred stock by discounting the expected dividends and the par value at maturity, considering the time value of money and the required rate of return.

Variables:
V0V_0:
Present value of the preferred stock
DtD_t:
Dividend at time t
rr:
Required rate of return
FF:
Par value at maturity
nn:
Number of periods until maturity
Units: currency

Asset-Based Valuation

Learning Outcome Statement:

describe asset-based valuation models and their use in estimating equity value

Summary:

Asset-based valuation models estimate a company's equity value by assessing the market or fair values of its assets and liabilities. These models are particularly effective for companies with tangible assets and minimal intangible assets. They provide a baseline or 'floor' value and are often used alongside other valuation methods for a comprehensive analysis. Asset-based valuation is crucial for companies with significant tangible assets but can be challenging when assets have indeterminate market values or in hyper-inflationary environments.

Key Concepts:

Asset-Based Valuation

This valuation method involves estimating the market or fair values of a company's assets and liabilities. It is suitable for companies with significant tangible assets and is used to provide a baseline value of the company.

Tangible vs Intangible Assets

Asset-based valuation is more straightforward for companies with tangible assets (like real estate, equipment) than for those with intangible assets (like brand reputation or intellectual property), which are harder to value.

Market vs Book Value

There can be significant differences between the book values recorded on the balance sheet and the actual market values of assets and liabilities. Accurate asset-based valuation depends on correct market value estimations.

Use in Different Company Types

While typically used for private companies, asset-based valuation can also be applied to public companies, financial institutions, and natural resource firms, especially in scenarios like liquidation or minimal operation.

Formulas:

Adjusted Book Value

ABV=MVassets−MVliabilitiesABV = MV_{assets} - MV_{liabilities}

This formula calculates the adjusted book value by subtracting the market value of liabilities from the market value of assets. It provides a baseline equity value of the company.

Variables:
ABVABV:
Adjusted Book Value
MVassetsMV_{assets}:
Market Value of Assets
MVliabilitiesMV_{liabilities}:
Market Value of Liabilities
Units: currency (e.g., USD)

Estimated Value and Market Price

Learning Outcome Statement:

evaluate whether a security, given its current market price and a value estimate, is overvalued, fairly valued, or undervalued by the market

Summary:

This LOS focuses on evaluating securities based on their estimated intrinsic value compared to their current market price. Analysts use various valuation models to determine if a security is overvalued, fairly valued, or undervalued. The process involves assessing the accuracy of the market price as an estimate of value and considering the analyst's confidence in the valuation model and inputs used.

Key Concepts:

Estimated Value vs. Market Price

Analysts compare the estimated intrinsic value of a security to its market price to determine if it is overvalued, fairly valued, or undervalued. This comparison forms the basis for investment decisions such as buy, sell, or hold recommendations.

Confidence in Valuation

The confidence an analyst has in the valuation model and the inputs significantly affects the investment decision. A high confidence level might lead to decisive actions based on small price-value discrepancies, whereas low confidence might require larger discrepancies before acting.

Convergence of Market Price to Intrinsic Value

Analysts must consider the likelihood and timeframe within which the market price of a security will converge to its estimated intrinsic value. This consideration is crucial for realizing the potential gains from investment decisions based on valuation discrepancies.

Reevaluation of Models and Inputs

If a significant number of securities appear overvalued or undervalued, analysts may need to reevaluate the models and inputs used in their valuation to ensure accuracy and reliability before making investment recommendations.

Dividend Discount Model (DDM) and Free-Cash-Flow-to-Equity Model (FCFE)

Learning Outcome Statement:

calculate the intrinsic value of a non-callable, non-convertible preferred stock

Summary:

The Dividend Discount Model (DDM) and Free-Cash-Flow-to-Equity Model (FCFE) are fundamental approaches in equity valuation. DDM focuses on expected dividends to value a stock, while FCFE models the cash flows available to equity shareholders after accounting for expenses, taxes, and reinvestment. The required rate of return, crucial for these models, can be estimated using the Capital Asset Pricing Model (CAPM) or other methods involving economic judgments or company bond yields.

Key Concepts:

Dividend Discount Model (DDM)

DDM values a stock based on the present value of expected future dividends. It is particularly applicable to companies that pay regular dividends.

Free-Cash-Flow-to-Equity (FCFE)

FCFE measures the cash flow available to equity shareholders after accounting for all expenses, taxes, and necessary reinvestment. It is used to assess the value of a stock based on these available cash flows.

