Stock Valuation and Risk

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CHAPTER 11

• Stock Valuation and Risk

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CHAPTER 11 OVERVIEW

• This chapter will
• A. Explain methods of valuing stocks and
  determining the stock required rate of return
• B. Identify the factors that affect stock prices
• C. Explain how analysts affect stock prices
• D. Explain how to measure the risk of stocks

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Common Stock Price

• For common stock, the future cash flows are
• Dividends
• Selling price
• These cash flows are highly uncertain.
• To find the value of common stock, we make
  assumptions about how dividends evolve in the
  future. We look at 3 set of assumptions
• Constant dividend stream
• Dividends grow at constant rate (constant
  dividend growth model)
• Non-constant dividend growth

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Constant dividend stream

• Same amount of dividend is paid for ever.
• Cash flow stream resembles a perpetuity.
• Common stock price, Pe
• Cost of equity capital, re

Common stock dividend
Cost of equity capital or required rate of return
on equity
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Dividends grow at constant rate 1

• Assume that dividends grow at a constant rate, g,
  per period forever.
• Given this assumption, the price of common stock
  equals

D1 D0(1 g)
D0 Dividend that the firm just paid
Required rate of return on equity
Dividend growth rate
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Dividends grow at constant rate 2

• Useful properties.
• All other things unchanged,
• If D0 increases (decreases), Pe increases
  (decreases).
• If g increases (decreases), Pe increases
  (decreases).
• If re increases (decreases), Pe decreases
  (increases).

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Dividends grow at constant rate 2

• By rearranging the above equation, we can find
  the required rate of return on equity
• For the constant growth model to work, re gt g.

Capital gains yield
Required rate of return on equity
Dividend yield
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Constant growth problems 1

• Jarrow Company will pay an annual dividend of 3
  per share one year from today. The dividend is
  expected to grow at a constant rate of 7
  permanently. The market requires 15 What is the
  current price of the stock (to 2 decimal places)?
• In this question D1 is already given to you.
• Verify that Price 37.5

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Constant growth problems 2

• Johnson Foods Inc. just paid a dividend of 10
  (i.e., D0 10.00). Its dividends are expected
  to grow at a 4 annual rate forever. If you
  require a 15 rate of return on investments of
  this risk level, what is Johnson Foodss current
  stock price? (to 2 decimal places)
• Straightforward application of price formula.
• Verify that price 94.55

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Constant growth problems 3

• The price of a stock in the market is 62. You
  know that the firm has just paid a dividend of 5
  per share (i.e., D0 5). The dividend growth
  rate is expected to be 6 percent forever. What is
  the investors required rate of return for this
  stock (to 2 decimal places)?
• Use re (D1/P) g.
• Verify that re 14.55

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Constant growth problems 4

• A firm is expected to pay a dividend of 5.00 on
  its stock next year. The price of this stock is
  40 and the investors required rate of return is
  20. The firms dividends grow at a constant
  rate. What is this constant dividend growth rate
  (g)?
• use re (D1/P) g
• Verify that g 7.5

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Constant growth problems 5

• In order to use the constant dividend growth
  model to value a stock it must be true that
• a. The required rate of return is less than the
  expected dividend growth rate.
• b. The expected dividend growth rate is greater
  than zero.
• c. The next dividend (D1) is expected to be
  greater than 1.00.
• d. The expected dividend growth rate is less than
  the required rate of return.

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Non-constant dividend growth 1

• With this assumption, dividends grow at different
  rates for different periods of time. Eventually,
  dividends will grow at a constant rate forever.
• Time line is very useful for valuing this type of
  stocks.
• To value such stocks, also need the constant
  growth formula.
• Best way to learn is through an example.

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Non-constant dividend growth 2

• ABC Co. is expected to pay dividends at the end
  of the next three years of 2, 3, 3.50,
  respectively. After three years, the dividend is
  expected to grow at 5 constant annual rate
  forever. If the required rate of return on this
  stock is 15, what is the current stock price?

