A%20philosophical%20basis%20for%20Valuation

1
A philosophical basis for Valuation

• Many investors believe that the pursuit of 'true
  value' based upon financial fundamentals is a
  fruitless one in markets where prices often seem
  to have little to do with value.
• There have always been investors in financial
  markets who have argued that market prices are
  determined by the perceptions (and
  misperceptions) of buyers and sellers, and not by
  anything as prosaic as cashflows or earnings.
• Perceptions matter, but they cannot be all that
  matter.
• Asset prices cannot be justified by merely using
  the bigger fool theory.

2
Misconceptions about Valuation

• Myth 1 A valuation is an objective search for
  true value
• Truth 1.1 All valuations are biased. The only
  questions are how much and in which direction.
• Truth 1.2 The direction and magnitude of the
  bias in your valuation is directly proportional
  to who pays you and how much you are paid.
• Myth 2. A good valuation provides a precise
  estimate of value
• Truth 2.1 There are no precise valuations
• Truth 2.2 The payoff to valuation is greatest
  when valuation is least precise.
• Myth 3 . The more quantitative a model, the
  better the valuation
• Truth 3.1 Ones understanding of a valuation
  model is inversely proportional to the number of
  inputs required for the model.
• Truth 3.2 Simpler valuation models do much
  better than complex ones.

3
Approaches to Valuation

• Discounted cashflow valuation Relates the value
  of an asset to the present value of expected
  future cashflows on that asset.
• Relative valuation Estimates the value of an
  asset by looking at the pricing of 'comparable'
  assets relative to a common variable like
  earnings, cashflows, book value or sales.
• Contingent claim valuation Uses option pricing
  models to measure the value of assets that share
  option characteristics.

4
Basis for all valuation approaches

• The use of valuation models in investment
  decisions (i.e., in decisions on which assets are
  under valued and which are over valued) are based
  upon
• a perception that markets are inefficient and
  make mistakes in assessing value
• an assumption about how and when these
  inefficiencies will get corrected
• In an efficient market, the market price is the
  best estimate of value. The purpose of any
  valuation model is then the justification of this
  value.

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Efficient Market Hypothesis (EMH)

• Definition 1 A market is said to be efficient
  with respect to some information set, It, if it
  is impossible to make economic profits on the
  basis of information set It.
• Economic profits Profits after adjusting for
  risk and transaction costs (such as, brokerage
  fees, investment advisory fees).
• Economic profits Actual return - Expected
  return - Transaction costs
• Expected Return CAPM provides one estimate of
  expected return. Other estimates Arbitrage
  Pricing Theory, Historical Industry Returns.

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EMH continued

• Models of Expected Returns
• CAPM Expected return on stock i Riskfree rate
  
  (Beta of i with respect to
  Market)(Expected return on Market - Riskfree
  rate)
• APT Expected return on stock i Riskfree rate
  
  (Beta of i with respect to Factor 1)(Expected
  return on Factor 1 - Riskfree rate)
  
  
  (Beta of i with respect to Factor
  2)(Expected return on Factor 2 - Riskfree rate)
  ...

7
EMH continued

• Models of Expected Returns
• Historical Industry Returns Expected Return on
  stock i Average historical return of other
  firms in the same industry as company i.

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EMH continued

• Information set
• Weak form of EMH Past history of prices of the
  particular security.
• Semistrong form of EMH All publicly available
  information.
• Strong form of EMH All public and private
  information.

9
Efficient Market Hypothesis

• Definition 2 If capital markets are efficient
  then purchase or sale of any security at the
  prevailing market price is a zero-NPV
  transaction.
• Definition 3 (Technical definition) The capital
  market is efficient with respect to an
  information set if and only if revealing that
  information to all investors would change neither
  equilibrium prices nor portfolios.

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Discounted Cash Flow Valuation

• What is it In discounted cash flow valuation,
  the value of an asset is the present value of the
  expected cash flows on the asset.
• Philosophical Basis Every asset has an intrinsic
  value that can be estimated, based upon its
  characteristics in terms of cash flows, growth
  and risk.
• Information Needed To use discounted cash flow
  valuation, you need
• to estimate the life of the asset
• to estimate the cash flows during the life of the
  asset
• to estimate the discount rate to apply to these
  cash flows to get present value

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Discounted Cashflow Valuation Basis for Approach

• where,
• n Life of the asset
• CFt Cashflow in period t
• r Discount rate reflecting the riskiness of
  the estimated cashflows

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Advantages of DCF Valuation

• Since DCF valuation, done right, is based upon an
  assets fundamentals, it should be less exposed
  to market moods and perceptions.
• If good investors buy businesses, rather than
  stocks (the Warren Buffett adage), discounted
  cash flow valuation is the right way to think
  about what you are getting when you buy an asset.
• DCF valuation forces you to think about the
  underlying characteristics of the firm, and
  understand its business. If nothing else, it
  brings you face to face with the assumptions you
  are making when you pay a given price for an
  asset.

