Risk, returns and WACC

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Risk, returns and WACC

• CAPM and the capital budgeting

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Todays plan

• Review what we have learned in the last lecture
• Risk
• Portfolio
• CAPM
• The security market line
• Portfolio rules
• The application of CAPM in capital budgeting
• WACC (Weighted Average Cost of Capital)

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What have we learned in the last lecture?

• How to measure investment performance?
• How to measure risk?
• Two kinds of risk?
• How to measure systematic risk?
• What is the heuristic meaning of the Beta?
• What is a portfolio?
• How to calculate a portfolio weight?
• What is the CAPM?
• What is the basic idea behind CAPM?
• What is the security market line?

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Measuring Market Risk

• Market Portfolio
• It is a portfolio of all assets in the economy.
  In practice a broad stock market index, such as
  the SP 500 is used to represent the market
  portfolio. The market return is denoted by Rm
• Beta (ß)
• Sensitivity of a stocks return to the return on
  the market portfolio,
• Mathematically,

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An intuitive example for Beta

• Turbo Charged Seafood has the following returns
  on its stock, relative to the listed changes in
  the return on the market portfolio. The beta of
  Turbo Charged Seafood can be derived from this
  information.

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Measuring Market Risk (example, continue)
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Measuring Market Risk (continue)

• When the market was up 1, Turbo average change
  was 0.8
• When the market was down 1, Turbo average
  change was -0.8
• The average change of 1.6 (-0.8 to 0.8) divided
  by the 2 (-1.0 to 1.0) change in the market
  produces a beta of 0.8. ß1.6/20.8

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Another example

• Suppose we have following information

Market
Stock A
Stock B
State
-6
-8
-10
bad
24
32
good
38
a. What is the beta for each stock?
b. What is the expected return for each stock if
each scenario is equally likely?
c. What is the expected return for each stock if
the probability for good economy is 20?
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Solution

• a.
• b.
• c.

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Betas for the market portfolio and risk-free
investment

• What is the beta of the market portfolio?
• What is the beta of the risk-free security?

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Market risk and risk premium

• Risk premium for bearing market risk
• The difference between the expected return
  required by investors and the risk-free asset.
• Example, the expected return on IBM is 10, the
  risk-free rate is 5, and the risk premium is 10
  -55
• If a security ( an individual security or a
  portfolio) has market or systematic risk,
  risk-averse investors will require a risk
  premium.

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CAPM (Capital Asset Pricing Model)

• The risk premium on each security is proportional
  to the market risk premium and the beta of the
  security.
• That is,

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Security market line (SML)

• The graphic representation of CAPM in the
  expected return and Beta plane

Security Market Line
Rm
rf
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Some true or false questions

• 1.A market index is used to measure performance
  of a broad-based portfolio of stocks.
• 2. Long-term corporate bonds are riskier than
  common stocks.
• 3.If one portfolio's variance exceeds that of
  another portfolio, its standard deviation will
  also be greater than that of the other portfolio.
• 4. Portfolio weights are always positive.

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Some true or false questions

• 5. Standard deviation can be calculated as the
  square of the variance.
• 6. Market risk can be eliminated in a stock
  portfolio through diversification.
• 7. Macro risks are faced by all common stock
  investors.
• 8. The risk that remains in a stock portfolio
  after efforts to diversify is known as unique
  risk.
• 9. We use the standard deviation or variance of
  stock prices to measure the risk of a stock.

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Portfolio rules

• Rule 1 The realized return of a portfolio will
  be an weighted average of the realized returns
  of the securities in the portfolio.
• Rule 2 The expected return of a portfolio will
  be an weighted average of the expected returns
  of the securities in the portfolio.
• Rule 3 The Beta of a portfolio will be an
  weighted average of the Betas of the securities
  in the portfolio.

