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CFA2: Equity

Asset valuation contributions

  • Graham and Dodd: estimation of investment’s intrinsic value by multiplying earnings power by an appropriate capitalization factor
  • Williams: present value of future cash flows, discounted at the opportunity cost of the capital
  • Markowitz: return depends on the systematic risk (modern portfolio theory)

Equity Valuation Process

Valuation: process of estimating an asset’s value based either on indicative future returns or by comparison with similar assets; use for following:

  1. Stock selection guide the purchase, holding or sale of stocks
  2. Reading the market identification of expectations
  3. Corporate actions valuation value determination of proposed M&A, divestitures, management buyouts (MBOs), and recapitalization efforts.
  4. Fairness opinions support professional opinions about the fairness of a price in M&A
  5. Planning and consulting evaluation of effects of proposed strategies on the firm’s stock price
  6. Communication with analysts and investors provides management, investors and analysts with a common basis upon company’s performance, current state and future plans
  7. Valuation of private business determine the value of firms or holdings in firms that are not publicly traded
  8. Portfolio management determine the value and risk of a portfolio of investments
  • Quantitative factors most appropriate and reliable information regarding the company’s financial disclosures and accounting information; highly objective in nature
  • Qualitative factors include the analyst’s viewpoint on business acumen and integrity of management as well as the transparency and quality of the company’s accounting practices: highly subjective

Importance of inputs quality in valuation

  • Quality of earnings analysis: investigation of the associated issues with accuracy and detail of firm's disclosures; requires examination of the firm’s income statement, balance sheet, and the notes to the financial statements; firms with more transparent earnings tend to have higher market values

Interpretation of footnotes and disclosures

  • Recognition of income: prepaid sales and advanced billing
  • Reclassifying gains and nonoperating income: distorts the results, often hiding underperformance or a decline in sales
  • Expense recognition and losses: delay of recognition of expenses, the capitalization of expenses, and the classification of operating expenses as nonoperating.
  • Amortization, depreciation, and discount rates: selection of amortization and depreciation methods, and choice of discount rates can defer expense recognition
  • Off-balance sheet issues: special purpose entities (SPEs), which can be used to increase sales or to obscure the nature and value of assets or liabilities
Ex ante alpha = realized return - expected return
Ex post alpha = historical HPR − historical return on similar assests
  • Going-concern value: based on the assumption that the firm continues operating, and the future dividends arise from its continued operation
  • Non-going concern: liquidation value based on the assumption that the firm will cease to operate and all of its assets will be sold
  • Absolute valuation model: estimation of an asset’s intrinsic value
    • Dividend discount models: determine present value of all of the cash flows expected in the future
    • Asset-based models: estimate a firm’s value as the sum of the market value of the assets it owns or controls; commonly used for firms that own natural resources
  • Relative valuation models: relate the value of an asset to that of another asset. e.g. EPS, P-E ratio

Ownership perspective

  • Premiums for control: ability of controlling shareholders to make financing decisions as a valuable factor
  • Discounts for lack of marketability: non-publicly traded shares will be discounted in value for a timely manner
  • Discounts for lack of liquidity: require additional time to sell the position; perceived cost of this delay deducted from the value

Markets and Instruments

Origins of national market organizations

  • Private bourses: established by individuals for the purpose of securities trading; most popular model today
  • Public bourses: public institutions with brokers appointed by the government; regulated by government officials
  • Bankers’ bourses: banks play the primary role in securities trading

Order-driven market (auction): price determined supply and demand for securities directly, using electronic central order book

+ Traders view all standing orders as trades are executed.
+ Liquidity is provided at a lower cost.
+ Low cost of trading.
+ Minimal human intervention.
+ Efficient system for small security trades.
- Lacks market depth.
- More market orders are placed as opposed to limit orders.

Price-driven market (dealer): price quoted continuously in bid-ask spread; inventory of securities maintained by market makers

+ Purchases are made at the lowest offering price.
+ Sales occur at the highest bid price.
- No centralized book of limit orders.
- Anonymity of trade is reduced

Execution costs

  • Commissions, fees, and taxes tangible execution costs, such as negotiated broker fees to handle and clear a trade, taxes imposed by various governments, fees for post-trade settlement, and soft dollars
  • Market impact intangible cost; price adjustment needed to purchase liquidity = price difference between the time the order is submitted and when the actual trade occurs; e.g. bid-ask spread
  • Opportunity cost intangible cost associated with the delay in or failure to complete an individual trade; significant for order-driven markets

