Equity Markets

1
Equity Markets Stock Valuation

• Chapter 7

2
Key Concepts and Skills

• Understand how stock prices depend on future
  dividends and dividend growth
• Be able to compute stock prices using the
  dividend growth model
• Understand how corporate directors are elected
• Understand how stock markets work
• Understand how stock prices are quoted

3
Chapter Outline

• Common Stock Valuation
• with focus on dividend growth models (DGM)
• Some Features of Common and Preferred Stocks
• The Stock Markets

4
Cash Flows to Stockholders

• If you buy a share of stock, you can receive cash
  in two ways
• 1) The company pays dividends
• 2) You sell your shares, either to another
  investor in the market or back to the company
• As with bonds, the price of the stock is the
  present value of these expected cash flows
• Price of stock (what you are willing to pay for
  it)
• PV of future sale price PV of cash flows
  (from dividends)

5
One Period Example

• Suppose you are thinking of purchasing the stock
  of More Oil, Inc. You expect the company to pay a
  2 dividend in one year and just after the
  dividend pay you believe that you can sell the
  stock for 14. If you require a return of 20 on
  investments of this risk, what is the maximum you
  would be willing to pay for this stock?
• Price PV of future price PV of dividend
• 14/1.22/1.211.66 1.666 13.33
• Or Price Income / (1r)t (14 2) / (1.2)1
  13.33
• With financial calculator
• FV 16 I/Y 20 N 1 CPT PV -13.33

Similar example is on pp. 197-198
6
Two Period Example

• Now, what if you decide to hold the stock for two
  years? In addition to the dividend in one year
  (2.00), you expect a dividend of 2.10 and a
  stock price of 14.70 at the end of year 2. You
  still require a return of 20.
• Now how much would you be willing to pay?
• Using cash flow calculation, adding up PVs of
  cash flows
• PV PV of future dividends PV of sale price
• 2/1.22.1/ (1.2)2 14.7/ (1.2)2
  1.661.45810.213.333
• With financial calculator
• CF00 C012 F011 C0216.80 F021 NPV I20
  CPT NPV13.33

Similar example is on p. 198
7
Three Period Example

• Finally, what if you decide to hold the stock for
  three periods? In addition to the dividends at
  the end of years 1 and 2, you expect to receive a
  dividend of 2.20 at the end of year 3 and you
  expect to sell the stocks at 16.5. You still
  require a return of 20.
• Now how much would you be willing to pay?
• Using cash flow calculation, adding up PVs of
  cash flows
• PV PV of dividend in year 1 PV of dividend
  in year 2
• PV of dividend in year 3 and PV of the sale
  price
• 2/1.2 2.10/1.22 2.20/1.23 16.5/1.23
  13.95
• With financial calculator
• CF0 0 C01 2 F01 1 C02 2.10 F02 1
  C03 17.64 F03 1 NPV I 20 CPT NPV
  13.947
• Note that for Cash Flow 3, you need to enter the
  sum of the dividend and sale price.

8
Developing The Model

• You could continue to push back when you would
  sell the stock
• You would find that the price of the stock is
  really just the present value of all expected
  future dividends (when we are thinking on a
  really long term holding the stock)
• So, how can we estimate all future dividend
  payments?

9
Estimating Dividends Special Cases

• Constant dividend
• The firm will pay a constant dividend forever
• This is like preferred stock
• The price is computed using the perpetuity
  formula
• Constant dividend growth
• The firm will increase the dividend by a constant
  percent every period (div11 div2div1(1g)
  div3 div2 (1g))
• Supernormal growth
• Dividend growth is not consistent initially, but
  settles down to a constant growth eventually
  (div12.5 div23 div31.2 div4div3(1g))

10
Zero Growth

• If dividends are expected at regular intervals
  forever, then this is like preferred stock and is
  valued as a perpetuity
• P0 D / R (recall the perpetuity PVC/r)
• Example 1. The stock of Paradise Co. pays 10 per
  share dividend every year. Your required rate of
  return is 20. How much are you willing to pay
  for this stock?
• Price D/r10/.250, thus you are willing to pay
  at most 50.
• Example 2. Suppose a stock is expected to pay a
  0.50 dividend every quarter and the required
  return is 10 with quarterly compounding. What is
  the price?
• Using the perpetuity formula to calculate the
  stock price
• P0 .50 / (.1 / 4) 20