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Example

• Suppose you have a portfolio of IBM and Dell with
  a beta of 1.2 and 2.2, respectively. If you put
  50 of your money in IBM, and the other in Dell,
  what is the beta of your portfolio
• Beta of your portfolio 0.51.2 0.52.21.7

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Project Risk and cost of the capital

• In capital budgeting, in order to calculate the
  NPV of the project, we need to measure the risk
  of the project and thus find out the discount
  rate (the cost of capital)
• We can use Beta of the project cash flows to
  measure the risk of the project and use CAPM to
  get the expected return required by investors

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Example 1

• Based on the CAPM, ABC Company has a cost of
  capital of 17. (4 1.3(10)). A breakdown of
  the companys investment projects is listed
  below.
• 1/3 Nuclear Parts ß2.0
• 1/3 Computer Hard Drive ß 1.3
• 1/3 Dog Food Production ß 0.6
• When evaluating a new dog food production
  investment, which cost of capital should be used
  and how much?

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Solution

• Since dog food projects may have similar
  systematic risk to the dog food division, we use
  a beta of 0.6 to measure the risk of the projects
  to be taken.
• Thus the expected return on the project or the
  cost of capital is 0.040.6(0.1)0.l or 10

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Example 2

• Stock A has a beta of .5 and investors expect it
  to return 5. Stock B has a beta of 1.5 and
  investors expect it to return 13. What is the
  market risk premium and the expected rate of
  return on the market portfolio?

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Solution

• According to the CAPM

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Example 3

• You have 1 million of your own money and borrow
  another 1 million at a risk-free rate of 4 to
  invest in the market portfolio. The expected
  return for the market portfolio is 12, what is
  the expected return on your portfolio?

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Solution

• We can use two approaches to solve it
• First, the expected rate of return of a portfolio
  is the weighed average of the expected rates of
  return of the securities in the portfolio.
• Second , the beta of a portfolio is the weighed
  average of the betas of the securities in the
  portfolio. Then use the CAPM to get the expected
  rate of return.

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Solution (continue)

• First approach
• Second approach

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The cost of capital

• Cost of Capital
• The expected return the firms investors require
  if they invest in securities or projects with
  comparable degrees of risk.

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WACC to approximate the cost of capital or
discount rate

• Weighted -average cost of capital

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Summary of WACC calculation

• Three steps in calculating WACC
• First step Calculate the portfolio weight using
  the market value.
• Second step Determine the required rate of
  return on each security in the portfolio.
• Third step Calculate a weighted average of these
  returns, or the expected return on the portfolio.

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WACC calculation(continue)

• In calculating WACC, we have to use market values
  of debt and equity.
• Even if you are given the book value of debt, you
  may convert this book value to market debt value
  to calculate WACC
• Why do we use market values of debt and equity,
  but not book values of debt and equity, in
  calculating WACC?

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The cost of capital for the bond

• The cost of capital for the bond
• It is the YTM, the expected return required by
  the investors.
• That is
• The expected return on a bond can also be
  calculated by using CAPM

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Example 2

• A bond with a face value of 2000 matures in 5
  years. The coupon rate is 8. If the market price
  for this bond is 1900.
• (a) What is the expected return on this bond or
  what is the cost of debt or interest rate for
  this bond?
• (b) Suppose that the YTM is 9, what is the
  market value of this bond?

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Solution

• (a)
• (b)

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The cost of capital for a stock

• The cost of capital for a stock is calculated by
  using
• CAPM
• Dividend growth model

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Example 3

• Sock A now pays a dividend of 1.5 per share
  annually, It is expected that dividend is going
  to grow at a constant rate of 2. The current
  price for stock A is 25 per share. What is the
  expected return or the cost of capital by
  investing in this stock?

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Solution
Using the dividend discount model, we have
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Example 4

• Geothermal Inc. has two securities debt and
  stocks. The market debt value is 194 million,
  but the firms market value is 647 million.
  Given that geothermal pays 8 for debt and 14
  for equity, what is the Company Cost of Capital
  (There is no corporate tax)?

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Solution
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Example 5

• Executive Fruit has issued debt, preferred stock
  and common stock. The market value of these
  securities are 4mil, 2mil, and 6mil,
  respectively. The required returns are 6, 12,
  and 18, respectively.
• What is the WACC for Executive Fruit, Inc.?

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Solution
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Example 6 (with tax)

• Geothermal Inc. has two securities debt and
  stocks. The market debt value is 194 million,
  but the firms market value is 647 million.
  Given that geothermal pays 8 for debt and 14
  for equity, what is the Company Cost of Capital
  if the tax rate is 50?

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Solution