Capital Asset Pricing Model (CAPM)

CAPM is used to estimate the required rate of return for a stock, incorporating the risk-free rate, the stock's beta, and the market risk premium.

Preferred Stock Valuation

Preferred stock is valued using a simplified DDM if it pays a fixed dividend and is non-callable and non-convertible. The model reduces to the present value of a perpetuity formula.

Formulas:

Required rate of return using CAPM

ri=rf+βi(Market risk premium)r_i = r_f + \beta_i (\text{Market risk premium})

This formula calculates the required rate of return for a stock based on its risk profile and the overall market risk.

Variables:
rir_i:
required rate of return on share i
rfr_f:
current expected risk-free rate of return
βi\beta_i:
beta of the stock i
MarketriskpremiumMarket risk premium:
expected return of the market in excess of the risk-free return
Units: percentage

Valuation of perpetual preferred stock

V0=D0rV_0 = \frac{D_0}{r}

This formula calculates the value of a non-callable, non-convertible perpetual preferred stock by treating it as a perpetuity.

Variables:
V0V_0:
current value of the stock
D0D_0:
annual dividend payment
rr:
required rate of return
Units: currency

Multistage Dividend Discount Models

Learning Outcome Statement:

calculate and interpret the intrinsic value of an equity security based on the Gordon (constant) growth dividend discount model or a two-stage dividend discount model, as appropriate

Summary:

Multistage Dividend Discount Models (DDMs) are used to estimate the intrinsic value of equity securities that experience different phases of growth. The two-stage DDM is particularly useful for companies transitioning from a high growth phase to a stable growth phase, while the Gordon growth model is used for companies with constant growth rates. These models help in understanding the value of a company by considering expected future dividends and growth rates.

Key Concepts:

Two-stage Dividend Discount Model

This model is used for companies expected to have a high growth rate for a finite period followed by a sustainable lower growth rate. It involves calculating the present value of dividends during the high growth period and the terminal value at the end of this period using a lower growth rate.

Gordon Growth Model

Applicable for companies with constant growth rates, this model estimates the terminal value of dividends growing at a sustainable rate into perpetuity. It is used to calculate the present value of expected future dividends.

Characteristics for Model Applicability

The choice between a constant growth model and a multistage growth model depends on the company's growth characteristics. Companies with stable, predictable growth are suitable for the Gordon model, while those with variable growth rates are better evaluated with multistage models.

Advantages and Disadvantages

Multistage models are flexible and can model complex growth patterns but are sensitive to the assumptions about growth rates and duration. Constant growth models are simpler and less sensitive to assumptions but may not accurately reflect companies with changing growth rates.

Formulas:

Two-stage Dividend Discount Model

V0=∑t=1nD0(1+gS)t(1+r)t+Vn(1+r)nV_0 = \sum_{t=1}^{n} \frac{D_0 (1 + g_S)^t}{(1 + r)^t} + \frac{V_n}{(1 + r)^n}

This formula calculates the present value of expected dividends during the high growth phase and the present value of the terminal value at the end of the high growth phase.

Variables:
V0V_0:
Present value of the stock
D0D_0:
Dividend at time 0
gSg_S:
Short-term growth rate
rr:
Required rate of return
VnV_n:
Terminal value at time n
nn:
Number of years in the high growth phase
Units: currency

Terminal Value using Gordon Growth Model

Vn=Dn+1r−gLV_n = \frac{D_{n+1}}{r - g_L}

This formula estimates the terminal value of the stock using the dividend expected at the end of the high growth phase and the sustainable long-term growth rate.

Variables:
VnV_n:
Terminal value at time n
Dn+1D_{n+1}:
Dividend at time n+1
rr:
Required rate of return
gLg_L:
Long-term growth rate
Units: currency

Dividend at time n+1

Dn+1=D0(1+gS)n(1+gL)D_{n+1} = D_0 (1 + g_S)^n (1 + g_L)

This formula calculates the expected dividend at time n+1, considering the growth during the high growth phase and the transition to the long-term growth rate.

Variables:
Dn+1D_{n+1}:
Dividend at time n+1
D0D_0:
Initial dividend
gSg_S:
Short-term growth rate
gLg_L:
Long-term growth rate
nn:
Number of years in the high growth phase
Units: currency
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