Chapter 7: Stock Valuation

proxy contest

When two or more groups are competing to collect proxies to prevail in a matter up for shareholder vote (such as election of directors).

1

(_____) (1) P_sub_0 = (Div_sub_1 + P_sub_1) / (1 + r_sub_E)

10

(_____) (10) New Investment = Earnings X Retention Rate

11

(_____) (11) Earnings Growth Rate = Change in Earnings / Earnings = Retention Rate X Return on New Investment

12

(_____) (12) g = Retention Rate X Return on New Investment

13

(_____) (13) P_sub_N = Div_sub_(N + 1) / (r_sub_E - g)

14

(_____) (14) P_sub_0 = PV (Future Dividends per Share)

5

(_____) (5) P_sub_0 = Div_sub_1 / (1 + r_sub_E) + Div_sub_2 / (1 + r_sub_E)^2 + Div_sub_3 / (1 + r_sub_E)^3 + ...

15

(_____) (15) *Total Payout Model*: P_sub_0 = PV (Future Total Dividends and Net Repurchases) / Shares Outstanding_sub_0

dividend-discount model

A model that values shares of a firm according to the present value of the future dividends the firm will pay.

floor broker

A person at the NYSE with a trading license who represents orders on the floor, balancing speed and price to get the best execution.

2

(_____) (2) r_sub_E = (Div_sub_1 + P_sub_1) / P_sub_0 - 1 = Div_sub_1 / P_sub_0 + (P_sub_1 - P_sub_0) / P_sub_0 = Dividend Yield + Capital Gain Rate

3

(_____) (3) P_sub_0 = Div_sub_1 / (1 + r_sub_E) + (Div_sub_2 + P_sub_2) / (1 + r_sub_E)^2

4

(_____) (4) *Dividend-Discount Model*: P_sub_0 = Div_sub_1 / (1 + r_sub_E) + Div_sub_2 / (1 + r_sub_E)^2 + ... + Div_sub_N / (1 + r_sub_E)^N + P_sub_N / (1 + r_sub_E)^N

6

(_____) (6) *Constant Dividend Growth Model*: P_sub_0 = Div_sub_1 / (r_sub_E - g) ... This formula requires that g < r_sub_E. Otherwise, the present value of the growing perpetuity is infinite. The implication here is that it is impossible for a stock's dividends to grow at a rate g > r_sub_E *forever*.

7

(_____) (7) r_sub_E = Div_sub_1 / P_sub_0 + g

8

(_____) (8) Div_sub_t = Earnings_sub_t / Shares Outstanding_sub_t X Dividend Payout Rate_sub_t = EPS_sub_t X Dividend Payout Rate_sub_t

9

(_____) (9) Change in Earnings = New Investment X Return on New Investment

Non-Dividend-Paying Stocks

*7.5 Limitations of the Dividend-Discount Model* -_____ --Many companies do not pay dividends, thus the dividend-discount model must be modified

Uncertain Dividend Forecasts

*7.5 Limitations of the Dividend-Discount Model* -_____ --The dividend-discount model values a stock based on a forecast of the future dividends, but a firm's future dividends carry a tremendous amount of uncertainty

A Simple Model of Growth

*Estimating Dividends in the Dividend-Discount Model*... *Dividends Versus Investment and Growth*... *_____* (A Simple Model of Growth)... the dividend each year is equal to the firm's earnings per share (EPS) multiplied by its dividend payout rate. The firm can, therefore, increase its dividend in three ways: 1. It can increase its earnings (net income). 2. It can increase its dividend payout rate. 3. It can decrease its number of shares outstanding... A firm can do one of two things with its earnings: It can pay them out to investors, or it can retain and reinvest them.

Profitable Growth

*Estimating Dividends in the Dividend-Discount Model*... *Dividends Versus Investment and Growth*... *_____* (Profitable Growth) Equation 12 shows that a firm can increase its growth rate by retaining more of its earnings. but if the firm retains more earnings, and as a result pays out a smaller fraction of those earnings as dividends, then according to Eq. 8 the firm may have to cut its dividend in the short run. If a firm wants to increase its share price, should it cut its dividend and invest more, or should it cut its investments and increase its dividend? Not surprisingly, the answer to this question will depend on the profitability of the firm's investments.