11
Dividend Growth Model

• Dividends are expected to grow at a constant
  percent per period (g is the constant growth
  rate)
• P0 D1 /(1R) D2 /(1R)2 D3 /(1R)3
• P0 D0(1g)/(1R) D0(1g)2/(1R)2
  D0(1g)3/(1R)3
• With a little algebra, this reduces to

12
DGM Example 1

• Suppose Big D, Inc. just paid a dividend of .50.
  It is expected to increase its dividend by 2 per
  year. If the market requires a return of 15 on
  assets of this risk, how much should the stock be
  selling for?
• To solve realize that D0.5 and g.02 and R.15
  and use the constant dividend growth model.
• The important assumption in this model that R has
  to be greater than g.

13
DGM Example 2

• Suppose TB Pirates, Inc. is expected to pay a 2
  dividend in one year. If the dividend is expected
  to grow at 5 per year and the required return is
  20, what is the price?
• P0 D1/ (R-g) 2 / (.2 - .05) 13.33
• Why isnt the 2 in the numerator multiplied by
  (1.05) in this example?
• Because the dividend given is a future dividend
  to be received a year from now. It is important
  that in the constant dividend model you use the
  future dividend.

14
Stock Price Sensitivity to Dividend Growth(g)
D1 2 R 20
If g .05 then Price2/(.20 - .05) 13.33 If g
.10 then Price2/(.20 - .10) 20
15
Stock Price Sensitivity to Required Return, R
D1 2 g 5
If R .08 then Price2/(.08 - .05) 66.66 If
R .20 then Price2/(.20 - .05) 13.33
16
Example 7.3 Gordon Growth Company - I

• Gordon Growth Company is expected to pay a
  dividend of 4 next period and dividends are
  expected to grow at 6 per year. The required
  return is 16.
• What is the current price? (note D14 g6
  R16)
• P0 4 / (.16 - .06) 40
• Remember we already have the dividend expected
  next year, so we dont multiply the dividend by
  1g

See example 7.3 on p. 201
17
Example 7.3 Gordon Growth Company II

• What is the price expected to be in year 4?
  (apply the DGM and use the applicable future
  dividend, D5)
• P4 D4(1 g) / (R g) D5 / (R g)
• P4 4(1.06)4 / (.16 - .06) 50.50
• Or alternatively P4 P0 (1g)4 40(1.06)4
  50.5
• Note that the DGM makes an implicit assumption
  that the stock price will grow at the same rate
  as the dividend. This tells us if the cash flows
  of an investment grow at a rate of g, so does the
  value of that investment.

18
Nonconstant Growth Problem 1

• Suppose a firm is just paid 1 in dividends and
  expected to increase dividends by 20 in one year
  and by 15 in two years. After that dividends
  will increase at a rate of 5 per year
  indefinitely. What is the price of the stock if
  the required rate of return is 20?
• Remember we have to find the PV of all expected
  future dividends.
• D1 1(1.2) 1.20
• D2 1.20(1.15) 1.38
• (D3 1.38(1.05) 1.449 we need D3 to calculate
  P2)
• Find the expected price at year 2, the dividend
  growth rate is constant after year 2 thus we can
  apply the DGM only for P2.
• P2 D3 / (R g) 1.449 / (.2 - .05) 9.66
• Find the present value of the expected future
  cash flows (calculate price)
• P0 1.20 / (1.2) (1.38 9.66) / (1.2)2 8.67

19
Nonconstant Growth Problem 2

• Suppose a firm currently pays no dividend. It is
  expected to pay dividend, .50 in five years for
  the first time. We expect that the dividend then
  will grow at the rate of 10 per year
  indefinitely. The required rate on similar
  companies is 20. What is the price of the stock?
• Remember we have to find the PV of all expected
  future dividends.
• The first dividend will be in 5 years, using the
  DGM we can calculate what the price would be inn
  four years (knowing that D5.5 g10 and R20)
  