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Disadvantages of DCF valuation

• Since it is an attempt to estimate intrinsic
  value, it requires far more inputs and
  information than other valuation approaches
• These inputs and information are not only noisy
  (and difficult to estimate), but can be
  manipulated by the savvy analyst to provide the
  conclusion he or she wants.
• For example
• An entrepreneur can get a high valuation by
  overestimating cashflows and/or underestimating
  discount rates.
• A venture capitalist can buy equity from an
  entrepreneur at a lower price by underestimating
  cashflows.
• An entrepreneur and venture capitalist can get a
  higher price for their IPO by overestimating
  cashflows and/or underestimating discount rates.

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Disadvantages of DCF valuation

• In an intrinsic valuation model, there is no
  guarantee that anything will emerge as under- or
  over-valued. Thus, it is possible in a DCF
  valuation model, to find every stock in a market
  to be over-valued. This can be a problem for
• equity research analysts, whose job it is to
  follow sectors and make recommendations on the
  most under- and over-valued stocks in that sector
• equity portfolio managers, who have to be fully
  (or close to fully) invested in equities

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When DCF Valuation works best

• This approach is easiest to use for assets
  (firms) whose
• cashflows are currently positive and
• can be estimated with some reliability for future
  periods, and
• where a proxy for risk that can be used to obtain
  discount rates is available.
• It works best for investors who either
• have a long time horizon, allowing the market
  time to correct its valuation mistakes and for
  price to revert to true value or
• are capable of providing the catalyst needed to
  move price to value, as would be the case if you
  were an activist investor or a potential acquirer
  of the whole firm

16
Relative Valuation

• What is it? The value of any asset can be
  estimated by looking at how the market prices
  similar or comparable assets.
• Philosophical Basis The intrinsic value of an
  asset is impossible (or close to impossible) to
  estimate. The value of an asset is whatever the
  market is willing to pay for it (based upon its
  characteristics)
• Information Needed To do a relative valuation,
  you need
• an identical asset, or a group of comparable or
  similar assets
• a standardized measure of value (in equity, this
  is obtained by dividing the price by a common
  variable, such as earnings or book value)
• and if the assets are not perfectly comparable,
  variables to control for the differences
• Market Inefficiency Pricing errors made across
  similar or comparable assets are easier to spot,
  easier to exploit and are much more quickly
  corrected.

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Advantages of Relative Valuation

• Relative valuation is much more likely to reflect
  market perceptions and moods than discounted cash
  flow valuation. This can be an advantage when it
  is important that the price reflect these
  perceptions as is the case when
• the objective is to sell a security at that price
  today (as in the case of an IPO)
• With relative valuation, there will always be a
  significant proportion of securities that are
  under- valued and over-valued.
• Since portfolio managers are judged based upon
  how they perform on a relative basis (to the
  market and other money managers), relative
  valuation is more tailored to their needs
• Relative valuation generally requires less
  information than discounted cash flow valuation
  (especially when multiples are used as screens)

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Disadvantages of Relative Valuation

• A portfolio that is composed of stocks which are
  undervalued on a relative basis may still be
  overvalued, even if the analysts judgments are
  right. It is just less overvalued than other
  securities in the market.
• Relative valuation is built on the assumption
  that markets are correct in the aggregate, but
  make mistakes on individual securities. To the
  degree that markets can be over or under valued
  in the aggregate, relative valuation will fail
• Relative valuation may require less information
  in the way in which most analysts and portfolio
  managers use it. However, this is because
  implicit assumptions are made about other
  variables (that would have been required in a
  discounted cash flow valuation). To the extent
  that these implicit assumptions are wrong the
  relative valuation will also be wrong.

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Disadvantages of Relative Valuation
Introduction DCF Valuation Relative Valuation
Real Option Valuation Conclusion

• Relative valuation may require less information
  in the way in which most analysts and portfolio
  managers use it. However, this is because
  implicit assumptions are made about other
  variables (that would have been required in a
  discounted cash flow valuation). To the extent
  that these implicit assumptions are wrong the
  relative valuation will also be wrong.

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Introduction DCF Valuation Relative Valuation
Real Option Valuation Conclusion

• Value of Firm
• FCFF1 expected free cash flow to the firm
• k firms cost of capital
• g growth in the expected free cash flow to the
  firm
• Dividing both sides by FCFF1 yields the
  Value/FCFF multiple for a stable growth firm

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Introduction DCF Valuation Relative Valuation
Real Option Valuation Conclusion

• The Value/FCFF multiple for a stable growth firm
• Value/FCFF increases as g increases.
• Value/FCFF decreases as k increases.
• k is a function of the firms line of business.

