Discount Rates in Valuation

1
Discount Rates in Valuation

• Where We Are Going
• We will study the discount rates used in these
  cash flow valuation models

Chapter 7
2
Third Phase of Security
Analysis
Business Analysis
GAAP Financial Statements
Financial Statement Analysis
Forecast Assumptions
Valuation
Time
Historical Periods
Valuation Date
Forecast Periods
3
What Does a Discount Rate Do?

• A discount rate is the rate of return demanded by
  a provider of capital
• Appropriate discount rate depends on which rate
  the capital provider is talking about

4
Discount Rates in Valuation

• Different valuation models use different
  discounts rates because they evaluate different
  cash flow components
• We choose the discount rate that is a just
  sufficient expected return to compensate the
  relevant capital suppliers

5
What Discount Rate to Use?Depends on the Model
As if the debt were converted to equity
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The Cost of Equity

• Is the building block for all other discount
  rates
• Has no promised rate of return
• Must use an asset pricing model to infer the
  demanded rate of return.
• CAPM is the most common model.

7
Capital Asset Pricing Model (CAPM)

• The key concept
• Investors are risk averse
• Investors will hold riskier portfolios if the
  expected return is sufficiently higher
• The risk of the investor's portfolio, not the
  risk of any individual security in the portfolio,
  drives the risk?return trade-off

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Estimating the Risk-Free Rate

• To estimate a company's cost of equity
  we need to estimate the
• Risk-free interest rate
• Equity risk premium
• Company's Beta

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The Cost of Equity
is the risk-free interest rate
is the equity risk premium
is the degree to which the stock's returns are
correlated with market movements, or systematic
risk
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The Cost of Equity Continued

• Estimating the Risk-free Interest Rate
• Begin with a long-term risk-free interest rate
  such as 30-year Treasury bonds
• Because in a corporate valuation context, the
  cash flow stream generally has a fairly long
  duration

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The Cost of Equity Continued

• Equity Risk Premium
• The additional expected return above the
  risk-free rate that an investor requires to hold
  an average-risk stock rather than a Treasury bond
• The most subjective task
• Many analysts use the average Historical
  Equity Premium Earned

12
The Cost of Equity Continued

• Equity Risk Premium Continued
• Historical Equity Premium Earned
• The excess return actually earned on stocks in a
  given period over (or under) the amount earned on
  the risk-free asset
• Assumes expected premium today is unchanged from
  the past
• It is what investors are expecting

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The Cost of Equity Continued

• Understanding Beta
• Beta measures a stock's correlation
  with the market
• It represents the firms sensitivity of market
  performance
• Systematic risk vs. Nonsystematic risk
• Ex. 7.3 scatter plot of a stock
• Ex. 7.4 scatter plot of portfolios

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Understanding Beta
Beta, A measure
of correlation with the market
Additional volatility unrelated to the market
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Estimating Beta

• Beta is estimated by regressing a firm's stock
  returns on the market's returns over a period of
  time
• Fitting a best fit line through a scatter plot
  such as that of Ex. 7.3

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Estimating Beta Continued

• Before running regression we must determine
• Return interval
• Daily returns or monthly returns
• Estimation period
• Such as trailing five years or one year period

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Return Interval

• A shorter return interval provides a
  more precise estimate of beta
• For a given time period, using a shorter return
  interval increases the number of independent
  observations

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Estimation Period

• A longer period increases number of observations
• But it is likely that the company was
  fundamentally different than it is currently
• Common approach is five years
• Shorter period is suitable for companies with
  substantial change over last five years
• Such as acquisition or divestiture

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The Weighted-Average Cost of Capital (WACC)

• Is used in the
• Free cash flow model
• Residual income model

20
The Weighted-Average Cost of Capital
Continued

• To obtain the weighted-average cost of capital
• Average the estimated cost of equity with the
  costs of all other capital claims

is the corporate
marginal tax rate
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Computing WACC with No Nonoperating Assets
Easy Company

• 0.0966

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The Weighted-Average Cost of Capital
Continued

• What if there is nonoperating asset?
• Applying the formula will usually generate a
  lower WACC, because the cost of equity is lowered
  by the extra cushion of equity
• Exhibit 7.10
• Treating nonoperating security as negative debt
• Because only net debt matters

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Computing Not So Easys WACC
0.0966
0.0966
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Unlevering Beta
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Beta Vs. Leverage
Unlevered beta 0.98
Beta when d 0.30 is 1.344
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The Unlevered Cost of Equity
To obtain the unlevered cost of equity

• Apply an unlevering formula to the cost of equity

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Issues With Private Companies

• For private companies
• Betas cannot be estimated directly from stock
  returns Instead, Use betas of comparable firms,
  adjusting for the capital structure differences

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Summary

• We have learned
• Why different valuation models use different
  discount rates
• The capital asset pricing model

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Summary Continued

• How to estimate the discount rate for each model
• How to alter the analysis of discount rates for
  private companies