• P4 D5 / (R-g) .5/ (.2-.1) 5
• If we know that the future price in 4 years is
  5, we can calculate the current price, by
  discounting the price back at the rate of 20.
• P0 P4 / (1R)4 5/1.24 2.41

See details on p. 202
20
Using the DGM to Find R

• Start with the DGM
• Rearrange and solve for R
• Total return Dividend yield capital gains
  yield

21
Finding the Required Return - Example

• Suppose a firms stock is selling for 10.50.
  They just paid a 1 dividend and dividends are
  expected to grow at 5 per year. What is the
  required return?
• R D1 / P0 g 1(1.05)/10.50 .05 15
• What is the dividend yield (D1/ P0)?
• 1(1.05) / 10.50 10
• What is the capital gains yield?
• g 5

Similar example on p. 204
22
Table 7.1
23
Features of Common Stock

• Voting Rights
• There are two distinctly different voting
  procedures
• Cumulative voting and straight voting
• Proxy voting
• Classes of stock
• Often one class of stock has the majority of
  voting right, while they represent only a small
  fraction of al shares outstanding
• Other Rights
• Share proportionally in declared dividends
• Share proportionally in remaining assets during
  liquidation
• Preemptive right first shot at new stock issue
  to maintain proportional ownership if desired

24
Dividend Characteristics

• Dividends are not a liability of the firm until a
  dividend has been declared by the Board
• Consequently, a firm cannot go bankrupt for not
  declaring dividends
• Dividends and Taxes
• Dividend payments are not considered a business
  expense, therefore, they are not tax deductible
• Dividends received by individuals are taxed as
  ordinary income
• Dividends received by corporations have a minimum
  70 exclusion from taxable income

25
Features of Preferred Stock

• Dividends
• Stated dividend that must be paid before
  dividends can be paid to common stockholders
• Dividends are not a liability of the firm and
  preferred dividends can be deferred indefinitely
• Most preferred dividends are cumulative any
  missed preferred dividends have to be paid before
  common dividends can be paid
• Preferred stock generally does not carry voting
  rights

26
Example with Preferred Stock

• ABC Company's preferred stock is selling for 30
  a share. If the required return is 8, what will
  the dividend be in a years from now?
• Now recall PV of a perpetuity C/ r
• For the preferred stock there is a guaranteed 8
  return as long as you hold the stock, thus
  forever in valuating a stock.
• PV30, because the stock is selling at 30 on
  the market
• PVpayment/r 30 D / .08 ? D 2.40

For other example go back to slide 9.
27
Stock Market

• Stock market Primary versus secondary market

• Dealers vs. Brokers
• Dealer maintains an inventory and stands ready
  to buy and sell any time
• Broker brings buyer and sellers together

28
Stock Markets

• New York Stock Exchange (NYSE)
• Members owner of seat on NYSE
• Commission brokers
• Specialists
• Floor brokers
• Operations
• Floor activity
• NASDAQ
• Not a physical exchange computer based
  quotation system
• Large portion of technology stocks
• Dealer market, no direct trading

29
Work the Web Example

• Electronic Communications Networks (ECN) provide
  trading in NASDAQ securities
• A network of web-sites, which allow investors to
  trade directly with each other.
• The Island allows the public to view the order
  book in real time
• Click on the web surfer and visit The Island!

30
Reading Stock Quotes

• Sample Quote
• 19.2 57.91 42.59 Coca-Cola KO .80 1.4 36
  26927 56.20 0.74
• What information is provided in the stock quote?

31
Reading Stock Quotes (contd)

• Sample Quote
• 19.2 57.91 42.59 Coca-Cola KO .80 1.4 36
  26927 56.20 0.74

Annual dividend, which is four times quarterly
div. of .20
Highest and lowest price during the last 52 weeks
P/E ratio, Coke sells at 36 times of earning
Closing price
Net change in closing price
Daily trading volume
Dividend yield Div/ Stock price
Stock price has risen 19.2 year to date
Company name and ticker
32
Quick Quiz

• You observe a stock price of 18.75. You expect a
  dividend growth rate of 5 and the most recent
  dividend was 1.50. What is the required return?
• What are some of the major characteristics of
  common stock?
• What are some of the major characteristics of
  preferred stock?
• Try to answer these questions on your own!