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Introduction DCF Valuation Relative Valuation
Real Option Valuation Conclusion

• The Value/FCFF multiple for a stable growth firm
• Hence, picking a certain number for the
  Value/FCFF ratio implies certain assumptions
  about k and g.
• Similarly, for
• Price/Earnings,
• Price/Sales,
• Price/EBITDA, etc.

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When relative valuation works best..

• This approach is easiest to use when
• there are a large number of assets comparable to
  the one being valued
• these assets are priced in a market
• there exists some common variable that can be
  used to standardize the price
• This approach tends to work best for investors
• who have relatively short time horizons
• are judged based upon a relative benchmark (the
  market, other portfolio managers following the
  same investment style etc.)
• can take actions that can take advantage of the
  relative mispricing for instance, a portfolio
  manager specializing in technology stocks can buy
  the under valued and sell the over valued assets

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Financial Data about Companies

• Go to http//libraries.colorado.edu/
• Type hoovers
• Go to this resource

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• Price/Cash Flow Ratio for different k (in bold)
  and g (in italics)

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Contingent Claim (Option) Valuation

• Options have several features
• They derive their value from an underlying asset,
  which has value
• The payoff on a call (put) option occurs only if
  the value of the underlying asset is greater
  (lesser) than an exercise price that is specified
  at the time the option is created. If this
  contingency does not occur, the option is
  worthless.
• They have a fixed life
• Any security or project that shares these
  features can be valued as an option.

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Direct Examples of Options

• Listed options, which are options on traded
  assets, that are issued by, listed on and traded
  on an option exchange.
• Warrants, which are call options on traded
  stocks, that are issued by the company. The
  proceeds from the warrant issue go to the
  company, and the warrants are often traded on the
  market.

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Indirect Examples of Options

• Equity in a deeply troubled firm - a firm with
  negative earnings and high leverage - can be
  viewed as an option to liquidate that is held by
  the stockholders of the firm. Viewed as such, it
  is a call option on the assets of the firm.
• The reserves owned by natural resource firms can
  be viewed as call options on the underlying
  resource, since the firm can decide whether and
  how much of the resource to extract from the
  reserve,
• The patent owned by a firm or an exclusive
  license issued to a firm can be viewed as an
  option on the underlying product (project). The
  firm owns this option for the duration of the
  patent.

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Advantages of Using Option Pricing Models

• Option pricing models allow us to value assets
  that we otherwise would not be able to value. For
  instance, equity in deeply troubled firms and the
  stock of a small, bio-technology firm (with no
  revenues and profits) are difficult to value
  using discounted cash flow approaches or with
  multiples. They can be valued using option
  pricing.
• Option pricing models provide us fresh insights
  into the drivers of value. In cases where an
  asset is deriving its value from its option
  characteristics, for instance, more risk or
  variability can increase value rather than
  decrease it.

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Disadvantages of Option Pricing Models

• When real options (which includes the natural
  resource options and the product patents) are
  valued, many of the inputs for the option pricing
  model are difficult to obtain. For instance,
  projects do not trade and thus getting a current
  value for a project or a variance may be a
  daunting task.
• The option pricing models derive their value from
  an underlying asset. Thus, to do option pricing,
  you first need to value the assets. It is
  therefore an approach that is an addendum to
  another valuation approach.

32
Discounted Cash Flow Valuation
33
Discounted Cashflow Valuation Basis for Approach

• where,
• n Life of the asset
• CFt Cashflow in period t
• r Discount rate reflecting the riskiness of
  the estimated cashflows

34
Equity Valuation versus Firm Valuation

• Value just the equity stake in the business
• Value the entire business, which includes,
  besides equity, the other claimholders in the
  firm

35
I.Equity Valuation

• The value of equity is obtained by discounting
  expected cashflows to equity, i.e., the residual
  cashflows after meeting all expenses, tax
  obligations and interest and principal payments,
  at the cost of equity, i.e., the rate of return
  required by equity investors in the firm.
• where,
• CF to Equityt Expected Cashflow to Equity in
  period t
• ke Cost of Equity
• The dividend discount model is a specialized case
  of equity valuation, and the value of a stock is
  the present value of expected future dividends.

