Principles of Corporate Finance

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					             The Value of
            Common Stocks




Oh, the ragman draws circles up and down the block. I’d ask him
what the matter was, but I know he don’t talk. - Dylan
                Stocks and stock markets

Primary Market:        Market in which firm sells
                       new shares to raise cash.

Secondary Market:      Market in which investors trade
                       existing shares among themselves.

Stock exchanges are secondary markets. They may either operate as auction
markets or dealer markets.

The New York Stock Exchange is an auction market; the specialist keeps a
record of orders to buy & sell stock.
If (say) you wish to sell IBM stock, the specialist will identify the buyer who is
prepared to pay the highest price.

NASDAQ is a dealer market. It consists of a network of dealers who quote
prices at which they will buy or sell.
     What determines a stock's true value?

n   Book Value records what a company has paid for its assets with a
    simple deduction for depreciation and no allowance for inflation.

n   Liquidation Value is what the company could realize by selling its
    assets and repaying debts. It does not measure the value of a going
    concern. It ignores intangible assets (e.g.., patents, brand name) and
    ignores that firms may be able to make profitable investments in the
    future.

n   True Value is market value, that is, the amount that investors are
    willing to pay for the firm. It depends on the earning power of existing
    assets and the profitability of future investments.
                           The expected return on a stock
Expected = Dividend + Capital
Return     Yield       Gain

            DIV 1           P1 - P 0
 r     =               +
            P0               P0

eg Blue Skies stock price (P0 ) = $75. Investors expect next
year a dividend (DIV1 ) of $3 & a price (P1 ) of $81.

       3          81 - 75
 r =        +                     = .12 or 12%
       75         75

Stock =      Cash payoff to investors
Price        1 + expected return

           DIV1 + P1
P0 =
            1+r
                              3 + 81
For Blue Skies: P0 =                        = $75
                               1.12
                        Stock price is equal to the
                     discounted stream of dividends
Stock =     Cash payoff to investors
Price       1 + expected return

              DIV 1 + P 1
P0    =
                     1+r

                             DIV2 + P 2
Similarly P      1   =
                               1+r

                             DIV 1           DIV2 + P2
Therefore P 0 =                         +
                                                       2
                             1+r             (1 + r)

We can also express P2 in terms of DIV3 & P3 etc. Thus

          DIV1             DIV2           DIV3
P =
 0
                     +              +              + ......
          1+r            (1 + r)2       (1 + r)3
      Valuing Common Stocks
Dividend Discount Model - Computation of today’s
  stock price which states that share value equals the
  present value of all expected future dividends.




 H - Time horizon for your investment.
         Valuing Common Stocks
Example
   Current forecasts are for XYZ Company to pay dividends of $3, $3.24,
   and $3.50 over the next three years, respectively. At the end of three
   years you anticipate selling your stock at a market price of $94.48.
   What is the price of the stock given a 12% expected return?
    Valuing Common Stocks
     Assuming No Growth
If we forecast no growth, and plan to hold out
stock indefinitely, we will then value the stock as
a PERPETUITY.




 Assumes all earnings are
 paid to shareholders.
       Constant-growth dividend discount model
             (the Gordon Growth model)
If dividends are expected to grow at a constant rate (g), the value of
the stock is

        DIV1
PV =
        (r – g)

Example:
Blue Skies is expected to pay a $3 dividend next year (DIV1 = 3).
Investors expect Blue Skies dividends to increase by 8% a year
indefinitely (g = .08). The discount rate is 12% (r = .12).