Methods of Reducing Trading Costs

  • Program trading
+ reduces execution costs by trading large baskets of securities that are deemed :+ less risky/diversification.
- unlikely to locate a counterparty for the large diversified basket of securities
  • Internal crossing
+ minimizes execution costs.
- likelihood
- fair transaction price establishment difficult
  • External crossing
+ very low execution costs and anonymous trades.
- opportunity cost can increase if the trade grows stale without an opposing order to execute
  • Principal trades
+ opportunity costs are reduced since liquidity is assured by the dealer
- the entire execution cost can be large; limits anonymous trades
  • Agency trades
+ minimizes opportunity costs and price impact costs
- commission could be too large
  • Futures contracts
+ high liquidity
- risk introduction for extreme beta values
  • Indications of interest
+ low execution costs
- less anonymity

American Depository Receipt(ADR): dollar-denominated negotiable certificate representing a specified number of shares in a foreign corporation; issued by U.S. banks; listed in the U.S. on the NYSE, AMEX, or Nasdaq exchange; trade like regular stocks

  • Level I: used by foreign companies that don’t qualify/wish to have their ADR listed on an exchange; trade solely on the OTC market; easy and inexpensive way for a company to gauge interest for its securities in North America; no SEC reporting requirements
  • Level II: listed/quoted on an exchange; SEC registration & reporting requirements; higher visibility trading volume
  • Level III: the most prestigious; an issuer floats a public offering of ADRs on a U.S. exchange
+ reduces administration and duty costs, international diversification.
- do not eliminate the currency and economic risks of the foreign country; availability
  • Reasons for a company to list its securities abroad:
  1. broader diversification of its capital across international boundaries
  2. concern over take-over acquisitions by domestic competitors
  3. access to additional resources
  4. additional advertising opportunities

Closed-end country fund invests in stocks from a single country; market price usually not equal to the fund’s NAV. 
Premium/discount determinants:

  • Foreign investment restrictions: restrictions // premium
  • Management fees and lack of liquidity: attractive for developing markets
  • Correlation with U.S. markets: market prices react slowly to changes in NAV

International Exchange Traded Funds: designed to track a market index performance

+ Achieve international diversification with high liquidity at a minimal cost
Tax-efficient due to very low portfolio turnover/cost
+ trade during the market hours
+ Can be shorted and margined
+ Allow investment without engaging in direct international security purchases
+ Specially designed to be utilized in active asset allocation strategies
- Stale pricing when in non-overlapping time zones
- high management fee
+ a simple way to access local foreign markets while achieving international diversification
+ fixed redemptions for portfolio managers
- may trade at a significant premium or discount to their NAV; NAV premium can increase uncertainty and risk; may be highly correlated with the U.S. stock market, which reduces the benefit of international diversification

Open-end funds

+ trade at NAV with no discount/premium
- shares must be redeemed by noon EST due to the international market closings
- time lag between the international market closings, redemptions, and NAV determination creates cash flow problems for managers
- cannot be sold short or margined

Return Concepts

Holding period return (increase in asset price + cash in-flow) / initial price

  • required return is the minimum expected return an investor requires given the asset’s characteristics.
  • If expected return is greater (less) than required return, the asset is undervalued (overvalued)
  • Mispricing can lead to a return from convergence of price to intrinsic value.
  • Discount rate: used to find the present value of an investment
  • Internal rate of return (IRR): equates the discounted cash flows to the current price; same as required return in efficient market

Equity risk premium return over the risk-free rate

required return for stock j = risk-free return + βj×(equity risk premium)

Historical estimate of the equity risk premium = mean return on a equity-market index - mean return on U.S. Treasury bills over a given time period

Forward-looking or ex ante estimates: use current information and expectations concerning economic and financial variables

+ does not rely on an assumption of stationarity
+ less subject to problems like survivorship bias.

Equity risk premium

  • Historical estimates: straightforward to compute, but not current
  • Forward-looking estimates: use current information, but needs to be updated periodically as new estimates are generated
  • Macroeconomic models: use current information, but only appropriate for developed countries where public equities represent a relatively large share of the economy
  • Survey estimates: easy to obtain, but there can be a wide disparity between opinions

Capital Asset Pricing Model: required return on stock j = current risk-free return + (equity risk premium) × (β of j)

Multifactor model: required return = RFR + Σ(risk premium)n

Fama-French model: required return of stock j = RFR + βmkt,j × market risk premium + βSMB,j × small-cap risk premium + βHML,j × value risk premium

Pastor-Stambaugh model: Fama-French model + liquidity factor

Macroeconomic multifactor models: use factors associated with economic variables that would affect the cashflows and/or discount rate of companies.