36
II. Firm Valuation

• The value of the firm is obtained by discounting
  expected cashflows to the firm, i.e., the
  residual cashflows after meeting all operating
  expenses and taxes, but prior to debt payments,
  at the weighted average cost of capital, which is
  the cost of the different components of financing
  used by the firm, weighted by their market value
  proportions.
• where,
• CF to Firmt Expected Cashflow to Firm in
  period t
• WACC Weighted Average Cost of Capital

37
Cash Flows and Discount Rates

• Assume that you are analyzing a company with the
  following cashflows for the next five years.
• Year CF to Equity Int Exp (1-t) CF to Firm
• 1 50 40 90
• 2 60 40 100
• 3 68 40 108
• 4 76.2 40 116.2
• 5 83.49 40 123.49
• Terminal Value 1603.008 2363.008
• Assume also that the cost of equity is 13.625
  and the firm can borrow long term at 10. (The
  tax rate for the firm is 50.)
• The current market value of equity is 1,073 and
  the value of debt outstanding is 800.

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Equity versus Firm Valuation

• Method 1 Discount CF to Equity at Cost of Equity
  to get value of equity
• Cost of Equity 13.625
• PV of Equity 50/1.13625 60/1.136252
  68/1.136253 76.2/1.136254 (83.491603)/1.13625
  5 1073
• Method 2 Discount CF to Firm at Cost of Capital
  to get value of firm
• Cost of Debt Pre-tax rate (1- tax rate) 10
  (1-.5) 5
• WACC 13.625 (1073/1873) 5 (800/1873)
  9.94
• PV of Firm 90/1.0994 100/1.09942
  108/1.09943 116.2/1.09944 (123.492363)/1.0994
  5 1873
• PV of Equity PV of Firm - Market Value of Debt
  
• 1873 - 800 1073

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First Principle of Valuation

• Never mix and match cash flows and discount
  rates.
• The key error to avoid is mismatching cashflows
  and discount rates, since discounting cashflows
  to equity at the weighted average cost of capital
  will lead to an upwardly biased estimate of the
  value of equity, while discounting cashflows to
  the firm at the cost of equity will yield a
  downward biased estimate of the value of the firm.

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Discounted Cash Flow Valuation The Steps

• Estimate the discount rate or rates to use in the
  valuation
• Discount rate can be either a cost of equity (if
  doing equity valuation) or a cost of capital (if
  valuing the firm)
• Discount rate can be in nominal terms or real
  terms, depending upon whether the cash flows are
  nominal or real
• Discount rate can vary across time.
• Estimate the current earnings and cash flows on
  the asset, to either equity investors (CF to
  Equity) or to all claimholders (CF to Firm)
• Estimate the future earnings and cash flows on
  the asset being valued, generally by estimating
  an expected growth rate in earnings.
• Estimate when the firm will reach stable growth
  and what characteristics (risk cash flow) it
  will have when it does.
• Choose the right DCF model for this asset and
  value it.

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Discounted Cash Flow Valuation The Inputs
42
The Key Inputs in DCF Valuation

• Discount Rate
• Cost of Equity, in valuing equity
• Cost of Capital, in valuing the firm
• Cash Flows
• Cash Flows to Equity
• Cash Flows to Firm
• Growth (to get future cash flows)
• Growth in Equity Earnings
• Growth in Firm Earnings (Operating Income)

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I. Estimating Discount Rates

• DCF Valuation

44
Estimating Inputs Discount Rates

• Critical ingredient in discounted cashflow
  valuation. Errors in estimating the discount rate
  or mismatching cashflows and discount rates can
  lead to serious errors in valuation.
• At an intuitive level, the discount rate used
  should be consistent with both the riskiness and
  the type of cashflow being discounted.
• Equity versus Firm If the cash flows being
  discounted are cash flows to equity, the
  appropriate discount rate is a cost of equity. If
  the cash flows are cash flows to the firm, the
  appropriate discount rate is the cost of capital.
• Currency The currency in which the cash flows
  are estimated should also be the currency in
  which the discount rate is estimated.
• Nominal versus Real If the cash flows being
  discounted are nominal cash flows (i.e., reflect
  expected inflation), the discount rate should be
  nominal

45
Estimating Inputs Discount Rates or Cost of
Capital (WACC)

• It will depend upon
• (a) the components of financing Debt, Equity
• (b) the cost of each component
• The cost of capital is the cost of each component
  weighted by its relative market value.
• WACC ke (E/(DE)) kd (D/(DE))
• where ke is cost of equity
• kd is cost of debt,
• E is market value of equity, D is typically book
  value of debt.

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I. Cost of Equity

• The cost of equity is the rate of return that
  investors require to make an equity investment in
  a firm. There are three approaches to estimating
  the cost of equity
• a dividend-growth model,
• a risk and return model (e.g., CAPM),
• industry average model (Historical Industry
  Returns).

