Discounted Cash Flow Valuation

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Discounted Cash Flow Valuation
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Challenges

• Defining and forecasting CFs
• Estimating appropriate discount rate

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Basic DCF model

• An assets value is the present value of its
  (expected) future cash flows

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Three alternative definitions of cash flow

• Dividend discount model
• Free cash flow model
• Residual income model

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Free cash flow

• Free cash flow to the firm (FCFF) is cash flow
  from operations minus capital expenditures
• Free cash flow to equity (FCFE) is cash flow from
  operations minus capital expenditures minus net
  payments to debtholders (interest and principal)

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FCF valuation

• PV of FCFF is the total value of the company.
  Value of equity is PV of FCFF minus the market
  value of outstanding debt.
• PV of FCFE is the value of equity.
• Discount rate for FCFF is the WACC. Discount
  rate for FCFE is the cost of equity (required
  rate of return for equity).

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Intro to Free Cash Flows

• Dividends are the cash flows actually paid to
  stockholders
• Free cash flows are the cash flows available for
  distribution.

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Defining Free Cash Flow

• Free cash flow to equity (FCFE) is the cash flow
  available to the firms common equity holders
  after all operating expenses, interest and
  principal payments have been paid, and necessary
  investments in working and fixed capital have
  been made.
• FCFE is the cash flow from operations minus
  capital expenditures minus payments to (and plus
  receipts from) debtholders.

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Valuing FCFE

• The value of equity can also be found by
  discounting FCFE at the required rate of return
  on equity (r)
• Since FCFE is the cash flow remaining for equity
  holders after all other claims have been
  satisfied, discounting FCFE by r (the required
  rate of return on equity) gives the value of the
  firms equity.
• Dividing the total value of equity by the number
  of outstanding shares gives the value per share.

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Discount rate determination

• Jargon
• Discount rate any rate used in finding the
  present value of a future cash flow
• Risk premium compensation for risk, measured
  relative to the risk-free rate
• Required rate of return minimum return required
  by investor to invest in an asset
• Cost of equity required rate of return on common
  stock

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Two major approaches for cost of equity

• Equilibrium models
• Capital asset pricing model (CAPM)
• Arbitrage pricing theory (APT)
• Bond yield plus risk premium method (BYPRP)

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CAPM

• Expected return is the risk-free rate plus a risk
  premium related to the assets beta
• E(Ri) RF ?iE(RM) RF
• The beta is ?i Cov(Ri,RM)/Var(RM)
• E(RM) RF is the market risk premium or the
  equity risk premium

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CAPM

• What do we use for the risk-free rate of return?
• Choice is often a short-term rate such as the
  30-day T-bill rate or a long-term government bond
  rate.
• We usually match the duration of the bond rate
  with the investment period, so we use the
  long-term government bond rate.
• Risk-free rate must be coordinated with how the
  equity risk premium is calculated (i.e., both
  based on same bond maturity).

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Equity risk premium

• Historical estimates Average difference between
  equity market returns and government debt
  returns.
• Choice between arithmetic mean return or
  geometric mean return
• Survivorship bias
• ERP varies over time
• ERP differs in different markets

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Equity risk premium

• Expectational method is forward looking instead
  of historical
• One common estimate of this type
• GGM equity risk premium estimate
• dividend yield on index based on year-ahead
  dividends
• consensus long-term earnings growth rate
• - current long-term government bond yield

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Sources of error in using models

• Three sources of error in using CAPM or APT
  models
• Model uncertainty Is the model correct?
• Input uncertainty Are the equity risk premium
  or factor risk premiums and risk-free rate
  correct?
• Uncertainty about current values of stock beta or
  factor sensitivities

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BYPRP method

• The bond yield plus risk premium method finds the
  cost of equity as
• BYPRP cost of equity
• YTM on the companys long-term debt
• Risk premium
• The typical risk premium added is 3-4 percent.

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Single-stage, constant-growth FCFE valuation model

• FCFE in any period will be equal to FCFE in the
  preceding period times (1 g)
• FCFEt FCFEt1 (1 g).
• The value of equity if FCFE is growing at a
  constant rate is
• The discount rate is r, the required return on
  equity. The growth rate of FCFF and the growth
  rate of FCFE are frequently not equivalent.

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Computing FCFF from Net Income

• This equation can be written more compactly as
• FCFF NI Depreciation Int(1 Tax rate)
  Inv(FC) Inv(WC)
• Or
• FCFF EBIT(1-tax rate) depreciation Cap.
  Expend. change in working capital change in
  other assets

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Forecasting free cash flows

• Computing FCFF and FCFE based upon historical
  accounting data is straightforward. Often times,
  this data is then used directly in a single-stage
  DCF valuation model.
• On other occasions, the analyst desires to
  forecast future FCFF or FCFE directly. In this
  case, the analyst must forecast the individual
  components of free cash flow. This section
  extends our previous presentation on computing
  FCFF and FCFE to the more complex task of
  forecasting FCFF and FCFE. We present FCFF and
  FCFE valuation models in the next section.