The build-up method: similar to the risk premium approach; does not use betas to adjust for the exposure to a factor; e.g. bond yield plus risk premium method

Beta estimation from regression of publicly-traded company's stock returns on index returns

  • Beta drift: adjusted β = 2/3 × (regression β) + 1/3 × 1.0 (mean reversion)

For thinly-traded stocks and non-publicly traded companies:

  1. identify publicly traded benchmark company
  2. estimate the beta of the benchmark company
  3. unlever the benchmark company’s beta
  4. relever the beta using the capital structure of the thinly-traded/non-public company.

Required return estimation

  • CAPM: simple but low explanatory power
  • Multifactor models: more explanatory power but complex and costly
  • Build-up models: simple and apply to closely held companies, but could be irrelevant(historical values)

Emerging market - premium for greater risk

  • Country spread model: uses a corresponding developed market as a benchmark; adds a premium for the emerging market risk; premium based on differences in bond yield
  • Country risk rating model: equity risk premium for developed countries and inputs associated with the emerging market

Weighted Average Cost of Capital (WACC) = wd (1-T) rd + we re

  • Appropriateness in measurement to involve real cash flows and real discount rate

Valuation Techniques

Information problem for foreign companies:

  • Delayed and infrequent release of financial statements
  • Financial statements only published in the domestic language
  • Inconsistent presentation.

Issues of differences raised for convergence project between IASB and FASB(U.S. GAAP): Consolidation methods, Business combinations, Financial instruments, Related party transactions, Pensions and post-retirement benefits, Capitalization of borrowing costs, Joint ventures, Leases, Intangible assets, Revenue recognition, Share-based payments, Insurance contracts

  • IAS requires lease capitalization

Country Analysis

  • Expected real economic growth the most significant influence on the risk and returns in national equity markets
  • [Short-run] focus on forecasting the stage in the business cycle and expected short-term economic growth
  • [Long-run] focus on sustainable economic growth expectations in GDP growth

Business Cycles

  • Motivation: forecast the turning points when the economy moves from one stage to another and then invest in those sectors or industries that are expected to perform best during that stage; opportunities to earn excess risk-adjusted returns
Business Cycle Stage Description Attractive Investments
Recovery Economy begins to recover from recession Cyclical stocks, Commodities,
Other risky assets
Early upswing Consumer confidence improves;
economic growth rate increases
Stocks, Real estate
Late upswing Peak growth rate;
also known as “boom” period
Bonds, Interest-sensitive stocks
Mature growth Economy slows Declining growth; 
interest rates fall
Bonds, Interest-sensitive stocks
Recession Low point of economic growth;
government eases monetary policy to stimulate growth
Stocks (late in cycle)
Commodities (late in cycle)
  • Industry analysis more significant for multinational firm that operates in the global industry

Return Analysis return potential assessment by analyzing firm’s sources of growth and how it maintains a competitive advantage

  • Global demand analysis
  • Industry life cycle
  • Competition structure analysis
    • N firm concentration ratio
    • Herfindahl index
  • Value chain
  • Degree of industry cooperation
  • Competitive advantage
  • Generic competitive strategies

Risk Analysis

  • Porter's five forces:
  1. Bargaining power of buyers.
  2. Bargaining power of suppliers.
  3. Threat of new entrants.
  4. Competition within the industry.
  5. Substitute products.
  • Additional factors:
  1. Value chain competition.
  2. Government intervention.
  3. Overall risk.

DuPont model: financial ratio analysis of past performance

    ROE = Net profit / Equity = Net profit/Pretax profit * Pretax profit/EBIT * EBIT/Sales * Sales/Assets * Assets/Equity

Discounted Cash Flow Valuation Models: intrinsic value of common equity share estimated using DDM

Franchise Value Method

  1. Tangible P/E value(static) = 1/r
  2. Franchise P/E value(growth)
    1. franchise factor = 1/r - 1/ROE
    2. growth factor = g/(r-g)
  3. Intrinsic P/E value = tangible P/E + franchise P/E

Effects of inflation: need to determine what portion of inflation in input prices the firm can pass on to its customers in the form of higher prices

P0/E1 = 1 / (real required return + (1-inflation flow-through rate)inflation rate)
  • full-flow-through firm: earnings reflect all price changes; earnings are growing at the inflation rate
  • inflation flow-through rate // firm value

Multifactor models

  • country factor: modeled using blocks of neighboring countries
  • industry factor: groups of similar industries or return on global index for that particular industry

Risk exposures factors(factor sensitivities)

  • Use specific information about the company
  • Estimate the factor sensitivities with multiple linear regression

Other factors that could be considered with extreme caution due to significant differences between countries