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I. Cost of Equity

• The dividend growth model (which specifies the
  cost of equity to be the sum of the dividend
  yield and the expected growth in earnings) is
  based upon the premise that the current price is
  equal to the value. It cannot be used in
  valuation, if the objective is to find out if an
  asset is correctly valued.
• P Present value of a stream of cash flows, D,
  growing at a rate of g.
• r Discount rate that reflects the riskiness of
  the cash flows D.
• P D / (r-g)
• r-g D/P

r D/P g
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I. Cost of Equity

• The dividend growth model (which specifies the
  cost of equity to be the sum of the dividend
  yield and the expected growth in earnings) is
  based upon the premise that the current price is
  equal to the value. It cannot be used in
  valuation, if the objective is to find out if an
  asset is correctly valued.
• A risk and return model, on the other hand, tries
  to answer two questions
• How do you measure risk?
• How do you translate this risk measure into a
  risk premium?
• Industry Average Returns
• Assumes future returns of the company will be
  similar to the past returns of firms in that
  industry.
• Needs no estimate of risk, or risk and return
  model.

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Measuring Cost of Capital

• It will depend upon
• (a) the components of financing Debt, Equity
• (b) the cost of each component
• The cost of capital is the cost of each component
  weighted by its relative market value.
• WACC ke (E/(DE)) kd (D/(DE))

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The Cost of Debt

• The cost of debt is the market interest rate that
  the firm has to pay on its borrowing. It will
  depend upon three components-
• (a) The general level of interest rates
• (b) The default premium
• (c) The firm's tax rate

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What the cost of debt is and is not..

• The cost of debt is
• the rate at which the company can borrow at today
• corrected for the tax benefit it gets for
  interest payments.
• Cost of debt kd Interest Rate on Debt (1 -
  Tax rate)
• The cost of debt is not
• the interest rate at which the company obtained
  the debt it has on its books.

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Estimating the Cost of Debt

• If the firm has bonds outstanding, and the bonds
  are traded, the yield to maturity on a long-term,
  straight (no special features) bond can be used
  as the interest rate.
• If the firm is rated, use the rating and a
  typical default spread on bonds with that rating
  to estimate the cost of debt.
• If the firm is not rated,
• and it has recently borrowed long term from a
  bank, use the interest rate on the borrowing or
• estimate a synthetic rating for the company, and
  use the synthetic rating to arrive at a default
  spread and a cost of debt
• The cost of debt has to be estimated in the same
  currency as the cost of equity and the cash flows
  in the valuation.

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Calculate the weights of each component

• Use target/average debt weights rather than
  project-specific weights.
• Use market value weights for debt and equity.
• The cost of capital is a measure of how much it
  would cost you to go out and raise the financing
  to acquire the business you are valuing today.
  Since you have to pay market prices for debt and
  equity, the cost of capital is better estimated
  using market value weights.
• Book values are often misleading and outdated.

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Estimating Market Value Weights

• Market Value of Equity should include the
  following
• Market Value of Shares outstanding
• Market Value of Warrants outstanding
• Market Value of Conversion Option in Convertible
  Bonds
• Market Value of Debt is more difficult to
  estimate because few firms have only publicly
  traded debt. There are two solutions
• Assume book value of debt is equal to market
  value
• Estimate the market value of debt from the book
  value

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II. Estimating Cash Flows

• DCF Valuation

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Steps in Cash Flow Estimation

• Estimate the current earnings of the firm
• Cash flows to equity look at earnings after
  interest expenses - i.e. net income
• Cash flows to the firm look at operating
  earnings after taxes
• Consider how much the firm invested to create
  future growth
• If the investment is not expensed, it will be
  categorized as capital expenditures. To the
  extent that depreciation provides a cash flow, it
  will cover some of these expenditures.
• Increasing working capital needs are also
  investments for future growth

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Earnings Checks

• When estimating cash flows, we invariably start
  with accounting earnings. To the extent that we
  start with accounting earnings in a base year, it
  is worth considering the following questions
• Are basic accounting standards being adhered to
  in the calculation of the earnings?
• Are the base year earnings skewed by
  extraordinary items - profits or losses? (Look at
  earnings prior to extraordinary items)
• Are the base year earnings affected by any
  accounting rule changes made during the period?
  (Changes in inventory or depreciation methods can
  have a material effect on earnings)
• Are the base year earnings abnormally low or
  high? (If so, it may be necessary to normalize
  the earnings.)
• How much of the accounting expenses are operating
  expenses and how much are really expenses to
  create future growth?

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Estimating Cashflows

• Free cashflow to Firm (FCFF) Cashflow to
• common shareholders,
• preferred shareholders, and
• debtholders.
• FCFF Free Cashflow to Equity
• Preferred dividends
• Interest expense (1 - tax rate)
  Principal repayments - New debt issues.

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Estimating Cashflows

• 1. Revenues - Operating expenses
• Earnings before interest, taxes,
  depreciation, and amort. (EBITDA)
• 2. EBITDA - Depreciation and Amortization
• Earnings before interest and taxes (EBIT)
• 3. EBIT - Interest Expenses
• Earnings before taxes
• 4. Earnings before taxes Taxes Net Income
• 5. Net Income Depreciation and Amortization
• Cashflow from Operations
• 6. Cashflow from operations - Working Capital
  change - Capital spending - Principal Repayments
  Proceeds from New Debt Issues Free Cashflow
  to Equity.

