Common Stock Pricing part 1

• Forms of Corporations

  private firms (closely held)

  • shares held by few investors not easily traded

  public firms

  • shares available to anyone and traded between investor
  • have held IPO
  • ability to raise capital
  • liquidity for investors
  • opportunity to cash out
• Rights of common shareholders

  what are shareholders?

  • owners

  what does that let them get?

  • dividends
  • voting rights
  • major decisions - mergers/acquisitions
  • board of directors - shareholder representative
  • Claim of:
  • net income and assets ( they are paid last)
• Value of a Stock

  value of an asset =

  • present value of expected future cash flows

  stock cash flows:

  • dividends
  • selling price

  so what do you really get?

  • dividends
• value of stock =

  PV of expected future dividends
• Dt =

  dividend expected at the end of year t
• D0

  = “last dividend” already paid by firm
• D1 =

  “next dividend” to be paid, the first future cash flow
• Pt =

  expected price at end of year t
• P0 =

  actual price or intrinsic value today
• g =

  expected dividend growth rate
• R =

  shareholder required return (CAPM)
• Perpetuity =

  infinite annuity
• the FV of a perpetuity is

  infinity
• PV Perp =

  PMT / i ~ PMT = PV x i
• How much must you deposit today at 10% interest to be able to pay out $100 per year forever, with the first payment in one year

  $1,000
• Constant dividend ( perpetuity for a stock)

  P0 = D1 / R
• Stock pays a constant dividend of $2 per share. If the required return is 15% what should the price be?

  $13.33
• Something that has a constant dividend is called a

  preferred stock
• P0 =

  D1/ R - g
• Dt =

  D0 (1 + g) ^t
• A stock just paid a dividend of $2 that is expected to grow at 5%. If the required return is 15%, what should the price be?

  $21
• A stock with a beta of 1.3 just paid a dividend of $1.50 that is expected to grow at 3%. If the risk-free rate is 2% and the market risk premium is 6%, what should the price of the stock be?

  $22.72
• What happens to the stock price if:

  dividend increases

  • price increases and Po increases

  growth increases

  • price increases and Po increases

  risk increases

  • price decreases and (R increases) Po decreases
• R =

  D1 / P0 + g
• D1 / P0

  represents the dividend yield
• g


  represents the capital gains yield
• Pt =

  D down t + 1 / R - g
• how would you get the price in five years

  P5 = D6 / R - g
• Pt =

  P0 ( 1 + g ) ^ t
• A stock just paid a dividend of $2 that is expected to grow at 5%. If the required return is 15% what will be the price in three years? (Hint: this is the first stock we did and the current price is $21.)

  $24.31
• the hardest to estimate is

  R because it can be market rate or your rate
• market R

  g is market expected growth for stock "implicit"
• your R

  g is your required growth for stock
• R =

  D0 (1 + g) / P0 + g
• A stock is priced at $45 and just paid a dividend of $1.50. The required return is 15%

  What growth rate does the market expect for this stock?

  - 11.29%

  If you expect the stock to grow at 10%, would you buy it? Why or why not?

  • no, need 11.29% growth to earn required return
• Your firm has a beta of 1.5 and just paid a dividend of $1.85 that is expected to grow at 4%. You are considering a new project that would increase your beta to 1.8 and increase your expected growth rate to 5%. The risk-free rate is 3% and the expected market return is 10%

  now = $20.25

  with project = $18.33

  No because it lowers stock price
• Your firm has a beta of 1.5 and just paid a dividend of $1.85 that is expected to grow at 4%. You are considering a new project that would increase your beta to 1.8 and increase your expected growth rate to 5%. The risk-free rate is 3% and the expected market return is 10%

  Given the new beta of 1.8, what is the minimum growth rate that makesthe project feasible?

  - 5.92%