  • momentum effect: past short-term performance of firms predicts the future short-term performance
  • size effect: returns for small firms are significantly different from the returns for large firms
  • value effect: returns on value stocks are different from growth stock returns (price to book value ratio)

U.S. Portfolio Strategy

Ten-year moving average provides a near-term historic benchmark against which current valuations can be measured; utilizes standard deviation of the distribution associated with the ten-year moving average

  • caution for stocks that have realized a downgrade in their growth prospects (undervalued)

Valuation metrics used in Multi-matrix valuation approach (Goldman Sachs research): enterprise value(EV) / sales, EV / EBITA, price / book, FCF yield, P/E, PEG, implied growth from DDM

  • negative coefficients will generate extreme valuation signals
  • correlation coefficients all positive and range from 0.1 to 0.9

PEG valuation technique

  • general rule: 1<PEG<2, considered expensive if PEG>2
  • only applicable to companies with normal/high earnings growth (denominator)

Porter's Five Forces

Choice of a competitive strategy:

  • Industry attractiveness: Is the industry attractive in terms of long-term profitability potential?
  • Competitive advantage: What determines a firm’s relative competitive position within an industry?

Analysis through Porter’s Five Forces:

  1. Threat of new entrants: Analyze threat of new entrants/entry barriers
  2. Threat of substitutes: Relative price of substitutes and switching costs
  3. Bargaining power of buyers: Influences prices that firms can charge
  4. Bargaining power of suppliers: Determines costs of raw materials and other inputs
  5. Rivalry among existing competitors: Look at industry growth, product differences, brand identity, and switching costs
  • Industry growth rate, technology and innovation, government, and complementary products and services are transient factors, which should be evaluated in terms of their influence on Porter's five forces.
  • Eliminating rivals is a risky strategy because the increased industry profits are likely to attract new competitors, increasing rivalry, reducing industry attractiveness in the long term

Strategic alternatives:

  • Positioning the company where the five forces appear to be the weakest
  • Projecting changes in the forces and exploiting industry changes that result
  • Inducing changes in the industry structure that will play to the strengths of the firm (where its factor exposure is weakest)

Industry analysis model 
1. Industry classification

Life cycle model: recognizing phases with associated differing degree of vitality
  • Pioneer: acceptance of the product/service uncertain; unclear strategy; significant capital needs; typically does not generate profits; high risk with a high rate of failures; Equity investors must be prepared to lose their entire investment
  • Growth: acceptance established; proper execution of a well-conceived strategy leads to accelerating sales and earnings; industry growth > general economy; profit margins above average; can prosper in all stages of the business cycle
  • Mature: industry growth corresponds general economy growth; average results; above-average growth must come from increased market share or acquisitions
  • Decline: Shifting tastes or technologies have overtaken the industry; product demand steadily decreases; Profit margins diminishing; participants consolidate, reinvent themselves, or fail
Business cycle reaction approach: classifies industries by behavior during various phases
  • Growth industry stocks: accelerating sales and high profit margins during all phases e.g. Biotech
  • Defensive industry stocks: much less cyclical than the overall market because demand relatively independent of the business cycle; often in the mature phase e.g. Food, beverage, and utility
  • Cyclical industry stocks: vary directly with the business cycle because product demand increase during the expansion and drop off significantly during the recessionary phase; e.g. Automobile, heavy equipment, and machine tool companies with high operating leverage

2. External factor review

  • Technology: concern for whether a competition from new technologies will supplant the old technology
  • Government: regulations, taxes, subsidies and litigation on environmental mendates
  • Social changes: fashion(short-term) and lifestyle(long-term) changes
  • Demography: demographic trends; relatively easy to predict; implications are not
  • Foreign Influences: a foreign competitor with a comparative advantage decimates industry; increasing prosperity in foreign countries creates new demand for output

3. Demand analysis: macroeconomic factors that affect industry revenue

  • GDP growth vs. growth in company revenues.
  • Knowledge of industry classification.
  • External factors.
  • A study of the firm’s customers.
  • A study of the industry’s inputs and outputs.