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Measuring Investment Expenditures

• Accounting rules categorize expenses into
  operating and capital expenses. In theory,
  operating expenses are expenses that create
  earnings only in the current period, whereas
  capital expenses are those that will create
  earnings over future periods as well. Operating
  expenses are netted against revenues to arrive at
  operating income.
• There are anomalies in the way in which this
  principle is applied. Research and development
  expenses are treated as operating expenses, when
  they are in fact designed to create products in
  future periods.
• Capital expenditures, while not shown as
  operating expenses in the period in which they
  are made, are depreciated or amortized over their
  estimated life. This depreciation and
  amortization expense is a non-cash charge when it
  does occur.
• The net cash flow from capital expenditures can
  be then be written as
• Net Capital Expenditures Capital Expenditures -
  Depreciation

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The Working Capital Effect

• In accounting terms, the working capital is the
  difference between current assets (inventory,
  cash and accounts receivable) and current
  liabilities (accounts payables, short term debt
  and debt due within the next year)
• A cleaner definition of working capital from a
  cash flow perspective is the difference between
  non-cash current assets (inventory and accounts
  receivable) and non-debt current liabilities
  (accounts payable).
• Any investment in this measure of working capital
  ties up cash. Therefore, any increases
  (decreases) in working capital will reduce
  (increase) cash flows in that period.
• When forecasting future growth, it is important
  to forecast the effects of such growth on working
  capital needs, and building these effects into
  the cash flows.

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III. Estimating Growth

• DCF Valuation

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Ways of Estimating Growth in Earnings

• Look at the past
• The historical growth in earnings per share is
  usually a good starting point for growth
  estimation
• Look at what others are estimating
• Analysts estimate growth in earnings per share
  for many firms. It is useful to know what their
  estimates are.
• Look at fundamentals
• Ultimately, all growth in earnings can be traced
  to two fundamentals - how much the firm is
  investing in new projects, and what returns these
  projects are making for the firm.

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I. Historical Growth in EPS

• Historical growth rates can be estimated in a
  number of different ways
• Arithmetic versus Geometric Averages
• Simple versus Regression Models
• Historical growth rates can be sensitive to
• the period used in the estimation
• In using historical growth rates, the following
  factors have to be considered
• how to deal with negative earnings
• the effect of changing size

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Arithmetic versus Geometric Growth Rates

• Year EPS Growth Rate
• 2000 1.50
• 2001 1.20 -20.00
• 2002 1.52 26.67
• 2003 1.63 7.24
• 2004 2.04 25.15
• 2005 2.53 24.02
• 2006 2.23 -11.86
• Arithmetic Average 8.54
• Geometric Average (2.23/1.50) (1/6) 1 6.83
  
• The arithmetic average will be higher than the
  geometric average rate
• The difference will increase with the standard
  deviation in earnings

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The Effects of Altering Estimation Periods

• Year EPS Growth Rate
• 2001 1.20
• 2002 1.52 26.67
• 2003 1.63 7.24
• 2004 2.04 25.15
• 2005 2.53 24.02
• 2006 2.23 -11.86
• Taking out 2000 from our sample, changes the
  growth rates materially
• Arithmetic Average from 2001 to 2006 14.24
• Geometric Average (2.23/1.20)(1/5) 13.19

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Dealing with Negative Earnings

• When the earnings in the starting period are
  negative, the growth rate cannot be estimated.
  (0.30/-0.05 -600)
• When earnings are negative, the growth rate is
  meaningless. Thus, while the growth rate can be
  estimated, it does not tell you much about the
  future.

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The Effect of Size on Growth

• Year Net Profit Growth Rate
• 2000 1.80
• 2001 6.40 255.56
• 2002 19.30 201.56
• 2003 41.20 113.47
• 2004 78.00 89.32
• 2005 97.70 25.26
• 2006 122.30 25.18
• Geometric Average Growth Rate 102

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Extrapolation and its Dangers

• Year Net Profit ( million)
• 2006 122.30
• 2007 247.05
• 2008 499.03
• 2009 1,008.05
• 2010 2,036.25
• 2011 4,113.23
• If net profit continues to grow at the same rate
  as it has in the past 6 years (2000-2006), the
  expected net income in 5 years (2011) will be
  4.113 billion!

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Propositions about Historical Growth

• Proposition 1 And in today already walks
  tomorrow.
• Coleridge
• Proposition 2 You cannot plan the future by the
  past
• Burke
• Proposition 3 Past growth carries the most
  information for firms whose size and business mix
  have not changed during the estimation period,
  and are not expected to change during the
  forecasting period.
• Proposition 4 Past growth carries the least
  information for firms in transition (from small
  to large, from one business to another..)

