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Chapter 6. Equities. Common Stock . Represents ownership of a business entity with claims on earnings and dividends Can have different classes of stock where one class can be given disproportionate powers Right to vote Proxy. Intrinsic Value .

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chapter 6
Chapter 6


common stock
Common Stock
  • Represents ownership of a business entity with claims on earnings and dividends
  • Can have different classes of stock where one class can be given disproportionate powers
  • Right to vote
    • Proxy
intrinsic value
Intrinsic Value
  • Present value of expected net cash flows that accrues to the owner of security
dividend discount model
Dividend Discount Model
  • Process of evaluating stocks on basis of present value of their expected stream of dividends
  • Also known as the dividend valuation model
intrinsic value of common stock
Intrinsic Value of Common Stock

P0 = price of stock today

dt = dividend during period t

r = required rate of return

H = holding period

PH = price of the stock at the end of the holding period

holding period model is misleading
Holding Period Model Is Misleading
  • Problem with defining price of stock in terms of dividends and selling price is that this is circular argument, as it begs the question of what determines selling price.
  • Selling price is present value of dividends to be paid forever thereafter.
dividend discount model1
Dividend Discount Model
  • Because model runs to infinity, it can’t be implemented without making additional assumptions about pattern of future dividends.
required rate of return
Required Rate of Return
  • Rate of return on an investment required by market to justify degree of risk incurred
  • Risk-free rate plus the risk premium
  • In equilibrium (quantity supplied equals quantity demanded), required rate of return equal to expected rate of return.
value cannot be based on earnings
Value Cannot Be Based on Earnings
  • Double counting
    • Earnings retained (i.e., reinvested) in firm should lead to higher earnings in future
    • Higher earnings are NOT additional value to investor, but simply a return on value of earnings previously invested
valuation of stocks that don t pay dividends
Valuation of Stocks That Don’t Pay Dividends
  • If they will never, ever pay a dividend:
    • Truly worthless
  • If they will start paying a dividend in the future:
    • Value today based on when they are expected to start paying dividends, and amount of payment at that time
gordon constant growth model
Gordon (Constant) Growth Model
  • Form of dividend discount model
  • Used to evaluate the intrinsic value of an asset based on assumptions of constant growth rate g of cash flow or dividends and a known discount rate r, where r>g.


gordon constant growth model continued
Gordon (Constant) Growth Model (continued)

Vo = d1/(r – g) = d0 x (1 + g)/(r – g)

where V0 = intrinsic value,

d1 = next year’s dividend,

g = growth rate of dividends, and

r = required rate of return.

dn = dn – 1(1+g) or dn = d0(1 + g)n

implications of growth model
Implications of Growth Model
  • Decrease in required rate of return (that is, discount rate), will cause value of stock to be higher
  • Increase in expected growth rate of dividends (g), will cause value of stock to be higher
  • Increase in next year’s expected dividend (d1) will cause value of stock to be higher
alternative meaning of g
Alternative Meaning of “g”
  • Can solve constant growth rate model for r:

r = d1/Vo + g

= dividend yield plus growth rate

  • Return to investor equals dividend yield plus expected percentage price change
  • If discount rate = expected return, then

dividend growth rate = expected percentage price change

zero growth model
Zero Growth Model
  • Assume dividends will never change (i.e., no growth) P = d / r

where P = intrinsic value of a stock whose dividends are expected to form a perpetuity

d = the constant, annual dividend

r = discount rate

selection of discount rate
Selection of Discount Rate
  • Sufficient to compensate investor for the riskiness of dividend stream
  • Frequently use CAPM:

ri = r f +  (r m – r f)

application of capm
Application of CAPM

Risk-free rate

  • interest rate on riskless investment, such as Treasury bill

Market portfolio

  • portfolio of all assets, but good surrogate is S&P 500
market price based ratios
Market-Price Based Ratios
  • Used to judge relative appropriateness of current stock price
    • Price-earnings ratio
    • Price-cash flow ratio
      • Price-free cash flow ratio
    • Price-sales ratio
    • Price-earnings/growth rate ratio
earnings per share eps
Earnings Per Share (EPS)
  • Net income of company, minus any preferred dividend requirements, divided by the number of outstanding common shares
  • Provides investor or potential investor with information on stability of dividends and capital gains potential
  • Considered one of most important indications of value of common stock
price earnings p e ratio
Price-Earnings (P/E) Ratio
  • Share price of stock divided by its actual or anticipated earnings per share
    • For trailing earnings, stock price relative to most recent 12-month earnings per share
      • Factual
    • For ex ante earnings, stock price relative to expected next 12-month earnings.
      • Fantasy
dividend payout ratio
Dividend Payout Ratio
  • Dividends on common stock paid out as percentage of net income (after preferred dividends)
growth model p e ratio
Growth Model & P/E Ratio

Where E0 = last year’s earnings

m = the payout ratio


P0 = E0 x m x (1 + g)/(r – g)

growth model p e ratio continued
Growth Model & P/E Ratio (continued)

Dividing through by last year’s earnings produces the price-to-past earnings ratio:

 P0 / E0 = m x (1 + g) / (r – g)or

P0 / [E0 x (1+g)] = m / (r – g)

P0 / E1 = m / (r – g)

characteristics of companies with high p e ratios
Characteristics of Companies with High P/E Ratios
  • High expected growth rate of earnings
  • Low discount rate (less risky)
  • Small spread between the discount rate and growth rate
growth stocks vs value stocks
Growth Stocks vs. Value Stocks
  • Growth stocks synonymous with above average PE ratios
  • Value stocks synonymous with below average PE ratios
  • Recent evidence suggests value stocks perform better than growth stocks the majority of the time
forecasting with p e ratio
Forecasting with P/E Ratio
  • Individual stock:
    • Forecast earnings per share
    • Forecast P/E ratio
    • Multiply the two together
  • Market:
    • Forecast earnings for index
    • Forecast P/E for that index
    • Multiply the two together
other equity instruments
Other Equity Instruments
  • Straight Preferred stock and Participating Preferred stock
  • Rights Offering
  • Warrants
  • Issued to raise new capital
  • Exercise Price < Market Price
    • Sometimes by a large margin
    • Hence, Intrinsic Value > 0
  • Short lifespan
  • Transferable
    • Trade on exchanges or OTC for larger companies
mechanics of dividends
Mechanics of Dividends
  • Declaration date
  • Ex-dividend date
  • Record date
  • Payment date
dividend patterns
Dividend Patterns
  • Many companies boast of number of years of consecutive dividend payments
  • Dividends paid on same date of each quarter
  • Dividend increases usually same quarter of each year
non traditional investments
Non-Traditional Investments
  • Collectables

–requires a market for the asset

  • Noncollectables

–items that are unique and expensive

  • Natural Resources

–depletion allowance on some mineral rights

  • Precious Metals

–rare metallic chemical element of high, durable economic value