4. Supply analysis: assume that supply will equal demand in long term; demand can be more or less than supply in short term
5. Profitability analysis: factors that affect industry pricing practices:

  • Product segmentation: firm’s ability to differentiate its product over varying market segments (e.g. branded vs. generic products), thus charge higher prices.
  • Industry concentration: fewer the competitors -> greater the concentration -> broadly coordinated pricing actions -> reducing price competition
  • Ease of industry entry: lower entry barriers -> reducing prices toward the marginal cost of production
  • Supply input price: dependency on limited natural resources (e.g. oil)

6. International competition and markets review

Emerging Markets

  • Emerging markets tend to experience high inflation -> distinction between real and nominal cash flows and discount rates
  • Income taxes - based on nominal earnings
  • real cash outflow from NWC not= change in real NWC
  • Nominal capital expenditures difficult to forecast because nominal sales - nominal capital expenditures not constant when inflation is high

Emerging markets company valuation on a real and nominal basis:

  1. Forecast real revenue, EBITDA, invested capital, and EBITA
  2. Forecast nominal revenue, EBITDA, invested capital, and NOPLAT
  3. Forecast real NOPLAT.
  4. Forecast nominal and real free cash flows
  5. Estimate firm value using a free cash flow model in both real and nominal terms by discounting at respective WACC

Support for adjustment in cash flow rather than adjusting the discount rate:

  • Country risks are diversifiable.
  • Companies respond differently to country risk.
  • Country risk is one-sided risk.
  • Identifying cash flow effects aids in risk management.

Guidelines to estimate WACC for an emerging markets company:

  • Risk-free rate = 10-year U.S. government bond yield + inflation differential from U.S.
  • Beta = industry beta from a globally-diversified market index.
  • The long-term global market risk premium = approximately 4.5% to 5.5%.
  • Pre-tax cost of debt = local risk-free rate + credit spread on comparably-rated U.S. corporate debt
  • Marginal tax rate = local taxes applied to debt interest
  • Capital structure weights approximated by industry average weights.
  • Add country risk premium to company's WACC if unadjusted cash flows are used for valuation
  • Do not use the sovereign risk premium to estimate the country risk premium - volatility specific to the company’s cash flow will usually be different than the volatility of government bond payments.
  • Varibility across different analysts
  • Analysts often overestimate - compare the expected returns implied by the CAPM model to historical real returns in the country.

Discounted Dividend Valuation

appropriate for: history of dividend payments, clear dividend policy, related to the earnings, minority shareholder perspective
+ theoretically justified
- difficult to implement for non-dividend paying firms

Gordon Growth Model

  • Conditions: dividend to be paid in one year, and expected to grow at a constant rate (g<r)
P0 = D1 / (r - g)
g = r - (D1/P0)
+ applicable to stable, mature, dividend-paying firms
+ appropriate for valuing market indexes
+ straightforward approach
+ determines price-implied growth rates, required rates of return, growth opportunity valuation
+ can be used to supplement other, more complex valuation methods
- very sensitive to estimates of growth rates and required rates of return, both of which are difficult to estimate with precision
- cannot be easily applied to non-dividend paying stocks
- unpredictable growth patterns

Present value of growth opportunities (PVGO): part of a stock’s total value that is derived from profitable growth opportunities

V0 = E/r + PVGO

Price-to-Earnings ratio (P/E) :most commonly used relative valuation indicator


Noncallable fixed-rate perpetual preferred stock: firms with no additional opportunities to earn excess earnings should distribute all to shareholders in dividend form. growth rate = 0

Two-stage models company grows at a high rate for a relatively short period of time (the first stage), and then reverts to a long-run perpetual, sustainable growth rate (the second stage)

H-models growth rate starts out high, and then declines linearly over the high-growth stage until it reaches the long-run average growth rate; appropriate for a firm that has little competition now, but expects increasing competition in the future

Three-stage models assume a constant growth rate in each of three distinct growth stages

Spreadsheet modeling allow for any pattern of growth given the adaptation of algorithms; appropriate for firms with a great deal of information and can project different growth rates for different periods.

Business growth pattern

  • Initial growth phase: rapidly increasing earnings, little or no dividends, heavy reinvestment
  • Transition phase: earnings&dividends increasing; competitive forces reduce profit opportunities, need for reinvestment
  • Mature phase: earnings grow at a stable but slower rate; payout ratios stabilizing; reinvestment matches depreciation and asset maintenance requirements

Terminal value estimation

  • Gordon growth model = discounted dividend
  • Price multiples = P/E * earnings estimate

Sustainable growth rate (SGR): earningis the rate at which earnings (and dividends) can continue to grow indefinitely

SGR = earnings retention ratio × ROE
PRATmodel.gif (PRAT model)

Spreadsheet modeling procedure

  1. Establish the base level of cash flows or dividends.
  2. Estimate changes in the firm's dividends for the foreseeable future.
  3. Estimate what normalized level of growth will occur at the end of the supernormal growth period, #allowing for an estimate of a terminal value.
  4. Discount and sum all projected dividends and the terminal value back to today.