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II. Analyst Forecasts of Growth

• While the job of an analyst is to find under and
  over valued stocks in the sectors that they
  follow, a significant proportion of an analysts
  time (outside of selling) is spent forecasting
  earnings per share.
• Most of this time, in turn, is spent forecasting
  earnings per share in the next earnings report
• While many analysts forecast expected growth in
  earnings per share over the next 5 years, the
  analysis and information (generally) that goes
  into this estimate is far more limited.
• Analyst forecasts of earnings per share and
  expected growth are widely disseminated by
  services such as Zacks and IBES, at least for U.S
  companies.

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How good are analysts at forecasting growth?

• Analysts forecasts of EPS tend to be closer to
  the actual EPS than simple time series models,
  but the differences tend to be small
• The advantage that analysts have over time series
  models
• tends to decrease with the forecast period (next
  quarter versus 5 years)
• tends to be greater for larger firms than for
  smaller firms
• tends to be greater at the industry level than at
  the company level
• Forecasts of growth (and revisions thereof) tend
  to be highly correlated across analysts.

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Are some analysts more equal than others?

• A study of All-America Analysts (chosen by
  Institutional Investor) found that
• There is no evidence that analysts who are chosen
  for the All-America Analyst team were chosen
  because they were better forecasters of earnings.
  (Their median forecast error in the quarter prior
  to being chosen was 30 the median forecast
  error of other analysts was 28)
• However, in the calendar year following being
  chosen as All-America analysts, these analysts
  become slightly better forecasters than their
  less fortunate brethren. (The median forecast
  error for All-America analysts is 2 lower than
  the median forecast error for other analysts.)
• Earnings revisions made by All-America analysts
  tend to have a much greater impact on the stock
  price than revisions from other analysts
• The recommendations made by the All America
  analysts have a greater impact on stock prices
  (3 on buys 4.7 on sells). For these
  recommendations the price changes are sustained,
  and they continue to rise in the following period
  (2.4 for buys 13.8 for the sells).

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The Five Deadly Sins of an Analyst

• Tunnel Vision Becoming so focused on the sector
  and valuations within the sector that they lose
  sight of the bigger picture.
• LemmingitisStrong urge felt by analysts to
  change recommendations and revise earnings
  estimates when other analysts do the same.
• Stockholm Syndrome Refers to analysts who start
  identifying with the managers of the firms that
  they are supposed to follow.
• Factophobia (generally is coupled with delusions
  of being a famous story teller) Tendency to base
  a recommendation on a story coupled with a
  refusal to face the facts.
• Dr. Jekyll/Mr.Hyde Analyst who thinks her
  primary job is to bring in investment banking
  business to the firm.

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Propositions about Analyst Growth Rates

• Proposition 1 There is far less private
  information and far more public information in
  most analyst forecasts than is generally claimed.
• Proposition 2 The biggest source of private
  information for analysts remains the company
  itself which might explain
• why there are more buy recommendations than sell
  recommendations (information bias and the need to
  preserve sources)
• why there is such a high correlation across
  analysts forecasts and revisions
• why All-America analysts become better
  forecasters than other analysts after they are
  chosen to be part of the team.
• Proposition 3 There is value to knowing what
  analysts are forecasting as earnings growth for a
  firm. There is, however, danger when they agree
  too much (lemmingitis) and when they agree too
  little (in which case the information that they
  have is so noisy as to be useless).

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IV. Growth Patterns

• Discounted Cashflow Valuation

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Stable Growth and Terminal Value

• When a firms cash flows grow at a constant
  rate forever, the present value of those cash
  flows can be written as
• Value Expected Cash Flow Next Period / (r - g)
• where,
• r Discount rate (Cost of Equity or Cost of
  Capital)
• g Expected growth rate
• This constant growth rate is called a stable
  growth rate and cannot be higher than the growth
  rate of the economy in which the firm operates.
• While companies can maintain high growth rates
  for extended periods, they will all approach
  stable growth at some point in time.
• When they do approach stable growth, the
  valuation formula above can be used to estimate
  the terminal value of all cash flows beyond.