       DIV1             3
PV =              =                 = $75
       (r – g)        (.12 - .08)

Note: The formula works only if g is less than r
    Estimating the capitalization rate
If dividends are expected to grow at a constant rate, g

                DIV1
         P0 =
                (r – g)

                DIV1
         r =              +   g
                 P0


If a firm earns a constant return on book equity and plows back a
constant proportion of earnings, then the dividend growth rate can be
estimated as follows:

DIVIDEND    = g = PLOWBACK                    x RETURN
GROWTH RATE       RATIO                         ON EQUITY

Also known as Sustainable Growth Rate – (i.e., steady rate at which a firm can
grow): plowback ratio X return on equity
     Valuing Common Stocks
Estimating the implied growth rate
 Example
   If a stock is selling for $100 in the stock market,
   what might the market be assuming about the
   growth in dividends?
                              Answer
                                The market is
                                assuming the dividend
                                will grow at 9% per
                                year, indefinitely.
PVGO- Growth versus No Growth
Suppose Blue Skies earns $5 a share, which it pays out
as dividends. DIV1 = $5 and g = 0. Then

        DIV 1         $5
PV =              =             = $41.67
        (r – g)       (.12 - .0)

$41.67 is the value of Blue Skies' assets in place (i.e., assuming no growth).

Suppose Blue Skies reinvests 40% of profits at a
return of 12% (that is the same rate as investors require):

g = plowback ratio x return on equity = .4 x .12 = .048

          .6 x $5
PV =                  = $41.67
        .12 - .048

NOTE: Firms that earn the required rate (r) on new investments, don't add value.

Recall Prior Estimated Price for Blue Skies = $75. If PV (assets in place) = $41.67,
then $75 - $41.67 = $33.33 = PV(Growth Opportunities) = PVGO
         Valuing Common Stocks
                 another PVGO example
Example
   Our company forecasts to pay a $8.33 dividend next year, which
   represents 100% of its earnings. This will provide investors with a
   15% expected return. Instead, we decide to plow back 40% of the
   earnings at the firm’s current return on equity of 25%. What is the
   value of the stock before and after the plowback decision?

No Growth                                     With Growth
Valuing Common Stocks another
            PVGO example continued
Example - continued
  If the company did not plowback some earnings, the stock
  price would remain at $55.56. With the plowback, the
  price rose to $100.00.

  The difference between these two numbers represents the
  net present value of a firm’s future investments. This is
 called the Present Value of Growth Opportunities (PVGO).
                 r is not EPS/P unless PVGO=0
STOCK PRICE =                   PV (average earnings under a
                                no-growth policy) plus
                                PV (growth opportunities)

             EPS1
     P0=                   +     PVGO
                 r

Thus
   EPS       1                    PVGO

     P
             =       r   (1 -       P
                                            )
         0                              0
If PVGO = 0, the earnings yield equals the capitalization rate.


PVGO IS POSITIVE ONLY IF THE FIRM CAN EARN MORE
THAN THE COST OF CAPITAL ON INVESTMENTS.
Estimated PVGOs
         Valuing a Business
Valuing a Business or Project




          PV (free cash flows)   PV (horizon value)
Example
              Valuing a Business
  Given the cash flows for Concatenator Manufacturing Division,
  calculate the PV of near term cash flows, PV (horizon value), and the
  total value of the firm. r=10% and g= 6%
              Valuing a Business
Example - continued
  Given the cash flows for Concatenator Manufacturing Division,
  calculate the PV of near term cash flows, PV (horizon value), and the
  total value of the firm. r=10% and g= 6%
              Valuing a Business
Example - continued
  Given the cash flows for Concatenator Manufacturing Division,
  calculate the PV of near term cash flows, PV (horizon value), and the
  total value of the firm. r=10% and g= 6%
           Accounting Ratios


1.   P0 = EPS x average P/EPS

2.   P0 = Book value per share x average P/book value per
                                               share

3.      P0 = EBITDA x average P/EBITDA
    Valuing the firm Summary
1. Calculate the PV of expected future dividends.
2. Calculate the PV of expected free cash flow.
3. Calculate the PV of earnings under no growth
   policy (perpetuity) plus the PV of growth
   opportunities.
4. Use Ratios to estimate current or horizon values.

				
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