Free Cash Flow Valuation

appropriate for: non-dividend paying, dividend not related to earnings, FCF corresponds to profitability, controlling shareholder perspective
+ applicable to many firms regardless of dividend policies or capital structures
- application very difficult; significant capital requirements may cause negative FCF

Free cash flow to the firm (FCFF): cash available to all of the firm’s investors, including stockholders, bondholders, and preferred stockholders after the firm buys and sell products, provides services, pays its operating expenses, and makes short and long-term investments.

  • useful for a company with negative FCFE

Free cash flow to equity (FCFE): cash available to stockholders after funding capital requirements, working capital needs, and debt financing requirements.

  • easier, more straight forward, volatile
Equity value = FCFE discounted at the required return on equity

Appropriate adjustments


Future FCF forecast

  • Calculate historical free cash flow and apply a growth rate under the assumption that growth will be constant and fundamental factors will be maintained
  • Forecast the underlying components of free cash flow. This often ties sales forecasts to future capital expenditures, depreciation expenses, and changes in working capital.
  • Importantly, capital expenditures have two dimensions: outlays that are needed to maintain existing capacity and marginal outlays that are needed to support growth. Thus, the first type of outlay is related to the current level of sales and the second type depends on the predicted sales growth.
  • appropriate choice for an acquisition target because the new owners will have discretion over its distribution
  • The Free Cash Flow to equity approach takes a control perspective which assumes immediate value recognition while dividend discount models take a minority perspective, under which value may not be realized until the dividend policy accurately reflects the firm’s long-run profitability.
  • Dividends, share repurchases, and share issues have no effect on either FCFF or FCFE.
  • Changes in leverage have only a minor effect on FCFE and no effect on FCFF.
    • decrease in leverage (repayment of debt) decreases FCFE and increases forecasted FCFE

FCF derivation

  • Net income is a poor proxy for FCFE. Net income includes noncash charges like depreciation that have to be added back to arrive at FCFE; it ignores cash flows that don’t appear on the income statement, such as investments in working capital and fixed assets as well as net borrowings.
FCFE = NI + NonCash Charges - FCInv - WCInv + net borrowing
  • EBITDA is a poor proxy for FCFF. EBITDA doesn’t reflect the cash taxes paid by the firm, and it ignores the cash flow effects of the investments in working capital and fixed capital.
FCFF = EBITDA (1 - tax) + (Depreciation × tax) - FCInv - WCInv

Single-stage FCFF model assumes that FCFF grows at a constant rate forever

FCFF singlestage.jpg

Two-stage model assumes two stages of growth: a high-growth rate for n years then another with a lower, constant growth rate forever

FCFF twostage.jpg

Sensitivity analysis shows how sensitive an analyst’s valuation results are to changes in each of a model’s inputs; assessment of various forecasting errors:

  • Estimatimation of future growth in FCFF and FCFE: Growth forecasts depend on a firm’s future profitability, which in turn depends on sales growth, changes in profit margin, position in the life cycle, its competitive strategy, and the overall profitability of the industry
  • The chosen base years for the FCFF or FCFE growth forecasts: A representative base year must be chosen, or all of the subsequent analysis and valuation will be flawed

Terminal value calculation

  • Single-stage model: forecast an FCFF or FCFE at the point in time at which cash flows begin to grow at the long-term, stable growth rate
  • Valuation multiples (e.g. P/E ratios): The terminal value in year n in terms of P/E would be expressed as:
terminal value in year n = (trailing P/E) × (earnings in year n)
terminal value in year n = (leading P/E) × (forecasted earnings in year n + 1)

FCFE vs. FCFF Preference

  • relatively stable capital structure -> FCFE is more direct and simpler
  • levered company with negative FCFE -> FCFF preferred

Price Multiples Estimation

Method of comparables: average multiple of similar stocks in the same peer group; relative valuation

  • Law of One Price: two similar assets should sell at comparable prices (i.e., multiples)

Method of forecasted fundamentals: ratio of the value of the stock from a discounted cash flow valuation model divided by some fundamental variable (e.g., earnings per share)

  • Value is equal to the present value of expected future cash flows discounted at the appropriate risk-adjusted rate of return
  • Price multiples: ratios of a common stock’s market price to some fundamental variable
  • Justified price multiple is what the multiple should be if the stock is fairly valued
    • actual multiple > justified price multiple, stock overvalued


  • trailing P/E = market price per share / EPS over previous 12 months; payout ratio(1+g)/(r-g)
  • leading P/E = market price per share / forecasted EPS over next 12 months; payout ratio/(r-g)
+ Earnings power, as measured by earnings per share (EPS), is the primary determinant of investment value.
+ popular in the investment community.
+ significantly related to long-run average stock returns
- Earnings can be negative, which produces a useless P/E ratio.
- Volatility, transitory portions cause difficulty in interpretation