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Growth Patterns

• A key assumption in all discounted cash flow
  models is the period of high growth, and the
  pattern of growth during that period. In general,
  we can make one of three assumptions
• there is no high growth, in which case the firm
  is already in stable growth
• there will be high growth for a period, at the
  end of which the growth rate will drop to the
  stable growth rate (2-stage)
• there will be high growth for a period, at the
  end of which the growth rate will decline
  gradually to a stable growth rate(3-stage)

Stable Growth
2-Stage Growth
3-Stage Growth
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Determinants of Growth Patterns

• Size of the firm
• Success usually makes a firm larger. As firms
  become larger, it becomes much more difficult for
  them to maintain high growth rates
• Current growth rate
• While past growth is not always a reliable
  indicator of future growth, there is a
  correlation between current growth and future
  growth. Thus, a firm growing at 30 currently
  probably has higher growth and a longer expected
  growth period than one growing 10 a year now.
• Barriers to entry and differential advantages
• Ultimately, high growth comes from high project
  returns, which, in turn, comes from barriers to
  entry and differential advantages.
• The question of how long growth will last and how
  high it will be can therefore be framed as a
  question about what the barriers to entry are,
  how long they will stay up and how strong they
  will remain.

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Stable Growth and Fundamentals

• The growth rate of a firm is driven by its
  fundamentals - how much it reinvests and how high
  project returns are. As growth rates approach
  stability, the firm should be given the
  characteristics of a stable growth firm.
• Model High Growth Firms Stable growth firms
• DDM 1. Pay no or low dividends 1. Pay high
  dividends
• 2. Have high risk 2. Have average risk
• 3. Earn high ROC 3. Earn ROC closer to WACC
• FCFE/ 1. Have high net cap ex 1. Have lower net
  cap ex
• FCFF 2. Have high risk 2. Have average risk
• 3. Earn high ROC 3. Earn ROC closer to WACC
• 4. Have low leverage 4. Have leverage closer to
  industry average

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V. Beyond Inputs Choosing and Using the Right
Model

• Discounted Cashflow Valuation

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Summarizing the Inputs

• In summary, at this stage in the process, we
  should have an estimate of the
• the current cash flows on the investment, either
  to equity investors (dividends or free cash flows
  to equity) or to the firm (cash flow to the firm)
• the current cost of equity and/or capital on the
  investment
• the expected growth rate in earnings, based upon
  historical growth, analysts forecasts and/or
  fundamentals.
• The next step in the process is deciding
• which cash flow to discount, which should
  indicate
• which discount rate needs to be estimated and
• what pattern we will assume growth to follow.

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Which cash flow should I discount?

• Use Equity Valuation
• (a) for firms which have stable leverage, whether
  high or not, and
• (b) if equity (stock) is being valued
• Use Firm Valuation
• (a) for firms which have leverage which is too
  high or too low, and expect to change the
  leverage over time, because debt payments and
  issues do not have to be factored in the cash
  flows and the discount rate (cost of capital)
  does not change dramatically over time.
• (b) for firms for which you have partial
  information on leverage (eg interest expenses
  are missing..)
• (c) in all other cases, where you are more
  interested in valuing the firm than the equity.
  (Value Consulting?)

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Given cash flows to equity, should I discount
dividends or FCFE?

• Use the Dividend Discount Model
• (a) For firms which pay dividends (and repurchase
  stock) which are close to the Free Cash Flow to
  Equity (over a extended period)
• (b)For firms where FCFE are difficult to estimate
  (Example Banks and Financial Service companies)
• Use the FCFE Model
• (a) For firms which pay dividends which are
  significantly higher or lower than the Free Cash
  Flow to Equity. (What is significant? ... As a
  rule of thumb, if dividends are less than 80 of
  FCFE or dividends are greater than 110 of FCFE
  over a 5-year period, use the FCFE model)
• (b) For firms where dividends are not available
  (Example Private Companies, IPOs)

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What discount rate should I use?

• Cost of Equity versus Cost of Capital
• If discounting cash flows to equity -gt Cost of
  Equity
• If discounting cash flows to the firm-gt Cost of
  Capital
• What currency should the discount rate (risk free
  rate) be in?
• Match the currency in which you estimate the risk
  free rate to the currency of your cash flows
• Should I use real or nominal cash flows?
• If discounting real cash flows-gt real cost of
  capital
• If nominal cash flows -gt nominal cost of capital
• If inflation is low (lt10), stick with nominal
  cash flows since taxes are based upon nominal
  income
• If inflation is high (gt10) switch to real cash
  flows

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Which Growth Pattern Should I use?

• Use a Stable Growth Model If your firm is
• large and already growing at a rate close to or
  lower than the overall growth rate of the
  economy, or
• constrained by regulation from growing at rate
  faster than the economy
• has the characteristics of a stable firm (average
  risk reinvestment rates)
• Use a 2-Stage Growth Model If your firm
• is large growing at a moderate rate (Overall
  growth rate 10) or
• has a single product barriers to entry with a
  finite life (e.g. patents)
• Use a 3-Stage Model If your firm
• is small and growing at a very high rate (gt
  Overall growth rate 10) or
• has significant barriers to entry into the
  business
• has firm characteristics that are very different
  from the norm

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