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Forecasting free cash flows

• Given that we have a variety of ways in which to
  derive free cash flow on a historical basis, it
  should come as no surprise that there are several
  methods of forecasting free cash flow.
• One approach is to compute historical free cash
  flow and apply some constant growth rate. This
  approach would be appropriate if free cash flow
  for the firm tended to grow at a constant rate
  and if historical relationships between free cash
  flow and fundamental factors were expected to be
  maintained.

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Forecasting FCFE

• If the firm finances a fixed percentage of its
  capital spending and investments in working
  capital with debt, the calculation of FCFE is
  simplified. Let DR be the debt ratio, debt as a
  percentage of assets. In this case, FCFE can be
  written as
• FCFE NI (1 DR)(Capital Spending
  Depreciation)
• (1 DR)Inv(WC)
• When building FCFE valuation models, the logic,
  that debt financing is used to finance a constant
  fraction of investments, is very useful. This
  equation is pretty common.

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Forecasting future dividends or FCFE

• Using stylized growth patterns
• Constant growth forever (the Gordon growth model)
• Two-distinct stages of growth (the two-stage
  growth model and the H model)
• Three distinct stages of growth (the three-stage
  growth model)

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Forecasting future dividends

• Forecast dividends for a visible time horizon,
  and then handle the value of the remaining future
  dividends either by
• Assigning a stylized growth pattern to dividends
  after the terminal point
• Estimate a stock price at the terminal point
  using some method such as a multiple of
  forecasted book value or earnings per share

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Gordon Growth Model

• Assumes a stylized pattern of growth,
  specifically constant growth
• Dt Dt-1(1g)
• Or
• Dt D0(1 g)t

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Gordon Growth Model

• PV of dividend stream is
• Which can be simplified to

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Gordon growth model

• Valuations are very sensitive to inputs.
  Assuming D1 0.83, the value of a stock is

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Other Gordon Growth issues

• Generally, it is illogical to have a perpetual
  dividend growth rate that exceeds the growth rate
  of GDP
• Perpetuity value (g 0)
• Negative growth rates are also acceptable in the
  model.

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Gordon Model P/E ratios

• If E is next years earnings (leading P/E)
• If E is this years earnings (trailing P/E)

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Using a P/E for terminal value

• The terminal value at the beginning of the second
  stage was found above with a Gordon growth model,
  assuming a long-term sustainable growth rate.
• The terminal value can also be found using
  another method to estimate the terminal value at
  t n. You can also use a P/E ratio, applied to
  estimated earnings at t n.

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Using a P/E for terminal value

• For DuPont, assume
• D0 1.40
• gS 9.3 for four years
• Payout ratio 40
• r 11.5
• Trailing P/E for t 4 is 11.0
• Forecasted EPS for year 4 is
• E4 1.40(1.093)4 / 0.40 1.9981 4.9952

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Using a P/E for terminal value
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Three-stage DDM

• There are two popular version of the three-stage
  DDM
• The first version is like the two-stage model,
  only the firm is assumed to have a constant
  dividend growth rate in each of the three stages.
  
• A second version of the three-stage DDM combines
  the two-stage DDM and the H model. In the first
  stage, dividends grow at a high, constant
  (supernormal) rate for the whole period. In the
  second stage, dividends decline linearly as they
  do in the H model. Finally, in stage three,
  dividends grow at a sustainable, constant rate.

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Spreadsheet modeling

• Spreadsheets allow the analyst to build very
  complicated models that would be very cumbersome
  to describe using algebra.
• Built-in functions such as those to find rates of
  return use algorithms to get a numerical answer
  when a mathematical solution would be impossible
  or extremely complicated.

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Strengths of multistage DDMs

• Can accommodate a variety of patterns of future
  dividend streams.
• Even though they may not replicate the future
  dividends exactly, they can be a useful
  approximation.
• The expected rates of return can be imputed by
  finding the discount rate that equates the
  present value of the dividend stream to the
  current stock price.

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Strengths of multistage DDMs

• Because of the variety of DDMs available, the
  analyst is both enabled and compelled to evaluate
  carefully the assumptions about the stock under
  examination.
• Spreadsheets are widely available, allowing the
  analyst to construct and solve an almost
  limitless number of models.

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Weaknesses of multistage DDMs

• Garbage in, garbage out. If the inputs are not
  economically meaningful, the outputs from the
  model will be of questionable value.
• Analysts sometimes employ models that they do not
  understand fully.
• Valuations are very sensitive to the inputs to
  the models.

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Forecasting growth rates

• There are three basic methods for forecasting
  growth rates
• Using analyst forecasts
• Using historical rates (use historical dividend
  growth rate or use a statistical forecasting
  model based on historical data)
• Using company and industry fundamentals

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Finding g

• The simplest model of the dividend growth rate
  is
• g b x ROE
• where g Dividend growth rate
• b Earnings retention rate (1 payout ratio)
• ROE Return on equity.