0. Chapter 7
Equity Markets and Stock Valuation

1. 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

2. Chapter Outline Common Stock Valuation
Some Features of Common and Preferred Stocks
The Stock Markets

3. Cash Flows to Stockholders
If you buy a share of stock, you can receive cash in two ways
The company pays dividends
You sell your shares, either to another investor in the market or back to the company
As with bonds, the price of the stock (today’s value) is the present value of these expected cash flows

4. One Period Example
Suppose you are thinking of purchasing the stock of Moore Oil, Inc. and you expect it to pay a $2 dividend in one year and you believe that you can sell the stock for $14 at that time. If you require a return of 20% on investments of this risk, what is the maximum you would be willing to pay for the stock today?
Compute the PV of the expected cash flows
FV = ; I/Y = ; N = ; PV =?=
Price = (14 + 2) / (1.2) = $13.33

5. Two Period Example
Now what if you decide to hold the stock for two years? In addition to the dividend in one year, you expect a dividend of $2.10 in two years (a 5% growth) and a stock selling price of $14.70 at the end of year 2. Now how much would you be willing to pay?
CF0 = ; CF1 = ; CF2 = ; I =
NPV=?=

6. 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 $2.205 at the end of year 3 and a stock price of $ Now how much would you be willing to pay for the stock today?
Or CF0 = ; CF1 = ; CF2 = ; CF3 = I = ; NPV = ? =

7. 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 cash flows (dividends)
So, how can we estimate all future dividend payments?

8. 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
Supernormal growth
Dividend growth is not consistent initially, but settles down to constant growth eventually

9. Zero Growth
If dividends are expected at regular intervals forever, then this is like preferred stock and is valued as a perpetuity
Price of Stock = constant dividend / rate of return
Or : P0 = D / R
Suppose stock is expected to pay a $0.50 dividend every quarter and the required return is 10% with quarterly compounding. What is the price?
P0 = / = ?
Remind the students that if dividends are paid quarterly, then the discount rate must be a quarterly rate.

10. Dividend Growth Model
Dividends are expected to grow at a constant percent per period.
P0 = D1 /(1+R) + D2 /(1+R)2 + D3 /(1+R)3 + …
P0 = D0(1+g)/(1+R) + D0(1+g)2/(1+R)2 + D0(1+g)3/(1+R)3 + …
With a little algebra, this reduces to:

11. Constant Growth Model Price of stock today = Divd pd @ year-end
Return – growth
where Divd year-end = Divd just pd today (1+growth rate)
Or Po = D1 / R-g
where D1 = D0 (1+g)

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 currently be selling for?
P0 =

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 today?
P0 =
Why isn’t the $2 in the numerator multiplied by (1.05) in this example?

14. Stock Price Sensitivity to Dividend Growth
D1 = $2; R = 20%
As the growth rate approaches the required return, the stock price increases dramatically.

15. Stock Price Sensitivity to Required Return
D1 = $2; g = 5%
As the required return approaches the growth rate, the price increases dramatically. This graph is a mirror image of the previous one.

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?
P0 =
Remember that we already have the dividend expected next year, so we don’t multiply the dividend by 1+g

17. Example 7.3 – Gordon Growth Company - II
What is the price expected to be in year 4?
P4 =
What is the implied return given the change in price during the four year period?
PV = ; FV = ; N = ; I/Y = ?
The price grows at the same rate as the dividends
Point out that the formula is completely general. The dividend in the numerator is always for one period later than the price we are computing. This is because we are computing a Present Value, so we have to start with a future cash flow. This is very important when discussing supernormal growth.
We know the dividend in one year is expected to be $4 and it will grow at 6% per year for four more years. So, D5 = 4(1.06)(1.06)(1.06)(1.06) = 4(1.06)4

18. Growth Problem 2
A company pays a $.25 dividend and 6%. The required return on the stock is 12%.
Find the dividends for the next three years
Find the price of the stock today
Find the price of the stock one year from now

19. SuperNormal Growth – Prob 1
A new start-up just paid a $.25 per share dividend, and expects to grow it at 30% for the next three years, after which it expects a constant 10% growth ongoing. The required return is 12 %. What’s the value of the stock today?

20. Supernormal Growth Problem Statement
Suppose a firm is 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. If the last dividend was $1 and the required return is 20%, what is the price of the stock today?
Remember that we have to find the PV of all expected future dividends.

21. Supernormal Growth – Example Solution
Compute the dividends until growth levels off
D1 = D0(1+g) = $1(1+.2) = $1.20
D2 = D1(1+g) = $1.20(1.15) = $1.38
D3 = D2(1+g) = $1.38(1.05) = $1.449
Find the expected future price based on when growth levels off. (D3 = 1st constant growth divd which gives us price at P2)
P2 = D3 / (R – g) = / ( ) = 9.66
Point out that P2 is the value, at year 2, of all expected dividends year 3 on.
The final step is exactly the same as the 2-period example at the beginning of the chapter. We can look at as if we buy it today receive the $1.20 dividend in 1 year, receive the $1.38 dividend in 2 years and then immediately sell it for $9.66.