  • P/B Ratio: P/B = market value of equity / book value of equity = market price per share / BV per share
  • book value of equity = common shareholders' equity = (total asset - total liabilities) - preferred stock:+ usually positive, even when the firm reports a loss and EPS is negative
  • Justified P/B ratio: P0/B0 = (ROE - g) / (r - g) increasing function of ROE
+ more stable than EPS, so it may be more useful than P/E when EPS is extreme or volatile
+ appropriate measure of net asset value for firms that primarily hold liquid assets. Examples include finance, investment, insurance, and banking firms.
+ useful in valuing companies that are expected to go out of business.
+ help explain differences in long-run average stock returns.
- P/Bs do not recognize the value of nonphysical assets, such as human capital.
- P/Bs can be misleading when there are significant differences in the asset size of the firms under consideration.


  • P/S = market value of equity / total sales = market price per share / sales per share:+ meaningful even for distressed firms, since sales revenue is always positive
  • P0/S0 = [(E0/S0)(1 - b)(1 + g)] / (r - g)
+ not as easy to manipulate or distort
+ not as volatile as P/E multiples. This may make P/S ratios more reliable in valuation analysis.
+ appropriate for valuing stocks in mature or cyclical industries and start-up companies with no record of earnings.
- High growth in sales does not necessarily indicate operating profits as measured by earnings and cash flow.
- P/S ratios do not capture differences in cost structures across companies.

Price/Cash Flow

  • earnings-plus-noncash-charges (CF), adjusted cash flow (adjusted CFO), free cash flow to equity (FCFE), and earnings before interest, taxes, depreciation, and amortization (EBITDA)
  • P/CF = market value of equity / CF = market price per share / cash flow per share
+ Cash flow is harder for managers to manipulate than earnings.
+ Price to cash flow is more stable than price to earnings.
+ Reliance on cash flow rather than earnings handles the problem of differences in the quality of reported earnings, which is a problem for P/E.
- Items affecting actual cash flow from operations are ignored when the EPS plus noncash charges estimate is used.
- From a theoretical perspective, free cash flow to equity (FCFE) is probably preferable to cash flow. However, FCFE is more volatile than straight cash flow.

Normalized EPS: P/Es adjusted for cyclical elements

  • Historical average EPS: Average EPS over the last complete business cycle.
  • Average return on equity: Average ROE over the last complete business cycle multiplied by the current book value per share.

Earnings yield (E/P)

  • Negative earnings render P/E ratios meaningless. In such cases, it is common to use normalized EPS and/or restate the ratio as the earnings yield (E/P) because price is never negative.
  • A high E/P suggests a cheap security.
  • A low E/P suggests an expensive E/P.

Fundamental factors of influence

  • Justified P/E increases as g increases or r decreases.
  • Justified P/B increases as ROE increases or the spread between ROE and r increases.
  • Justified P/S increases as profit margin increases or g increases.
  • Justified P/CF increases as g increases or r decreases.

Method of comparables approach compares a stock’s price multiple to a benchmark:

  1. Select and calculate the multiple that will be used.
  2. Select the benchmark stock and calculate the mean or median of its multiple over the group of comparable stocks.
  3. Compare the stock’s multiple to the benchmark.
  4. Examine whether any observed difference between the multiples of the stock and the benchmark are explained by the underlying determinants of the multiple, and make appropriate valuation adjustments.

Frequently encountered P/E benchmarks include:

  • P/E of another stock of a company in a similar industry with similar operating characteristics.
  • Average or median P/E of peer group within the company’s industry.
  • Average or median P/E for the industry.
  • P/E of an equity index.
  • Average historical P/E for the stock.

Importance of fundamentals in comparables method

  • The basic idea of the method of comparables is to compare a stock’s price multiple to the benchmark. Firms with multiples below the benchmark are undervalued, and firms with multiples above the benchmark are overvalued.
  • make sure that the stock is comparable to the benchmark: it should have similar expected growth and similar risk and return

PEG ratio captures the relationship between earnings growth and P/E (P/E ratio /g)

Alternative definitions of cash flow

  • Earnings-plus-non-cash-charges (CF) is equal to net income + depreciation + amortization. A limitation of this measure is that it ignores some items that affect cash flow.
  • Cash flow from operations (CFO) is often adjusted by adding back after-tax interest costs, because CFO by itself includes items related to financing and investing activities.
Adjusted CFO = CFO + [(net cash interest outflow) × (1 - tax rate)]
  • Free cash flow to equity (FCFE) is the preferred way, but is more volatile than straight cash flow.
FCFE = CFO - FCInv + net borrowing
  • Earnings before interest, taxes, depreciations, and amortization (EBITDA) is better suited as an indicator for total company value rather than just equity value.
  • Common differences in international accounting treatment: goodwill, deferred income taxes, foreign exchange adjustments, R&D, pension expense, and tangible asset revaluations.
  • P/adjusted CFO and P/FCFE least affected by accounting differences