Changing Growth Rates

*Estimating Dividends in the Dividend-Discount Model*... *_____* (Changing Growth Rates) Successful young firms often have very high initial earnings growth rates. During this period of high growth, firms often retain 100% of their earnings to exploit profitable investment opportunities. As they mature, their growth slows to rates more typical of established companies. At that point, their earnings exceed their investment needs and they begin to pay dividends. We cannot use the constant dividend growth model to value the stock of such a firm for two reasons: 1. These firms often pay *no* dividends when they are young. 2. Their growth rate continues to change over time until they mature. However, we can use the general form of the dividend-discount model to value such a firm by applying the constant growth model to calculate the future share price of the stock P_sub_N once the firm matures and its expected growth rate stabilizes... The constant dividend growth model (Eq. 13) is just a special case of the general dividend-discount formula (Eq. 4). We can always value all the streams of dividends using Eq. 4. However, if we assume constant growth, we can apply the growing perpetuity shortcut to all or part of the dividend stream, depending on whether the constant growth starts now or at some point in the future... Table 1 summarizes the dividend-discount model, including how to apply the shortcut for constant growth.

Constant Dividend Growth

*Estimating Dividends in the Dividend-Discount Model*... *_____* (Constant Dividend Growth)... Comparing Eq. 7 with Eq. 2, we see that g equals the expected capital gain rate. In other words, with constant expected dividend growth rate, the expected growth rate of the share price matches the growth rate of the dividends. -If the firm chooses to keep its dividend payout rate constant, then *the growth in its dividends will equal the growth in its earnings*

Dividends Versus Investment and Growth

*Estimating Dividends in the Dividend-Discount Model*... *_____* (Dividends Versus Investment and Growth) In Eq. 6, the firm's share price increases with the current dividend level, Div_sub_1, and the expected growth rate, g. To maximize its share price, a firm would like to increase both these quantities. Often, however, the firm faces a tradeoff: Increasing growth may require investment, and money spent on investment cannot be used to pay dividends. The constant dividend growth model provides insight into this tradeoff.

Cumulative Versus Non-Cumulative Preferred Stock

*Preferred Stock*... *_____* (Cumulative Versus Non-Cumulative Preferred Stock) There are two types of preferred stock: *cumulative* and *non-cumulative*.

A Multiyear Investor

*The Dividend-Discount Model*... *_____* (A Multiyear Investor)... Equations 1 and 3 are different: As a two-year investor we care about the dividend and stock price in year 2, but these terms do not appear in Eq. 1. Does this difference imply that a two-year investor will value the stock differently than a one-year investor? The answer to that question is no. A one-year investor does not care about the dividend and stock price in year 2 directly. She will care about them indirectly, however, because they will affect the price for which she can sell the stock at the end of year 1... Thus, the formula for the stock price for a two-year investor is the same as that for a sequence of two one-year investors.

A One-Year Investor

*The Dividend-Discount Model*... *_____* (A One-Year Investor) There are two potential sources of cash flows from owning a stock: 1. The firm might pay out cash to its shareholders in the form of a dividend. -*dividend payments (Div) given by the firm* 2. The investor might generate cash by selling the shares at some future date -*by selling it to another investor when the price of the stock goes up.*

Dividend Yields, Capital Gains, and Total Returns

*The Dividend-Discount Model*... *_____* (Dividend Yields, Capital Gains, and Total Returns)... Equation 2 states that the stock's total return should equal the equity cost of capital. In other words, *the expected total return of the stock should equal the expected return of other investments available in the market with equivalent risk*.

Dividend-Discount Model Equation

*The Dividend-Discount Model*... *_____* (Dividend-Discount Model Equation)... Equation 4 applies to a single N-year investor, who will collect dividends for N years and then sell the stock, or to a series of investors who hold the stock for shorter periods and then resell it. Note that Eq. 4 holds for *any* horizon N... For the special case in which the firm eventually pays dividend and is never acquired or liquidated, it is possible to hold the shares forever. In this scenario, rather than having a stopping point where we sell the shares, we rewrite Eq. 4 to show that dividends go on into the future... That is, *the price of the stock is equal to the present value of all of the expected future dividends it will pay*.

Limitations of the Dividend-Discount Model

*_____* (Limitations of the Dividend-Discount Model) The dividend-discount model has two fundamental limitations that we will now address: its reliance on dividend forecasts and lack of applicability to non-dividend paying stocks.

Putting It All Together

*_____* (Putting It All Together)... First, how would an investor decide whether to buy or sell Nike stock? She would value the stock using her own expectations... Based on that conclusion, she would sell or buy the stock, and time would reveal whether her expectations were better than the market's. Second, how could Nike stock suddenly be worth 11% more after Nike's announcement in March of 2013? As investors digested the news in Nike's announcement and updated their expectations, they would have determined that the previous day's closing price was too low based on the new information about future earnings growth. Buying pressure would then drive the stock price up until the buys and sells came into balance. Third, what should Nike's managers do to raise the stock price further? The only way to raise the stock price is to make value-increasing decisions.