Dividends grow at 5 forever
2.00
3.00
3.50
T 0
T 1
T 2
T 3
T 4
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What to do?

• Use constant growth formula to find stock price
  at the end of year 3. Call this stock price P3.
• Add P3 to dividend received at t3. This sum is
  the cash flow for t3. Find PV of this cash flow.
  
• Find PV of dividends at t1, t2.
• Current stock price sum of 2 and 3.

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Apply the method

• P3 (3.5 x (1.05))/(0.15 0.05) 36.75
• At t3, cash flow is 36.75 3.50 40.25
• Current stock price,

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Another type of non-constant growth problem

• Malcolm Manufacturing, Inc. just paid a 2.00
  annual dividend (that is, D0 2.00). Investors
  believe that the firm will grow at 10 annually
  for the next 2 years and 6 annually forever
  thereafter. Assuming a required return of 15,
  what is the current price of the stock (to 2
  decimal places)?
• Use timeline to see the problem better.
• Verify that stock price 25.29

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Factors That Affect Stock Prices

• 1. Economic Factors
• a. Impact of Economic Growth
• b. Impact of Interest Rates
• 2. Market Related Factors
• a. Investor Sentiment

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Factors That Affect Stock Prices

• 3. Firm-Specific Factors
• a. Dividend Policy Changes
• b. Earnings Surprises
• c. Acquisitions and Divestitures

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Stock Market Efficiency

• Forms of Efficiency
• a. Weak-Form Efficiency
• b. Semistrong-Form Efficiency
• c. Strong-Form Efficiency

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Risk return relationship for equity security 1

• To find the risk premium for an equity security,
  we make use of a theoretical model in finance,
  called the Capital Asset Pricing Model (CAPM,
  pronounced as cap M).

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Risk return relationship for equity security 2

• The CAPM says that the risk premium on equity is
  defined as
• b(rm rf )

tells you how sensitive a stock is to movements
in a large, diversified portfolio
expected return on the diversified portfolio
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Risk return relationship for equity security 3

• Required rate of return for an equity security
• risk-free rate b(rm rf )
• Required rate of return on equity is also known
  as
• Cost of equity
• Discount rate

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Beta

• Measures a stocks market risk, and shows a
  stocks volatility relative to the market.

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Comments on beta

• If beta 1.0, the security is just as risky as
  the average stock (the market).
• If beta gt 1.0, the security is riskier than
  average.
• If beta lt 1.0, the security is less risky than
  average.
• Most stocks have betas in the range of 0.5 to 1.5.

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Calculating betas

• Well-diversified investors are primarily
  concerned with how a stock is expected to move
  relative to the market in the future.
• Without a crystal ball to predict the future,
  analysts are forced to rely on historical data.
  A typical approach to estimate beta is to run a
  regression of the securitys past returns against
  the past returns of the market.
• The slope of the regression line is defined as
  the beta coefficient for the security.

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Illustrating the calculation of beta
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Chapter 12 (Stock Market Transactions)

• 1. Placing an Order
• a. Market Order
• b. Stop-Loss Order
• c. Stop-Buy Order
• d. Placing an Order Online
• 2. Margin Trading
• 3. Short Selling

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Assignment 7 (continue)

• 1. Chapter 11
• Questions and Applications 3 4 5 9
• Problems 9 10 11
• 2. Additional problems
• Davidson Company will pay an annual dividend of
  6 per share one year from today. The dividend is
  expected to grow at a constant rate of 15 percent
  permanently. The market requires 24 percent
  return on the company. What is the current price
  of the stock (to 2 decimal places)?

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Additional problems

• The price of a stock in the market is 32. You
  know that the firm has just paid a dividend of
  0.75 per share (i.e., D0 0.75). The dividend
  growth rate is expected to be 6 percent forever.
  What is the investors required rate of return
  for this stock?
• Brett Creative Media is expected to pay dividends
  at the end of the next three years of 0.5, 1.5,
  2, respectively. After three years, the dividend
  is expected to grow at a 5 constant annual rate
  forever. If the required rate of return on this
  stock is 10, what is the current stock price?