22. SuperNormal Growth Solution part 2
Find the present value of the expected future cash flows
Find PV of supernormal divd D2 of $1.38
Find PV of supernormal divd D1 of $1.20
Find PV of expected future stock price P2 of $9.66
Sum PV’s to get price of stock today Po

23. Quick Quiz – Part I
What is the value of a stock that is expected to pay a constant dividend of $2 per year if the required return is 15%?
What is the stock price if the company starts increasing dividends by 3% per year, beginning with the next dividend? The required return stays at 15%.
Zero growth – 2 / .15 = 13.33
Constant growth: 2(1.03) / ( ) = $17.17

24. Required Return
Return the investor in stock demands is function of dividend return and capital gains return.
Req’d return = Divd yield + capital gains yield
R = (Divd end of period / price of stock today) + growth in value from beginning to end of period
R = D1/P0 + g

25. Using the Discounted Growth Model (DGM) to Find Rate of Return
Start with the DGM:
Point out that D1 / P0 is the dividend yield and g is the capital gains yield

26. Finding the Required Return - Example
Suppose a firm’s stock is selling for $ They just paid a $1 dividend and dividends are expected to grow at 5% per year. What is the required return?
P0 = D1 / (R-g) Or: R=D1/P0 + g
What is the dividend yield?
What is the capital gains yield?
R= 15%,
Div yield = 10%, CGY = 5%

27. Table 7.1 - Summary of Stock Valuation

28. Feature of Common Stock
Voting Rights
Proxy voting
Classes of stock
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
Shareholders have the right to vote for the board of directors and other important issues.
Cumulative voting increases the likelihood of minority shareholders getting a seat on the board.
Proxy votes are similar to absentee ballots. Proxy fights occur when minority owners are trying to get enough votes to obtain seats on the Board or affect other important issues that are coming up for the vote.
Different classes of stock can have different rights. Owners may want to issue a nonvoting class of stock if they want to make sure that they maintain control of the firm.

29. 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
Dividend exclusion: If corporation A owns less than 20% of corporation B stock, then 30% of the dividends received from corporation B are taxable. If A owns between 20% and 80% of B, then 20% of the dividends received are taxable. If A owns more than 80%, a consolidated statement can be filed and dividends received from B are essentially untaxed.

30. 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
Point out that there are a lot of features of preferred stock that are similar to debt. In fact, many new issues have sinking funds that effectively convert what was a perpetual security into an equity security with a definite maturity. However, for tax purposes, preferred stock is equity and dividends are not a tax deductible expense.

31. Stock Market Dealers vs. Brokers New York Stock Exchange (NYSE) NASDAQ
Members
Operations
Floor activity
NASDAQ
Not a physical exchange – computer based quotation system
Large portion of technology stocks
Dealer: maintains an inventory and stands ready to trade at quoted bid (price at which they will buy) and ask (price at which they will sell) prices. Make their profit from the difference between the bid and ask prices, called the bid-ask spread. The smaller the spread the more competition and the more liquid the stock. The move to decimalization allows for a smaller bid-ask spread. There will be more discussion of this later.
Broker: a broker matches buyers and sellers. They perform the search function for a fee (commission). They do not hold an inventory of securities.
Video: The Financial Markets video discusses how capital is raised in the market and shows the open-outcry market at the CBOT.
www: Check out the NYSE and NASDAQ web sites by clicking on the hot links. Students are often amazed at all of the information that is available.
NYSE:
Specialists manage the order flow by keeping the limit order book. The limit order book lists the trades that investors have given to their brokers that include desired trading prices. The specialist is also a dealer that holds an inventory in their assigned stock, they post bid and ask prices and they are supposed to maintain and orderly market.
Other participants on the floor of the exchange include floor traders that own exchange seats, commission brokers and floor brokers.

32. Reading Stock Quotes Sample Quote
52 Weeks Yld VOL NET
HI LO STOCK SYM DIV % PE S HI LO CLOS CHG
McDonalds MCD –088
Note that stock quotes have now moved to decimals instead of fractions
What information is provided in the stock quote?
This quote was taken from the Sept. 14, 2000 Wall Street Journal
See the instructor’s manual for a discussion about the switch to decimal pricing.
WWW: Click on the web surfer icon to go to CNBC.com. Quotes are available as well as a stock ticker that can be personalized for stocks of interest.
Have the students identify the following information in the quote above:
52-week high: $49.56
52-week low: $27.81
Ticker symbol: MCD
Annual dividend: $0.22 What was the last quarterly dividend? .22 / 4 = $0.055
Dividend yield: .8 = .22 / 28.31
P/E ratio: 19 = closing price / last 4 quarters of earnings. What has EPS been for the last 4 quarters?
19 = / EPS; EPS = $1.49
Volume: 7,764,100 volume is quoted in round lots (100’s)
Daily high: $29.50
Daily low: $28.06
Closing price: $28.31
Change from the previous close: -$0.88. What was the closing price the previous day? = $29.19

33. Quick Quiz – Part II
You observe a stock price of $ 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?
r = [1.5(1.05)/18.75] = 13.4%