Cost of equity

1
Cost of equity

• Issues of the risk-free rate, the market risk
  premium, and beta

2
Intro

• Cost of capital risk-free rate firm-specific
  risk premium
• WACC wdkd(1-t) weke wpskps
• Discuss
• 1)      cost of equity, ke
• 2)      cost of debt, kd, and
• 3)      market value weights

3
Cost of equity

• CAPM
• ke,i rf ?i (rm rf)
• Measurement of cost of equity is important
  practical issue because
• Large gaps exist between theory and practice in
  estimating the cost of equity
• For many firms, equity composes the majority of
  its capital.

4
The Issues

• 1)      What is the maturity of the risk-free
  rate that should be used (i.e., 3-month, 1-year,
  10-year, 30-year)?
• 2)      How large is the market risk premium?
• 3)      Does the market risk premium change over
  time (i.e., do market conditions change the
  premium)?
• 4)      How do we measure beta?

5
Maturity of risk-free rate

• Maturity of risk-free rate should reflect the
  maturity of project being analyzed
• For valuing equity, choose long-term Treasury
  rate (i.e., 10 or 30 years)
• Data sources Bondsonline, Federal Reserve Banks
  (any)

6
How large is the market risk premium?

• Traditional approach historic averages
• Ibbotson data back to 1926
• Arithmetic averages
• Geometric averages
• Which risk-free rate (short vs. long)?
• Is the historic premium too high?
• Data source Historic returns spreadsheet

7
Does the market risk premium change over time?

• Lower premium in 1800s
• Considerable difference based on periods of
  measurement (1990s?)
• Confusion realized returns are a function of
  changes in risk premium AND cash flow factors
• Measure implied premium using current market
  price data
• Data Implied returns spreadsheet and how to

8
Measurement of beta

• Beta measures systematic risk of individual
  stock (or of portfolio).
• Standard methodology
• The regression coefficient, ?i, on the market
  return is beta.
• Issues complicating measurement

9
Issues complicating beta measurement

• What is market?
• How many observations?
• What time frame should be used?
• How large is the estimation error?
• What if measurement yields unreasonable cost of
  equity estimate?
• Example Columbia Sportswear (COLM)

10
Alternative approach to single-firm regression
beta

• Bottom-up beta
• Uses comparable firm betas as starting point
• Basic process
• Unlever the industry beta using industry
  leverage ratio and tax rate
• Use the unlevered industry beta, along with
  firms own leverage ratio and tax rate to
  calculate its levered beta

11
Unlevering and levering betas

• Unlevering a levered beta
• In this equation, we are working with industry
  data
• Levering an unlevered beta
• In this equation, we are working with the
  unlevered industry beta, firm-specific leverage
  and tax rate