Stocks

- What is a stock?
- Cash flows to stockholders
- Company pays a dividend
- Stockholder sells shares

- Difficulties with stock valuation
- Cash flows aren’t known in advance
- earnings split between reinvestment and dividends
- required rate of return is not observable

- Security has no maturity

- Cash flows aren’t known in advance

Example

- Suppose you are thinking of purchasing the stock of Moore Oil, Inc. 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?
- 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 and a stock price of $\$$14.70 at the end of year. Now how much would you be willing to pay?

Generalizing

- $P0 = \frac{D1+P1}{1+R} = \frac{D1}{1+R} + \frac{P1}{1+R}$
- $P0 = \frac{D1}{1+R} + \frac{D2}{(1+R)^2} + \frac{P2}{(1+R)^2}$
- $P0 = \frac{D1}{1+R} + \frac{D2}{(1+R)^2} + \frac{D3}{(1+R)^3} + \frac{P3}{(1+R)^3}$
- $P0 = \frac{D1}{1+R} + \frac{D2}{(1+R)^2} + \frac{D3}{(1+R)^3} + \frac{D4}{(1+R)^4} + \ldots$

Special Cases

- Zero Growth - the dividend is constant
- $P0 = \frac{D}{1+R} + \frac{D}{(1+R)^2} + \frac{D}{(1+R)^3} + \frac{D}{(1+R)^4} + \ldots$
- In this case, a stock is just a perpetuity.
- $P0 = D/R$

- Constant Growth - the dividend for a company always grows at a steady rate
- $D1 = D0 \times (1+g)$, $D2 = D1 \times (1+g) = D0 \times (1+g)^2$, etc.
- $P0 = \frac{D0(1+g)}{1+R} + \frac{D0(1+g)^2}{(1+R)^2} + \frac{D0(1+g)^3}{(1+R)^3} + \frac{D0(1+g)^4}{(1+R)^4} + \ldots$
- In this case, a stock is just a growing perpetuity.
- $P0 = D0(1+g)/(R-g) = D1/(R-g)$
- We call this formula the
**Gordon Model**or the**Dividend Growth Model**. - What happens if $R = g$ or $R$ < $g$?
- An example:
- Suppose Big D, Inc., just paid a dividend (D0) of $0.50 per share. 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?

- Non-constant Growth - break the problem into pieces you can evaluate
- An example:
- Suppose a firm is expected to increase dividends by 20% in one year and by 15% for 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?

- An example:

Components of Required Return

- We can rearrange the dividend growth model to yield the following: $R = D1/P0 + g$.
- Required return is a function of:
- $D1/P0$ - Dividend yield
- $g = P1/P0$ - Capital gains yield

- Suppose a stock is selling for $\$$10.50. It just paid a $\$$1 dividend, and dividends are expected to grow at 5% per year.
- What is the required return?
- What is the dividend yield?
- What is the capital gains yield?

Stocks Without Dividends

- What is a stockholders claim if a stock doesn’t pay dividends?
- We can take a piece of information we know and, with some assumptions, calculate a price.
- P = Benchmark PE Ratio $\times$ EPS
- P = Benchmark PS Ratio $\times$ Sales per share

Stock Features

- Voting Rights
- Shareholders control the corporation through the right to elect the directors.
- Directors are elected at an annual shareholders’ meeting.
- One share, one vote (generally)
- Cumulative vs. Straight Voting
- cumulative voting - a procedure in which a shareholder may cast all votes for one member of the board of directors (enables minority participation)
- straight voting - a procedure in which a shareholder may cast all votes for each member of the board of directors
- Suppose a corporation has two shareholders: Smith with 20 shares and Jones with 80 shares. There are to be 4 directors elected to the board. Will Smith be one of them.
- If the vote is cumulative, Smith casts 80 votes while Jones casts 320. Smith will finish fourth at worst.
- If the vote is straight, directors are elected one at a time and Jones elects all the candidates.
- $1/(N+1)$ (cumulative) vs. 50% plus one share (straight) to get a director elected.

- Staggered Boards
- Directors have staggered terms.
- Makes it more difficult for a minority to elect a director.
- Makes takeover attempts less likely since a takeover will require a majority of directors.
- Can provide ``institutional memory."

- Proxy Voting
- grants of authority by one shareholder allowing another individual to vote his/her shares
- management has incentive to hoard proxies

- Classes of Stock
- 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.

- 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

Dividends

- 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.
- Tax Treatment
**not**a business expense so**not**tax deductible- Dividends received by individuals are taxable.
- Dividends received by corporations have a minimum 70% exclusion from taxable income.

Preferred Stock

- Has dividend priority over common stock
- Often has fixed dividend rate
- Dividends are not a liability of the firm, and preferred dividends can be deferred indefinitely
- However, most preferred dividends are
**cumulative**- any missed preferred dividends have to be paid before common dividends can be paid - Sometimes issued without voting rights

Stock Markets

- 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)
- Broker - matches buyers and sellers for a fee
- NYSE
- Largest stock market in the world
- 1366 exchange members
- Commission brokers - execute customer orders to buy and sell stock
- Specialists (market makers) - act as dealers in a small number of securities
- Floor brokers - execute orders for commission broers on a fee basis
- Floor traders - trade using their own money

- Operations - attract and process
**order flow**(flow of customer orders to buy and sell securities)

- NASDAQ
- Not a physical exchange - it is a computer based quotation system
- Multiple market makers rather than specialists