Share Repurchases and the Total Payout Model

*_____* (Share Repurchases and the Total Payout Model)... Share repurchases have two consequences for the dividend-discount model. First, the more cash the firm uses to repurchase shares, the less cash it has available to pay dividends. Second, by repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis... We can apply the same simplifications to the total payout method that we obtained by assuming constant growth in Section 3. The only change is that *we will discount total dividends and share repurchases and use the growth rate of earnings (rather than earnings per share) when forecasting the growth of the firm's total payouts*. When the firm uses share repurchases, this method can be more reliable and easier to apply than the dividend-discount model. -Share Repurchases --The firm uses excess cash to buy back its own stock ---Two Consequences: ----1. The more cash the firm uses to repurchase shares, the less cash it has available to pay dividends ----2. By repurchasing shares, the firm decreases its share count, which increases its earnings and dividends on a per-share basis

Stock Basics

*_____* (Stock Basics)... In this section, we explain what a stock market quote is and introduce the two types of stocks, *common* and *preferred*.

The Mechanics of Stock Trades

*_____* (The Mechanics of Stock Trades)... A *market order* means you do not specify a price, rather you want the order to execute immediately at the most favorable price available. If instead you wanted to specify a maximum price you were willing to pay, and you were willing to wait until the shares were available at that price, you would place a *limit order*... In market parlance, 100 shares is a "round lot" and would be considered a small order. Small orders such as this would typically be transmitted electronically to the stock exchange via a system called the *Super Display Book System* (Which replaced the old SuperDOT system in 2009)... Recall that a specialist holds a trading license at the NYSE and acts as a market maker for a particular stock, maintaining orderly trading and stepping in to provide liquidity when needed. The small order would automatically execute against the specialist's inventory in a few *milliseconds*... In the rest of this chapter, we discuss one traditional approach to valuing a stock, the *dividend-discount model*.

notation

*_____* (notation) Div_sub_t = dividends paid in year t EPS_sub_t = earnings per share on date t g = expected dividend growth rate N = terminal date or forecast horizon P_sub_t = stock price at the end of year t PV = present value r_sub_E = equity cost of capital

Stock Price

- Value = market price ? -If not, why are they different? --Market efficiency: information, sentiment -*The stock price today= the PV of future cash flows*

total payout model

A method that values shares of a firm by discounting the firm's *total payouts* to equity holders (that is, *all* the cash distributed as dividends *and* stock repurchases) and then dividing by the current number of shares outstanding. -Values all of the firm's equity, rather than a single share! -Two steps: --1. Find the PV of the total payouts (dividends and share repurchases) --2. Divide this by the number of shares, to obtain the share price

constant dividend growth model

A model for valuing a stock by viewing its dividends as a constant growth perpetuity. -A commonly used approximation is to assume that in the long run, dividends will grow at a constant rate (g) *forever*.

common stock

A share/form of *ownership* in the corporation, which confers rights to any common dividends as well as rights to vote on election of directors, mergers, and other major events. -They are the type of stock that most people are thinking of when they use the term "stock." -Since stocks are partial ownership of a corporation, they are also known as "*shares*."

share repurchase

A transaction in which a firm uses cash to buy back its own stock.

ticker symbol

A unique abbreviation assigned to a publicly traded company.

proxy

A written authorization for someone to vote your shares.

capital gain rate

An expression of capital gain as a percentage of the initial price of the asset.

classes

Different types of common stock for the same company, often carrying different voting rights.

annual meeting

Meeting held once per year where shareholders vote on directors and other proposals as well as ask managers questions.

cumulative preferred stock

Preferred stock where all missed preferred dividends must be paid before any common dividends can be paid.

non-cumulative preferred stock

Preferred stock where missed dividends do not accumulate. Only the current dividend is owed before common dividends can be paid.

preferred stock

Stock with preference over common shares in payment of dividends and in liquidation. -They are another form of a piece of ownership of a corporation -No voting rights -Fixed dividends -Equity or Debt?

capital gain

The amount by which the selling price of an asset exceeds its initial purchase price.

dividend yield

The expected annual dividend of a stock divided by its current price; the percentage return an investor expects to earn from the dividend paid by the stock.

equity cost of capital

The expected rate of return available in the market on other investments that have equivalent risk to the risk associated with the firm's shares.

retention rate

The fraction of a firm's current earnings that the firm retains.

dividend payout rate

The fraction of a firm's earnings that the firm pays out as dividends each year.

total return

The sum of a stock's dividend yield and its capital gain rate.

cumulative voting

Voting for directors where each shareholder is allocated votes equal to the number of open spots multiplied by his or her number of shares.

straight voting

Voting for directors where shareholders must vote for each director separately, with each shareholder having as many votes as shares held.