## Ch. 8: Stock Valuation

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

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?

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