Momentum indicators relate market price/fundamental variable to the time series of historical/expected value

  • Unexpected earnings surprise = difference between reported earnings and expected earnings
  • Standardized unexpected earnings(SUE) = measured as earnings surprise / standard deviation of earnings surprise
  • Relative strength indicators compare a stock's price or return performance during a given time period with its own historical performance or with some group of peer stocks

Residual Income Valuation

appropriate for: negative FCF, transparent financial reporting and high quality earnings
+ applicable to firms with negative FCF and non-dividend-paying firms
- requires in-depth analysis of the firm’s accounting accruals

Residual income(economic profit): net income - stockholders’ opportunity cost of capital; deducts all capital costs

Economic value added(EVA®) = value added to shareholders by management during a given year


Adjustments to the accounting statements:

  • Capitalize and amortize R&D charges and add them back to earnings to calculate NOPAT.
  • Add back charges on strategic investments that will generate returns far into the future.
  • Capitalize, but do not amortize goodwill, add amortization expense back to get NOPAT, and add accumulated amortization back to capital.
  • Eliminate deferred taxes and consider only cash taxes as an expense.
  • Treat operating leases as capital leases and adjust non-recurring items.

Market value added(MVA) = market value of a firm’s long-term debt&equity - book value of invested capital supplied by investors

MVA = market value - invested capital(Book value)

Valuation with residual income models is relatively less sensitive to terminal value estimates, which reduces forecast error; depends on current book value

Fundamental determinants/drivers of residual income:


RI model // price-to-book value(P/B) ratio

  • ROE > re -> RI > 0
  • market value > book value -> justified P/B ratio > 1

Residual income growth rate


Continuing residual income: expected RI over the long-term 
Common assumptions:

  • RI expected to persist at its current level forever
  • RI expected to drop immediately to zero
  • RI expected to decline to a long-run average level consistent with a mature industry
  • RI expected to decline over time as ROE falls to the cost of equity -> RI=0

Continuing residual income estimation requires analysis of firm's position in the industry and structure of the industry

Higher persistence factors:

  • Low dividend payouts.
  • Historically high residual income persistence in the industry.

Lower persistence factors:

  • High return on equity.
  • Significant levels of nonrecurring items.
  • High accounting accruals.

Multi-stage residual income model

  1. forecast residual income over a short-term horizon
  2. then make some simplifying assumptions about the pattern of residual income growth over the long term

Present Value of continuing residual income in year T - 1 = RIt / (1+r-w)

  • RI expected to persist at the current level forever -> w = 1.
  • RI expected to drop immediately to zero -> w = 0.
  • RI expected to decline over time after year T as ROE -> cost of equity capital, then the persistence factor(w): 0<w<1

Premium over book value (PT-BT) = present value of continuing residual income in year T, and the present value of continuing residual income in year T - 1 is: PVcontinuing residual income|T = (PT-BT)+RIT / (1+r)

Strengths and Weaknesses

+ Terminal value does not dominate the intrinsic value estimate
+ RI models use available accounting data
+ applicable to firms that do not pay dividends or that do not have positive expected FCF
+ applicable even when cash flows are highly volatile
+ focus on economic rather than just accounting profitability
- rely on accounting data that can be manipulated.
- reliance on accounting data requires numerous and significant adjustments.
- assume that clean surplus relation holds or that its failure to hold has been properly taken into account

Appropriate for:

  • A firm does not pay dividends, cash flows too volatile to be sufficiently predictable
  • Expected free cash flows are negative for the foreseeable future
  • Terminal value forecast highly uncertain -> DDM or FCF less useful

Not suitable for:

  • clean surplus accounting relation is violated significantly
  • significant uncertainty on book value estimates and RoE

Major accounting issues

  1. Violations of the clean surplus relationship
    • Changes in the market value of long-term investments
    • Foreign currency translation adjustments
    • The minimum liability adjustment in pension accounting
  2. Balance sheet adjustments for fair value
    • Inventory, deferred tax assets and liabilities, pension plan assets and liabilities
    • Operating leases, special-purpose entities, reserves and allowances, and intangible assets
  3. Intangible assets
  4. Non-recurring items
  5. Aggressive accounting practices
  6. International accounting differences
    • Availability of reliable earnings forecasts
    • Systematic violations of the clean surplus assumption
    • Poor quality accounting rules that result in delayed recognition of value changes